From bd21045741224254c41a5ab1fb1c2cdd0cdf129e Mon Sep 17 00:00:00 2001 From: Robert Jeutter Date: Thu, 8 Apr 2021 21:18:53 +0200 Subject: [PATCH] fixing images and minor bugs --- Programmierparadigmen.pdf | Bin 6747412 -> 9667368 bytes Programmierparadigmen.tex | 7913 +++++++++++++++++-------------------- README.md | 2 +- 3 files changed, 3639 insertions(+), 4276 deletions(-) diff --git a/Programmierparadigmen.pdf b/Programmierparadigmen.pdf index ae6dae0ab72d496634c08aca8450dcf908e4cd9a..a3a8b19a2ca08558da9178303b0b90666fa62501 100644 GIT binary patch delta 3729349 zcmZtMQ*bU!v?kzW$F}y4ZQHhO+jjEBwr$(CZQHh;`A?mxxthE8qN{J#s<*42>ZFTI zkg|{&&^UHDHfTC&6I(N9b9@FSrqp>~ZVEuOs*c?zJEHe%?b_%|gto9EVX@G>Pz|0y zCaxuOJ39G;;AYfxBQ;b~Qp?XX8x@l+w01g>g0R%q`u6&IF{p`h9C8uGY&oG)+}K^H z)V^HYm;`DY7IN{B2(nxeemVvdg@kGdF%Yq?xuWDD6orkrNs)dY>M_3}$MM&Wye?o* zN5UgqN}ixmgSLF`O(ia5Q#&yvw2Ls>BtCv+twdZcA|eYG8@S&*NJlZfUtGR?N?M8% z1`|zLbxc$#d9bBmLYxsxg`RDUT&ND5!X&I8zZCXXI-Dy?vWTK6!y)Gnt&}~%UF{Na 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zGv!UNwv+I4fBc~ypyLpYxKxN%HTC&Refr;U|F0DIUVttuKP|(@_0XHwN@fzww3omn VVl-YpZgwsX0VEn48C6-N{|~|H@!9|Y diff --git a/Programmierparadigmen.tex b/Programmierparadigmen.tex index 5608c53..f0876bf 100644 --- a/Programmierparadigmen.tex +++ b/Programmierparadigmen.tex @@ -32,15 +32,47 @@ {\geometry{top=1cm,left=1cm,right=1cm,bottom=1cm} } } - \lstset{literate=% - {Ö}{{\"O}}1 - {Ä}{{\"A}}1 - {Ü}{{\"U}}1 - {ß}{{\ss}}1 - {ü}{{\"u}}1 - {ä}{{\"a}}1 - {ö}{{\"o}}1 - } + + \definecolor{commentsColor}{rgb}{0.497495, 0.497587, 0.497464} + \definecolor{keywordsColor}{rgb}{0.000000, 0.000000, 0.635294} + \definecolor{stringColor}{rgb}{0.558215, 0.000000, 0.135316} + \lstset{ + backgroundcolor=\color{white}, % choose the background color; you must add \usepackage{color} or \usepackage{xcolor} + basicstyle=\ttfamily, % the size of the fonts that are used for the code + breakatwhitespace=false, % sets if automatic breaks should only happen at whitespace + breaklines=true, % sets automatic line breaking + captionpos=b, % sets the caption-position to bottom + commentstyle=\color{commentsColor}\textit, % comment style + deletekeywords={...}, % if you want to delete keywords from the given language + escapeinside={\%*}{*)}, % if you want to add LaTeX within your code + extendedchars=true, % lets you use non-ASCII characters; for 8-bits encodings only, does not work with UTF-8 + frame=tb, % adds a frame around the code + keepspaces=true, % keeps spaces in text, useful for keeping indentation of code (possibly needs columns=flexible) + keywordstyle=\color{keywordsColor}\bfseries, % keyword style + language=Python, % the language of the code (can be overrided per snippet) + otherkeywords={*,...}, % if you want to add more keywords to the set + numbers=left, % where to put the line-numbers; possible values are (none, left, right) + numbersep=5pt, % how far the line-numbers are from the code + numberstyle=\tiny\color{commentsColor}, % the style that is used for the line-numbers + rulecolor=\color{black}, % if not set, the frame-color may be changed on line-breaks within not-black text (e.g. comments (green here)) + showspaces=false, % show spaces everywhere adding particular underscores; it overrides 'showstringspaces' + showstringspaces=false, % underline spaces within strings only + showtabs=false, % show tabs within strings adding particular underscores + stepnumber=1, % the step between two line-numbers. If it's 1, each line will be numbered + stringstyle=\color{stringColor}, % string literal style + tabsize=2, % sets default tabsize to 2 spaces + title=\lstname, % show the filename of files included with \lstinputlisting; also try caption instead of title + columns=fixed, % Using fixed column width (for e.g. nice alignment) + %identifierstyle=\color{red}, + literate= + {Ö}{{\"O}}1 + {Ä}{{\"A}}1 + {Ü}{{\"U}}1 + {ß}{{\ss}}1 + {ü}{{\"u}}1 + {ä}{{\"a}}1 + {ö}{{\"o}}1 + } % Turn off header and footer \pagestyle{empty} @@ -99,27 +131,22 @@ \setlength{\columnsep}{2pt} \section{Einleitung} -\paragraph{Was ist ein Paradigma?} +\subsection{Was ist ein Paradigma?} \begin{itemize*} - \item Paradigma - aus dem Altgriechischen Beispiel, Muster; Erzählung mit beispielhaftem Charakter (laut Duden) + \item Paradigma aus dem Altgriechischen "Beispiel, Muster", Erzählung mit beispielhaftem Charakter (laut Duden) \item Programmierparadigmen beschreiben grundsätzliche Arten wie Computer-Programme formuliert werden können \item Programmiersprachen können einzelne oder viele Konzepte aufgreifen \begin{itemize*} \item Keine verbreitete Sprache greift alle behandelten Konzepte auf \item Betrachtung unterschiedlicher Sprachen \end{itemize*} - \item Ziel der Veranstaltung: Weiten der in Algorithmen und Programmierung eingeführten Sichten hin zu einem Werkzeugkoffer zur Lösung realer Probleme... + \item Warum unterschiedliche Paradigmen? Komplexität von Software schlecht beherrschbar \end{itemize*} -\paragraph{Warum unterschiedliche Paradigmen?} -Komplexität von Software schlecht beherrschbar -\paragraph{Was bedeutet das?} +\subsection{Was bedeutet das?} \begin{itemize*} - \item Programmierer schreiben, testen und dokumentieren zwischen 325 und 750 Codezeilen pro Monat - \begin{itemize*} - \item maximal 360.000 Zeilen in 40 Jahren! - \end{itemize*} + \item Programmierer schreiben, testen und dokumentieren (nur) zwischen 325 und 750 Codezeilen pro Monat \item Komplexität muss verborgen werden, z.B. durch \begin{itemize*} \item Kapselung @@ -130,7 +157,7 @@ Komplexität von Software schlecht beherrschbar \item Theoretische Rahmenbedingungen (Turing-Mächtigkeit, Satz von Rice) behalten Gültigkeit! \end{itemize*} -\paragraph{Welche Paradigmen existieren?} +\subsection{Welche Paradigmen existieren?} \begin{itemize*} \item Grundlegend \begin{itemize*} @@ -138,7 +165,7 @@ Komplexität von Software schlecht beherrschbar \item Applikative Algorithmen \item Deduktive Algorithmen \end{itemize*} - \item Aber Vielzahl weiterer Formen + \item aber Vielzahl weiterer Formen \begin{itemize*} \item teilweise ergänzend, unterschiedliche Kategorisierung möglich \item Bsp: prozedural, deklarativ, objekt-orientiert, datenstromorientiert, parallele \& verteilte Programmierung... @@ -155,9 +182,9 @@ Komplexität von Software schlecht beherrschbar \end{itemize*} \end{itemize*} - +\newpage \section{Objektorientierung und weiterführende Konzepte} -\subsection{Ziel des Kapitels} +\subsection{Ziele} Einführen von Mechanismen zur Handhabung von komplexeren Code \begin{itemize*} \item Systematisiertes \& schnelles Testen @@ -169,13 +196,13 @@ Einführen von Mechanismen zur Handhabung von komplexeren Code \end{itemize*} \subsection{Unit-Testing} -\paragraph{Motivation} +\subsubsection{Motivation} \begin{itemize*} \item Große Software-Systeme entwickeln sich über lange Zeiträume \item Wie können Änderungen an komplexen Code-Basen beherrscht werden? \item Veränderung über Zeit + Komplexität der Software \begin{itemize*} - \item Änderungen führen mglw. zu Auswirkungen, die für Einzelne nicht immer überschaubar sind + \item Änderungen führen möglicherweise zu Auswirkungen, die für Einzelne nicht immer überschaubar sind \item Software muss nach Änderung von Grund auf durchgetestet werden \end{itemize*} \item Verbreitetes Vorgehen: zusätzlichen Code schreiben, der eigentlichen Code automatisch "überprüft" @@ -189,9 +216,9 @@ Einführen von Mechanismen zur Handhabung von komplexeren Code \end{itemize*} \end{itemize*} -\paragraph{Eigenschaften von Unit-Tests} +\subsubsection{Eigenschaften von Unit-Tests} \begin{itemize*} - \item Software schlecht als Ganzes testbar -> Zergliederung von Software in sinnvolle Einheiten + \item Software schlecht als Ganzes testbar $\rightarrow$ Zergliederung von Software in sinnvolle Einheiten \item Individuelle Tests dieser Einheiten \item Dabei: reproduzierbar \& vollautomatisierbar \begin{itemize*} @@ -199,17 +226,10 @@ Einführen von Mechanismen zur Handhabung von komplexeren Code \end{itemize*} \item Messung der Vollständigkeit der Tests schwierig \item Üblich: Messung von Überdeckung (Coverage) in Bezug auf Anzahl Funktionen, Code-Zeilen oder Verzweigungen - \item Gute Praxis: Wenn ein Bug beim Testen oder Live-Betrieb auftritt -> Schreiben eines zusätzlichen Tests, um Wiederauftreten zu erkennen + \item Gute Praxis: Wenn ein Bug beim Testen oder Live-Betrieb auftritt $\rightarrow$ Schreiben eines zusätzlichen Tests, um Wiederauftreten zu erkennen \end{itemize*} -\begin{itemize*} - \item reproduzierbar \& vollautomatisierbar - \item Wann immer Änderungen in komplexen Programmen vorgenommen werden, möglichst vollständiger Test, da Programmierer nicht mehr alles überblicken - \item Messung von Überdeckung (Coverage) in Bezug auf Anzahl Funktionen, Code-Zeilen oder Verzweigungen - \item Wenn ein Bug beim Testen oder Live-Betrieb auftritt $\rightarrow$ Schreiben eines zusätzlichen Tests, um Wiederauftreten zu erkennen -\end{itemize*} - -\paragraph{Richtiges Abstraktionsniveau bei Unit Testing} +\subsubsection{Richtiges Abstraktionsniveau bei Unit Testing} \begin{itemize*} \item Um die Tests auszuführen, müssen jeweils entsprechende Hauptprogramme generiert werden ("Test Suites") \item Hauptschwierigkeiten von Unit-Tests: @@ -234,18 +254,8 @@ Einführen von Mechanismen zur Handhabung von komplexeren Code \end{itemize*} \end{itemize*} -Zwei wesentliche Möglichkeiten: -\begin{itemize*} - \item Individuelles Testen von Klassen: Vernachlässigt Zusammenspiel zwischen Klassen - \item Gemeinsames Testen von Klassen: Erfordert Eingreifen in gekapselte Funktionalitäten -\end{itemize*} - Klasse -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] public class Multi { int mul(int a, int b) { return a * b; @@ -254,11 +264,7 @@ public class Multi { \end{lstlisting} Testklasse -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] import static org.junit.jupiter.api.Assertions.*; class MultiTest { @org.junit.jupiter.api.Test @@ -271,7 +277,6 @@ class MultiTest { \end{lstlisting} \subsection{Reflections} - \begin{itemize*} \item Normaler Ablauf: Programm schreiben, compilieren, ausführen \begin{itemize*} @@ -295,21 +300,13 @@ class MultiTest { API verstreut über verschiedene Packages, z.B. java.lang.Class, java.lang.instrument, java.lang.reflect -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] Class cls = "test".getClass(); System.out.println("Die Klasse heisst " + cls.getName()); // Die Klasse heisst java.lang.String \end{lstlisting} -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] // import java.lang.reflect.Method; Method[] methods = cls.getMethods(); for (Method m : methods) @@ -318,11 +315,7 @@ System.out.println(m.getName()); Kurz: Programm zur Laufzeit inspizieren oder verändern -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] static class Foo { private String h = "Hallo"; public void greet() { System.out.println(h); } @@ -341,7 +334,7 @@ public static void main(String[] args) { \end{lstlisting} -\paragraph{Annotationen} +\subsubsection{Annotationen} \begin{itemize*} \item Annotationen erlauben Anmerkungen an Klassen \& Methoden \item Beginnen mit @ @@ -350,29 +343,20 @@ public static void main(String[] args) { \item Häufig genutzt, wenn zusätzlicher Code geladen wird (Java EE) \item Oder um Unit-Tests zu markieren... \end{itemize*} - -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] -class MultiTest { -@org.junit.jupiter.api.Test -void mul() { - ... -\end{lstlisting} -Annotationen erlauben Anmerkungen an Klassen \& Methoden, Beginnen mit @ -Einige wenige vordefinierte z.B. @Override - Nachteile: \begin{itemize*} \item Geringe Geschwindigkeit weil Zugriff über Programmcode erfolgt \item Kapselung kann umgangen werden \end{itemize*} +\begin{lstlisting}[language=java] +class MultiTest { +@org.junit.jupiter.api.Test +void mul() { + ... +\end{lstlisting} - -\paragraph{Reflektionen über Reflections} +\subsubsection{Reflektionen über Reflections} \begin{itemize*} \item Reflections sind ein sehr mächtiges Werkzeug, aber Einsatz sollte wohldosiert erfolgen \item Nachteile: @@ -394,8 +378,6 @@ Nachteile: \end{itemize*} \end{itemize*} - - \subsection{Assertions/Pre-/Postconditions/Invarianten} \begin{itemize*} \item Kann man interne Zustände testen, ohne invasive Techniken wie Reflections? @@ -408,11 +390,7 @@ Nachteile: \end{itemize*} \end{itemize*} -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[ language=java ] class Stack { public void push(Object o) { ... @@ -423,10 +401,6 @@ public void push(Object o) { } \end{lstlisting} - - -An sinnvollen Stellen im Programmcode testen, ob Annahmen/Zusicherungen (Assertions) stimmen... - Aber: Ausführungsgeschwindigkeit niedriger \begin{itemize*} \item Zeitverlust stark abhängig von Programm/Programmiersprache @@ -439,11 +413,7 @@ Aber: Ausführungsgeschwindigkeit niedriger \item Aktivierung der Tests über Start mit java -ea \item Benötigt spezielle "if"-Bedingung: assert \end{itemize*} -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] class Stack { public void push(Object o) { ... @@ -452,8 +422,7 @@ class Stack { } \end{lstlisting} - -\paragraph{Welche braucht man?} +\subsubsection{Welche braucht man?} \begin{itemize*} \item Woran erkennt man beim Programmieren bzw. (erneutem) Lesen von Code, dass man eine Assertion hinzufügen sollte? \item Eine einfache Heuristik - Die "Eigentlich"-Regel: @@ -463,7 +432,7 @@ class Stack { \end{itemize*} \end{itemize*} -\paragraph{Spezielle Assertions: Pre- \& Postconditions} +\subsubsection{Spezielle Assertions: Pre- \& Postconditions} \begin{itemize*} \item Methoden/Programmabschnitte testen Bedingung vor und nach Ausführung \item Einige Sprachen bieten spezialisierte Befehle: requires und ensures @@ -479,38 +448,30 @@ class Stack { \item Ziel mancher Sprachen: Formale Aussagen über Korrektheit \end{itemize*} -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] class Stack { -public void push(Object o) { - assert o != null // precondition - ... - assert empty() == false // postcondition -} + public void push(Object o) { + assert o != null // precondition + ... + assert empty() == false // postcondition + } ... } \end{lstlisting} -\paragraph{Klasseninvarianten} +\subsubsection{Klasseninvarianten} \begin{itemize*} \item Bei OO-Programmierung sind Vor- und Nachbedingungen nur eingeschränkt sinnvoll - \item Bedingungen oft besser auf Objekt-Ebene -> interner Zustand + \item Bedingungen oft besser auf Objekt-Ebene $\rightarrow$ interner Zustand \item Invarianten spezifizieren Prüfbedingungen - \item In Java nicht nativ unterstützt: + \item In Java nicht nativ unterstützt \begin{itemize*} \item Erweiterungen, wie Java Modeling Language \item Simulation \end{itemize*} \end{itemize*} -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] class Stack { void isValid() { for(Object o : _objs) // Achtung: O(n) Aufwand! @@ -523,18 +484,7 @@ public void push(Object o) { } \end{lstlisting} - \subsection{Exceptions} - -Signifikantes Element vieler Sprachen: Wie wird mit Fehlern umgegangen? -Fehler können unterschiedliche Gründe haben -Besser für Code-Komplexität: Fehlerprüfungen an zentralerer Stelle -\begin{itemize*} - \item Abbrechen und Programm-Stack "abbauen" bis (zentrale) Fehlerbehandlung greift - \item Dabei Fehler sinnvoll gruppieren - \item Java (und viele mehr): try/catch/throw-Konstrukt -\end{itemize*} - \begin{itemize*} \item Wie wird mit Fehlern umgegangen? \item gut für Code-Komplexität: Fehlerprüfungen an zentralerer Stelle @@ -547,44 +497,29 @@ Besser für Code-Komplexität: Fehlerprüfungen an zentralerer Stelle \item throw übergibt ein Objekt vom Typ Throwable an Handler, dabei zwei Unterarten: \item Error: Sollte nicht abgefangen werden z.B. Fehler im Byte-Code, Fehlgeschlagene Assertions \item Exceptions: Programm muss Exception fangen oder in Methode vermerken, + \begin{itemize*} + \item Checked Exception: Programm muss Exception fangen oder in Methode vermerken + \item Runtime Exceptions: Müssen nicht (aber sollten) explizit behandelt werden, bspw. ArithmeticException oder IndexOutOfBoundsException + \end{itemize*} \end{itemize*} \end{itemize*} -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily -] +\begin{lstlisting}[language=java] private void readFile(String f) { -try { -Path file = Paths.get("/tmp/file"); -if(Files.exists(file) == false) - throw new IOException("No such dir"); -array = Files.readAllBytes(file); -} catch(IOException e) { -// do something about it -} + try { + Path file = Paths.get("/tmp/file"); + if(Files.exists(file) == false) + throw new IOException("No such dir"); + array = Files.readAllBytes(file); + } catch(IOException e) { + // do something about it + } } \end{lstlisting} - -throw übergibt ein Objekt vom Typ Throwable an Handler, dabei zwei Unterarten: -\begin{itemize*} - \item Error: Sollte nicht abgefangen werden z.B. Fehler im Byte-Code, Fehlgeschlagene Assertions - \item Exceptions: - \begin{itemize*} - \item Checked Exception: Programm muss Exception fangen oder in Methode vermerken - \item Runtime Exceptions: Müssen nicht (aber sollten) explizit behandelt werden, bspw. ArithmeticException oder IndexOutOfBoundsException - \end{itemize*} -\end{itemize*} - -\paragraph{Checked Exceptions} +\subsubsection{Checked Exceptions} Deklaration einer überprüften Exception: -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] void dangerousFunction() throws IOException { ... if(onFire) @@ -603,27 +538,19 @@ Sollte man checked oder unchecked Exceptions verwenden? \end{itemize*} Abfangen mehrerer unterschiedlicher Exceptions -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] try { -dangerousFunction(); + dangerousFunction(); } catch(IOException i) { -// handle that nasty error + // handle that nasty error } catch(Exception e) { -// handle all other exceptions + // handle all other exceptions } \end{lstlisting} Aufräumen nach einem try-catch-Block: Anweisungen im finally-Block werden immer ausgeführt, d.h. auch bei return in try- oder catch-Block (oder fehlerloser Ausführung) -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] try { dangerousFunction(); } catch(Exception e) { @@ -641,73 +568,53 @@ try { \item Parametrisierung eines Software-Elementes (Methode, Datenstruktur, Klasse, ...) durch einen oder mehrere Typen \end{itemize*} Beispiel: -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] int min(int a, int b) { -return a < b ? a : b; + return a < b ? a : b; } float min(float a, float b) { -return a < b ? a : b; + return a < b ? a : b; } String min(String a, String b) { // lexikographisch -return a.compareTo(b) < 0 ? a : b; + return a.compareTo(b) < 0 ? a : b; } \end{lstlisting} - -\paragraph{Grenzen von Typsubstitution} +\subsubsection{Grenzen von Typsubstitution} Kann ein Objekt einer Oberklasse (eines Typs) durch ein Objekt seiner Unterklasse (Subtyps) ersetzt werden? Möglicher Ausweg: Klassenhierarchie mit zentraler Basisklasse -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] void sort(Object[] feld) { ... } //z.B. java.lang.Object void sort(java.util.Vector feld) { ... } //alternativ (nutzt intern Object) \end{lstlisting} Möglicher Ausweg 2: Nutzung primitiver Datentypen nicht direkt möglich -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] Object[] feld = new Object[10]; //Object[] != int[] feld[0] = new Integer(42); int i = ((Integer) feld[0]).intValue(); //erfordert Wrapper-Klassen wie java.lang.Integer \end{lstlisting} +Weiteres Problem: Typsicherheit -Weiteres Problem: Typsicherheit
Typ-Substituierbarkeit: Kann ein Objekt einer Oberklasse (eines Typs) durch ein Objekt seiner Unterklasse (Subtyps) ersetzt werden? + Beispiel (isSubtyp): short $\rightarrow$ int $\rightarrow$ long + Viele Programmiersprachen ersetzen Typen automatisch, d.h. diese wird auch für shorts und ints verwendet -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] long min(long a, long b) { -return a < b ? a : b; + return a < b ? a : b; } \end{lstlisting} - Kreis-Ellipse-Problem: Modellierung von Vererbungsbeziehungen \begin{itemize*} \item "Ist ein Kreis eine Ellipse?" "Oder eine Ellipse ein Kreis?" \item Annahme: Kreis := Ellipse mit Höhe = Breite \end{itemize*} -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] Circle c = new Circle(); c.skaliereX(2.0); //skalieren aus Klasse Circle c.skaliereY(.5); //is das noch ein Kreis? @@ -718,59 +625,50 @@ Verwandte Probleme: Rechteck-Quadrat, Set-Bag \subsubsection{Ko- und Kontravarianz} Geg.: Ordnung von Datentypen von spezifisch $\rightarrow$ allgemeiner -Gleichzeitige Betrachtung einer Klassenhierarchie, die Datentypen verwendet + \begin{itemize*} - \item Kovarianz: Erhaltung der Ordnung der Typen - \item Kontravarianz: Umkehrung der Ordnung - \item Invarianz: keines von beiden -\end{itemize*} -In objektorientierten Programmiersprachen im Allgemeinen -\begin{itemize*} - \item Kontravarianz: für Eingabeparameter - \item Kovarianz: für Rückgabewerte und Ausnahmen - \item Invarianz: für Ein- und Ausgabeparameter -\end{itemize*} -Anwendung für -\begin{itemize*} - \item Parameter - \item Rückgabetypen - \item Ausnahmetypen - \item Generische Datenstrukturen + \item Gleichzeitige Betrachtung einer Klassenhierarchie, die Datentypen verwendet + \begin{itemize*} + \item Kovarianz: Erhaltung der Ordnung der Typen + \item Kontravarianz: Umkehrung der Ordnung + \item Invarianz: keines von beiden + \end{itemize*} + \item In objektorientierten Programmiersprachen im Allgemeinen + \begin{itemize*} + \item Kontravarianz: für Eingabeparameter + \item Kovarianz: für Rückgabewerte und Ausnahmen + \item Invarianz: für Ein- und Ausgabeparameter + \end{itemize*} + \item Anwendung für + \begin{itemize*} + \item Parameter + \item Rückgabetypen + \item Ausnahmetypen + \item Generische Datenstrukturen + \end{itemize*} \end{itemize*} Beispiel: Basierend auf Meyer‘s SKIER-Szenario -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] class Student { -String name; -Student mate; -void setRoomMate(Student s) { ... } + String name; + Student mate; + void setRoomMate(Student s) { ... } } \end{lstlisting} Wie überschreibt man in einer Unterklasse Girl oder Boy die Methode "setRoomMate" in elternfreundlicher Weise? Von Eltern sicher gewollt - Kovarianz: -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] class Boy extends Student { -void setRoomMate(Boy b) { ... } + void setRoomMate(Boy b) { ... } } class Girl extends Student { -void setRoomMate(Girl g) { ... } + void setRoomMate(Girl g) { ... } } \end{lstlisting} Was passiert mit folgendem Code? -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] Boy kevin = new Boy("Kevin"); Girl vivian = new Girl("Vivian"); kevin.setRoomMate(vivian); @@ -779,89 +677,61 @@ kevin.setRoomMate(vivian); \begin{itemize*} \item Verwendet setRoomMate der Basisklasse \item setRoomMate Methoden der abgeleiteten Klassen überladen nur Spezialfälle $\rightarrow$ gültig - \item In C++ und Java keine Einschränkung der Typen zur Compile-Zeit \item Kovarianz so nur in wenigen Sprachen implementiert (z.B. Eiffel über redefine); Überprüfung auch nicht immer statisch! \item Auch bekannt als catcall-Problem (cat = changed availablility type) \end{itemize*} Ausweg: Laufzeitüberprüfung -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] class Girl extends Student { -... -public void setRoomMate(Student s) { //student wird aufgerufen! nicht boy oder girl, dadurch koennen die methoden der klasse verwendet werden - if (s instanceof Girl) - super.setRoomMate(s); - else - throw new ParentException("Oh Oh!"); -} + ... + public void setRoomMate(Student s) { //student wird aufgerufen! nicht boy oder girl, dadurch koennen die methoden der klasse verwendet werden + if (s instanceof Girl) + super.setRoomMate(s); + else + throw new ParentException("Oh Oh!"); + } } \end{lstlisting} - Nachteil: Nur zur Laufzeit überprüfung -\paragraph{Ko- und Kontravarianz für Rückgabewerte} +\subsubsection{Ko- und Kontravarianz für Rückgabewerte} Kovarianz (gängig): -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] public class KlasseA { -KlasseA ich() { return this; } + KlasseA ich() { return this; } } public class KlasseB extends KlasseA { -KlasseB ich() { return this; } + KlasseB ich() { return this; } } \end{lstlisting} Kontravarianz macht wenig Sinn und kommt (gängig) nicht vor -In objektorientierten Programmiersprachen im Allgemeinen -\begin{itemize*} - \item Kontravarianz: für Eingabeparameter - \item Kovarianz: für Rückgabewerte und Ausnahmen - \item Invarianz: für Ein- und Ausgabeparameter -\end{itemize*} - \subsection{Liskovsches Substitutionsprinzip (LSP)} Barbara Liskov, 1988 bzw. 1993, definiert stärkere Form der Subtyp-Relation, berücksichtigt Verhalten: -> Wenn es für jedes Objekt $o_1$ eines Typs S ein Objekt $o_2$ des Typs T gibt, so dass für alle Programme P, die mit Operationen von T definiert sind, das Verhalten von P unverändert bleibt, wenn $o_2$ durch $o_1$ ersetzt wird, dann ist S ein Subtyp von T.' -Subtyp darf Funktionalität eines Basistyps nur erweitern, aber nicht einschränken.
+ +Wenn es für jedes Objekt $o_1$ eines Typs S ein Objekt $o_2$ des Typs T gibt, so dass für alle Programme P, die mit Operationen von T definiert sind, das Verhalten von P unverändert bleibt, wenn $o_2$ durch $o_1$ ersetzt wird, dann ist S ein Subtyp von T. +Subtyp darf Funktionalität eines Basistyps nur erweitern, aber nicht einschränken. + Beispiel: Kreis-Ellipse $\rightarrow$ Kreis als Unterklasse schränkt Funktionalität ein und verletzt damit LSP Typsicherheit -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] String s = GMethod.thisOrThat("Java", "C++"); Integer i = GMethod.thisOrThat(new Integer(42), new Integer(23)); \end{lstlisting} - -\paragraph{Generics in Java (Typsicherheit)} +\subsubsection{Generics in Java (Typsicherheit)} Motivation: Parametrisierung von Kollektionen mit Typen -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] LinkedList liste = new LinkedList(); liste.add("Generics"); String s = liste.get(0); \end{lstlisting} auch für Iteratoren nutzbar -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] Iterator iter = liste.iterator(); while(iter.hasNext()) { String s = iter.next(); @@ -870,27 +740,18 @@ while(iter.hasNext()) { \end{lstlisting} oder mit erweiterter for-Schleife -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] for(String s : liste) { -System.out.println(s); + System.out.println(s); } \end{lstlisting} - Deklaration: Definition mit Typparameter -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] class GMethod { -static T thisOrThat(T first, T second) { - return Math.random() > 0.5 ? first : second; -} + static T thisOrThat(T first, T second) { + return Math.random() > 0.5 ? first : second; + } } \end{lstlisting} @@ -900,192 +761,131 @@ static T thisOrThat(T first, T second) { \item nur Referenzdatentypen (Klassennamen), keine primitiven Datentypen Anwendung: \item explizite Angabe des Typparameters - \begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] + \begin{lstlisting}[language=java] String s = GMethod.thisOrThat("Java", "C++"); Integer>thisOrThat(new Integer(42), new Integer(23)); -\end{lstlisting} - + \end{lstlisting} \item automatische Typinferenz durch Compiler - \begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] + \begin{lstlisting}[language=java] String s = GMethod.thisOrThat("Java", "C++"); Integer i = GMethod.thisOrThat(new Integer(42), new Integer(23)); -\end{lstlisting} + \end{lstlisting} \end{itemize*} - -\paragraph{Eingrenzung von Typparametern} +\subsubsection{Eingrenzung von Typparametern} Festlegung einer Mindestfunktionalität der einzusetzenden Klasse, z.B. durch Angabe einer Basisklasse \begin{itemize*} \item Instanziierung von T muss von Comparable abgeleitet werden (hier ein Interface, dass wiederum generisch ist, daher Comparable) \item Verletzung wird vom Compiler erkannt \end{itemize*} -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] static> T min(T first, T second) { -return first.compareTo(second) < 0 ? first : second; + return first.compareTo(second) < 0 ? first : second; } \end{lstlisting} Angabe des Typparameters bei der Klassendefinition: -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] class GArray { -T[] data; -int size = 0; -public GArray(int capacity) { ... } -public T get(int idx) { return data[idx]; } -public void add(T obj) { ... } + T[] data; + int size = 0; + public GArray(int capacity) { ... } + public T get(int idx) { return data[idx]; } + public void add(T obj) { ... } } \end{lstlisting} -Achtung: new T[n] ist unzulässig! Grund liegt in der Implementierung von Generics: +Achtung: new $T[n]$ ist unzulässig! Grund liegt in der Implementierung von Generics + Es gibt zwei Möglichkeiten der internen Umsetzung generischen Codes: \begin{itemize*} \item Code-Spezialisierung: jede neue Instanziierung generiert neuen Code \begin{itemize*} - \item Array → ArrayString, Array → ArrayInteger + \item Array $\rightarrow$ ArrayString, Array $\rightarrow$ ArrayInteger \item Problem: Codegröße \end{itemize*} \item Code-Sharing: gemeinsamer Code für alle Instanziierungen \begin{itemize*} - \item Array → Array, Array → Array + \item Array $\rightarrow$ Array, Array $\rightarrow$ Array \item Probleme: keine Unterstützung primitiver Datentypen \& keine Anpassung von Algorithmen an Typ \end{itemize*} \end{itemize*} Java: Code-Sharing durch Typlöschung (Type Erasure) + Typen beim Übersetzen geprüft, aber keinen Einfluss auf Code -sichert auch Kompatibilität zu nicht generischem Code (Java-Version < 1.5) Bsp.: ArrayList vs. ArrayList + +sichert auch Kompatibilität zu nicht generischem Code (Java-Version < 1.5) + +Bsp.: ArrayList vs. ArrayList Beispiel: Reflektion (Metaklassen) zur Erzeugung nutzen; danach Konstruktionsaufruf -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] public GArray(Class clazz, int capacity) { -data = (T[]) Array.newInstance(clazz, capacity); + data = (T[]) Array.newInstance(clazz, capacity); } - GArray array = new GArray(String.class, 10); \end{lstlisting} - -\paragraph{Kovarianz generischer Typen} +\subsubsection{Kovarianz generischer Typen} einfache Felder in Java sind kovariant -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] Object[] feld = new Object[10]; feld[0] = "String"; feld[1] = new Integer(42); \end{lstlisting} Instanziierungen mit unterschiedliche Typen sind jedoch inkompatibel -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] GArray anArray = new GArray(); GArray anotherArray = (GArray) anArray; \end{lstlisting} - \subsubsection{Wildcards} Wildcard "?" als Typparameter und abstrakter Supertyp für alle Instanziierungen -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] GArray aRef; aRef = new GArray(); aRef = new GArray(); \end{lstlisting} - aber nicht: -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] GArray aRef = new GArray(); \end{lstlisting} hilfreich insbesondere für generische Methoden -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] // dieser Methode ist der genaue Typ egal static void pO(GArray ia) { -for(Object o : ia) { - System.out.print(o); -} + for(Object o : ia) { + System.out.print(o); + } } // floats wollen wir mit Genauigkeit 2 haben static void pF(GArray ia) { -for(Float f : ia) { - System.out.printf("%5.2f\n", f); -} + for(Float f : ia) { + System.out.printf("%5.2f\n", f); + } } \end{lstlisting} - Beschränkte Wildcards \begin{itemize*} \item nach "unten" in der Klassenhierarchie $\rightarrow$ Kovarianz - \begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] + \begin{lstlisting}[language=java] ? extends Supertyp \end{lstlisting} - - Anwendungsbeispiel: Sortieren eines generischen Feldes erfordert Unterstützung der Comparable-Schnittstelle - \begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] + \item Anwendungsbeispiel: Sortieren eines generischen Feldes erfordert Unterstützung der Comparable-Schnittstelle + \begin{lstlisting}[language=java] void sortArray(GArray array) { ... } \end{lstlisting} - \item nach "oben" in der Klassenhierarchie $\rightarrow$ Kontravarianz - \begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] + \begin{lstlisting}[language=java] ? super Subtyp -\end{lstlisting} - - Anwendungsbeispiel: Feld mit ganzen Zahlen und Objekten - \begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] + \end{lstlisting} + \item Anwendungsbeispiel: Feld mit ganzen Zahlen und Objekten + \begin{lstlisting}[language=java] GArray array; // Zuweisungskompatibel zu ... array = new GArray(); @@ -1093,13 +893,11 @@ array = new GArray(); array = new GArray(); // aber nur erlaubt: Object obj = array.get(0); -\end{lstlisting} - + \end{lstlisting} \end{itemize*} PECS = Producer extends, Consumer super $\rightarrow$ Producer liest nur sachen, Consumer legt daten/Objekte/... ab - \subsection{Objektorientierung am Beispiel C++} \begin{itemize*} \item Ziel von C++: volle Kontrolle über Speicher \& Ausführungsreihenfolgen sowie skalierbarere Projekt-Größe @@ -1120,15 +918,10 @@ PECS = Producer extends, Consumer super $\rightarrow$ Producer liest nur sachen, \end{itemize*} \end{itemize*} -> C makes it easy to shoot yourself in the foot; C++ makes it harder, but when you do it blows your whole leg off. [Bjarne Stroustrup] - +"C makes it easy to shoot yourself in the foot; C++ makes it harder, but when you do it blows your whole leg off." [Bjarne Stroustrup] Wichtige Makrobefehle: -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=C++] #include "X.hpp" // Datei X.hpp aus Projekt-Ordner #include // Datei cstdio aus System-Includes @@ -1146,41 +939,29 @@ playMinesweeper(); #endif \end{lstlisting} - \subsubsection{C++ Klassen} Header Foo.hpp deklariert Struktur und Schnittstelle -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=C++] public: // Block ohne Zugriffsbeschränkung Foo(); // Konstruktor ~Foo(); // Destruktor protected: // Block von Dingen, auf die auch abgeleitete Klassen zugreifen dürfen int num; // Member-Variable -}; // WICHTIGES Semikolon! \end{lstlisting} - Implementierung in getrennter Datei Foo.cpp -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -\#include "Foo.hpp" // Klassen Deklaration einbinden -\#include // Einbinden von Funktionen der stdlib +\begin{lstlisting}[language=C++] +#include "Foo.hpp" // Klassen Deklaration einbinden +#include // Einbinden von Funktionen der stdlib Foo::Foo() : // Implementierung des Konstuktors von Foo -num(5) { // Statische Initialisierung von num, Code in Klammern {} kann auch initialisieren -std::cout << "c" << std::endl; + num(5) { // Statische Initialisierung von num, Code in Klammern {} kann auch initialisieren + std::cout << "c" << std::endl; } Foo::~Foo() { -std::cout << "d" << std::endl; + std::cout << "d" << std::endl; } \end{lstlisting} - \begin{itemize*} \item Reine Implementierung auch im Header möglich, aber Trennung von Implementierung und Deklaration erlaubt schnelleres Kompilieren \item Trennung nicht immer möglich (später mehr Details), aber im Allgemeinen zu bevorzugen @@ -1193,11 +974,11 @@ std::cout << "d" << std::endl; \end{itemize*} \item Schlüsselworte private, protected und public vergleichbar zu Java, werden aber vor ganze Blöcke geschrieben \begin{itemize*} - \item Kapselung nur auf Ebene von Klassen $rightarrow$ Klassen sind immer public + \item Kapselung nur auf Ebene von Klassen $\rightarrow$ Klassen sind immer public \item protected erlaubt nur der Klasse selber und Unterklassen den Zugriff \end{itemize*} \item Zugriffe außerhalb der Klassenstruktur können durch friend- Deklaration erlaubt werden (teilweise verrufen!) - \item Auch *final* ähnlich zu Java $\rightarrow$ Verhindert weiteres Ableiten von Klassen + \item Auch final ähnlich zu Java $\rightarrow$ Verhindert weiteres Ableiten von Klassen \item Schlüsselwort const markiert Methoden, die Objekte nicht verändern $\rightarrow$ Erlauben die Übergabe von Nur-Lesen-Referenzen \item Größere Unterschiede zu Java: \begin{itemize*} @@ -1220,21 +1001,16 @@ std::cout << "d" << std::endl; \begin{itemize*} \item Parametertypen (oder const-Markierung) müssen sich unterscheiden! \item Nur Veränderung des Rückgabewertes nicht ausreichend - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] + \begin{lstlisting}[language=C++] class Foo { public: void doMagic(int i); void doMagic(std::string s); }; - \end{lstlisting} + \end{lstlisting} \end{itemize*} \end{itemize*} - \subsubsection{C++ Präprozessor} C/C++-Code kann vor dem Übersetzen durch einen Präprozessor verändert werden \begin{itemize*} @@ -1256,11 +1032,7 @@ C/C++-Code kann vor dem Übersetzen durch einen Präprozessor verändert werden \end{itemize*} Beispiele: -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=C++] #include "X.hpp" // Datei X.hpp aus Projekt-Ordner #include // Datei cstdio aus System-Includes @@ -1278,33 +1050,22 @@ playMinesweeper(); #endif \end{lstlisting} - \subsubsection{Include Guards} Eine (oft hässliche) Eigenschaft des \#include-Befehls: kein Überprüfen ob eine Datei vorher bereits eingebunden wurde. Problematisches Beispiel: -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=C++] #include "Bar.hpp" //in "Bar.hpp" ist "Foo.hpp" bereits inkludiert worden #include "Foo.hpp" //Fehler weil kallse Foo bereits deklariert wurde \end{lstlisting} Common Practice: Include-Guards um alle Header-Dateien -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=C++] #ifndef FOO_HPP #define FOO_HPP ... #endif \end{lstlisting} - \subsubsection{Speichermanagement} - \begin{itemize*} \item Programmspeicher enthält Code und Daten, vom Betriebssystem i.A. auf virtuelle Adressbereiche abgebildet \item Unterschiedliche Varianten von Datenspeicher: @@ -1319,7 +1080,8 @@ Common Practice: Include-Guards um alle Header-Dateien \item Für den Heap bietet nur Java automatisches Speicher-Mgmt. \end{itemize*} -\paragraph{Eigenschaften des Stack-Speichers:} +\paragraph{Eigenschaften des Stack-Speichers} + \begin{itemize*} \item Variablen/Objekte haben klare Lebensdauer $\rightarrow$ Werden immer gelöscht wenn Funktion verlassen wird $\rightarrow$ Man kann Speicher nicht "aufheben" \item In der Regel sehr schnell, weil im Prozessor-Cache @@ -1328,17 +1090,14 @@ Common Practice: Include-Guards um alle Header-Dateien \end{itemize*} \paragraph{Heap: Keine klare Struktur} + \begin{itemize*} \item Anlegen: in C++ \& Java mit new \item Um angelegten Speicher anzusprechen: Zeiger und Referenzen \begin{itemize*} \item In Java automatisch Zeiger \item In C++ Zeiger durch * hinter Typ - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] + \begin{lstlisting}[language=C++] int main() { int* i = new int[3]; int* j = new int; @@ -1375,161 +1134,67 @@ Common Practice: Include-Guards um alle Header-Dateien Beispiele \begin{itemize*} \item Anlegen eines Objects auf dem Heap: - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] - std::string* s = new std::string("wiz!"); - delete s; - \end{lstlisting} - + \begin{lstlisting}[language=C++] + std::string* s = new std::string("wiz!"); + delete s; + \end{lstlisting} \item Allokation von Feldern: - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] - int* i = new int[29]; // gültige Indicies 0-28 - i[0] = 23; - delete [] i; // nicht mit delete i; verwechseln! - \end{lstlisting} - + \begin{lstlisting}[language=C++] + int* i = new int[29]; // gültige Indicies 0-28 + i[0] = 23; + delete [] i; // nicht mit delete i; verwechseln! + \end{lstlisting} \item Zeiger können durch \& auf beliebige Variablen ermittelt werden - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] - int i = 0; - int* j = \&i; // \&-Operator erzeugt Zeiger; j darf nicht gelöscht werden - \end{lstlisting} - + \begin{lstlisting}[language=C++] + int i = 0; + int* j = \&i; // \&-Operator erzeugt Zeiger; j darf nicht gelöscht werden + \end{lstlisting} \item Zeiger können durch * dereferenziert werden - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] - int i = 0; - int* j = \&i; // \&-Operator erzeugt Zeiger - *j = 1; // Zugriff auf Variableninhalt - \end{lstlisting} - + \begin{lstlisting}[language=C++] + int i = 0; + int* j = \&i; // \&-Operator erzeugt Zeiger + *j = 1; // Zugriff auf Variableninhalt + \end{lstlisting} \item Zugriff auf Methoden/Member Variablen - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] - std::string* s = new std::string("wiz"); - (*s).push_back('?'); // manuelles Derefenzieren - s->push_back('?'); // -> Operator - delete s; - \end{lstlisting} - + \begin{lstlisting}[language=C++] + std::string* s = new std::string("wiz"); + (*s).push_back('?'); // manuelles Derefenzieren + s$\rightarrow$push_back('?'); // $\rightarrow$ Operator + delete s; + \end{lstlisting} \item C++ übergibt alles als Kopie - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] - void set(std::string s) { s = "foo"; } - int main() { - std::string s = "bar"; - set(s); - std::cout << s; // gibt bar aus - return 0; - } - \end{lstlisting} - + \begin{lstlisting}[language=C++] + void set(std::string s) { s = "foo"; } + int main() { + std::string s = "bar"; + set(s); + std::cout << s; // gibt bar aus + return 0; + } + \end{lstlisting} \item Zeiger können verwendet werden, um schreibend zuzugreifen - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] - void set(std::string* s) { *s = "foo"; } - int main() { - std::string s = "bar"; - set(\&s); - std::cout << s; // gibt foo aus - return 0; - } - \end{lstlisting} - - \item Zeiger erlauben syntaktisch sehr viele Dinge mit unvorhersehbaren Nebenwirkungen - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] - std::string* magicStr() { - std::string s("wiz!"); - return \&s; // gibt Speicher auf Stack weiter; Tun Sie das nie! - } - int main() { - std::string* s = magicStr(); - std::cout << *s; // Stack ist bereits überschrieben! - return 0; - } - \end{lstlisting} -\end{itemize*} -Allokation von Feldern: -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -int* i = new int[29]; // gültige Indicies 0-28 -i[0] = 23; -delete [] i; // nicht mit delete i; verwechseln! -\end{lstlisting} -Zeiger können durch \& auf beliebige Variablen ermittelt werden -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -int i = 0; -int* j = \&i; // \&-Operator erzeugt Zeiger; j darf nicht gelöscht werden -\end{lstlisting} -Zeiger können durch * dereferenziert werden -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -int i = 0; -int* j = \&i; // \&-Operator erzeugt Zeiger -*j = 1; // Zugriff auf Variableninhalt -\end{lstlisting} -Zugriff auf Methoden/Member Variablen -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -std::string* s = new std::string("wiz"); -(*s).push_back('?'); // manuelles Derefenzieren -s$\rightarrow$push_back('?'); // $\rightarrow$ Operator -delete s; -\end{lstlisting} -Zeiger können verwendet werden, um schreibend zuzugreifen -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -void set(std::string* s) { *s = "foo"; } -int main() { + \begin{lstlisting}[language=C++] + void set(std::string* s) { *s = "foo"; } + int main() { std::string s = "bar"; set(\&s); std::cout << s; // gibt foo aus return 0; -} -\end{lstlisting} - + } + \end{lstlisting} + \item Zeiger erlauben syntaktisch sehr viele Dinge mit unvorhersehbaren Nebenwirkungen + \begin{lstlisting}[language=C++] + std::string* magicStr() { + std::string s("wiz!"); + return \&s; // gibt Speicher auf Stack weiter; Tun Sie das nie! + } + int main() { + std::string* s = magicStr(); + std::cout << *s; // Stack ist bereits überschrieben! + return 0; + } + \end{lstlisting} +\end{itemize*} Warum wirken sich Speicherfehler so unvorhersehbar aus? \begin{itemize*} @@ -1542,15 +1207,12 @@ Warum wirken sich Speicherfehler so unvorhersehbar aus? \end{itemize*} \paragraph{Bessere Alternative: Referenzen} + \begin{itemize*} \item Zeigen ebenfalls auf Speicher, Compiler stellt aber sicher, dass Speicher gültig ist (wenn man nicht in Zeiger wandelt etc.)! \item Markiert durch Suffix \& \item Beispiel: - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] + \begin{lstlisting}[language=C++] void set(std::string\& s) { s = "foo"; } int main() { std::string s = "bar"; @@ -1559,72 +1221,45 @@ void set(std::string\& s) { s = "foo"; } return 0; } \end{lstlisting} - - \item Dereferenzierung durch * und -> nicht notwendig + \item Dereferenzierung durch * und $\rightarrow$ nicht notwendig \item Referenzen sind toll, haben aber eine Einschränkung: - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] - std::string\& magicStr() { - std::string s("wiz!"); - return s; //< FEHLER + \begin{lstlisting}[language=C++] + std::string& magicStr() { + std::string s("wiz!"); + return s; //< FEHLER + } + \end{lstlisting} + \begin{lstlisting}[language=C++] + std::string& magicStr() { + static std::string s("wiz!"); + return s; // klappt prima } \end{lstlisting} - - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] - std::string\& magicStr() { - static std::string s("wiz!"); - return s; // klappt prima - } -\end{lstlisting} - \item Per Referenz übergebene Rückgabewerte müssen im Speicher noch existieren, wenn Methodenaufruf abgeschlossen ist... \begin{itemize*} \item OK für globale Variablen, Member-Variablen, statische Variablen... \item Nicht-OK für Speicher der wirklich dynamisch alloziert werden muss \end{itemize*} \item Allgemein bleiben nur Zeiger und Heap: - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -std::string* magicStr() { - std::string* s = new std::string("wiz!"); - return s; // klappt prima, aber: aufpassen wann s gelöscht - // werden kann und vollständig vergessen wurde! -} -\end{lstlisting} - - - \item Konvertierung von Zeigern zu Referenzen mit "*"-Operator: - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] + \begin{lstlisting}[language=C++] + std::string* magicStr() { + std::string* s = new std::string("wiz!"); + return s; // klappt prima, aber: aufpassen wann s gelöscht + // werden kann und vollständig vergessen wurde! + } + \end{lstlisting} + \item Konvertierung von Zeigern zu Referenzen mit $*$-Operator: + \begin{lstlisting}[language=C++] std::string\& s = *magicStr(); // Konvertieren in Referenz; Delete nicht mehr möglich std::string s2 = *magicStr(); // Konvertieren in Referenz \& Kopie! Delete nicht direkt möglich -\end{lstlisting} - - \item Konvertierung von Referenzen zu Zeigern mit "\&"-Operator: - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] - std::string s("bla"); - std::string* sStar = \&s; // Konvertieren in Zeiger -\end{lstlisting} + \end{lstlisting} + \item Konvertierung von Referenzen zu Zeigern mit $\&$-Operator: + \begin{lstlisting}[language=C++] + std::string s("bla"); + std::string* sStar = \&s; // Konvertieren in Zeiger + \end{lstlisting} \end{itemize*} - \begin{itemize*} \item Abschließende Bemerkungen zum Speicher \begin{itemize*} @@ -1637,26 +1272,21 @@ std::string* magicStr() { \item Statische Code Analyse nutzen: z.B. http://cppcheck.sourceforge.net \item malloc/free sind Äquivalente in Sprache C und nicht typsicher! \end{itemize*} - \item Verbreitetes Vorgehen in C++ (Pattern): Resource Acquisition Is Initialization (RAII) \begin{itemize*} \item Speicher (oder Ressourcen im Allgemeinen) wird nur im Konstruktor einer Klasse reserviert \item Destruktor gibt Speicher frei \item Sicheres (Exceptions!), nachvollziehbares Konstrukt \item Beispiel: (Funktioniert leider noch nicht immer) - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] + \begin{lstlisting}[language=C++] class MagicString { - std::string* s; - public: - MagicString() : s(new std::string("wiz!")) {} - std::string* magicStr() { return s; } - ~MagicString() { delete s; } + std::string* s; + public: + MagicString() : s(new std::string("wiz!")) {} + std::string* magicStr() { return s; } + ~MagicString() { delete s; } }; - \end{lstlisting} + \end{lstlisting} \end{itemize*} \end{itemize*} @@ -1664,68 +1294,57 @@ std::string* magicStr() { \begin{itemize*} \item Vermeiden von Mehrfachimplementierungen \item Vermeiden von Dopplung interner Daten - \item Vererbung syntaktisch ebenfalls ähnlich zu Java: - \begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] -class Foo { - public: - int magic() const { return 23; } - int enchanting() const { return 0xbeef; } -}; -class FooBar : public Foo { - public: - int magic() const { return 42; } -}; -\end{lstlisting} + \item Vererbung syntaktisch ebenfalls ähnlich zu Java + \begin{lstlisting}[language=java] + class Foo { + public: + int magic() const { return 23; } + int enchanting() const { return 0xbeef; } + }; + class FooBar : public Foo { + public: + int magic() const { return 42; } + }; + \end{lstlisting} \end{itemize*} \begin{itemize*} \item Unterschied zu Java: Methoden "liegen" bei C++ statisch im Speicher \begin{itemize*} - \item D.h. f.magic(); ruft statisch magic-Methode in Klasse Foo auf, weil f eine Referenz vom Typ Foo ist + \item D.h. $f.magic();$ ruft statisch magic-Methode in Klasse Foo auf, weil f eine Referenz vom Typ Foo ist \item Vermeidet Mehrfachimplementierungen, realisiert aber keine einheitliche Schnittstelle! \end{itemize*} \item Nach Überschreiben einer Methode wollen wir meist, dass genutzte Methode nicht vom Referenztyp abhängt, sondern vom Objekttyp \begin{itemize*} \item Idee zu jedem Objekt speichern wir Zeiger auf zu nutzende Methoden - \item Tabelle wird *vtable* bezeichnet + \item Tabelle wird $vtable$ bezeichnet \item Markierung von Methoden, für die ein Zeiger vorgehalten wird, mit Schlüsselwort virtual \item Funktionierendes Beispiel: - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] - class Foo { - public: - virtual int magic() const { return 23; } - }; - class FooBar : public Foo { - public: - int magic() const override { return 42; } - }; - int r(const Foo\& f) { return f.magic(); } - int main() { - return r(FooBar()); // yeah gibt 42 zurück! - } - \end{lstlisting} + \begin{lstlisting}[language=C++] + class Foo { + public: + virtual int magic() const { return 23; } + }; + class FooBar : public Foo { + public: + int magic() const override { return 42; } + }; + int r(const Foo\& f) { return f.magic(); } + int main() { + return r(FooBar()); // yeah gibt 42 zurück! + } + \end{lstlisting} \item virtual-Markierung genügt in Oberklasse, alle abgeleiteten Methoden ebenfalls "virtuell" \item override-Markierung optional, aber hätte vor fehlendem virtual gewarnt! \end{itemize*} \end{itemize*} + Definierte Programmierschnittstellen durch Überschreiben von Methoden/abstrakte Methoden; Vermeiden von Dopplung interner Daten. Unterschied zu Java: Methoden "liegen" bei C++ statisch im Speicher -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=C++] class Stromfresser { -public: + public: Stromfresser() { std::cerr << "Mjam" << std::endl; } @@ -1741,24 +1360,18 @@ int main() { \end{lstlisting} Mit virtual: "Mjam", ohne virtual: "Mjam Mjam" - \paragraph{Mehrfachvererbung} \begin{itemize*} \item C++ unterstützt keine Interfaces - \item Aber C++ unterstützt Mehrfachvererbung! Pro Interface eine Basisklasse -> mit abstrakten Methoden erstellen + \item Aber C++ unterstützt Mehrfachvererbung! Pro Interface eine Basisklasse $\rightarrow$ mit abstrakten Methoden erstellen \item Gute Praxis: Explizites Überschreiben - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -class NiceFooBar : public Foo, public Bar { - // erlaube NiceFooBar().magic() - int magic() const override { return Bar::magic(); } -}; -\end{lstlisting} - + \begin{lstlisting}[language=C++] + class NiceFooBar : public Foo, public Bar { + // erlaube NiceFooBar().magic() + int magic() const override { return Bar::magic(); } + }; + \end{lstlisting} \begin{itemize*} \item Wegen Mehrfachvererbung: kein super:: \item Stattdessen immer NameDerBasisKlasse:: @@ -1781,38 +1394,37 @@ Komposition statt Vererbung \item Engl.: Prefer composition over inheritance \end{itemize*} -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=C++] class Automatisierungsmodul { -public: - void steuere() = 0; -}; + public: + void steuere() = 0; + }; +} class Roboter : public Automatisierungsmodul{ -public: - void steuere() { /* call HAL */ } -}; + public: + void steuere() { /* call HAL */ } + }; +} class DumbDevice : public Automatisierungsmodul { -public: - void steuere() { /* do nothing */ } -}; + public: + void steuere() { /* do nothing */ } + }; +} class Geraet { -protected: - Automatisierungsmodul* _a; - Geraet(Automatisierungsmodul* a, Saeuberungsmodul* s): _a(a), _s(s) {} -public: - void steuere() { _a->steuere(); } -}; + protected: + Automatisierungsmodul* _a; + Geraet(Automatisierungsmodul* a, Saeuberungsmodul* s): _a(a), _s(s) {} + public: + void steuere() { _a$\rightarrow$steuere(); } + }; +} \end{lstlisting} \subsubsection{Operator-Overloading} - \begin{itemize*} - \item In Java: Unterschied zwischen "==" und "equals()" bei String-Vergleich - \item In C++: "=="-Operator für String-Vergleich - \item Umsetzung: Hinzufügen einer Methode mit Namen *operatorx* wobei für x unter anderem zulässig: $+ - * / \% ^ \& | ~ ! = < > += -= *= /= \%= ^= \&= |= << >> >>= <<= == != <= >= <=> \&\& || ++ -- , ->* -> () []$ + \item In Java: Unterschied zwischen $==$ und $equals()$ bei String-Vergleich + \item In C++: $==$-Operator für String-Vergleich + \item Umsetzung: Hinzufügen einer Methode mit Namen $operator x$ wobei für x unter anderem zulässig: $+ - * / \% ^ \& | ~ ! = < > += -= *= /= \%= ^= \&= |= << >> >>= <<= == != <= >= <=> \&\& || ++ -- , ->* -> () []$ \item Vereinfacht Nutzung komplexer Datentypen teilweise sehr stark \item Aber: Erfordert Disziplin beim Schreiben von Code \begin{itemize*} @@ -1826,12 +1438,8 @@ public: \end{itemize*} \end{itemize*} -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -class MagicString { // Remember me? +\begin{lstlisting}[language=C++] +class MagicString { std::string* s; public: MagicString() : s(new std::string("wiz!")) {} @@ -1850,7 +1458,6 @@ public: }; \end{lstlisting} - \subsubsection{Templates} \begin{itemize*} \item Generische Datentypen werden in C++ mit Templates realsiert @@ -1859,22 +1466,14 @@ public: \item Einfaches Beispiel (mit Typen, ähnl. zu Generics, primitive Typen ok!): \end{itemize*} -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily -] -template // typename keyword -> deklariert T als Typ +\begin{lstlisting}[language=C++] +template // typename keyword $\rightarrow$ deklariert T als Typ T max(T a, T b) { -return (a > b ? a : b); + return (a > b ? a : b); } \end{lstlisting} -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily -] +\begin{lstlisting}[language=C++] int i = 10; int j = 2; int k = max(j, i); // explizit @@ -1882,82 +1481,59 @@ int l = max(j, i); // automat. Typinferenz durch Parametertypen \end{lstlisting} \begin{itemize*} - \item Ein wichtiges Grundkonzept von Templates: Substitution failure is not an error (SFINAE) es -> wird solange nach passenden Templates (in lexikogr. Reihenfolge) gesucht bis Parameter passen (sonst Fehler!) + \item Ein wichtiges Grundkonzept von Templates: Substitution failure is not an error (SFINAE) es $\rightarrow$ wird solange nach passenden Templates (in lexikogr. Reihenfolge) gesucht bis Parameter passen (sonst Fehler!) \item Sehr häufig verwendetes Konstrukt \& mächtiger als es scheint, aber schwer zu beherrschen \begin{itemize*} \item Wir können alternativ versuchen, durch SFINAE zu verhindern, dass Funktionen doppelt definiert sind \item Trick: Einführen eines Pseudoparameters, der nicht benutzt wird - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily -] -template -T quadrieren(T i, typename T::Val pseudoParam = 0) { -T b(i); b *= i; return b; -} -\end{lstlisting} - + \begin{lstlisting}[language=C++] + template + T quadrieren(T i, typename T::Val pseudoParam = 0) { + T b(i); b *= i; return b; + } + \end{lstlisting} \item Trick: Einführen eines Hilfstemplates (sogenannter trait): wenn arithmetic::Cond definiert ist, muss T = int sein - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily -] -template struct arithmetic {}; -template<> struct arithmetic { using Cond = void*; }; -\end{lstlisting} - + \begin{lstlisting}[language=C++] + template struct arithmetic {}; + template<> struct arithmetic { using Cond = void*; }; + \end{lstlisting} \item Definition einer Funktion, die nur für int instanziiert werden kann: - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily -] -template -T quadrieren(T i, typename arithmetic::Cond = nullptr) { -return i * i; -} -\end{lstlisting} + \begin{lstlisting}[language=C++] + template + T quadrieren(T i, typename arithmetic::Cond = nullptr) { + return i * i; + } + \end{lstlisting} \end{itemize*} \end{itemize*} \subsubsection{Container} - \begin{itemize*} \item Templates werden an vielen Stellen der C++ Standard-Bibliothek verwendet \item Container implementieren alle gängigen Datenstrukturen \item Prominente Beispiele: - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -template class vector; // dynamisches Array -template class list; // doppelt verkette Liste -template class set; // geordnete Menge basiert auf Baum -template class map; // Assoziatives Array, -\end{lstlisting} + \begin{lstlisting}[language=C++] + template class vector; // dynamisches Array + template class list; // doppelt verkette Liste + template class set; // geordnete Menge basiert auf Baum + template class map; // Assoziatives Array, + \end{lstlisting} \item Alle Templates sind stark vereinfacht dargestellt, weitere Parameter haben Standardwerte, die z.B. Speicherverhalten regeln \end{itemize*} - \paragraph{Container Enumerieren} + \begin{itemize*} \item Je nach Struktur unterschiedlicher Zugriff \item Oft über Iteratoren vom Typ Container::iterator, bspw. vector::iterator \end{itemize*} -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=C++] std::vector v{ 1, 2, 3 }; // Initialisierung über Liste // normale for-Schleife, Beachte: Überladene Operatoren ++ und * for(std::vector::iterator i = v.begin(); i != v.end(); ++i) { std::cout << *i << std::endl; } - // auto erlaubt Typinferenz -> Code lesbarer, aber fehleranfälliger + // auto erlaubt Typinferenz $\rightarrow$ Code lesbarer, aber fehleranfälliger for(auto i = v.begin(); i != v.end(); ++i) { std::cout << *i << std::endl; } @@ -1967,36 +1543,36 @@ template class map; // Assoziatives Array, } \end{lstlisting} - \paragraph{Container Einfügen} + \begin{itemize*} \item Unterschiedliche Operationen je nach Container-Typ - \item std::vector::push\_back() fügt neues Element am Ende ein + \item $std::vector::push\_back()$ fügt neues Element am Ende ein \begin{itemize*} \item Allokiert ggf. neuen Speicher \item Exisitierende Pointer können dadurch invalidiert werden!!! \end{itemize*} - \item std::list zusätzlich push\_front() fügt Element am Anfang ein - \item std::set, std::map, ... + \item $std::list \text{ zusätzlich } push\_front()$ fügt Element am Anfang ein + \item $std::set$, $std::map$, ... \begin{itemize*} - \item insert() fügt Element ein, falls es nicht existiert (Optional mit Hinweis wo ungefähr eingefügt werden soll) - \item operator[] erlaubt Zugriff aber auch Überschreiben alter Elemente - \item emplace() Einfügen, ohne Kopien zu erzeugen (nicht behandelt) + \item $insert()$ fügt Element ein, falls es nicht existiert (Optional mit Hinweis wo ungefähr eingefügt werden soll) + \item $operator[]$ erlaubt Zugriff aber auch Überschreiben alter Elemente + \item $emplace()$ Einfügen, ohne Kopien zu erzeugen (nicht behandelt) \end{itemize*} \end{itemize*} \paragraph{Container Löschen} + \begin{itemize*} \item Unterschiedliche Operationen je nach Container-Typ \item Allgemein: erase(Container::iterator) (Vorsicht ggf. werden Iterator/Zeiger auf Objekte dadurch ungültig!) - \item std::vector::resize() löscht implizit letzte Elemente bei Verkleinerung - \item std::vector::pop\_back()entfernt letztes Element - \item std::list hat zusätzlich pop\_front() - \item std::set, std::map, ... löschen nur mit erase() + \item $std::vector::resize()$ löscht implizit letzte Elemente bei Verkleinerung + \item $std::vector::pop\_back()$ entfernt letztes Element + \item $std::list$ hat zusätzlich $pop\_front()$ + \item $std::set$, $std::map$, ... löschen nur mit $erase()$ \end{itemize*} \subsubsection{Shared Pointer} - \begin{itemize*} \item Synonym: Smart Pointer \item Ziel: Sichereres Verwenden von Speicher @@ -2004,11 +1580,7 @@ template class map; // Assoziatives Array, \item Realisierung mit RAII, Templates, Operator-Überladung \item Beispiel, wie shared\_ptr sich verhalten sollten \end{itemize*} -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=C++] using stringP = shared_ptr; stringP hello() { // gibt kopie der referenz zurück return stringP(new std::string("Hello!")); @@ -2017,7 +1589,7 @@ stringP hello() { // gibt kopie der referenz zurück int main() { stringP x = hello(); stringP y(x); // Erstellen einer weiteren Referenz - std::cout << y->length(); + std::cout << y$\rightarrow$length(); return 0; // Original-String wird gelöscht wenn letzte Ref. weg } @@ -2029,7 +1601,7 @@ public: shared_ptr(T* t) : p(t), r(new int) { *r = 1; } // Referenz durch andere Referenz erzeugen shared_ptr(const shared_ptr\& sp) : p(sp.p), r(sp.r) { ++(*r); } - T* operator->() const { // benutzen wie einen richtigen Zeiger + T* operator$\rightarrow$() const { // benutzen wie einen richtigen Zeiger return p; } ~shared_ptr() { @@ -2038,14 +1610,10 @@ public: delete p; } } -}; // TODO operator= implementieren! +}; \end{lstlisting} -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=C++] template class shared_ptr { // Vereinfacht! T* p; // Zeiger auf eigentliches Objekt int*r; // Referenzzähler @@ -2064,7 +1632,6 @@ public: }}}; \end{lstlisting} - \subsubsection{Vergleich mit Java} \begin{itemize*} \item Unterschiede im Aufbau: @@ -2099,11 +1666,7 @@ public: \end{itemize*} \end{itemize*} -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=java] [Hello.java] package hello; // say that we are part of a package public class Hello { // declare a class called Hello: @@ -2115,11 +1678,7 @@ package hello; // say that we are part of a package } // end of class Hello \end{lstlisting} -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=C++] [Hello.cpp] // include declarations for I/O library where cout object is specified in namespace std:: #include @@ -2141,15 +1700,14 @@ int main(int argc, char* argv[]) { \item Code kann völlig unlesbar werden! Viele Features sollten nur eingesetzt werden wenn sich dadurch ein wirklicher Vorteil ergibt! \end{itemize*} - \subsection{Objektorientierung am Beispiel Java} \begin{itemize*} - \item Bekannt: + \item Bekannt \begin{itemize*} \item Grundlegendes Verständnis von Java \item Kapselung durch Klassen und Vererbung \end{itemize*} - \item Ziele: + \item Ziele \begin{itemize*} \item Verständnis der Probleme bei Vererbung und Typersetzbarkeit in objektorientierten Programmiersprachen \item Kennenlernen der Grundideen generischer und abstrahierender Konzepte in Objekt-orientierter Programmierung (OOP) @@ -2159,9 +1717,10 @@ int main(int argc, char* argv[]) { \end{itemize*} \paragraph{Unit-Testing in Java} + \begin{itemize*} \item De facto Standard: JUnit Framework - \item "Best Practice" für einfachen Einsatz: + \item Best Practice für einfachen Einsatz: \begin{itemize*} \item Java Code in ein oder mehrere Klassen im Ordner src speichern \item Im Ordner tests jeweils eine Klasse anlegen, die Funktionen einer Implementierungsklasse prüft @@ -2172,7 +1731,7 @@ int main(int argc, char* argv[]) { \item Viele weitere Features, z.B. Deaktivieren von Tests, Timeouts, GUI Coverage, Mocks \end{itemize*} - +\newpage \section{Einführung in Funktionale Programmierung} Sind $v_1, ..., v_n$ Unbestimmte vom Typ $T_1, ..., T_n$ (bool oder int) und ist $t(v_1,...,v_n)$ ein Term, so heißt $f(v_1,...,v_n)= t(v_1,...,v_n)$ eine Funktionsdefinition vom Typ $T$. $T$ ist dabei der Typ des Terms. @@ -2182,10 +1741,7 @@ Kategorien der funktionalen Sprachen \begin{itemize*} \item Ordnung der Sprache \begin{itemize*} - \item Erster Ordnung: - \begin{itemize*} - \item Funktionen können (nur) definiert und aufgerufen werden - \end{itemize*} + \item Erster Ordnung: Funktionen können (nur) definiert und aufgerufen werden \item Höherer Ordnung: \begin{itemize*} \item Funktionen können außerdem als Parameter an Funktionen übergeben werden und/oder Ergebnisse von Funktionen sein. @@ -2209,71 +1765,38 @@ Kategorien der funktionalen Sprachen \item Realisiert "Sharing" (im Unterschied zur Normalform-Reduktion - dort werden gleiche Ausdrücke immer wieder erneut berechnet). \end{itemize*} \end{itemize*} + \item Typisierung: + \begin{itemize*} + \item Stark typisiert: Die verbreiteten funktionalen Programmiersprachen sind stark typisiert, d.h. alle Typfehler werden erkannt. + \begin{description*} + \item[Statisch typisiert] Typprüfung wird zur Übersetzungszeit ausgeführt. + \item[Dynamisch typisiert] Typprüfung wird zur Laufzeit ausgeführt + \end{description*} + \item Untypisiert: Reiner Lambda-Kalkül (später) + \end{itemize*} \end{itemize*} \subsection{Applikaive Algorithmen} -Grundidee: +Grundidee \begin{itemize*} \item Definition zusammengesetzter Funktionen durch Terme: $f(x) = 5x + 1$ \item Unbestimmte: \begin{itemize*} - \item x, y, z, . . . vom Typ int - \item q, p, r , . . . vom Typ bool + \item $x, y, z, . . .$ vom Typ int + \item $q, p, r , . . .$ vom Typ bool \end{itemize*} \item Terme mit Unbestimmten (z.B. Terme vom Typ int: $x, x - 2, 2x + 1, (x + 1)(y - 1)$) - \item Terme vom Typ bool $p, p \vee true, (p V true) \Rightarrow (q V false)$ + \item Terme vom Typ bool $p, p \vee true, (p \vee true) \Rightarrow (q \vee false)$ \end{itemize*} -> Sind $v_1, ..., v_n$ Unbestimmte vom Typ $\tau_1,...,\tau_n$ (bool oder int) und ist $t(v_1, ..., v_n)$ ein Term, so heißt $f(v_1, ..., v_n) = t(v_1, ..., v_n)$ eine Funktionsdefinition vom Typ $\tau$ . $\tau$ ist dabei der Typ des Terms. +Sind $v_1, ..., v_n$ Unbestimmte vom Typ $\tau_1,...,\tau_n$ (bool oder int) und ist $t(v_1, ..., v_n)$ ein Term, so heißt $f(v_1, ..., v_n) = t(v_1, ..., v_n)$ eine Funktionsdefinition vom Typ $\tau .\tau$ ist dabei der Typ des Terms. \begin{itemize*} \item Erweiterung der Definition von Termen \item Neu: Aufrufe definierter Funktionen sind Terme \end{itemize*} -> Ein applikativer Algorithmus ist eine Menge von Funktionsdefinitionen. Die erste Funktion $f_1$ wird wie beschrieben ausgewertet und ist die Bedeutung (Semantik) des Algorithmus. - -\begin{itemize*} - \item Kategorisierung nach unterschiedlichen Kriterien - \item Ordnung der Sprache - \begin{itemize*} - \item Erster Ordnung: - \begin{itemize*} - \item Funktionen können (nur) definiert und aufgerufen werden - \end{itemize*} - \item Höherer Ordnung: - \begin{itemize*} - \item Funktionen können außerdem als Parameter an Funktionen übergeben werden und/oder Ergebnisse von Funktionen sein. - \item Funktionen sind hier auch Werte! - erstklassige Werte; - \item Erstklassig: Es gibt keine Einschränkungen. - \item Umgekehrt: Wert ist eine Funktion ohne Parameter - \end{itemize*} - \end{itemize*} - \item Auswertungsstrategie: - \begin{itemize*} - \item Strikte Auswertung: - \begin{itemize*} - \item Synonyme: strict evaluation, eager evaluation, call by value, applikative Reduktion - \item Die Argumente einer Funktion werden vor Eintritt in die Funktion berechnet (ausgewertet) - wie z.B. in Pascal oder C. - \end{itemize*} - \item Bedarfsauswertung: - \begin{itemize*} - \item Synonyme: Lazy evaluation, call by need - \item Funktionsargumente werden unausgewertet an die Funktion übergeben - \item Erst wenn die Funktion (in ihrem Körper) die Argumente benötigt, werden die eingesetzten Argumentausdrücke berechnet, und dann nur einmal. - \item Realisiert "Sharing" (im Unterschied zur Normalform-Reduktion - dort werden gleiche Ausdrücke immer wieder erneut berechnet). - \end{itemize*} - \end{itemize*} - \item Typisierung: - \begin{itemize*} - \item Stark typisiert: Die verbreiteten funktionalen Programmiersprachen sind stark typisiert, d.h. alle Typfehler werden erkannt. - \begin{itemize*} - \item Statisch typisiert: Typprüfung wird zur Übersetzungszeit ausgeführt. - \item Dynamisch typisiert: Typprüfung wird zur Laufzeit ausgeführt - \end{itemize*} - \item Untypisiert: Reiner Lambda-Kalkül (später) - \end{itemize*} -\end{itemize*} +Ein applikativer Algorithmus ist eine Menge von Funktionsdefinitionen. Die erste Funktion $f_1$ wird wie beschrieben ausgewertet und ist die Bedeutung (Semantik) des Algorithmus. \subsection{Die funktionale Programmiersprache Erlang} \begin{itemize*} @@ -2283,6 +1806,7 @@ Grundidee: \end{itemize*} \paragraph{Arbeiten mit Erlang} + \begin{itemize*} \item Erlang-Programme werden durch Definition der entsprechenden Funktionen in Modulen erstellt \item Module können in den Erlang-Interpreter geladen und von diesem in Zwischencode übersetzt werden @@ -2290,22 +1814,35 @@ Grundidee: \end{itemize*} Modul "fakultaet.erl": -\begin{lstlisting}[ - language=erlang, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=erlang] -module(fakultaet). -export([fak/1]). -fak(0) -> 1; -fak(N) when N > 0 -> (N) * fak(N-1). +fak(0) $\rightarrow$ 1; +fak(N) when N > 0 $\rightarrow$ (N) * fak(N-1). \end{lstlisting} -Laden in Interpreter mittels: ``c(fakultaet)`` +Laden in Interpreter mittels: $c(fakultaet)$ -Testen der Funktion, z.B. mit: ``fakultaet:fak(5)`` +Testen der Funktion, z.B. mit: $fakultaet:fak(5)$ \paragraph{Elemente von Erlang} + +Kurz: +\begin{itemize*} + \item Kommentare: werden mit \% eingeleitet und erstrecken sich bis Zeilenende + \item Ganzzahlen (Integer): 10, -234, \$A, \$Char, 16\#AB10F + \item Gleitkommazahlen (Floats): 17.368, -56.34, 12.34E-10 + \item Atoms (Atoms): abcdf, start\_with\_lower\_case, 'Blanks are quoted' \#Konstanten mit eigenem Namen als Wert + \item Tupel (Tupels): {123, bcd}, {abc, {def, 'joe', 234}, als} \#können feste Anzahl von Dingen speichern + \item Listen (Lists): [123, xzy], [{person, 'Joe', 'Armstrong},{person...}] \#können variable Anzahl von Dingen speichern + \item Variablen: Abc, A\_long\_variable \#fangen mit Großbuchstaben an; zur Speicherung von Werten; können nur einmal gebunden werden + \item Komplexe Datenstrukturen: beliebige komplexe Datenstrukturen können erzeugt werden (durch einfaches Hinschreiben) + \item Case-Ausdrücke: + \begin{lstlisting} + case Expression of Pattern1 [when Guard1] -> Expr_seq1; ... end + \end{lstlisting} +\end{itemize*} + Ganzzahlen (Integer): \begin{itemize*} \item 10 @@ -2329,44 +1866,44 @@ Atome (Atoms): \item abcef \item start\_with\_a\_lower\_case\_letter \item "Blanks can be quoted" - \item "Anything inside quotes" + \item \"Anything inside quotes" \item Erläuterungen: \begin{itemize*} \item Atome sind Konstanten, die Ihren eigenen Namen als Wert haben \item Atome beliebiger Länge sind zulässig \item Jedes Zeichen ist innerhalb eines Atoms erlaubt \item Einige Atome sind reservierte Schlüsselwörter und können nur in der von den Sprachentwicklern gewünschen Weise verwendet werden als Funktionsbezeichner, Operatoren, Ausdrücke etc. - \item Reserviert sind: *after and andalso band begin bnot bor bsl bsr bxor case catch cond div end fun if let not of or orelse query receive rem try when xor* + \item Reserviert sind: \textit{after and andalso band begin bnot bor bsl bsr bxor case catch cond div end fun if let not of or orelse query receive rem try when xor} \end{itemize*} \end{itemize*} Tupel (Tuples): \begin{itemize*} - \item {123, bcd} % Ein Tupel aus Ganzzahl und Atom - \item {123, def, abc} - \item {person, 'Joe', 'Armstrong'} - \item {abc, {def, 123}, jkl} - \item {} + \item \{123, bcd\} \% Ein Tupel aus Ganzzahl und Atom + \item \{123, def, abc\} + \item \{person, 'Joe', 'Armstrong'\} + \item \{abc, {def, 123}, jkl\} + \item \{\} \item Erläuterungen: \begin{itemize*} \item Können eine feste Anzahl von "Dingen" speichern \item Tupel beliebiger Größe sind zulässig - \item Kommentare werden in Erlang mit % eingeleitet und erstrecken sich dann bis zum Zeilenende + \item Kommentare werden in Erlang mit \% eingeleitet und erstrecken sich dann bis zum Zeilenende \end{itemize*} \end{itemize*} Listen: \begin{itemize*} - \item [123, xyz] - \item [123, def, abc] - \item [{person, 'Joe', 'Armstrong'}, {person, 'Robert', 'Virding'}, {person, 'Mike', 'Williams'}] - \item "abcdefgh" wird zu [97,98,99,100,101,102,103,104] - \item "" wird zu [] + \item $[123, xyz]$ + \item $[123, def, abc]$ + \item $[\{person, 'Joe', 'Armstrong'\}, \{person, 'Robert', 'Virding'\}, \{person, 'Mike', 'Williams'\}]$ + \item \"abcdefgh\" wird zu $[97,98,99,100,101,102,103,104]$ + \item " " wird zu $[ ]$ \item Erläuterungen: \begin{itemize*} \item Listen können eine variable Anzahl von Dingen speichern \item Die Größe von Listen wird dynamisch bestimmt - \item "..." ist eine Kurzform für die Liste der Ganzzahlen, die die ASCIICodes der Zeichen innerhalb der Anführungszeichen repräsentieren + \item \"...\" ist eine Kurzform für die Liste der Ganzzahlen, die die ASCIICodes der Zeichen innerhalb der Anführungszeichen repräsentieren \end{itemize*} \end{itemize*} @@ -2381,14 +1918,14 @@ Variablen: \item Keine "Funny Characters" \item Variablen werden zu Speicherung von Werten von Datenstrukturen verwendet \item Variablen können nur einmal gebunden werden! - \item Der Wert einer Variablen kann also nicht mehr verändert werden, nachdem er einmal gesetzt wurde: *N = N + 1 VERBOTEN!* - \item Einzige Ausnahmen: Die anonyme Variable "\_" (kein Lesen möglich) und das Löschen einer Variable im Interpreter mit f(N). + \item Der Wert einer Variablen kann also nicht mehr verändert werden, nachdem er einmal gesetzt wurde: $N = N + 1$ VERBOTEN! + \item Einzige Ausnahmen: Die anonyme Variable "\_" (kein Lesen möglich) und das Löschen einer Variable im Interpreter mit $f(N)$. \end{itemize*} \end{itemize*} Komplexe Datenstrukturen: \begin{itemize*} - \item [{{person,'Joe', 'Armstrong'}, {telephoneNumber, [3,5,9,7]}, {shoeSize, 42}, {pets, [{cat, tubby},{cat, tiger}]}, {children,[{thomas, 5},{claire,1}]}}, {{person,'Mike','Williams'}, {shoeSize,41}, {likes,[boats, beer]}, ... }] + \item $[\{\{person,'Joe', 'Armstrong'\}, \{telephoneNumber, [3,5,9,7]\}, \{shoeSize, 42\}, \{pets, [\{cat, tubby\},\{cat, tiger\}]\}, \{children,[\{thomas, 5\},\{claire,1\}]\}\}, \{\{person,'Mike','Williams'\}, \{shoeSize,41\}, \{likes,[boats, beer]\}, ... \}]$ \item Erläuterungen: \begin{itemize*} \item Beliebig komplexe Strukturen können erzeugt werden @@ -2434,16 +1971,12 @@ Funktionsaufrufe: \end{itemize*} Modul-Deklaration: -\begin{lstlisting}[ - language=erlang, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=erlang] -module(demo). -export([double/1]). - double(X) -> times(X, 2). - times(X, N) -> X * N. - \end{lstlisting} + double(X) $\rightarrow$ times(X, 2). + times(X, N) $\rightarrow$ X * N. +\end{lstlisting} \begin{itemize*} \item Erläuterungen: \item Die Funktion double kann auch außerhalb des Moduls verwendet werden, times ist nur lokal in dem Modul verwendbar @@ -2471,17 +2004,13 @@ Eingebaute Funktionen (Built In Functions, BIFs) \end{itemize*} Definition von Funktionen: -\begin{lstlisting}[ - language=erlang, - showspaces=false, - basicstyle=\ttfamily - ] -func(Pattern1, Pattern2, ...) -> +\begin{lstlisting}[language=erlang] +func(Pattern1, Pattern2, ...) $\rightarrow$ ... ; % Vor dem ; steht der Rumpf -func(Pattern1, Pattern2, ...) -> +func(Pattern1, Pattern2, ...) $\rightarrow$ ... ; % Das ; kündigt weitere Alternativen an ... % Beliebig viele Alternativen möglich -func(Pattern1, Pattern2, ...) -> +func(Pattern1, Pattern2, ...) $\rightarrow$ ... . % Am Ende muss ein Punkt stehen! \end{lstlisting} Erläuterungen: @@ -2493,13 +2022,13 @@ Erläuterungen: \item Der entsprechende Anweisungsrumpf wird sequentiell ausgeführt \end{itemize*} -Was passiert wenn wir mathstuff:factorial() mit einem negativen Argument aufrufen? Der Interpreter reagiert nicht mehr? +Was passiert wenn wir $mathstuff:factorial()$ mit einem negativen Argument aufrufen? Der Interpreter reagiert nicht mehr? \begin{itemize*} \item Erste Reaktion: rette das Laufzeitsystem durch Eingabe von CTRL-G \begin{itemize*} \item User switch command \begin{enumerate*} - \item --> h + \item -$\rightarrow$ h \item c [nn] - connect to job \item i [nn] - interrupt job \item k [nn] - kill job @@ -2508,7 +2037,7 @@ Was passiert wenn wir mathstuff:factorial() mit einem negativen Argument aufrufe \item r [node [shell]] - start remote shell \item q - quit erlang \item ? | h - this message - \item --> + \item -$\rightarrow$ \end{enumerate*} \item Liste durch Eingabe von j alle Jobnummern auf \item Beende den entsprechenden Shell-Job durch k @@ -2521,54 +2050,53 @@ Was passiert wenn wir mathstuff:factorial() mit einem negativen Argument aufrufe \item "Beschütze" die Funktion vor Endlosrekursion durch Ergänzung eines sogenannten Wächters (Guards) bei dem entsprechenden Fallmuster (Pattern) \item Erläuterungen: \begin{itemize*} - \item Der Guard wird durch das Atom when und eine Bedingung vor dem Pfeil -> formuliert + \item Der Guard wird durch das Atom when und eine Bedingung vor dem Pfeil $\rightarrow$ formuliert \item Vollständig "beschützte" Klauseln können in beliebiger Reihenfolge angeordnet werden \item Achtung: Ohne Guard führt diese Reihenfolge zu Endlosschleifen \end{itemize*} \item Beispiele für Guards: - \begin{itemize*} - \item number(X) % X is a number - \item integer(X) % X is an integer - \item float(X) % X is a float - \item atom(X) % X is an atom - \item tuple(X) % X is a tuple - \item list(X) % X is a list - \item length(X) == 3 % X is a list of length 3 - \item size(X) == 2 % X is a tuple of size 2. - \item X > Y + Z % X is > Y + Z - \item X == Y % X is equal to Y - \item X =:= Y % X is exactly equal to Y (i.e. 1 == 1.0 succeeds but 1 =:= 1.0 fails) - \end{itemize*} + \begin{lstlisting}[language=erlang] + number(X) % X is a number + integer(X) % X is an integer + float(X) % X is a float + atom(X) % X is an atom + tuple(X) % X is a tuple + list(X) % X is a list + length(X) == 3 % X is a list of length 3 + size(X) == 2 % X is a tuple of size 2. + X > Y + Z % X is > Y + Z + X == Y % X is equal to Y + X =:= Y % X is exactly equal to Y (i.e. 1 == 1.0 succeeds but 1 =:= 1.0 fails) + \end{lstlisting} \item Alle Variablen in einem Wächter müssen zuvor gebunden werden \end{itemize*} \end{itemize*} Traversieren ("Ablaufen") von Listen: -\begin{lstlisting} - average(X) -> sum(X) / len(X). - sum([H|T]) -> H + sum(T); % summiert alle Werte auf - sum([]) -> 0. - len([_|T]) -> 1 + len(T); % Wert des Elements - len([]) -> 0. % interessiert nicht +\begin{lstlisting}[language=erlang] +average(X) -> sum(X) / len(X). +sum([H|T]) -> H + sum(T); % summiert alle Werte auf +sum([]) -> 0. +len([_|T]) -> 1 + len(T); % Wert des Elements +len([]) -> 0. % interessiert nicht \end{lstlisting} \begin{itemize*} \item Die Funktionen sum und len verwenden das gleiche Rekursionsmuster \item Zwei weitere gebräuchliche Rekursionsmuster: \begin{lstlisting} - double([H|T]) -> [2*H|double(T)]; % verdoppelt alle - double([]) -> []. % Listenelemente - - member(H, [H|_]) -> true; % prüft auf - member(H, [_|T]) -> member(H, T); % Enthaltensein - member(_, []) -> false. % in Liste - \end{lstlisting} + double([H|T]) -> [2*H|double(T)]; % verdoppelt alle + double([]) -> []. % Listenelemente + member(H, [H|_]) -> true; % prüft auf + member(H, [_|T]) -> member(H, T); % Enthaltensein + member(_, []) -> false. % in Liste + \end{lstlisting} \end{itemize*} Listen und Akkumulatoren: \begin{lstlisting} - average(X) -> average(X, 0, 0). - average([H|T], Length, Sum) -> average(T, Length + 1, Sum + H); - average([], Length, Sum) -> Sum / Length. + average(X) -> average(X, 0, 0). + average([H|T], Length, Sum) -> average(T, Length + 1, Sum + H); + average([], Length, Sum) -> Sum / Length. \end{lstlisting} \begin{itemize*} \item Interessant sind an diesem Beispiel: @@ -2580,31 +2108,31 @@ Listen und Akkumulatoren: "Identisch" benannte Funktionen mit unterschiedlicher Parameterzahl: \begin{lstlisting} - sum(L) -> sum(L, 0). - sum([], N) -> N; - sum([H|T], N) -> sum(T, H+N). - \end{lstlisting} + sum(L) -> sum(L, 0). + sum([], N) -> N; + sum([H|T], N) -> sum(T, H+N). +\end{lstlisting} \begin{itemize*} \item Erläuterungen - \item Die Funktion sum/1 summiert die Elemente einer als Parameter übergebenen Liste - \item Sie verwendet eine Hilfsfunktion, die mit sum/2 benannt ist + \item Die Funktion $sum/1$ summiert die Elemente einer als Parameter übergebenen Liste + \item Sie verwendet eine Hilfsfunktion, die mit $sum/2$ benannt ist \item Die Hilfsfunktion hätte auch irgendeinen anderen Namen haben können - \item Für Erlang sind sum/1 und sum/2 tatsächlich unterschiedliche Funktionsnamen + \item Für Erlang sind $sum/1$ und $sum/2$ tatsächlich unterschiedliche Funktionsnamen \end{itemize*} Shell-Kommandos: -\begin{itemize*} - \item h() \item history . Print the last 20 commands. - \item b() \item bindings. See all variable bindings. - \item f() \item forget. Forget all variable bindings. - \item f(Var) \item forget. Forget the binding of variable X. This can ONLY be used as a command to the shell \item NOT in the body of a function! - \item e(n) \item evaluate. Evaluate the n:th command in history. - \item e(-1) Evaluate the previous command. - \item Erläuterungen: Die Kommandozeile kann wie mit dem Editor Emacs editiert werden (werl.exe unterstützt zusätzlich Historie mit Cursortasten) -\end{itemize*} +\begin{lstlisting}[language=erlang] + h() history . Print the last 20 commands. + b() bindings. See all variable bindings. + f() forget. Forget all variable bindings. + f(Var) forget. Forget the binding of variable X. This can ONLY be used as a command to the shell - NOT in the body of a function! + e(n) evaluate. Evaluate the n:th command in history. + e(-1) Evaluate the previous command. +\end{lstlisting} +Erläuterungen: Die Kommandozeile kann wie mit dem Editor Emacs editiert werden (werl.exe unterstützt zusätzlich Historie mit Cursortasten) Spezielle Funktionen: -\begin{lstlisting} +\begin{lstlisting}[language=erlang] apply(Func, Args) apply(Mod, Func, Args) % old style, deprecated \end{lstlisting} @@ -2616,9 +2144,9 @@ apply(Mod, Func, Args) % old style, deprecated \item Die Stelligkeit der Funktion ist gleich der Länge der Argumentliste \item Beispiel: \begin{lstlisting} - ` 1> apply( lists1,min_max,[[4,1,7,3,9,10]]). -> {1, 10} - \end{lstlisting} - \item Bemerkung: Die Funktion min\_max erhält hier ein Argument + ` 1> apply( lists1,min_max,[[4,1,7,3,9,10]]). -> {1, 10} + \end{lstlisting} + \item Bemerkung: Die Funktion $min\_max$ erhält hier ein Argument \end{itemize*} Anonyme Funktionen: @@ -2642,114 +2170,22 @@ Anonyme Funktionen: \end{itemize*} Modul fakultaet.erl: -\begin{lstlisting}[ - language=erlang, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=erlang] -module(fakultaet). -export([fak/1]). fak(0) $\rightarrow$ 1; fak(N) when N > 0 $\rightarrow$ (N) * fak(N-1). \end{lstlisting} Laden in den Interpreter mittels: -\begin{lstlisting}[ - language=erlang, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=erlang] c(fakultaet). \end{lstlisting} Testen der Funktion, z.B. mit: -\begin{lstlisting}[ - language=erlang, - showspaces=false, - basicstyle=\ttfamily - ] +\begin{lstlisting}[language=erlang] fakultaet:fak(5). \end{lstlisting} -\paragraph{Elemente von Erlang} -\begin{itemize*} - \item Kommentare: werden mit \% eingeleitet und erstrecken sich bis Zeilenende - \item Ganzzahlen (Integer): 10, -234, \$A, \$Char, 16\#AB10F - \item Gleitkommazahlen (Floats): 17.368, -56.34, 12.34E-10 - \item Atoms (Atoms): abcdf, start\_with\_lower\_case, 'Blanks are quoted' \#Konstanten mit eigenem Namen als Wert - \item Tupel (Tupels): {123, bcd}, {abc, {def, 'joe', 234}, als} \#können feste Anzahl von Dingen speichern - \item Listen (Lists): [123, xzy], [{person, 'Joe', 'Armstrong},{person...}] \#können variable Anzahl von Dingen speichern - \item Variablen: Abc, A\_long\_variable \#fangen mit Großbuchstaben an; zur Speicherung von Werten; können nur einmal gebunden werden - \item Komplexe Datenstrukturen: beliebige komplexe Datenstrukturen können erzeugt werden (durch einfaches Hinschreiben) - \item Pattern Matching - \begin{itemize*} - \item {B, C, D} = {10, foo, bar} \#bindet B zu 10, C zu foo und D zu bar - \item {A, A, B} = {abc, def, ghi} \#schlägt fehl A=!A - \item [A, B, C, D] = [1, 2, 3] \#schlägt fehl; Länge des ersten Patterns zu groß - \item [A, B | C] = [1, 2, 3, 4, 5] \#bindet A zu 1, B zu 2, C zu [3, 4, 5] - \item [A, \_, B ] = [1, 2, 3] \#bindet A zu 1, B zu 3; 2 anonyme Variable $\rightarrow$ kann nie ausgelesen werden - \end{itemize*} - \item Funktionsaufrufe - \begin{itemize*} - \item module:func(Arg\_1, Arg\_2,...) - \item func(Arg\_1, Arg\_2,...) - \end{itemize*} - \item Modul Deklaration - \begin{lstlisting}[ - language=erlang, - showspaces=false, - basicstyle=\ttfamily - ] - -module(demo). - -export([double/1]). - double(X) $\rightarrow$ times(X, 2). - times(X, N) $\rightarrow$ X * N. - \end{lstlisting} - \item Eingebaute Funktionen (Built In Functions, BIFs) - \begin{itemize*} - \item date() - \item time() - \item length([1,2,3,4,5]) - \item size({a,b,c}) - \item atom\_to\_list(an\_atom) - \item list\_to\_tuple([1,2,3,4]) - \item integer\_to\_list(2234) - \item tuple\_to\_list({}) - \end{itemize*} - \item Definition von Funktionen: func(Pattern1, Pattern2,...) $\rightarrow$ ...; ... . \#";" kündigt weitere Alternativen an. Am Ende muss "." stehen - \item Guards (Wächter): - \begin{lstlisting}[ - language=erlang, - showspaces=false, - basicstyle=\ttfamily - ] - factorial(N) when N > 0 $\rightarrow$ N* factorial(N-1); - \end{lstlisting} - \begin{itemize*} - \item number(X) % X is a number - \item integer(X) % X is an integer - \item float(X) % X is a float - \item atom(X) % X is an atom - \item tuple(X) % X is a tuple - \item list(X) % X is a list - \item length(X) == 3 % X is a list of length 3 - \item size(X) == 2 % X is a tuple of size 2. - \item X > Y + Z % X is > Y + Z - \item X == Y % X is equal to Y - \item X =:= Y % X is exactly equal to Y - \end{itemize*} - \item Traversieren ("Ablaufen") von Liste: - \begin{itemize*} - \item sum([H|T]) $\rightarrow$ H + sum(T); sum([]) $\rightarrow$ 0. - \item len([\_|T]) $\rightarrow$ 1 + len(T); len([]) $\rightarrow$ 0. - \end{itemize*} - \item Case-Ausdrücke: - \begin{lstlisting} - case Expression of Pattern1 [when Guard1] $\rightarrow$ Expr_seq1; ... end - \end{lstlisting} -\end{itemize*} - - -\subsubsection{Kalküle} -Kalküle sind +\subsection{Kalküle} \begin{itemize*} \item Minimalistische Programmiersprachen zur Beschreibung von Berechnungen, \item mathematische Objekte, über die Beweise geführt werden können. @@ -2764,8 +2200,7 @@ Beispiele weiterer Kalküle: \item $\pi$-Kalkül (Milner) für nebenläufige, mobile Programme \end{itemize*} - -\subsection{Lambda Kalkül} +\subsubsection{Lambda Kalkül} Kalküle sind minimalistische Programmiersprachen zur Beschreibung von Berechnungen, mathematische Objekte, über die Beweise geführt werden können Hier: $\lambda$-Kalkül (Church, Landin) für sequentielle (funktionale /imperative Sprachen) @@ -2777,19 +2212,20 @@ Die Klasse $\bigwedge$ der Lambda-Terme ist die kleinste Klasse, welche die folg \item Wenn $M, N \in \bigwedge$ sind, dann ist $(MN) \in \bigwedge$ (Funktionsanwendung) \end{itemize*} -%| Bezeichnung | Notation | Beispiele | -%| -\item | -\item | -\item | -%| Variablen | x | x y | -%| Abstraktion | $\lambda x.t$ | $\lambda y.0$ $\lambda f. \lambda x. \lambda y.fyx$ | -%| Funktionsanwendung | $t_1t_2$ | $f42$ | $(\lambda x.x + 5) 7$ | +\begin{tabular}{l | l | l} + Bezeichnung & Notation & Beispiele \\\hline + Variablen & x & x y \\ + Abstraktion & $\lambda x.t$ & $\lambda y.0$ $\lambda f. \lambda x. \lambda y.fyx$ \\ + Funktionsanwendung & $t_1t_2$ & $f42$, $(\lambda x.x + 5) 7$ \\ +\end{tabular} $\lambda$-Abstraktionen: $\lambda x. t$ bindet die Variable x im Ausdruck t -Die Menge der freien Variablen eines Terms M wird mit FV(M) bezeichnet und ist wie folgt induktiv definiert: +Die Menge der freien Variablen eines Terms M wird mit $FV(M)$ bezeichnet und ist wie folgt induktiv definiert: \begin{itemize*} \item $FV(x)={x}$ \item $FV(MN) = FV(M) \cup FV(N)$ - \item $FV(\lambda x.M) = FV(M) - {x}$ + \item $FV(\lambda x.M) = FV(M) - \{x\}$ \end{itemize*} Ein Lambda-Term ohne freie Variablen heißt Kombinator \begin{itemize*} @@ -2799,61 +2235,52 @@ Ein Lambda-Term ohne freie Variablen heißt Kombinator \end{itemize*} \paragraph{Das untypisierte Lambdakalkül} + \begin{itemize*} \item Turing-mächtiges Modell funktionaler Programme \item Auch: Beschreibung sequentieller imperativer Konstrukte \end{itemize*} \subitem\colorbox{lightgray}{ \begin{minipage}[h]{0.9\linewidth} - Definition der $\lambda$-Terme: + Definition der $\lambda$-Terme:\\ Die Klasse $\Lambda$ der Lambda-Terme ist die kleinste Klasse, welche die folgenden Eigenschaften erfüllt: \begin{itemize*} - \item Wenn x eine Variable ist, dann ist x $\in \Lambda$ - \item Wenn M $\in \Lambda$ ist, dann ist ($\lambda$xM) $\in \Lambda$ (Abstraktion) - \item Wenn M, N $\in \Lambda$ sind, dann ist (MN) $\in \Lambda$ (Funktionsanwendung) - + \item Wenn $x$ eine Variable ist, dann ist $x \in \Lambda$ + \item Wenn $M\in \Lambda$ ist, dann ist $(\lambda xM) \in \Lambda$ (Abstraktion) + \item Wenn $M, N\in \Lambda$ sind, dann ist $(MN) \in \Lambda$ (Funktionsanwendung) \end{itemize*} - \end{minipage} } \begin{itemize*} \item Um Klammern zu sparen verwendet man oft eine alternative Notation: $\lambda$x.M - \item Bei mehreren zu bindenden Variablen: $\lambda$xyz.M = ($\lambda$x($\lambda$y($\lambda$zM))) + \item Bei mehreren zu bindenden Variablen: $\lambda xyz.M = (\lambda x(\lambda y(\lambda zM)))$ \end{itemize*} \subitem\colorbox{lightgray}{ \begin{minipage}[h]{0.9\linewidth} $\lambda$-Terme\\ \\ \begin{tabular}[h]{lcr} - \textbf {Bezeichnung} & \textbf{Notation} & \textbf{Beispiele} \\ - Variablen & x & x \enspace y \\ - Abstraktion & $\lambda$x.t & $\lambda$y.0 \enspace $\lambda$f. $\lambda$x. $\lambda$y.fyx \\ - Funktionsanwendung & $t_1t_2$ & f 42 \enspace ( $\lambda$x.x+5)7 + \textbf {Bezeichnung} & \textbf{Notation} & \textbf{Beispiele} \\ + Variablen & $x$ & $x \enspace y$ \\ + Abstraktion & $\lambda$x.t & $\lambda y.0 \enspace \lambda f. \lambda x. \lambda y.fyx$ \\ + Funktionsanwendung & $t_1t_2$ & $f 42 \enspace ( \lambda x.x+5)7$ \end{tabular} - \\\\ (weitere primitive Operationen nach Bedarf) 17, True, +, · \end{minipage} } - Variablenkonvention -\begin{tabular}[h]{ll} - x ,y ,f & \enspace \enspace sind korrekte Programmvariablen \\ - x, y, z & \enspace \enspace sind Meta-Variablen für Programmvariablen \\ - t, t', $t_1$, $t_2$ & \enspace \enspace bezeichnen immer einen Term - +\begin{tabular}[h]{l l} + $x ,y ,f$ & \enspace sind korrekte Programmvariablen \\ + $x, y, z$ & \enspace sind Meta-Variablen für Programmvariablen \\ + $t, t', t_1, t_2$ & \enspace bezeichnen immer einen Term \end{tabular} Funktionsanwendung ist linksassoziativ und bindet stärker als Abstraktion +$$\lambda x.fxy = \lambda x.((fx)y)$$ -\begin{center} - $\lambda$x.fxy = $\lambda$x.((fx)y) -\end{center} Abstraktion ist rechtsassoziativ: - -\begin{center} - $\lambda$.x$\lambda$.y.fxy = ($\lambda$x.($\lambda$.fxy)) -\end{center} +$$\lambda.x\lambda.y.fxy = (\lambda x.( \lambda.fxy))$$ \subsubsection{Strukturelle Induktion} \begin{itemize*} @@ -2863,70 +2290,56 @@ Abstraktion ist rechtsassoziativ: \end{itemize*} \item Beispiel: Jeder Term in $\Lambda$ ist wohl geklammert \begin{itemize*} - \item \color{blue}{Induktionsanfang:} \color{black} trivial, da jede Variable ein wohlgeklammerter Lambda-Term ist. - \item \color{blue} Induktionsannahme: \color{black} M,N sind wohlgeklammerte Lambda-Terme - \item \color{blue} Induktionsschritt: \color{black} dann sind auch die Terme (MN) und ($\lambda$xM) wolgeklammert. + \item \color{blue}Induktionsanfang: \color{black} trivial, da jede Variable ein wohlgeklammerter Lambda-Term ist. + \item \color{blue} Induktionsannahme: \color{black} $M,N$ sind wohlgeklammerte Lambda-Terme + \item \color{blue} Induktionsschritt: \color{black} dann sind auch die Terme $(MN)$ und ($\lambda xM$) wolgeklammert. \end{itemize*} \end{itemize*} - \subsubsection{Variablenbindung bei Abstraktion} - Variablenbindung in Haskell (erlaubt anonyme Lambda-Funktionen): \\ -\color{blue}Anonyme Funktion: \color{black} \textbackslash x -$>$ (\textbackslash y -$>$ y $+$ 5) (x $+$ 3)\\ -\color{blue} let-Ausdruck: \color{black} let x = 5 in x+y\\ +\color{blue}Anonyme Funktion: \color{black} \textbackslash $x ->(\backslash y -> y+5) (x+3)$\\ +\color{blue} let-Ausdruck: \color{black} let $x = 5 in x+y$\\ -Analog bei $\lambda$-Abstraktionen: $\lambda$x.t bindet die Variable x im Ausdruck t\\ +Analog bei $\lambda$-Abstraktionen: $\lambda x.t$ bindet die Variable $x$ im Ausdruck t\\ Beispiele: \begin{itemize*} - \item $\lambda$x.$\lambda$y.fyx bindet x in $\lambda$y.fyx, das selbst x in fyx bindet. - \item f ist frei in $\lambda$x.$\lambda$y.fyx. + \item $\lambda x.\lambda y.fyx$ bindet $x$ in $\lambda y.fyx$, das selbst $x$ in $fyx$ bindet. + \item f ist frei in $\lambda x.\lambda y.fyx.$ \end{itemize*} -\ \\ -Innere Abstraktionen können äußere Variablen verdecken: \ \\ + +Innere Abstraktionen können äußere Variablen verdecken: +$$(\lambda x.\lambda y.\lambda z.f( \lambda x.z+x)(y x)) (\lambda y.y+x)$$ + \begin{center} - ($\lambda$x.$\lambda$y.$\lambda$z.f($\lambda$x.z+x)(y x)) ($\lambda$y.y+x) -\end{center} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-002} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-Lambda_Abstraktion} \end{center} \subsubsection{Freie und gebundene Variablen} \begin{itemize*} \item Die Menge der \color{blue} freien Variablen \color{black} eines Terms M wird mit FV(M) bezeichnet und ist wie folgt induktiv definiert: \begin{itemize*} - \item FV(x) = \{x\} - \item FV(MN) = FV(M) $\cup $ FV(N) - \item FV($\lambda$x.M) = FV(M) - \{x\} + \item $FV(x) = \{x\}$ + \item $FV(MN) = FV(M) \cup FV(N)$ + \item $FV(\lambda x.M) = FV(M) - \{x\}$ \end{itemize*} \item Übung: Definieren sie analog die Menge der gebundenen Variablen GV(M) \item Ein Lambda-Term ohne freie Variablen heißt \color{blue}Kombinator \color{black} \item Einige besonders wichtige Kombinatoren haben eigene Namen: \begin{itemize*} \item Identitätsfunktion:\enspace\enspace \enspace \enspace\enspace\enspace\enspace I $\equiv$ $\lambda$x.x - \item Konstanten-Funktional: \enspace K $\equiv$ $\lambda$xy.x - \item Fixpunkt-Kombinator: \enspace\enspace Y $\equiv$ $\lambda$f.($\lambda$x.f(x x)) ($\lambda$x.f(x x)) + \item Konstanten-Funktional: \enspace $K \equiv\lambda xy.x$ + \item Fixpunkt-Kombinator: \enspace $Y\equiv\lambda f.(\lambda x.f(x x)) (\lambda x.f(x x))$ \end{itemize*} \end{itemize*} - \subsubsection{Ausführung von $\lambda$ Termen} -\begin{itemize*} - \item Redex: Ein $\lambda $-Term der Form $(\lambda x. t_1 ) t_2$ heißt Redex. - \item $\beta$ -Reduktion: $\beta$ -Reduktion entspricht der Ausführung der Funktionsanwendung auf einem Redex: $(\lambda x. t_1 ) t_2 \Rightarrow t_1 [x \rightarrow t_2 ]$ - \item Substitution: $t_1 [x \rightarrow t_2 ]$ erhält man aus dem Term $t_1$ , wenn man alle freien Vorkommen von $x$ durch $t_2$ ersetzt. - \item Normalform: Ein Term, der nicht weiter reduziert werden kann, heißt in Normalform. -\end{itemize*} - -Beispiel: $(\lambda x.x)y \Rightarrow x[x \rightarrow y] = y$ - - \colorbox{lightgray}{ \begin{minipage}[h]{1.0\linewidth} \begin{tabular}{|p{4cm}|p{7cm}|} - Redex & Ein $\lambda$-Term der Form ($\lambda$x.$t_1$)$t_2$ heißt Redex. \\[\normalbaselineskip] - $\beta$-Reduktion & $\beta$-Reduktion entspricht der Ausführung der Funktionanwendung auf einem Redex: \\[\normalbaselineskip] - & ($\lambda$x.$t_1$)$t_2$ $\Rightarrow$ $t_1$[x $\rightarrow$ $t_2$] \\[\normalbaselineskip] - Substitution & $t_1$[x $\rightarrow$ $t_2$] erhält man aus dem Term $t_1$, wenn man alle freien Vorkommen von x durch $t_2$ ersetzt. \\[\normalbaselineskip] + Redex & Ein $\lambda$-Term der Form ($\lambda x.t_1)t_2$ heißt Redex. \\[\normalbaselineskip] + $\beta$-Reduktion & entspricht der Ausführung der Funktionanwendung auf einem Redex: \\[\normalbaselineskip] + & ($\lambda x.t_1)t_2 \Rightarrow t_1[x \rightarrow t_2]$ \\[\normalbaselineskip] + Substitution & $t_1[x \rightarrow t_2]$ erhält man aus dem Term $t_1$, wenn man alle freien Vorkommen von x durch $t_2$ ersetzt. \\[\normalbaselineskip] Normalform & Ein Term, der nicht weiter reduziert werden kann, heißt in Normalform \end{tabular} \end{minipage} @@ -2938,1878 +2351,1769 @@ Beispiele: ($\lambda$x.x($\lambda$x.x))(yz) $\Rightarrow$ (x($\lambda$x.x))[x $\rightarrow$ (yz)] = ((yz)($\lambda$x.x) \end{center} - \subsubsection{Braucht man primitive Operationen?} Nicht unbedingt - Kodierung mit Funktionen höherer Ordnung \\ Beispiel: let \\ \hspace*{14.5mm}let x = $t_1$ in $t_2$ wird zu ($\lambda x. t_2 )t_1$ \\ Beispiel: let x = g y in f x berechnet f(g y)\\ -\hspace*{14.5mm} ($\lambda$x.fx)(g y) $\Rightarrow$ f(g y) +\hspace*{14.5mm} ($\lambda x.fx)(g y) \Rightarrow f(g y)$ -\subsection{Äquivalenz} -$\alpha$-Äquivalenz: $t_1$ und $t_2$ heißen $\alpha$-äquivalent $(t_1 t_2)$, wenn $t_1$ in $t_2$ durch konsistente Umbenennung der $\lambda$-gebundenen Variablen überführt werden kann. - -$\eta $-Äquivalenz: Terme $\lambda x. f\ x$ und $f$ heißen $\eta $-äquivalent $(\lambda x. f x = f )$ falls $x$ nicht freie Variable von f ist - -\paragraph{$\alpha$-Äquivalenz} -Namen gebundener Variablen -\begin{itemize*} - \item dienen letztlich nur der Dokumentation - \item entscheidend sind die Bindungen -\end{itemize*} - -\colorbox{lightgray}{ - \begin{minipage}[h]{1.0\linewidth} - $\alpha$-Äquivalenz \\ - $ t_1$ und $t_2$ heißen $\alpha$-Äquivalent ($t_1$ $\stackrel{\alpha}{=}$ $t_2$), wenn $t_1$ in $t_2$ durch konsistente Umbenennung der $\lambda$-gebundenen Variablen überführt werden kann. - \end{minipage} -} - -Beispiele: -\begin{center} - $\lambda$ x.x $\stackrel{\alpha}{=}$ $\lambda$ y.y \linebreak - $\lambda$x.$\lambda$z.f($\lambda$y.zy)x $\stackrel{\alpha}{=}$ $\lambda$y.$\lambda$x.f($\lambda$z.xz)y -\end{center} -\ \\ -aber -\begin{center} $\lambda$x.$\lambda$z.f($\lambda$y.zy)x $\stackrel{\alpha}{\neq}$ $\lambda$x.$\lambda$z.g($\lambda$y.zy)x\\ $\lambda$z.$\lambda$z.f($\lambda$y.zy)z $\stackrel{\alpha}{\neq}$ $\lambda$x.$\lambda$z.f($\lambda$y.zy)x -\end{center} - -\paragraph{$\eta$-Äquivalenz} -Extensionalitäts-Prinzip: -\begin{itemize*} - \item Zwei Funktionen sind gleich, falls Ergebnis gleich für alle Argumente -\end{itemize*} -\colorbox{lightgray} { - \begin{minipage}[h]{1.0\linewidth} - $\eta$-Äquivalenz \\ - Terme $\lambda$x.fx und f heißen $\eta$-äquivalent ($\lambda$x.fx $\stackrel{\eta}{=}$ f), falls x nicht freie Variable von f ist. - \end{minipage} -} - -Beispiele: -\begin{center} $\lambda$x.$\lambda$y.f z x y $\stackrel{\eta}{=}$ $\lambda$x.f z x \newline \newline - f z $\stackrel{\eta}{=}$ $\lambda$x.f z x \newline \newline $\lambda$x.x $\stackrel{\eta}{=}$ $\lambda$x.($\lambda$x.x)x \newline \newline -\end{center} -aber -\begin{center} $\lambda$x.f x x $\stackrel{\eta}{\neq}$ f x -\end{center} - -\subsection{Kodierung boolscher Werte} -Church Booleans -\begin{itemize*} - \item True wird zu: $C_{true} = \lambda t.\lambda f.t$ - \item False wird zu: $C_{false} = \lambda t.\lambda f.f$ - \item If-then-else wird zu: $If = \lambda a.a$ -\end{itemize*} - -Bsp: -\begin{lstlisting} + \subsection{Äquivalenz} + \paragraph{$\alpha$-Äquivalenz} + + Namen gebundener Variablen + \begin{itemize*} + \item dienen letztlich nur der Dokumentation + \item entscheidend sind die Bindungen + \end{itemize*} + + \colorbox{lightgray}{ + \begin{minipage}[h]{1.0\linewidth} + $\alpha$-Äquivalenz \\ + $ t_1$ und $t_2$ heißen $\alpha$-Äquivalent ($t_1 \stackrel{\alpha}{=} t_2$), wenn $t_1$ in $t_2$ durch konsistente Umbenennung der $\lambda$-gebundenen Variablen überführt werden kann. + \end{minipage} + } + + Beispiele: + \begin{center} + $$\lambda x.x \stackrel{\alpha}{=} \lambda y.y$$ + $$\lambda x.\lambda z.f(\lambda y.zy)x \stackrel{\alpha}{=} \lambda y.\lambda x.f(\lambda z.xz)y$$ + \end{center} + aber + \begin{center} + $$\lambda x.\lambda z.f(\lambda y.zy)x \stackrel{\alpha}{\neq} \lambda x.\lambda z.g(\lambda y.zy)x$$ + $$\lambda z.\lambda z.f(\lambda y.zy)z\stackrel{\alpha}{\neq} \lambda x.\lambda z.f(\lambda y.zy)x$$ + \end{center} + + \paragraph{$\eta$-Äquivalenz} + + Extensionalitäts-Prinzip: + \begin{itemize*} + \item Zwei Funktionen sind gleich, falls Ergebnis gleich für alle Argumente + \end{itemize*} + \colorbox{lightgray} { + \begin{minipage}[h]{1.0\linewidth} + $\eta$-Äquivalenz \\ + Terme $\lambda$x.fx und f heißen $\eta$-äquivalent ($\lambda$x.fx $\stackrel{\eta}{=}$ f), falls x nicht freie Variable von f ist. + \end{minipage} + } + + Beispiele: + $$\lambda x.\lambda y.f z x y \stackrel{\eta}{=}\lambda x.f z x$$ + $$f z \stackrel{\eta}{=}\lambda x.f z x$$ + $$\lambda x.x \stackrel{\eta}{=}\lambda x.(\lambda x.x)x$$ + aber $$\lambda x.f x x \stackrel{\eta}{\neq} f x$$ + + \subsection{Kodierung boolscher Werte} + Church Booleans + \begin{itemize*} + \item True wird zu: $C_{true} = \lambda t.\lambda f.t$ + \item False wird zu: $C_{false} = \lambda t.\lambda f.f$ + \item If-then-else wird zu: $If = \lambda a.a$ + \end{itemize*} + + Beispiel + \begin{lstlisting} if True then x else y \end{lstlisting} -ergibt: $(\lambda a.a)(\lambda t- \lambda f.t) x y = (\lambda t.\lambda f.t) xy = (\lambda f.x)y \Rightarrow x$ + ergibt: $(\lambda a.a)(\lambda t- \lambda f.t) x y = (\lambda t.\lambda f.t) xy = (\lambda f.x)y \Rightarrow x$ -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-003.png} -\end{center} - -\begin{itemize*} - \item if True then x else y ergibt: - \subitem ($\lambda$\color{blue}a.a\color{black})(\color{red} $\lambda$t.$\lambda$f.t\color{black}) x y $\Rightarrow$ ($\lambda$\color{blue}t\color{black}.$\lambda$f.\color{blue}t\color{black}) \color{red}x\color{black} y $\Rightarrow$ ($\lambda$\color{blue}f\color{black}.x)\color{red}y\color{black} $\Rightarrow$ x - \item $b_1$ \&\& $b_2$ ist äquivalent zu if $b_1$ then $b_2$ else False - \subitem $\Rightarrow$ $b_1$ \&\& $b_2$ wird zu ($\lambda$a.a) $b_1$ $b_2$ $C_false$ - \subitem $\Rightarrow$ $b_1$ \&\& $b_2$ wird zu ($\lambda$a.a) $b_1$ $b_2$ ($\lambda$t.$\lambda$f.f) - \item True \&\& True ergibt: - \subitem \color{white} $\Rightarrow$ \color{black}($\lambda$\color{blue}a.a\color{black})\color{red}$C_true$ \color{black} $C_true$ ($\lambda$t.$\lambda$f.f) - \subitem $\Rightarrow$ ($\lambda$\color{blue}t\color{black}.$\lambda$f.\color{blue}t\color{black})\color{red}($\lambda$t.$\lambda$f.t)\color{black}($\lambda$t.$\lambda$f.f) - \subitem $\Rightarrow$ ($\lambda$\color{blue}f\color{black}.($\lambda$t.$\lambda$f.t)) \color{red}($\lambda$t.$\lambda$f.f)\color{black} $\Rightarrow$ $\lambda$t.$\lambda$f.f = $C_true$ -\end{itemize*} - -\begin{itemize*} - \item $b_1 \lor b_2$ entspricht: - \subitem if $b_1$ then True else $b_2$ - \item $\neg b_1$ entspricht: - \subitem if $b_1$ then False else True - \item $b_1 \Rightarrow b_2$ entspricht: - \subitem if $b_1$ then $b_2$ else True -\end{itemize*} - -\subsection{Kodierung natürlicher Zahlen} -Eine natürliche Zahl drückt aus, wie oft etwas geschehen soll. + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-Lambda_Abstraktion.png} + \end{center} + + \begin{itemize*} + \item if True then x else y ergibt: + \subitem ($\lambda$\color{blue}a.a\color{black})(\color{red} $\lambda$t.$\lambda$f.t\color{black}) x y $\Rightarrow$ ($\lambda$\color{blue}t\color{black}.$\lambda$f.\color{blue}t\color{black}) \color{red}x\color{black} y $\Rightarrow$ ($\lambda$\color{blue}f\color{black}.x)\color{red}y\color{black} $\Rightarrow$ x + \item $b_1$ \&\& $b_2$ ist äquivalent zu if $b_1$ then $b_2$ else False + \subitem $\Rightarrow$ $b_1$ \&\& $b_2$ wird zu ($\lambda$a.a) $b_1$ $b_2$ $C_false$ + \subitem $\Rightarrow$ $b_1$ \&\& $b_2$ wird zu ($\lambda$a.a) $b_1$ $b_2$ ($\lambda$t.$\lambda$f.f) + \item True \&\& True ergibt: + \subitem \color{white} $\Rightarrow$ \color{black}($\lambda$\color{blue}a.a\color{black})\color{red}$C_true$ \color{black} $C_true$ ($\lambda$t.$\lambda$f.f) + \subitem $\Rightarrow$ ($\lambda$\color{blue}t\color{black}.$\lambda$f.\color{blue}t\color{black})\color{red}($\lambda$t.$\lambda$f.t)\color{black}($\lambda$t.$\lambda$f.f) + \subitem $\Rightarrow$ ($\lambda$\color{blue}f\color{black}.($\lambda$t.$\lambda$f.t)) \color{red}($\lambda$t.$\lambda$f.f)\color{black} $\Rightarrow$ $\lambda$t.$\lambda$f.f = $C_true$ + \item $b_1 \lor b_2$ entspricht: + \subitem if $b_1$ then True else $b_2$ + \item $\neg b_1$ entspricht: + \subitem if $b_1$ then False else True + \item $b_1 \Rightarrow b_2$ entspricht: + \subitem if $b_1$ then $b_2$ else True + \end{itemize*} + + \subsection{Kodierung natürlicher Zahlen} + Eine natürliche Zahl drückt aus, wie oft etwas geschehen soll. $c_0 = \lambda s.\lambda z.z$; $c_1=\lambda s.\lambda z.sz$; $c_2=\lambda s.\lambda z.s(sz)$;...;$c_n=\lambda s.\lambda z.s^n z$ -Arithmetische Operationen -Addition: $plus = \lambda m. \lambda n. \lambda s. \lambda z. m s (n s z)$ -Multiplikation: $times = \lambda m. \lambda n. \lambda s. n (m s) = \lambda m. \lambda n. \lambda s. \lambda z. n (m s) z$ -Exponentiation: $exp = \lambda m. \lambda n. n m = \lambda m. \lambda n. \lambda s. \lambda z. n m s z$ -Vorgänger: $pred = \lambda n.\lambda s.\lambda x. n (\lambda y.\lambda z. z (y s))(K x)$ -Subtraktion: $sub = \lambda n.\lambda m. m pred n$ -Nullvergleich: $isZero = \lambda n. n (\lambda x. C false ) C true$ + Arithmetische Operationen + \begin{itemize} + \item Addition: $plus = \lambda m. \lambda n. \lambda s. \lambda z. m s (n s z)$ + \item Multiplikation: $times = \lambda m. \lambda n. \lambda s. n (m s) = \lambda m. \lambda n. \lambda s. \lambda z. n (m s) z$ + \item Exponentiation: $exp = \lambda m. \lambda n. n m = \lambda m. \lambda n. \lambda s. \lambda z. n m s z$ + \item Vorgänger: $pred = \lambda n.\lambda s.\lambda x. n (\lambda y.\lambda z. z (y s))(K x)$ + \item Subtraktion: $sub = \lambda n.\lambda m. m pred n$ + \item Nullvergleich: $isZero = \lambda n. n (\lambda x. C false ) C true$ + \end{itemize} + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-kodierung-natürlicher-zahlen} + \end{center} + + succ($c_2$) = ($\lambda$\color{blue}n\color{black}.$\lambda s.\lambda z.s$ (\color{blue}n\color{black} s z)) \color{red} ($\lambda$s.$\lambda z.s (s z))$ \color{black} + \subitem $\Rightarrow\lambda s.\lambda z.s ((\lambda$\color{blue}s\color{black}.$\lambda z.$ \color{blue} s \color{black}(\color{blue}s\color{black} z)) s z) + \subitem $\Rightarrow\lambda s.\lambda z.s((\lambda$\color{blue}z\color{black}.s (s \color{blue}z\color{black}))\color{red}z\color{black}) + \subitem $\Rightarrow\lambda s.\lambda z.s(s(s z)) = c_3$ -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-004} -\end{center} + \subsection{Rechnen mit Church - Zahlen } + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-diamant-eigenschaft} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-01.png} + + Idee zu exp: \\ + \subitem exp $c_m c_n \Rightarrow c_n c_m \Rightarrow (\lambda.\color{blue}s\color{black}.\lambda z.s^n z)\color{red}(\lambda s. \lambda z.s^m z)$ \color{black} + \subsubitem $\Rightarrow \lambda z.(\lambda s. \lambda z.s^m z)^n z$ + \subitem (per Induktion über n) $\stackrel{\alpha \beta \eta}{\Rightarrow}\lambda s.\lambda z. \lambda z.{s^m}^n z = {c_m}^n$ -succ($c_2$) = ($\lambda$\color{blue}n\color{black}.$\lambda$s.$\lambda$z.s (\color{blue}n\color{black} s z)) \color{red} ($\lambda$s.$\lambda$z.s (s z)) \color{black} -\subitem $\Rightarrow$ $\lambda$s.$\lambda$z.s (($\lambda$\color{blue}s\color{black}.$\lambda$z. \color{blue} s \color{black}(\color{blue}s\color{black} z)) s z) -\subitem $\Rightarrow$ $\lambda$s.$\lambda$z.s(($\lambda$\color{blue}z\color{black}.s (s \color{blue}z\color{black}))\color{red}z\color{black}) -\subitem $\Rightarrow$ $\lambda$s.$\lambda$z.s(s(s z)) = $c_3$ - -\subsection{Rechnen mit Church - Zahlen } - -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-005} -\end{center} - -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-006} -\end{center} - -Idee zu exp: - -\subitem exp $c_m c_n \Rightarrow c_n c_m \Rightarrow (\lambda.\color{blue}s\color{black}.\lambda z.s^n z)\color{red}(\lambda s. \lambda z.s^m z)$ \color{black} -\subsubitem $\Rightarrow \lambda z.(\lambda s. \lambda z.s^m z)^n z$ -\subitem (per Induktion über n) $\stackrel{\alpha \beta \eta}{\Rightarrow}$ $\lambda s.\lambda z. \lambda z.{s^m}^n z = {c_m}^n$ - -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-007} -\end{center} - -\subitem isZero($c_0$) = ($\lambda$\color{blue}n\color{black}.\color{blue}n\color{black}($\lambda$x.$C_{false}$)$C_{true}$)\color{red} ($\lambda$s.$\lambda$z.z)\color{black} -\subsubitem $\Rightarrow (\lambda s. \lambda z. z)\color{red} (\lambda x.C_{false})\color{black} C_{true}$ -\subsubitem $\Rightarrow (\lambda \color{blue} z.z \color{black}) \color{red} C_{true} \Rightarrow C_{true}$ -(Bemerkung: I und K sind die Identitätsfunktion bzw. das Konstanten-Funktional) - -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-008} -\end{center} - - -\subsection{Auswertungsstrategien} -Wenn es in einem Term mehrere Redexe gibt, welchen reduziert man dann? - -\begin{center} - ($\lambda$x.x)(($\lambda$x.x)($\lambda$z.($\lambda$x.x)z))\\ - \ ($\lambda$\color{blue}x.x\color{black})\color{red}(($\lambda$x.x)($\lambda$z.($\lambda$x.x)z)) \color{black}\\ - ($\lambda$x.x)(($\lambda$\color{blue}x.x\color{black})\color{red}($\lambda$z.($\lambda$x.x)z)\color{black})\\ - ($\lambda$x.x)(($\lambda$x.x)($\lambda$z.($\lambda$\color{blue}x.x\color{black})\color{red}z\color{black})\\ -\end{center} - -\begin{center} - ($\lambda$x.x)(($\lambda$x.x)($\lambda$z.($\lambda$x.x)z))\\ -\end{center} - -Volle $\beta$-Reduktion: Jeder Redex kann jederzeit reduziert werden - -\begin{center} - ($\lambda$x.x)(($\lambda$x.x)($\lambda$z.($\lambda$\color{blue}x.x\color{black})\color{red}z\color{black}))\\ - $\Rightarrow$ ($\lambda$x.x)(($\lambda$\color{blue}x.x\color{black})\color{red}($\lambda$z.z)\color{black})\\ - $\Rightarrow$($\lambda$\color{blue}x.x\color{black})\color{red}($\lambda$z.z)\color{black}) \\ - $\Rightarrow$ ($\lambda$z.z)\color{black} $\nRightarrow$ -\end{center} - -\begin{center} - ($\lambda$x.x)(($\lambda$x.x)($\lambda$z.($\lambda$x.x)z))\\ -\end{center} - -Volle $\beta$-Reduktion: Jeder Redex kann jederzeit reduziert werden \newline Normalreihenfolge: Immer der linkeste äußerste Redex wird reduziert - -\begin{center} - ($\lambda$x.x)(($\lambda$\color{blue}x.x\color{black})\color{red}($\lambda$z.($\lambda$x.x)z))\color{black}\\ - $\Rightarrow$ ($\lambda$\color{blue}x.x\color{black})\color{red}($\lambda$z.($\lambda$x.x)z)\color{black}\\ - $\Rightarrow$$\lambda$z.($\lambda$\color{blue}x.x\color{black})\color{red}z\color{black} \\ - $\Rightarrow$ ($\lambda$z.z)\color{black}) $\nRightarrow$ -\end{center} - -\subsection{Fixpunktsatz und Rekursion} - -\subsubsection{Divergenz} - -Bisherige Beispiele werten zu einer Normalform aus. \\ -Aber: -\begin{center} - $\omega = (\lambda \color{blue}x.x x\color{black})\color{red}(\lambda x.x x) \color{black} \rightarrow (\lambda x.x x)(\lambda x.x x)$ -\end{center} + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-Arithmetische-Operationen} + \end{center} + + \subitem $isZero(c_0) = (\lambda\color{blue}n\color{black}.\color{blue}n\color{black}(\lambda x.C_{false})C_{true})\color{red} (\lambda s.\lambda z.z)\color{black}$ + \subsubitem $\Rightarrow (\lambda s. \lambda z. z)\color{red} (\lambda x.C_{false})\color{black} C_{true}$ + \subsubitem $\Rightarrow (\lambda \color{blue} z.z \color{black}) \color{red} C_{true} \Rightarrow C_{true}$ + (Bemerkung: I und K sind die Identitätsfunktion bzw. das Konstanten-Funktional) + + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-Arithmetische-Operationen-2} + \end{center} + + \subsection{Auswertungsstrategien} + Wenn es in einem Term mehrere Redexe gibt, welchen reduziert man dann? + $$(\lambda x.x)((\lambda x.x)(\lambda z.(\lambda x.x)z))$$ + $$(\lambda \color{blue}x.x\color{black})\color{red}((\lambda x.x)(\lambda z.(\lambda x.x)z)) \color{black}$$ + $$(\lambda x.x)((\lambda \color{blue}x.x\color{black})\color{red}(\lambda z.(\lambda x.x)z)\color{black})$$ + $$(\lambda x.x)((\lambda x.x)(\lambda z.(\lambda \color{blue}x.x\color{black})\color{red}z\color{black})$$ + $$(\lambda x.x)((\lambda x.x)(\lambda z.(\lambda x.x)z))$$ + + Volle $\beta$-Reduktion: Jeder Redex kann jederzeit reduziert werden + $$(\lambda x.x)((\lambda x.x)(\lambda z.(\lambda \color{blue}x.x\color{black})\color{red}z\color{black}))$$ + $$\Rightarrow(\lambda x.x)((\lambda\color{blue}x.x\color{black})\color{red}(\lambda z.z)\color{black})$$ + $$\Rightarrow(\lambda \color{blue}x.x\color{black})\color{red}(\lambda z.z)\color{black})$$ + $$\Rightarrow(\lambda z.z)\color{black} \nRightarrow$$ + $$(\lambda x.x)((\lambda x.x)(\lambda z.(\lambda x.x)z))$$ + + Volle $\beta$-Reduktion: Jeder Redex kann jederzeit reduziert werden \\ + Normalreihenfolge: Immer der linkeste äußerste Redex wird reduziert + $$(\lambda x.x)((\lambda\color{blue}x.x\color{black})\color{red}(\lambda z.(\lambda x.x)z))\color{black}$$ + $$\Rightarrow(\lambda \color{blue}x.x\color{black})\color{red}(\lambda z.(\lambda x.x)z)\color{black}$$ + $$\Rightarrow\lambda z.(\lambda\color{blue}x.x\color{black})\color{red}z\color{black}$$ + $$\Rightarrow(\lambda z.z)\color{black}) \nRightarrow$$ + + \subsection{Fixpunktsatz und Rekursion} + \subsubsection{Divergenz} + Bisherige Beispiele werten zu einer Normalform aus. Aber: + $$\omega = (\lambda \color{blue}x.x x\color{black})\color{red}(\lambda x.x x) \color{black} \rightarrow (\lambda x.x x)(\lambda x.x x)$$ + $\lambda x.xx$ wendet sein Argument auf das Argument selbst an $\Rightarrow$ dadurch reproduziert $\omega$ sich selbst. -\newline -\newline -\colorbox{lightgray}{ - \begin{minipage}[h]{1.0\linewidth} - Divergenz: \\ - Terme, die nicht zu einer Normalform auswerten, divergieren. - Diese modellieren unendliche Ausführungen. - \end{minipage} -} - -\subsubsection{Der Fixpunktsatz} -\colorbox{lightgray}{ - \begin{minipage}[h]{1.0\linewidth} - Fixpunktsatz \\ - Für alle F $\in \Lambda$ existiert ein X $\in \lambda$ sodass gilt: F X = X - \end{minipage} -} -\newline -\begin{itemize*} - \item Der Fixpunktsatz besagt, dass im Lambda-Kalkül jeder Term einen Fixpunkt hat, d.h. einen Wert, der auf sich selber abgebildet wird. - \item Beweis: - \begin{itemize*} - \item Zu jedem beliebigen F sei W = $\lambda$x.F(x x) und X = (W W) - \item Dann gilt: X $\equiv$ WW $\equiv$ ($\lambda$x.F(x x)) W $\equiv$ F(W W) $\equiv$ F X - \end{itemize*} - \item Bemerkungen: - \begin{itemize*} - \item Für einige Lambda-Terme ist die Identifikation eines Fixpunktes einfach, z.B. für den Term $\lambda$x.x (alle Terme sind Fixpunkte) - \item Für andere Terme, wie $\lambda$xy.xy (= $\lambda$x.$\lambda$y.xy) ist das nicht so klar - \item Der Beweis des Fixpunktsatzes ist konstruiv, d.h. er liefert zu jedem Lambda-Term einen Fixpunkt - \end{itemize*} -\end{itemize*} -\subsubsection{Anwendung des Fixpunktsatzes} -\begin{itemize*} - \item Aufgabe: Berechne den Fixpunkt zum Term $\lambda$xy.xy - \begin{itemize*} - \item Lösungsansatz: W $\equiv$ $\lambda$x.($\lambda$\color{blue}x\color{black}y.\color{blue}x\color{black}y)\color{red}(xx) \color{black} $\equiv$ $\lambda x.\lambda y.(x x)y \equiv \lambda xy.(xx)y$ - \item Damit ist der gesuchte Fixpunkt X $\equiv ((\lambda xy.(xx)y)(\lambda xy.(xx)y))$ - \item Nachrechnen: - \begin{description*} - \item[ \space ] $(\lambda xy.xy) ((\lambda xy.(xx)y) (\lambda xy.(xx)y))$ - \item[$\equiv$] $(\lambda \color{blue}x\color{black}.\lambda y. \color{blue} x \color{black} y) \color{red} ((\lambda xy.(xx)y) (\lambda xy.(xx)y)$ \color{black} - \item[$\equiv$] $\lambda \color{blue}y \color{black}.((\lambda xy.(xx)y)) (\lambda xy.(xx)y) \color{red}y\color{black}$ - \item[$\equiv$] $(\lambda xy.(xx)y)(\lambda xy.(xx)y)$ - \item[$\equiv$] X - \end{description*} - \end{itemize*} - \item Bemerkung: Der so für die Identitätsfunktion $\lambda x.x$ konstruierte Fixpunkt ist übrigens $(\lambda x.xx)(\lambda x.xx)$, er spielt die besondere Rolle des Standardterms $\bot$ für nicht-terminierende Ausführungen -\end{itemize*} -\subsubsection{Der Fixpunkt-Kombinator} - -\colorbox{lightgray}{ - \begin{minipage}[h]{1.0\linewidth} - Im Ergebnis unserer Diskussion des Fixpunktsatzes definieren wir den Fixpunkt-Kombinator wie folgt: \\ - \begin{center} - $Y \equiv \lambda f.(\lambda x.f(xx)) (\lambda x.f(xx))$ - \end{center} - \end{minipage} -} -\begin{itemize*} - \item Dieser Kombinator spielt eine wichtige Rolle bei der Definition rekursiver Funktionen im Lambda-Kalkül, wie wir im folgenden sehen werden - \item Für jeden Lambda-Term M gilt: Y M = M (Y M) - \begin{itemize*} - \item Beweisidee: zeige, dass beide Terme auf einen identischen Term reduziert werden können - \end{itemize*} - \item Der Term Y ist übrigens nicht der einzige Kombinator, der Fixpunkte zu Lambda-Termen konstruiert - \begin{itemize*} - \item A. Turing: $\Theta \equiv (\lambda xy.y(xxy)) (\lambda xy.y(xxy))$ - \end{itemize*} -\end{itemize*} - -\subsubsection{Rekursion im Lambda-Kalkül} -\begin{itemize*} - \item Die bisher definierten Funktionen waren alle nicht-rekursiv - \item Viele Funktionen kann man aber nur unter Zuhilfenahme von Rekursion (bzw. Iteration) beschreiben - \item In üblichen Programmiersprachen werden rekursive Funktionsdefinitionen durch die Verwendung von Namen für Funktionen möglich - man verwendet hierbei einfach den Namen der gerade zu definierenden Funktion im Rumpf der Definition: - \begin{itemize*} - \item fun fak(i) -$>$ if (i = 0) then 1 else i * fak(i-1). - \end{itemize*} - \item Im Lambda-Kalkül gibt es jedoch keine Namen für Funktionen: - \begin{itemize*} - \item Daher stellt man eine rekursive Funktion f mittels einer Funktion G dar, die einen zusätzlichen Parameter g hat, an den man dann G selber bildet - \item Schaut kompliziert aus, ist es auch (Q-Q) - \item Warum so kompliziert? Damit die Definition von G im eigenen Rumpf verfügbar ist - - \end{itemize*} -\end{itemize*} -\subsubsection{Rekursive Funktionen sind Fixpunkte} -\begin{itemize*} - \item Rekursive Funktion von g - \begin{itemize*} - \item g = $\lambda$n.…g…n… Rumpf verwendet g - - \end{itemize*} - \item Daraus gewinnt man das Funktional - \begin{itemize*} - \item G = $\lambda$g.$\lambda$n.…g…n… - \end{itemize*} - \item Falls G einen Fixpunkt g* hat, d.h. G(g*) = g*, so - \begin{itemize*} - \item g* = G(g*) = $\lambda$n.…g*…n - \end{itemize*} - \item Vergleiche: g = $\lambda$n.…g…n… -\end{itemize*} -\begin{center} - Rekursive Definition $\Leftrightarrow$ Fixpunkt des Funktionals -\end{center} -\begin{itemize*} - \item Beispiel: Fakultät - \begin{itemize*} - \item g = $\lambda$ n. if isZero n then $c_1$ else (times n g(pred n)) - rekursiv - \item G = $\lambda$g.$\lambda$n.if isZero n then $c_1$ else (times n g(pred n)) - funktional - \end{itemize*} -\end{itemize*} -\subsubsection{Der Fixpunktkombinator dient als Rekursionsoperator} -Wir berechnen den gesuchten Fixpunkt des Funktionals G mit dem Fixpunktkombinator, der somit als Rekusrionsoperator dient: \\ - -\color{blue} Rekursionsoperator - -\begin{center} - $Y = \lambda f.(\lambda x.f(xx))(\lambda x.f(xx))$ - \color{black} \newline \newline - $Y f = (\lambda \color{blue}f\color{black}.(\lambda x.\color{blue}f\color{black}(xx))(\lambda x.\color{blue}f\color{black}(xx))) \color{red}f\color{black}$ \\ - $\Rightarrow (\lambda \color{blue}x\color{black}.f(\color{blue}xx\color{black})) \color{red}(\lambda x.f(xx))\color{black}$ \\ - $\Rightarrow f((\lambda x.f(xx)) (\lambda x.f(xx)) \Leftarrow f(Yf) ())$ -\end{center}\color{black} -\subitem also \space\space\space \space f(Yf) $\stackrel{\beta}{=}$ Yf \\ -d.h. \space\space\space Yf ist Fixpunkt von f - -\subsubsection{Beispiel: Fakultät im Lambda-Kalkül} - -\begin{center} - \includegraphics[width=1.0\linewidth]{Assets/Programmierparadigmen-002} -\end{center} - -\subsection{Ausdrucksstärke des Lambdakalküls} -\begin{itemize*} - \item Im Folgenden wollen wir zeigen, dass der Lambda-Kalkül genau die rekursiven Funktionen beschreibt - \item Eine numerische Funktion ist eine Abbildung f: $\mathbb{N}^k \rightarrow \mathbb{N}$ mit k$ \in \mathbb{N} \cap \{0\}$ - \item Wir definieren hierzu: - \begin{itemize*} - \item Anfangsfunktionen: - \begin{itemize*} - \item Projektion: $U_i^k (n_1,n_2,…,n_k) = n_i$ für $1<=i<=k$ - \item Nullfunktion: Z(n) = 0 - \item Nachfolger: S(n) = n+1 - \end{itemize*} - \item Minimalisierung: - \begin{itemize*} - \item Für eine Relation P(m) bezeichne $\mu$m[P(m)] die kleinste Zahl m sodass P(m) gilt. - \end{itemize*} - \end{itemize*} - \item Bemerkung: im Folgenden notieren wir $n_1,n_2,…,n_k$ kurz als $\overline{n_k}$ - \item Eine numerische Funktion ist Lambda-definierbar, wenn es einen Kombinator M gibt, sodass M $\overline{n_k}$ = f($\overline{n_k}$) -\end{itemize*} - -\begin{itemize*} - \item Im folgenden sei C eine Klasse von numerischen Funktionen, und es gelte $g,h,h_1,h_2,…,h_m \in C$ - \item Wir definieren nun die folgenden Eigenschaften: - \begin{itemize*} - \item C ist \color{blue} abgeschlossen unter Komposition\color{black}, wenn für jede Funktion f, die über f($\overline{n_k}$) := $g(h_1(\overline{n_k}),…,h_m(\overline{n_k}))$ definiert ist, gilt $f \in C$ - \item C ist \color{blue} abgeschlossen unter primitiver Rekursion\color{black}, wenn für jede Funktion f, die über - \begin{center} - f(0,$\overline{n_k}$) = g($\overline{n_k}$) \\ - f(j+1, $\overline{n_k}$) = h(f(j,$\overline{n_k}$),j,$\overline{n_k}$) - \end{center} - definiert ist, gilt: $f \in C$ - \item C ist \color{blue} abgeschlossen unter unbeschränkter Minimalisierung \color{black}, wenn für jede Funktion f, die über f($\overline{n_k}$) = $\mu$m[g($\overline{n_k}$,m)= 0] definiert ist (wobei für alle $\overline{n_k}$ ein m existiere, sodass g($\overline{n_k}$,m) = 0 ist), gilt $f \in C$ - \end{itemize*} -\end{itemize*} - -\colorbox{lightgray}{\begin{minipage}[h]{1.0\linewidth} - Definition: \\ - Die Klasse der rekursiven Funktionen ist die kleinste Klasse numerischer Funktionen, die alle oben genannten Anfangsfunktionen enthält und abgeschlossen ist unter Komposition, primitiver Rekursion und unbeschränkter Minimalisierung - \end{minipage}} -\newline -\begin{itemize*} - \item \color{blue} Lemma 1: Die Anfangsfunktionen sind Lambda-definierbar \color{black} - \item Beweis: - \begin{itemize*} - \item $U_i^k$ = $\lambda x_1 x_2 … x_k.x_i$ - \item S = $\lambda n.\lambda s. \lambda z.s(nsz)$ (siehe succ bei Churchzahlen) - \item Z = $\lambda fx.x$ (siehe $c_0$ bei Churchzahlen) - \end{itemize*} -\end{itemize*} - -\begin{itemize*} - \item \color{blue} Lemma 2: Die Lambda-definierbaren Funktionen sind abgeschlossen unter primitiver Rekursion \color{black} - \item Beweis: Sei f definiert über - \begin{center} - f(0,$\overline{n_k}$) = g($\overline{n_k}$)\\ - f(j+1, $\overline{n_k}$) = h(f(j, $\overline{n_k}$),j,$\overline{n_k}$) - \end{center} - und seien g und h Funktionen (die per Induktionsvoraussetzung) durch die Lambda-terme G und H berechnet werden - \begin{itemize*} - \item Intuitiv kann f berechnet werden, indem man überprüft ob j = 0 ist, und wenn ja g($\overline{n_k}$), ansonsten h(f(j, $\overline{n_k}$),j,$\overline{n_k}$) - \item Ein Term M hierfür existiert laut Fixpunktsatz und es gilt: - $M \equiv Y (\lambda f\:x\: \overline{y_k}.if(isZero \: x)(G\:\overline{y_k})(H(f(pred\: x)\overline{y_k})(pred \: x)\overline{y_k}))$ - \end{itemize*} -\end{itemize*} - -\begin{itemize*} - \item \color{blue} Lemma 3: Die Lambda-definierbaren Funktionen sind abgeschlossen unter unbeschränkter Minimalisierung \color{black} - \item Beweis: - \begin{itemize*} - \item Sei f über f($\overline{n_k}$) = $\mu$m[g($\overline{n_k}$,m) = 0] definiert, wobei g (per Induktionsvoraussetzung) durch den Lambda-Term G berechnet wird - \item Intuitiv kann man f berechnen, indem man bei 0 beginnend für m überprüft, ob g($\overline{n_k}$,m) = 0 ist, und wenn ja m ausgibt, ansonsten die Überprüfung mit m+1 fortsetzt - \item Ein Term für eine solche Funktion kann laut Fixpunktsatz konstruiert werden und man erhält mit Anwendung des Fixpunktkombinators zunächst: \\ - $N \equiv Y (\lambda f \: \overline{x_k} \: y. if(isZero \: (G \: \overline{x_k} \: y))y(f\:\overline{x_k}\:(succ \: y)))$ - \item Nun definiert man die Funktion f durch den folgenden Term M: \\ - $M \equiv \lambda \overline{x_k}.N \: \overline{x_k} \: c_0$ - \end{itemize*} -\end{itemize*} - -\begin{center} - \includegraphics[width=1.0\linewidth]{Assets/Programmierparadigmen-004.png} -\end{center} -\begin{itemize*} - \item Aus den Lemmata 1 bis 3 folgt nun der Satz:\\ + \colorbox{lightgray}{ \begin{minipage}[h]{1.0\linewidth} - Alle rekursiven Funktionen sind Lambda-definierbar - \end{minipage}} -\end{itemize*} - - -\subsection{Berechnungsreihenfolgen und Konfluenz} -\subsubsection{Noch einmal Auswertungsstrategien} -\begin{itemize*} - \item Bei unserer initialen Betrachtung der Auswertungsstrategien haben wir die volle $\beta$-Rekursion und die Normalreihenfolge kennengelernt - \item Nun wollen wir unsere Betrachtungen hierzu noch einmal vertiefen und definieren zunächst: - \begin{itemize*} - \item Ein Redex wird als \color{blue} "äußerst" (outermost) \color{black} bezeichnet, wenn er nicht Teil eines anderen Redex ist. - \item Ein Redex wird als \color{blue} "innerst" (innermost) \color{black} bezeichnet, wenn er keinen eigenständigen Redex beinhaltet - \end{itemize*} - \item Mit diesen Begriffen können im folgenden die gebräuchlichsten Auswertungsstrategien formuliert werden - \begin{itemize*} - \item \color{blue} Normal Order: \color{black} Evaluiere Argumente so oft, wie sie verwendet werden - \item \color{blue} Applicative Order: \color{black} Evaluiere Argumente einmal - \item \color{blue} Lazy Evaluation: \color{black} Evaluiere Argumente höchstens einmal - \end{itemize*} - \item Eine zentrale Kernfrage: \color{blue} Welche Auswertungsstrategie führt (möglichst schnell) zu einem nicht weiter reduzierbaren Term? - \color{black} - \begin{itemize*} - \item Bei unserer beispielhaften Berechnung des Terms Fak $c_2$ haben wir nach der initialen Anwendung des Fixpunktkombinators zunächst den Term isZero $c_2$ reduziert. - \item Ebenso hätten wird den weiter innen stehenden Fixpunktkombinator zuerst erneut anwenden können(bei voller $\beta$-Reduktion kann jeder Term jederzeit reduziert werden). - \item Auf diese Weise hätten wir unendlich oft vorgehen, damit einen immer länger werdenden Term ableiten können und somit nicht das gewünschte Resultat $c_2$ berechnet. - \end{itemize*} - \item Eine weitere Kernfrage: Angenommen mehrere unterschiedliche Reduktionsreihenfolgen führen zu einem nicht weiter zu reduzierenden Ergebnis - \color{blue} führen all diese Reihenfolgen zum gleichen Ergebnis? \color{black} - \item Wir definieren zuerst einen zentralen begriff in diesem Zusammenhang: - \colorbox{lightgray}{\begin{minipage}[h]{1.0\linewidth} - Ein Transitiosnsystem (D, $\rightarrow*$) heißt genau dann konfluent, wenn für alle $t,t_1,t_2 \in D$ gilt: wenn $ t \rightarrow* t_1$ und $t \rightarrow* t_2$, dann gibt es ein $t' \in D$ mit $t_1 \rightarrow* t'$ und $t_2 \rightarrow* t'$ - \end{minipage}} - \item Wenn der Lambda-Kalkül konfluent ist, kann hieraus gefolgert werden, dass unterschiedliche Reduktionsreihenfolgen, die zu einer nicht mehr weiter zu reduzierenden Form führen, somit auf den gleichen Term führen müssen. - \item Achtung: hieraus kann nicht gefolgert werden, dass alle Reduktionsreihenfolgen auf den gleichen Term führen, da dies ja nur für "terminierende" Reduktionsreihenfolgen gilt! -\end{itemize*} -\subsubsection{Church-Rosser-Eigenschaft} -\color{blue} Satz (Church-Rosser) \newline Der untypisierte $\lambda$-Kalkül ist konfluent: Wenn $t \stackrel{*}{\Rightarrow} t_1$ und $t \stackrel{*}{\Rightarrow} t_2$, dann gibt es ein t' mit $t_1 \stackrel{*}{\Rightarrow} t'$ und $t_2 \stackrel{*}{\Rightarrow} t'$ - -\begin{center} - \includegraphics[width=0.25\linewidth]{Assets/Programmierparadigmen-009} -\end{center} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-010} -\end{center} -\color{black} -Beweisidee: Definiere $\stackrel{\rightarrow}{\rightarrow}$ als "parallele" $\beta$-Reduktion. -\begin{itemize*} - \item Es gilt: $\Rightarrow \subseteq \stackrel{\rightarrow}{\rightarrow} \subseteq \stackrel{*}{\Rightarrow}$ - \item Zeige Diamant Eigenschaft für $\stackrel{\rightarrow}{\rightarrow}$ -\end{itemize*} -\begin{center} - \includegraphics[width=0.25\linewidth]{Assets/Programmierparadigmen-011} + Divergenz: \\ + Terme, die nicht zu einer Normalform auswerten, divergieren. + Diese modellieren unendliche Ausführungen. + \end{minipage} + } -\end{center} -\subsubsection{Eindeutigkeit der Normalform} -\color{blue} Korollar (Eindeutigkeit der Normalform) \newline -Die Normalform eines $\lambda$-Terms ist - sofern sie existiert - eindeutig. \color{black} -\newline -\newline -Beweis: -\begin{itemize*} - \item $t_1$ und $t_2$ Normalformen von t, d.h. $t \stackrel{*}{\Rightarrow} t_1 \nRightarrow$ und $t \stackrel{*}{\Rightarrow} t_2 \nRightarrow$ - \item Nach Chruch-Rosser gibt es t' mit $t_1 \stackrel{*}{\Rightarrow} t'$ und $t_2 \stackrel{*}{\Rightarrow} t'$ - \item Nach Annahme $t_1 \nRightarrow$ und $t_2 \nRightarrow$, also $t_1 = t' = t_2$ -\end{itemize*}\ \newline -\color{blue} -Bei terminierenden $\beta$-Reduktionen ist irrelevant, welchen Redex man zuerst reduziert!\color{black} -\subsection{Auswertung von Parametern in Programmiersprachen} -\subsubsection{Behandlung von Parametern in Programmiersprachen} -\begin{itemize*} - \item Die Art und Weise, wie in einer Programmiersprache Parametter übergeben - d.h. wie die Reihenfolge und die Zeitpunkte ihrer Auswertung gehandhabt - werden, hat Einfluss auf wichtige Eigenschaften der Sprache: - \begin{itemize*} - \item Effizienz der Berechnungen - \item Termininerungsverhalten - \item Ausdruckskraft - \end{itemize*} - \item Hierbei ist es insbesondere von Interesse, wie Parameter gehandhabt werden, deren Werte undefiniert sind (z.B. 1/0)\newline + \subsubsection{Der Fixpunktsatz} \colorbox{lightgray}{ \begin{minipage}[h]{1.0\linewidth} - Wir definieren zunächst den zentralen begriff "strikt": \newline Eine n-stellige Funktion heißt strikt im k-ten Argument ($1<=k<=n$), wenn gilt: f($x_1,x_2,…,x_{k-1},\bot,x_{k+1},…,x_n$) = $\bot$ - \end{minipage}} - \item Ein undefiniertes Argument führt hier zu einem undefinierten Resultat - \item Grundsätzlich kann man die Auswertungsstrategien von Programmiersprachen in strikte und nicht-strikte Strategien einteilen; sehr gebräuchlich sind dabei insbesondere: - \begin{itemize*} - \item Call by Value: Ausdrücke, die Parameter bei einem Funktionsaufruf beschreiben, werden vor der Übergabe an die Funktion vollständig ausgewertet - \item Call by Name: Ausdrücke, die Parameter bei einem Funktionsaufruf beschreiben, werden nicht bei Übergabe, sondern erst dann ausgewertet, wenn sie in der aufgerufenen Funktion tatsächlich benötigt werden - \end{itemize*} - \item Beide Varianten haben spezifische Vor- und Nachteile: - \begin{itemize*} - \item Call by Value: weniger Berechnungsaufwand, wenn ein Parameter mehr als einmal im Funktionsrumpf vorkommt; weniger Speicheraufwand bei der Übergabe - \item Call by Name: weniger Berechnungsaufwand, wenn ein Argument nicht zum Ergebnis beiträgt; höherer Aufwand bei Übergabe - \end{itemize*} - \item Die Programmiersprache Erlang realisiert grundsätzlich eine strikte Handhabung von Parametern, da sie die Strategie Call by Value verwendet - \item Allerdings wird bei der Definition einer Funktion der resultierende Wert erst dann berechnet, wenn die Funktion ausgewertet wird - \begin{itemize*} - \item Das erlaubt über den Umweg zusätzlicher Funktionsdefinitionen auch die Realisierung einer nicht-strikten Auswertungsstrategie - ermöglicht Nachbildung der sogenannten Lazy-Evaluation - \item hierbei wird ein nicht-strikt zu evaluierendes Argument als Resultat einer anonymen nullstelligen Funktion (ohne Parameter) "verpackt" - \item Im Rumpf der eigentlichen Funktion wird diese Funktion dann ausgewertet (= aufgerufen), wenn feststeht, dass dieses Argument für die Berechnung des Ergebnisses benötigt wird - \item Andere funktionale Sprachen wie Haskell oder Gofer verwenden Call by Name und realisieren damit grundsätzlich Lazy-Evaluation - \end{itemize*} - \ \linebreak - \begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-012} - \end{center} - \begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-013} - \end{center} - \item Erläuterungen: - \begin{itemize*} - \item Im zweiten Beispiel wird der Rückgabewert der übergebenen Funktionne nur ausgewertet, wenn sie im Rumpf der auszuführenden Funktion aufgerufen werden - \item Innerhalb von Erlang-Modulen kann man sich mit Hilfe einer Macro-Definition Schreibarbeit sparen: \newline -define(DELAY(E), fun() -$>$ E end). \newline check() -$>$ test2(true, ?DELAY(3), ?DELAY(4/0)). - \end{itemize*} - \item Je nachdem, ob und wie häufig ein übergebener Parameter im Funktionsrumpf benötigt wird, können bei Lazy-Evaluation Berechnungen - \begin{itemize*} - \item komplett eingespart oder - \item (in identischer Form) wiederholt erforderlich werden - \item Unter Umständen kann man in der betreffenden Funktion durch Einführung einer temporären Variable redundante Mehrfachberechnungen einsparen ($\rightarrow$ Call by Need) - \end{itemize*} - \item Die Parameterübergabe ist bei Call by Name in der Regel aufwändiger als bei Call by Value - \begin{itemize*} - \item Die meisten Programmiersprachen (Java, C, C++, Pascal etc.) verwenden daher Call by Value ($\rightarrow$ strikte Auswertung) - \item Eine Ausnahme wird oft bei dem IF-Konstrukt gemacht (der auszuführende Code ist hier ja meist auch kein Parameter) - \end{itemize*} - \item Zu Ausdrucksstärke: während strikte Funktionen durch die Strategie Call by Value realisiert werden, ist es nicht so, dass Lazy Evaluation es erlaubt, alle nicht-strikten Funktionen zu realisieren - \begin{itemize*} - \item Die folgenden Gleichungen definieren eine nicht-strikte Multiplikation $\otimes$ auf der Basis der Multiplikation · für Zahlen:\newline \begin{center} - 0 $\otimes$ y = 0 \newline - x $\otimes$ 0 = 0 \newline - x $\otimes$ y = x · y \newline - \end{center} - \item Wenn ein Arguemnt undefiniert ist, dann liefert $\otimes$ ein Ergebnis, sofern das andere Argument zu 0 evaluiert wird ($\rightarrow$ fak(-1) $\otimes$ (fak(3)-6)) - \item Implementiert werden kann die Funktion nur durch eine Art von paralleler Auswertung mit Abbruch der anderen Berechnung sobald 0 als Resultat berechnet und zurückgegeben wurde - \end{itemize*} - \item Wir betrachten nun die Beziehungen zwischen Parameterbehandlung in Programmiersprachen und Reduktion von Lambda-Termen -\end{itemize*} -\subsubsection{Auswertungsstrategien \& Programmiersprachen} -\color{blue} Werte in Programmiersprachen wie Haskell: \color{black} -\begin{itemize*} - \item Primitive Werte: 2, True - \item Funktionen: (\textbackslash x $\rightarrow$ x), (\&\&), (x $\rightarrow$(\textbackslash y $\rightarrow$ y+y)x) -\end{itemize*} -\ \newline -\color{blue} Werte im $\lambda$-Kalkül: -\color{black} \begin{itemize*} - \item Abstraktionen: $c_2 = \lambda s. \lambda z.s\;(s\;z),\;\;\; C_{true} = \lambda t- \lambda f.t,\;\;\; \lambda x.x,\;\;\; \newline \lambda b_1. \lambda b_2.\;b_1\; b_2 (\lambda t.\lambda f.\;f),\;\;\; \lambda x.\;(\lambda y.\;plus\; yy)x$ -\end{itemize*} -\color{blue} Auswertungsstrategie: \color{black} Keine weitere Reduzierung von Werten \newline -Reduziere keine Redexe unter Abstraktionen (umgeben von $\lambda$):\newline -$\Rightarrow$ call-by-name, call-by-value -\subsubsection{Call-By-Name} -Call-By-Name: Reduziere linkesten äußersten Redex -\begin{itemize*} - \item Aber nicht falls von einem $\lambda$ umgeben \newline - \subitem $(\lambda y. (\lambda x.y(\lambda z.z)x))\color{red} ((\lambda x.x)(\lambda y.y))$ \color{black} \newline - \subitem $(\lambda x.((\lambda \color{blue}x.x\color{black}) \color{red}(\lambda y.y)\color{black})(\lambda z.z)x)$ - \begin{center} - Intuition: Reduziere Argumente erst, wenn benötigt - \end{center} + Fixpunktsatz \\ + Für alle $F\in\Lambda$ existiert ein $X\in\lambda$ sodass gilt: $F X = X$ + \end{minipage} + } -\end{itemize*} -Auswertung in Haskell: \color{blue} Lazy-Evaluation = call-by-name (+sharing) -\color{black} \begin{itemize*} - \item Standard-Auswertungsstrategie für Funktionen/Konstruktoren - \item[] listOf x = x : listOf x - \item[] 3: listOf 3 $\nRightarrow$ - \item[] - \item[] (div 1 0) : (6 : []) - \item[] tail ((div 1 0): (6 : [])) $\Rightarrow$ 6 : [] $\nRightarrow$ -\end{itemize*} -\subsubsection{Call-By-Value} -Call-By-Value: Reduziere linkesten Redex -\begin{itemize*} - \item der nicht einen $\lambda$ umgibt - \item und dessen Argument ein \color{blue} Wert \color{black} ist - \subsubitem $(\lambda y.(\lambda x.y(\lambda z.z)x)((\lambda \color{blue} x.x \color{black})\color{red}(\lambda y.y)\color{black})$ - \subsubitem $\Rightarrow (\lambda \color{blue}y\color{black}(\lambda x. \color{blue}y\color{black}(\lambda z.z)x))\color{red}(\lambda y.y)\color{black}$ - \subsubitem $\Rightarrow (\lambda x.(\lambda y.y(\lambda z.z)x)) \nRightarrow$ - \item[] Intuition: Argumente vor Funktionsaufruf auswerten - \item[] Auswertungsstrategie vieler Sprachen: Java, C, Scheme, ML, … - \item[] Arithmetik in Haskell: Auswertung by-value - \item[] prodOf(x) = y * prodOf x - \item[] 3 * prodOf 3 $\Rightarrow$ 3 * (3 * prodOf 3) $\Rightarrow$ … - \item[] ((div 1 0) * 6) * 0 $\Rightarrow$ $\bot$ - \item[] ((div 2 2 ) * 6) * 0 $\Rightarrow$ ((1 * 6) * 0) $\Rightarrow$ 6 * 0 $\Rightarrow$ 0 $\nRightarrow$ \end{itemize*} -\subsubsection{Vergleich der Auswertungsstrategien} -\color{blue} Call-by-name vs. Call-by-value \color{black} -\begin{itemize*} - \item Werten nicht immer zur Normalform aus $\lambda x.(\lambda y.y)x$ - \item Gibt es Normalform, dann darauf $\beta$-reduzierbar (Church-Rosser) - \item Call-by-name terminiert öfter - \item[] $Y(\lambda y.z) = \lambda f. (\lambda x.f(x\;x))(\lambda x.f(x\;x))\color{red}(\lambda y.z)\color{black}$ \newline - \subitem $ \Rightarrow \lambda x.(\lambda y.z(x\;x))\color{red} (\lambda x.(\lambda y.z)(x\;x))$ \newline - \subitem $\Rightarrow (\lambda y.z)\color{red}((\lambda x.(\lambda y.z)(x\;x)) (\lambda x.(\lambda y.z (x\;x)))\color{black} \stackrel{cbn}{\Rightarrow} z$ - \subitem \newline - \subitem $\stackrel{cbv}{\Rightarrow} (\lambda y.z)((\lambda x.(\lambda y.z)(x\;x))\color{red}(\lambda x.(\lambda y.z (x\;x))\color{black})$ - \subitem $\stackrel{cbv}{\Rightarrow} (\lambda y.z)((\lambda y.z)((\lambda x.(\lambda y.z)(x\;x)) \color{red} (\lambda x.(\lambda y.z(x\;x)) \color{black}))$ -\end{itemize*} -\color{blue} Standardisierungssatz \newline -Wenn t eine Normalform hat, dann findet Normalreihenfolgenauswertung diese. -\color{black} -\subsubsection{Abschließende Bemerkungen} -\begin{itemize*} - \item Der Lambda-Kalkül wurde in den dreißiger Jahren des 20. Jahrhunderts von Alonzo Church erfunden, um damit grundsätzliche Betrachtungen über berechenbare Funktionen anzustellen - \item Trotz der Einfachheit der dem Kalkül zugrunde liegenden Regeln, realisiert er ein universelles Berechnungsmodell - \item Der Lambda-Kalkül hat die Entwicklung zahlreicher, für die Informatik wichtiger Konzepte beeinflusst \begin{itemize*} - \item Funktionale Programmiersprachen (die minimalen Funktionen von Lisp wurden auf Grundlage des Lambda-Kalküls definiert) - \item Forschund zu Typsystemen für Programmiersprachen - \item Repräsentation von Logik-Termen im Lambda-Kalkül führte zu Theorembeweisen für Logiken höherer Stufen + \item Der Fixpunktsatz besagt, dass im Lambda-Kalkül jeder Term einen Fixpunkt hat, d.h. einen Wert, der auf sich selber abgebildet wird. + \item Beweis: + \begin{itemize*} + \item Zu jedem beliebigen F sei $W =\lambda x.F(x x)$ und $X = (W W)$ + \item Dann gilt: $X\equiv WW \equiv(\lambda x.F(x x)) W \equiv F(W W) \equiv F X$ + \end{itemize*} + \item Bemerkungen: + \begin{itemize*} + \item Für einige Lambda-Terme ist die Identifikation eines Fixpunktes einfach, z.B. für den Term $\lambda x.x$ (alle Terme sind Fixpunkte) + \item Für andere Terme, wie $\lambda xy.xy (= \lambda x.\lambda y.xy)$ ist das nicht so klar + \item Der Beweis des Fixpunktsatzes ist konstruiv, d.h. er liefert zu jedem Lambda-Term einen Fixpunkt + \end{itemize*} \end{itemize*} - \item Manche Puristen vertreten gelegentlich die Ansicht, dass funktionale Programmiersprachen nicht viel mehr sind, als "Lambda-Kalkül mit etwas syntaktischem Zucker" -\end{itemize*} - -\subsection{Zusammenfassung} -\begin{itemize*} - \item Funktionale Programmierung folgt einem verallgemeinerten Konzept der Funktionsauswertung - \item Die Programmiersprache Erlang ist dynamisch typisiert und unterstützt auch Funktionen höherer Ordnung - \item Manche Algorithmen lassen sich in Erlang aufgrund der mächtigen Listenkonstrukte und des flexiblen Pattern Matching sehr kompakt formulieren ($\rightarrow$ Potenzmenge, Quicksort) - \item Das heißt jedoch nicht, dass sehr kompakter Code auch zu sehr effizientem Laufzeit- und/oder Speicherbedarf führt - teilweise muss der Code relativ geschickt optimiert werden, um einigermaßen effiziente Lösungen zu erhalten ($\rightarrow$ Quicksort) - \item Manche Aufgaben, die in imperativen Programmiersprachen sehr effizient und einfach lösbar sind ($\rightarrow$ Teilen einer Liste in gleich große Hälften) sind mittels Listen nur recht umständlich und aufwendig lösbar - \item Es gilt in der Praxis also abzuwägen, für welche Aufgaben eine funktionale Sprache eingesetzt werden soll -\end{itemize*} - -\section{Multithreading und parallele Programmierung} -\subsection{Grundlagen} -\subsubsection{Lernziele} -\begin{itemize*} - \item Programmierung paralleler Algorithmen und Verfahren als Paradigma - \item Verständnis grundlegender Architekturen und Modelle - \item Praktische Erfahrungen mit Erlang, Java und C++ -\end{itemize*} - -\subsubsection{Grundbegriffe} -\begin{itemize*} - \item Prozess := Programm in Ausführung; Ausführungsumgebung für ein Programm; hat eigenen Adressraum; Prozessor kann immer nur einen Prozess ausführen - \item Thread ("Faden") := leichtgewichtige Ausführungseinheit oder Kontrollfluss (Folge von Anweisungen) innerhalb eines sich in Ausführung befindlichen Programms; "leichtgewichtig" im Vergleich zu Betriebssystemprozess; Threads eines Prozesses teilen sich Adressraum; Thread kann von CPU oder Core ausgeführt werden - \item Shared Memory := Kommunikation (über Variablen im) gemeinsamen Speicher; Prozess kann direkt auf Speicher eines anderen Prozesses zugreifen; erfordert explizite Synchronisation, z.B. über kritische Abschnitte - \item Message Passing := Prozesse mit getrennten Adressräumen; Zugriff nur auf eigenen Speicher; Kommunikation durch explizites Senden/Empfangen von Nachrichten; implizite Synchronisation durch Nachrichten - \item Parallelisierungsarten + + \subsubsection{Anwendung des Fixpunktsatzes} \begin{itemize*} - \item Instruktionsparallelität: parallele Ausführung mehrerer Operationen durch eine CPU-Instruktion; explizit: Vektorinstruktionen, SIMD; implizit: Pipelining von Instruktionen - \item Taskparallelität: Ausnutzung inhärenter Parallelität durch simultane Ausführung unabhängiger Aufgaben - \item Datenparallelität: Gemeinsame Operation auf homogener Datenmenge; Zerlegung eines Datensatzes in kleinere Abschnitte + \item Aufgabe: Berechne den Fixpunkt zum Term $\lambda xy.xy$ + \begin{itemize*} + \item Lösungsansatz: $W\equiv\lambda x.(\lambda\color{blue}x\color{black}y.\color{blue}x\color{black}y)\color{red}(xx) \color{black} \equiv\lambda x.\lambda y.(x x)y \equiv \lambda xy.(xx)y$ + \item Damit ist der gesuchte Fixpunkt $X\equiv((\lambda xy.(xx)y)(\lambda xy.(xx)y))$ + \item Nachrechnen: + \begin{description*} + \item[ \space ] $(\lambda xy.xy) ((\lambda xy.(xx)y) (\lambda xy.(xx)y))$ + \item[$\equiv$] $(\lambda \color{blue}x\color{black}.\lambda y. \color{blue} x \color{black} y) \color{red} ((\lambda xy.(xx)y) (\lambda xy.(xx)y)$ \color{black} + \item[$\equiv$] $\lambda \color{blue}y \color{black}.((\lambda xy.(xx)y)) (\lambda xy.(xx)y) \color{red}y\color{black}$ + \item[$\equiv$] $(\lambda xy.(xx)y)(\lambda xy.(xx)y)$ + \item[$\equiv$] X + \end{description*} + \end{itemize*} + \item Bemerkung: Der so für die Identitätsfunktion $\lambda x.x$ konstruierte Fixpunkt ist übrigens $(\lambda x.xx)(\lambda x.xx)$, er spielt die besondere Rolle des Standardterms $\bot$ für nicht-terminierende Ausführungen \end{itemize*} -\end{itemize*} - -\subsubsection{The free launch is over} -Taktfrequenz wächst nur noch langsam -\begin{itemize*} - \item Physikalische Gründe: Wärmeentwicklung, Energiebedarf, Kriechströme,… -\end{itemize*} -Auswege -\begin{itemize*} - \item Hyperthreading: + + \subsubsection{Der Fixpunkt-Kombinator} + \colorbox{lightgray}{ + \begin{minipage}[h]{1.0\linewidth} + Im Ergebnis unserer Diskussion des Fixpunktsatzes definieren wir den Fixpunkt-Kombinator wie folgt: $$Y \equiv \lambda f.(\lambda x.f(xx)) (\lambda x.f(xx))$$ + \end{minipage} + } \begin{itemize*} - \item Abarbeitung mehrerer Threads auf einer CPU (5-15 \% Performancegewinn) - \item Einfache Hardwareunterstützung (einige Register) + \item Dieser Kombinator spielt eine wichtige Rolle bei der Definition rekursiver Funktionen im Lambda-Kalkül, wie wir im folgenden sehen werden + \item Für jeden Lambda-Term M gilt: $Y M = M (Y M)$ + \begin{itemize*} + \item Beweisidee: zeige, dass beide Terme auf einen identischen Term reduziert werden können + \end{itemize*} + \item Der Term Y ist übrigens nicht der einzige Kombinator, der Fixpunkte zu Lambda-Termen konstruiert + \begin{itemize*} + \item A. Turing: $\Theta \equiv (\lambda xy.y(xxy)) (\lambda xy.y(xxy))$ + \end{itemize*} \end{itemize*} - \item Multicore: + + \subsubsection{Rekursion im Lambda-Kalkül} \begin{itemize*} - \item Mehrere CPUs auf einem Chip - \item Billiger als echte Mehrprozessorsysteme - \end{itemize*} - \item Caching: - \begin{itemize*} - \item Vergrößerung L1, L2, L3 Cache - \item Speicherzugriff 10-50 $\cdot$ teurer als Cachezugriff - \end{itemize*} -\end{itemize*} - -\subsubsection{Konsequenzen und Trends} -\begin{itemize*} - \item Applikationen müssen nebenläufig programmiert werden um CPU auszunutzen $\rightarrow$ Many-Core-Systeme - \item CPU-Begrenzung von Applikationen - \item Effizienz und Performanceoptimierung werden immer wichtiger - \item Unterstützung von Nebenläufigkeit/Parallelität durch Programmiersprachen -\end{itemize*} - -\subsubsection{Einordnung} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0014} -\end{center} - -\subsubsection{Architekturen} -SIMD, SMP, NUMA, Cluster, Grid -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0015} -\end{center} - -\subsubsection{Multiprozessorsysteme} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0016} -\end{center} -\begin{itemize*} - \item Zugriff über Bus auf gemeinsamen Speicher - \item jeder Prozessor mit eigenen Caches -\end{itemize*} - -\subsubsection{Multicore-Systeme} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0017} -\end{center} -\begin{itemize*} - \item mehrere Prozessorkerne auf einem Chip - \item Kerne typischerweise mit eigenen L1/L2-Caches und gemeinsamen L3-Cache -\end{itemize*} - -\subsubsection{Symmetrisch vs. Nicht-symmetrisch} -%| SMP (Symmetric Multi Processing) | NUMA (Non-Uniform Memory-Access) | -%| -\item | -\item | -%| Speicherbandbreite begrenzt und von allen Prozessoren gemeinsam genutzt | jedem Prozessor sind Teile des Speichers zugeordnet | -%| Skalierbarkeit begrenzt | lokaler Zugriff ist schneller als entfernter | -%| Single Socket-Lösung | Mehr-Socket-Board | - -SMP \newline Symmetric Multi Processing \newline -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0018} -\end{center} -\begin{itemize*} - \item Speicherbandbreite begrenzt und von allen Prozessoren gemeinsam genutzt - \item Skalierbarkeit begrenzt - \item Single Socket Lösung -\end{itemize*} -NUMA \newline -Non-Uniform Memory Access \newline -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0019} -\end{center} -\begin{itemize*} - \item jedem Prozessor sind Teile des Speichers zugeordnet - \item lokaler Zugriff ist schneller als entfernter - \item Typisch für Multi-Socket Systeme -\end{itemize*} - -\subsubsection{CPU vs. GPU} -\begin{itemize*} - \item GPU = Graphics Processing Units - \item Hochparallele Prozessorarchitekturen (nicht nur) für Grafikrendering -\end{itemize*} -\begin{center} - \includegraphics[width=0.95\linewidth]{Assets/Programmierparadigmen-0020} -\end{center} - -\subsubsection{Flynn's Architekturklassifikation} -\begin{center} - \includegraphics[width=0.95\linewidth]{Assets/Programmierparadigmen-0021} -\end{center} - -\subsubsection{Maße zur Leistungsbewertung} -\begin{itemize*} - \item Maße für Laufzeitgewinn durch Parallelisierung - \item $T_n$ = Laufzeit des Programms mit n Prozessoren/Kernen - \item Speedup - \begin{center} - \begin{displaymath} - Speedup = {{T_1} \over {T_n}} - \end{displaymath} - \end{center} - \item Effizienz - \begin{center} - \begin{displaymath} - Effizienz = {Speedup \over n} - \end{displaymath} - \end{center} -\end{itemize*} - -Maße zur Leistungsbewertung -Maße für den Laufzeitengewinn durch Parallelisierung -\begin{itemize*} - \item $T_n=$ Laufzeit des Programms mit n Prozessoren/Kernen - \item Speedup:= $\frac{T_1}{T_n}$ - \item Effizienz:= $\frac{Speedup}{n}$ -\end{itemize*} - - -\subsubsection{Amdahlsches Gesetz} -\begin{itemize*} - \item[] Berücksichtigung parallelisierbarer und serieller Anteile im Programmablauf - \item n Prozessoren - \item p = paralleler Anteil - \item s = serieller Anteil - \item p+s = 1 - \item Maximaler Speedup - \begin{gather} - Speedup_{max} = {T_1 \over T_n} \\ - = {{s+p}\over{s+{p \over n}}} \\ - = {1 \over {s+{p \over n}}} - \end{gather} - $Speedup_{max}=\frac{T_1}{T_n}=\frac{1}{s+\frac{p}{n}}$ -\end{itemize*} -\begin{center} - \includegraphics[width=0.35\linewidth]{Assets/Programmierparadigmen-0022} -\end{center} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0023} -\end{center} - -\subsubsection{Prozesse und Threads} -Prozess := Programm in Ausführung; Ausführungsumgebung für ein Programm -\begin{itemize*} - \item hat eigenen Adressraum - \item Prozessor kann immer nur einen Prozess ausführen -\end{itemize*} -Thread ("Faden") := leichtgewichtige Ausführungsreinheit oder Kontrollfluss (Folge von Anweisungen) innerhalb eines sich in Ausführung befindlichen Programms -\begin{itemize*} - \item "leichtgewichtig" im Vergleich zu Betriebssystemprozess - \item Threads eines Prozesses teilen sich den Adressraum - \item Thread kann von einer CPU oder einem Core ausgeführt werden -\end{itemize*} - -\subsubsection{Shared Memory vs Message Passing} -Art der Kommunikation zwischen Prozessen oder Threads \newline -Shared Memory -\begin{itemize*} - \item Kommunikation (über Variable im) gemeinsamen Speicher - \item Prozess kann direkt auf Speicher eines anderen Prozesses zugreifen - \item erfordert explizite Synchronisation, z.B. über zeitkritische Abschnitte -\end{itemize*} -Message Passing -\begin{itemize*} - \item Prozesse mit getrennten Adressräumen; Zugriff nur auf eigenen Speicher - \item Kommunikation durch explizites Senden/Empfangen von Nachrichten -\end{itemize*} - -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0024} -\end{center} - -\subsubsection{Programmiermodelle} -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-0025} -\end{center} - -\subsubsection{Parallelisierungsarten} -Instruktionsparallelität: -\begin{itemize*} - \item parallele Ausführung mehrerer Operationen durch eine CPU-Instruktion - \item explizit: Vektorinstruktionen, SIMD - \item implizit: Pipelining von Instruktionen -\end{itemize*} -Taskparallelität -\begin{itemize*} - \item Ausnutzung inhärenter Parallelität durch simultane Ausführung unabhängiger Aufgaben -\end{itemize*} -Datenparalelität: -\begin{itemize*} - \item Gemeinsame Operation auf homogener Datenmenge - \item Zerlegung eines Datensatzes in kleinere Abschnitte -\end{itemize*} - -\subsubsection{Instruktionsparallelität: SIMD} -\begin{itemize*} - \item Autovektorisierung durch Compiler - \item explizite Instruktionen -\end{itemize*} -Beispiel: Addition zweier Vektoren - -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-0026} -\end{center} - -\subsubsection{Taskparallelität} -\begin{itemize*} - \item Unabhängikeit von Teilprozessen $\rightarrow$ Desequentialisierung - \item Beispiel: Quicksort -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0027} -\end{center} - -\subsubsection{Datenparallelität} -\begin{itemize*} - \item homogene Datenmenge: Felder, Listen, Dokumentenmenge,… - \item Verteilung der Daten - \item alle Prozessoren führen gleiches Programm auf jeweils eigenen Daten aus - \item Beispiel: Matrixaddition S = A + B -\end{itemize*} -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-0028} -\end{center} - -\subsubsection{Herausforderungen} -\begin{itemize*} - \item Zerlegung eines Problems in parallel verarbeitbare Teile - \begin{itemize*} - \item Beispiel: Suche in einer Datenbank mit 1 TB Größe - \item Annahme: 100 MB/Sekunde mit einem Prozessor = 175 Minuten - \item bei paralleler Suche durch 10 Prozessoren = 17.5 Minuten - \item Übertragbar auf andere Probleme, z.B. Sortieren, Suche in Graphen? - \end{itemize*} - \item Synchronisation konkurrierender Zugriffe auf gemeinsame Ressourcen - \begin{itemize*} - \item Beispiel: Produzent-Konsument-Beziehung - \item Annahme: Datenaustausch über gemeinsame Liste - \item Fragestellungen: Benachrichtigung über neues Element in der Liste, Konsument entnimmt Element während Produzent einfügt - \item Wechselseitiger Ausschluss - \end{itemize*} - \item außerdem: Fehlersuche, Optimierung -\end{itemize*} - -\subsubsection{Zusammenfassung} -\begin{itemize*} - \item Parallele Verarbeitung als wichtiges Paradigma moderner Software - \item verschiedene parallele - \begin{itemize*} - \item Hardwarearchitekturen und - \item Programmiermodelle - \end{itemize*} - \item Herausforderungen: - \begin{itemize*} - \item Problemzerlegung - \item Synchronisation - \item … - \end{itemize*} - \item im Weiteren: konkrete Methoden und Techniken in Erlang und C++ -\end{itemize*} - -\subsection{Parallele Programmierung in Erlang} -\subsubsection{Unterstützung paralleler Programmierung in Erlang} -\begin{itemize*} - \item Leichtgewichtige Prozesse und Message Passing - \item SMP-Support (Symmetric Multi Processing) - \item Ziele für effiziente Parallelisierung - \begin{itemize*} - \item Problem in viele Prozesse zerlegen \newline(aber nicht zu viele …) - \item Seiteneffekte vermeiden \newline (würde Synchronisation erfordern …) - \item Sequentiellen Flaschenhals vermeiden - \newline (Zugriff auf gemeinsame Ressourcen: IO, Registrierung von Prozessen, …) - \begin{center} - \color{orange} Small Messages, Big Computation! \color{black} - \end{center} - \end{itemize*} -\end{itemize*} - -\subsubsection{Prozesse in Erlang} -\begin{itemize*} - \item Erlang VM = Betriebssystemprozess - \item Erlang-Prozess = Thread innerhalb der Erlang VM - \begin{itemize*} - \item kein Zugriff auf gemeinsame Daten, daher "Prozess" - \end{itemize*} - \item jede Erlang-Funktion kann einen Prozess bilden - \item Funktion spawn erzeugt einen Prozess, der die Funktion Fun ausführt - \begin{lstlisting} - Pid = spawn(fun Fun/0) + \item Die bisher definierten Funktionen waren alle nicht-rekursiv + \item Viele Funktionen kann man aber nur unter Zuhilfenahme von Rekursion (bzw. Iteration) beschreiben + \item In üblichen Programmiersprachen werden rekursive Funktionsdefinitionen durch die Verwendung von Namen für Funktionen möglich - man verwendet hierbei einfach den Namen der gerade zu definierenden Funktion im Rumpf der Definition: + \begin{lstlisting} + \item fun fak(i) -> if (i = 0) then 1 else i * fak(i-1). \end{lstlisting} - \item Resultat = Prozessidentifikation Pid, mittels der man dem Prozess Nachrichten schicken kann. - \item über self() kann man die eigene Pid ermitteln - \item Übergabe von Arghumenten an den Prozess bei der Erzeugung - \begin{lstlisting} - Pid = spawn(fun() -> any_func(Arg1, Arg2, ...) end) - \end{lstlisting} -\end{itemize*} - -\paragraph{Beispiele} -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-029} -\end{center} - -\subsubsection{SMP Erlang} -{\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-030} - \end{center} -} -\begin{itemize*} - \item 4 Betriebssystemthreads (hier 2 Kerne mit Hyperthreading) - \item kann mit -smp [disable $\mid$ enable $\mid$ auto] beeinflusst werden - \item +S [Anzahl] bestimmt Anzahl der Scheduler - \begin{itemize*} - \item sollte nicht größer als Anzahl der Kerne/Prozessoren sein + \item Im Lambda-Kalkül gibt es jedoch keine Namen für Funktionen: + \begin{itemize*} + \item Daher stellt man eine rekursive Funktion f mittels einer Funktion G dar, die einen zusätzlichen Parameter g hat, an den man dann G selber bildet + \item Schaut kompliziert aus, ist es auch (Q-Q) + \item Warum so kompliziert? Damit die Definition von G im eigenen Rumpf verfügbar ist + \end{itemize*} + \end{itemize*} + + \subsubsection{Rekursive Funktionen sind Fixpunkte} + \begin{itemize*} + \item Rekursive Funktion von g + \begin{itemize*} + \item $g = \lambda n.…g…n…$ Rumpf verwendet g + \end{itemize*} + \item Daraus gewinnt man das Funktional + \begin{itemize*} + \item $G = \lambda g.\lambda n.…g…n…$ + \end{itemize*} + \item Falls G einen Fixpunkt g* hat, d.h. $G(g*) = g*$, so + \begin{itemize*} + \item $g* = G(g*) = \lambda n.…g*…n$ + \end{itemize*} + \item Vergleiche: $g = \lambda n.…g…n…$ \end{itemize*} -\end{itemize*} - -\subsubsection{Scheduler in Erlang} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-031} -\end{center} - -\subsubsection{Message Passing in Erlang: Senden einer Nachricht} - -\begin{lstlisting} - Pid ! Message -\end{lstlisting} - -\begin{itemize*} - \item an Prozess Pid wird die Nachricht Message gesendet - \item der Prozess muss eine Empfangsoperation ausführen. damit ihn die Nachricht erreichen kann \begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-032} + Rekursive Definition $\Leftrightarrow$ Fixpunkt des Funktionals \end{center} - \item trifft eine Nachricht ein, wird versucht, diese mit einem Pattern und ggf. vorhandenen Guard zu "matchen" - \item erstes zutreffendes Pattern (inkl. Guard) bestimmt, welcher Ausdruck ausgewertet wird - \item trifft kein Pattern zu, wird die Nachricht für spätere Verwendung aufgehoben und Prozess wartet auf die nächste Nachricht ($\rightarrow$ "selective receive") -\end{itemize*} - -\begin{lstlisting}[ - language=erlang, - showspaces=false, - basicstyle=\ttfamily - ] -receive - Pattern1 [when Guard1] $\rightarrow$ Expressions1; - Pattern2 [when Guard2] $\rightarrow$ Expressions2; - ... -end -\end{lstlisting} - -\subsubsection{Ein einfacher Echo-Server} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-033} -\end{center} - -\paragraph{Erklärungen} -\begin{itemize*} - \item Funktion loop() realisiert einen (nur bedingt nützlichen) Echo-Dienst, der jede empfangene Nachricht unverändert an den Absender zurückschickt, bis er nach Empfang von stop endet - \item Funktion run() \begin{itemize*} - \item[1.] startet den Echoserver (Zeile 4) - \item[2.] schickt ihm als nächstes eine Nachricht (Zeile 5) - \item[3.] wartet auf eine Antwort (Zeile 6) - \item[4.] gibt diese aus (Zeile 7) - \item[5.] schickt dann stop an den Echoserver (Zeile 9) + \item Beispiel: Fakultät + \begin{itemize*} + \item $g = \lambda n. $ if isZero n then $c_1$ else (times n g(pred n)) - rekursiv + \item $G = \lambda g.\lambda n.$ if isZero n then $c_1$ else (times n g(pred n)) - funktional + \end{itemize*} \end{itemize*} - \item Aufruf in der Funktion loop() erfolgt endrekursiv, daher wird kein wachsender Aufrufstapel angelegt (Hinweis: grundsätzlich zu beachten, da sonst der Speicherbedarf stetig wächst) -\end{itemize*} - -\subsubsection{Ansätze zur Parallelisierung} -\begin{itemize*} - \item[] Beispiel: Berechnung einer (zufällig generierten) Liste von Fibonaccizahlen + + \subsubsection{Der Fixpunktkombinator dient als Rekursionsoperator} + Wir berechnen den gesuchten Fixpunkt des Funktionals G mit dem Fixpunktkombinator, der somit als Rekusrsionsoperator dient: + + \color{blue} Rekursionsoperator \color{black} + $$Y = \lambda f.(\lambda x.f(xx))(\lambda x.f(xx))$$ + $$Y f = (\lambda \color{blue}f\color{black}.(\lambda x.\color{blue}f\color{black}(xx))(\lambda x.\color{blue}f\color{black}(xx))) \color{red}f\color{black}$$ + $$\Rightarrow (\lambda \color{blue}x\color{black}.f(\color{blue}xx\color{black})) \color{red}(\lambda x.f(xx))\color{black}$$ + $$\Rightarrow f((\lambda x.f(xx)) (\lambda x.f(xx)) \Leftarrow f(Yf) ())$$ + \color{black} + \subitem also \space\space\space \space $f(Yf) \stackrel{\beta}{=} Yf$ \\ + d.h. \space\space\space Yf ist Fixpunkt von f + + \paragraph{Beispiel: Fakultät im Lambda-Kalkül} + \includegraphics[width=.4\linewidth]{Assets/Programmierparadigmen-Lambda_Abstraktion} + + \subsection{Ausdrucksstärke des Lambdakalküls} \begin{itemize*} + \item Im Folgenden wollen wir zeigen, dass der Lambda-Kalkül genau die rekursiven Funktionen beschreibt + \item Eine numerische Funktion ist eine Abbildung $f:\mathbb{N}^k \rightarrow \mathbb{N}$ mit $k\in\mathbb{N} \cap \{0\}$ + \item Wir definieren hierzu: + \begin{itemize*} + \item Anfangsfunktionen: + \begin{itemize*} + \item Projektion: $U_i^k (n_1,n_2,…,n_k) = n_i$ für $1<=i<=k$ + \item Nullfunktion: $Z(n) = 0$ + \item Nachfolger: $S(n) = n+1$ + \end{itemize*} + \item Minimalisierung: + \begin{itemize*} + \item Für eine Relation $P(m)$ bezeichne $\mu m[P(m)]$ die kleinste Zahl m sodass P(m) gilt. + \end{itemize*} + \end{itemize*} + \item Bemerkung: im Folgenden notieren wir $n_1,n_2,…,n_k$ kurz als $\overline{n_k}$ + \item Eine numerische Funktion ist Lambda-definierbar, wenn es einen Kombinator M gibt, sodass $M\overline{n_k} = f(\overline{n_k})$ + \end{itemize*} + + \begin{itemize*} + \item Im folgenden sei C eine Klasse von numerischen Funktionen, und es gelte $g,h,h_1,h_2,…,h_m \in C$ + \item Wir definieren nun die folgenden Eigenschaften: + \begin{itemize*} + \item C ist \color{blue} abgeschlossen unter Komposition\color{black}, wenn für jede Funktion f, die über $f(\overline{n_k}):= g(h_1(\overline{n_k}),…,h_m(\overline{n_k}))$ definiert ist, gilt $f \in C$ + \item C ist \color{blue} abgeschlossen unter primitiver Rekursion\color{black}, wenn für jede Funktion f, die über + $$f(0,\overline{n_k}) = g(\overline{n_k})$$ + $$f(j+1, \overline{n_k}) = h(f(j,\overline{n_k}),j,\overline{n_k})$$ + definiert ist, gilt: $f \in C$ + \item C ist \color{blue} abgeschlossen unter unbeschränkter Minimalisierung \color{black}, wenn für jede Funktion f, die über $f(\overline{n_k})=\mu m[g(\overline{n_k},m)= 0]$ definiert ist (wobei für alle $\overline{n_k}$ ein m existiere, sodass $g(\overline{n_k},m) = 0$ ist), gilt $f \in C$ + \end{itemize*} + \end{itemize*} + + \colorbox{lightgray}{\begin{minipage}[h]{1.0\linewidth} + Definition: \\ + Die Klasse der rekursiven Funktionen ist die kleinste Klasse numerischer Funktionen, die alle oben genannten Anfangsfunktionen enthält und abgeschlossen ist unter Komposition, primitiver Rekursion und unbeschränkter Minimalisierung + \end{minipage} + } + + \begin{itemize*} + \item \color{blue} Lemma 1: Die Anfangsfunktionen sind Lambda-definierbar \color{black} + \item Beweis: + \begin{itemize*} + \item $U_i^k = \lambda x_1 x_2 … x_k.x_i$ + \item $S = \lambda n.\lambda s. \lambda z.s(nsz)$ (siehe succ bei Churchzahlen) + \item $Z = \lambda fx.x$ (siehe $c_0$ bei Churchzahlen) + \end{itemize*} + \end{itemize*} + + \begin{itemize*} + \item \color{blue} Lemma 2: Die Lambda-definierbaren Funktionen sind abgeschlossen unter primitiver Rekursion \color{black} + \item Beweis: Sei f definiert über + \begin{center} + $$f(0,\overline{n_k}) = g(\overline{n_k})$$ + $$f(j+1, \overline{n_k}) = h(f(j, \overline{n_k}),j,\overline{n_k})$$ + \end{center} + und seien g und h Funktionen (die per Induktionsvoraussetzung) durch die Lambda-terme G und H berechnet werden + \begin{itemize*} + \item Intuitiv kann f berechnet werden, indem man überprüft ob j = 0 ist, und wenn ja $g(\overline{n_k})$, ansonsten $h(f(j, \overline{n_k}),j,\overline{n_k})$ + \item Ein Term M hierfür existiert laut Fixpunktsatz und es gilt: + $M \equiv Y (\lambda f\:x\: \overline{y_k}.if(isZero \: x)(G\:\overline{y_k})(H(f(pred\: x)\overline{y_k})(pred \: x)\overline{y_k}))$ + \end{itemize*} + \end{itemize*} + + \begin{itemize*} + \item \color{blue} Lemma 3: Die Lambda-definierbaren Funktionen sind abgeschlossen unter unbeschränkter Minimalisierung \color{black} + \item Beweis: + \begin{itemize*} + \item Sei f über $f(\overline{n_k}) = \mu m[g(\overline{n_k},m) = 0]$ definiert, wobei g (per Induktionsvoraussetzung) durch den Lambda-Term G berechnet wird + \item Intuitiv kann man f berechnen, indem man bei 0 beginnend für m überprüft, ob $g(\overline{n_k},m) = 0$ ist, und wenn ja m ausgibt, ansonsten die Überprüfung mit $m+1$ fortsetzt + \item Ein Term für eine solche Funktion kann laut Fixpunktsatz konstruiert werden und man erhält mit Anwendung des Fixpunktkombinators zunächst: $$N \equiv Y (\lambda f \: \overline{x_k} \: y. if(isZero \: (G \: \overline{x_k} \: y))y(f\:\overline{x_k}\:(succ \: y)))$$ + \item Nun definiert man die Funktion f durch den folgenden Term M: $$M \equiv \lambda \overline{x_k}.N \: \overline{x_k} \: c_0$$ + \end{itemize*} + \end{itemize*} + + \begin{center} + \includegraphics[width=.4\linewidth]{Assets/Programmierparadigmen-kodierung-natürlicher-zahlen} + \end{center} + \begin{itemize*} + \item Aus den Lemmata 1 bis 3 folgt nun der Satz:\\ + \colorbox{lightgray}{ + \begin{minipage}[h]{1.0\linewidth} + Alle rekursiven Funktionen sind Lambda-definierbar + \end{minipage}} + \end{itemize*} + + + \subsection{Berechnungsreihenfolgen und Konfluenz} + \subsubsection{Noch einmal Auswertungsstrategien} + \begin{itemize*} + \item Bei unserer initialen Betrachtung der Auswertungsstrategien haben wir die volle $\beta$-Rekursion und die Normalreihenfolge kennengelernt + \item Nun wollen wir unsere Betrachtungen hierzu noch einmal vertiefen und definieren zunächst: + \begin{itemize*} + \item Ein Redex wird als \color{blue} "äußerst" (outermost) \color{black} bezeichnet, wenn er nicht Teil eines anderen Redex ist. + \item Ein Redex wird als \color{blue} "innerst" (innermost) \color{black} bezeichnet, wenn er keinen eigenständigen Redex beinhaltet + \end{itemize*} + \item Mit diesen Begriffen können im folgenden die gebräuchlichsten Auswertungsstrategien formuliert werden + \begin{itemize*} + \item \color{blue} Normal Order: \color{black} Evaluiere Argumente so oft, wie sie verwendet werden + \item \color{blue} Applicative Order: \color{black} Evaluiere Argumente einmal + \item \color{blue} Lazy Evaluation: \color{black} Evaluiere Argumente höchstens einmal + \end{itemize*} + \item Eine zentrale Kernfrage: \color{blue} Welche Auswertungsstrategie führt (möglichst schnell) zu einem nicht weiter reduzierbaren Term? + \color{black} + \begin{itemize*} + \item Bei unserer beispielhaften Berechnung des Terms Fak $c_2$ haben wir nach der initialen Anwendung des Fixpunktkombinators zunächst den Term isZero $c_2$ reduziert. + \item Ebenso hätten wird den weiter innen stehenden Fixpunktkombinator zuerst erneut anwenden können(bei voller $\beta$-Reduktion kann jeder Term jederzeit reduziert werden). + \item Auf diese Weise hätten wir unendlich oft vorgehen, damit einen immer länger werdenden Term ableiten können und somit nicht das gewünschte Resultat $c_2$ berechnet. + \end{itemize*} + \item Eine weitere Kernfrage: Angenommen mehrere unterschiedliche Reduktionsreihenfolgen führen zu einem nicht weiter zu reduzierenden Ergebnis - \color{blue} führen all diese Reihenfolgen zum gleichen Ergebnis? \color{black} + \item Wir definieren zuerst einen zentralen begriff in diesem Zusammenhang: + \colorbox{lightgray}{\begin{minipage}[h]{1.0\linewidth} + Ein Transitiosnsystem $(D,\rightarrow*)$ heißt genau dann konfluent, wenn für alle $t,t_1,t_2 \in D$ gilt: wenn $ t \rightarrow* t_1$ und $t \rightarrow* t_2$, dann gibt es ein $t' \in D$ mit $t_1 \rightarrow* t'$ und $t_2 \rightarrow* t'$ + \end{minipage}} + \item Wenn der Lambda-Kalkül konfluent ist, kann hieraus gefolgert werden, dass unterschiedliche Reduktionsreihenfolgen, die zu einer nicht mehr weiter zu reduzierenden Form führen, somit auf den gleichen Term führen müssen. + \item Achtung: hieraus kann nicht gefolgert werden, dass alle Reduktionsreihenfolgen auf den gleichen Term führen, da dies ja nur für "terminierende" Reduktionsreihenfolgen gilt! + \end{itemize*} + + \subsubsection{Church-Rosser-Eigenschaft} + \color{blue} Satz (Church-Rosser) \\ + Der untypisierte $\lambda$-Kalkül ist konfluent: Wenn $t \stackrel{*}{\Rightarrow} t_1$ und $t \stackrel{*}{\Rightarrow} t_2$, dann gibt es ein t' mit $t_1 \stackrel{*}{\Rightarrow} t'$ und $t_2 \stackrel{*}{\Rightarrow} t'$ + \color{black} + + \begin{center} + \includegraphics[width=0.25\linewidth]{Assets/Programmierparadigmen-diamant-eigenschaft.png} + \includegraphics[width=0.25\linewidth]{Assets/Programmierparadigmen-010.png} + \end{center} + + Beweisidee: Definiere $\stackrel{\rightarrow}{\rightarrow}$ als "parallele" $\beta$-Reduktion. + \begin{itemize*} + \item Es gilt: $\Rightarrow \subseteq \stackrel{\rightarrow}{\rightarrow} \subseteq \stackrel{*}{\Rightarrow}$ + \item Zeige Diamant Eigenschaft für $\stackrel{\rightarrow}{\rightarrow}$ + \end{itemize*} + + \subsubsection{Eindeutigkeit der Normalform} + \color{blue} Korollar (Eindeutigkeit der Normalform) \newline + Die Normalform eines $\lambda$-Terms ist - sofern sie existiert - eindeutig. \color{black} + \newline + \newline + Beweis: + \begin{itemize*} + \item $t_1$ und $t_2$ Normalformen von t, d.h. $t \stackrel{*}{\Rightarrow} t_1 \nRightarrow$ und $t \stackrel{*}{\Rightarrow} t_2 \nRightarrow$ + \item Nach Chruch-Rosser gibt es t' mit $t_1 \stackrel{*}{\Rightarrow} t'$ und $t_2 \stackrel{*}{\Rightarrow} t'$ + \item Nach Annahme $t_1 \nRightarrow$ und $t_2 \nRightarrow$, also $t_1 = t' = t_2$ + \end{itemize*}\ \newline + \color{blue} + Bei terminierenden $\beta$-Reduktionen ist irrelevant, welchen Redex man zuerst reduziert!\color{black} + \subsection{Auswertung von Parametern in Programmiersprachen} + \subsubsection{Behandlung von Parametern in Programmiersprachen} + \begin{itemize*} + \item Die Art und Weise, wie in einer Programmiersprache Parametter übergeben - d.h. wie die Reihenfolge und die Zeitpunkte ihrer Auswertung gehandhabt - werden, hat Einfluss auf wichtige Eigenschaften der Sprache: + \begin{itemize*} + \item Effizienz der Berechnungen + \item Termininerungsverhalten + \item Ausdruckskraft + \end{itemize*} + \item Hierbei ist es insbesondere von Interesse, wie Parameter gehandhabt werden, deren Werte undefiniert sind (z.B. 1/0)\newline + \colorbox{lightgray}{ + \begin{minipage}[h]{1.0\linewidth} + Wir definieren zunächst den zentralen begriff "strikt": \newline Eine n-stellige Funktion heißt strikt im k-ten Argument $(1<=k<=n)$, wenn gilt: $f(x_1,x_2,…,x_{k-1},\bot,x_{k+1},…,x_n)=\bot$ + \end{minipage}} + \item Ein undefiniertes Argument führt hier zu einem undefinierten Resultat + \item Grundsätzlich kann man die Auswertungsstrategien von Programmiersprachen in strikte und nicht-strikte Strategien einteilen; sehr gebräuchlich sind dabei insbesondere: + \begin{itemize*} + \item Call by Value: Ausdrücke, die Parameter bei einem Funktionsaufruf beschreiben, werden vor der Übergabe an die Funktion vollständig ausgewertet + \item Call by Name: Ausdrücke, die Parameter bei einem Funktionsaufruf beschreiben, werden nicht bei Übergabe, sondern erst dann ausgewertet, wenn sie in der aufgerufenen Funktion tatsächlich benötigt werden + \end{itemize*} + \item Beide Varianten haben spezifische Vor- und Nachteile: + \begin{itemize*} + \item Call by Value: weniger Berechnungsaufwand, wenn ein Parameter mehr als einmal im Funktionsrumpf vorkommt; weniger Speicheraufwand bei der Übergabe + \item Call by Name: weniger Berechnungsaufwand, wenn ein Argument nicht zum Ergebnis beiträgt; höherer Aufwand bei Übergabe + \end{itemize*} + \item Die Programmiersprache Erlang realisiert grundsätzlich eine strikte Handhabung von Parametern, da sie die Strategie Call by Value verwendet + \item Allerdings wird bei der Definition einer Funktion der resultierende Wert erst dann berechnet, wenn die Funktion ausgewertet wird + \begin{itemize*} + \item Das erlaubt über den Umweg zusätzlicher Funktionsdefinitionen auch die Realisierung einer nicht-strikten Auswertungsstrategie - ermöglicht Nachbildung der sogenannten Lazy-Evaluation + \item hierbei wird ein nicht-strikt zu evaluierendes Argument als Resultat einer anonymen nullstelligen Funktion (ohne Parameter) "verpackt" + \item Im Rumpf der eigentlichen Funktion wird diese Funktion dann ausgewertet (= aufgerufen), wenn feststeht, dass dieses Argument für die Berechnung des Ergebnisses benötigt wird + \item Andere funktionale Sprachen wie Haskell oder Gofer verwenden Call by Name und realisieren damit grundsätzlich Lazy-Evaluation + \end{itemize*} + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-012.png} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-013.png} + \end{center} + \item Erläuterungen: + \begin{itemize*} + \item Im zweiten Beispiel wird der Rückgabewert der übergebenen Funktionne nur ausgewertet, wenn sie im Rumpf der auszuführenden Funktion aufgerufen werden + \item Innerhalb von Erlang-Modulen kann man sich mit Hilfe einer Macro-Definition Schreibarbeit sparen: + \begin{lstlisting}[language=erlang] + -define(DELAY(E), fun() -> E end). + check() -> test2(true, ?DELAY(3), ?DELAY(4/0)). + \end{lstlisting} + \end{itemize*} + \item Je nachdem, ob und wie häufig ein übergebener Parameter im Funktionsrumpf benötigt wird, können bei Lazy-Evaluation Berechnungen + \begin{itemize*} + \item komplett eingespart oder + \item (in identischer Form) wiederholt erforderlich werden + \item Unter Umständen kann man in der betreffenden Funktion durch Einführung einer temporären Variable redundante Mehrfachberechnungen einsparen ($\rightarrow$ Call by Need) + \end{itemize*} + \item Die Parameterübergabe ist bei Call by Name in der Regel aufwändiger als bei Call by Value + \begin{itemize*} + \item Die meisten Programmiersprachen (Java, C, C++, Pascal etc.) verwenden daher Call by Value ($\rightarrow$ strikte Auswertung) + \item Eine Ausnahme wird oft bei dem IF-Konstrukt gemacht (der auszuführende Code ist hier ja meist auch kein Parameter) + \end{itemize*} + \item Zu Ausdrucksstärke: während strikte Funktionen durch die Strategie Call by Value realisiert werden, ist es nicht so, dass Lazy Evaluation es erlaubt, alle nicht-strikten Funktionen zu realisieren + \begin{itemize*} + \item Die folgenden Gleichungen definieren eine nicht-strikte Multiplikation $\otimes$ auf der Basis der Multiplikation · für Zahlen: + $$0 \otimes y = 0$$ + $$x \otimes 0 = 0$$ + $$x \otimes y = x · y$$ + \item Wenn ein Arguemnt undefiniert ist, dann liefert $\otimes$ ein Ergebnis, sofern das andere Argument zu 0 evaluiert wird ($\rightarrow fak(-1) \otimes (fak(3)-6)$) + \item Implementiert werden kann die Funktion nur durch eine Art von paralleler Auswertung mit Abbruch der anderen Berechnung sobald 0 als Resultat berechnet und zurückgegeben wurde + \end{itemize*} + \item Wir betrachten nun die Beziehungen zwischen Parameterbehandlung in Programmiersprachen und Reduktion von Lambda-Termen + \end{itemize*} + + \subsubsection{Auswertungsstrategien \& Programmiersprachen} + \color{blue} Werte in Programmiersprachen wie Haskell: \color{black} + \begin{itemize*} + \item Primitive Werte: 2, True + \item Funktionen: ($\backslash x \rightarrow x$), ($\&\&$), ($x\rightarrow(\backslash y\rightarrow y+y)x$) + \end{itemize*} + + \color{blue} Werte im $\lambda$-Kalkül: + \color{black} \begin{itemize*} + \item Abstraktionen: $c_2 = \lambda s. \lambda z.s\;(s\;z),\;\;\; C_{true} = \lambda t- \lambda f.t,\;\;\; \lambda x.x,\;\;\; \newline \lambda b_1. \lambda b_2.\;b_1\; b_2 (\lambda t.\lambda f.\;f),\;\;\; \lambda x.\;(\lambda y.\;plus\; yy)x$ + \end{itemize*} + \color{blue} Auswertungsstrategie: \color{black} Keine weitere Reduzierung von Werten \newline + Reduziere keine Redexe unter Abstraktionen (umgeben von $\lambda$):\newline +$\Rightarrow$ call-by-name, call-by-value + \subsubsection{Call-By-Name} + Call-By-Name: Reduziere linkesten äußersten Redex + \begin{itemize*} + \item Aber nicht falls von einem $\lambda$ umgeben \newline + \subitem $(\lambda y. (\lambda x.y(\lambda z.z)x))\color{red} ((\lambda x.x)(\lambda y.y))$ \color{black} \newline + \subitem $(\lambda x.((\lambda \color{blue}x.x\color{black}) \color{red}(\lambda y.y)\color{black})(\lambda z.z)x)$ + \begin{center} + \item Intuition: Reduziere Argumente erst, wenn benötigt + \end{center} + \end{itemize*} + + Auswertung in Haskell: \color{blue} Lazy-Evaluation = call-by-name (+sharing)\color{black} + \begin{itemize*} + \item Standard-Auswertungsstrategie für Funktionen/Konstruktoren + \item listOf x = x : listOf x + \item 3: listOf 3 $\nRightarrow$ + \item (div 1 0) : (6 : []) + \item tail ((div 1 0): (6 : [])) $\Rightarrow$ 6 : [] $\nRightarrow$ + \end{itemize*} + + \subsubsection{Call-By-Value} + Call-By-Value: Reduziere linkesten Redex + \begin{itemize*} + \item der nicht einen $\lambda$ umgibt + \item und dessen Argument ein \color{blue} Wert \color{black} ist + \subsubitem $(\lambda y.(\lambda x.y(\lambda z.z)x)((\lambda \color{blue} x.x \color{black})\color{red}(\lambda y.y)\color{black})$ + \subsubitem $\Rightarrow (\lambda \color{blue}y\color{black}(\lambda x. \color{blue}y\color{black}(\lambda z.z)x))\color{red}(\lambda y.y)\color{black}$ + \subsubitem $\Rightarrow (\lambda x.(\lambda y.y(\lambda z.z)x)) \nRightarrow$ + \item Intuition: Argumente vor Funktionsaufruf auswerten + \item Auswertungsstrategie vieler Sprachen: Java, C, Scheme, ML, … + \item Arithmetik in Haskell: Auswertung by-value + \item $prodOf(x) = y * prodOf x$ + \item $3 * prodOf 3 \Rightarrow 3 * (3 * prodOf 3) \Rightarrow$ … + \item $((div \space1 \space 0) * 6) * 0 \Rightarrow \bot$ + \item $((div \space2 \space 2) * 6) * 0 \Rightarrow ((1 * 6) * 0) \Rightarrow 6 * 0\Rightarrow 0 \nRightarrow$ + \end{itemize*} + + \subsubsection{Vergleich der Auswertungsstrategien} + \color{blue} Call-by-name vs. Call-by-value \color{black} + \begin{itemize*} + \item Werten nicht immer zur Normalform aus $\lambda x.(\lambda y.y)x$ + \item Gibt es Normalform, dann darauf $\beta$-reduzierbar (Church-Rosser) + \item Call-by-name terminiert öfter + \item $Y(\lambda y.z) = \lambda f. (\lambda x.f(x\;x))(\lambda x.f(x\;x))\color{red}(\lambda y.z)\color{black}$ \newline + \subitem $ \Rightarrow \lambda x.(\lambda y.z(x\;x))\color{red} (\lambda x.(\lambda y.z)(x\;x))$ \newline + \subitem $\Rightarrow (\lambda y.z)\color{red}((\lambda x.(\lambda y.z)(x\;x)) (\lambda x.(\lambda y.z (x\;x)))\color{black} \stackrel{cbn}{\Rightarrow} z$ + \subitem \newline + \subitem $\stackrel{cbv}{\Rightarrow} (\lambda y.z)((\lambda x.(\lambda y.z)(x\;x))\color{red}(\lambda x.(\lambda y.z (x\;x))\color{black})$ + \subitem $\stackrel{cbv}{\Rightarrow} (\lambda y.z)((\lambda y.z)((\lambda x.(\lambda y.z)(x\;x)) \color{red} (\lambda x.(\lambda y.z(x\;x)) \color{black}))$ + \end{itemize*} + \color{blue} Standardisierungssatz \newline + Wenn t eine Normalform hat, dann findet Normalreihenfolgenauswertung diese. + \color{black} + + \subsubsection{Abschließende Bemerkungen} + \begin{itemize*} + \item Der Lambda-Kalkül wurde in den dreißiger Jahren des 20. Jahrhunderts von Alonzo Church erfunden, um damit grundsätzliche Betrachtungen über berechenbare Funktionen anzustellen + \item Trotz der Einfachheit der dem Kalkül zugrunde liegenden Regeln, realisiert er ein universelles Berechnungsmodell + \item Der Lambda-Kalkül hat die Entwicklung zahlreicher, für die Informatik wichtiger Konzepte beeinflusst + \begin{itemize*} + \item Funktionale Programmiersprachen (die minimalen Funktionen von Lisp wurden auf Grundlage des Lambda-Kalküls definiert) + \item Forschund zu Typsystemen für Programmiersprachen + \item Repräsentation von Logik-Termen im Lambda-Kalkül führte zu Theorembeweisen für Logiken höherer Stufen + \end{itemize*} + \item Manche Puristen vertreten gelegentlich die Ansicht, dass funktionale Programmiersprachen nicht viel mehr sind, als "Lambda-Kalkül mit etwas syntaktischem Zucker" + \end{itemize*} + + \subsection{Zusammenfassung} + \begin{itemize*} + \item Funktionale Programmierung folgt einem verallgemeinerten Konzept der Funktionsauswertung + \item Die Programmiersprache Erlang ist dynamisch typisiert und unterstützt auch Funktionen höherer Ordnung + \item Manche Algorithmen lassen sich in Erlang aufgrund der mächtigen Listenkonstrukte und des flexiblen Pattern Matching sehr kompakt formulieren ($\rightarrow$ Potenzmenge, Quicksort) + \item Das heißt jedoch nicht, dass sehr kompakter Code auch zu sehr effizientem Laufzeit- und/oder Speicherbedarf führt - teilweise muss der Code relativ geschickt optimiert werden, um einigermaßen effiziente Lösungen zu erhalten ($\rightarrow$ Quicksort) + \item Manche Aufgaben, die in imperativen Programmiersprachen sehr effizient und einfach lösbar sind ($\rightarrow$ Teilen einer Liste in gleich große Hälften) sind mittels Listen nur recht umständlich und aufwendig lösbar + \item Es gilt in der Praxis also abzuwägen, für welche Aufgaben eine funktionale Sprache eingesetzt werden soll + \end{itemize*} + + \newpage + \section{Multithreading und parallele Programmierung} + \subsection{Grundlagen} + \subsubsection{Lernziele} + \begin{itemize*} + \item Programmierung paralleler Algorithmen und Verfahren als Paradigma + \item Verständnis grundlegender Architekturen und Modelle + \item Praktische Erfahrungen mit Erlang, Java und C++ + \end{itemize*} + + \subsubsection{Grundbegriffe} + \begin{itemize*} + \item Prozess := Programm in Ausführung; Ausführungsumgebung für ein Programm; hat eigenen Adressraum; Prozessor kann immer nur einen Prozess ausführen + \item Thread ("Faden") := leichtgewichtige Ausführungseinheit oder Kontrollfluss (Folge von Anweisungen) innerhalb eines sich in Ausführung befindlichen Programms; "leichtgewichtig" im Vergleich zu Betriebssystemprozess; Threads eines Prozesses teilen sich Adressraum; Thread kann von CPU oder Core ausgeführt werden + \item Shared Memory := Kommunikation (über Variablen im) gemeinsamen Speicher; Prozess kann direkt auf Speicher eines anderen Prozesses zugreifen; erfordert explizite Synchronisation, z.B. über kritische Abschnitte + \item Message Passing := Prozesse mit getrennten Adressräumen; Zugriff nur auf eigenen Speicher; Kommunikation durch explizites Senden/Empfangen von Nachrichten; implizite Synchronisation durch Nachrichten + \item Parallelisierungsarten + \begin{itemize*} + \item Instruktionsparallelität: parallele Ausführung mehrerer Operationen durch eine CPU-Instruktion; explizit: Vektorinstruktionen, SIMD; implizit: Pipelining von Instruktionen + \item Taskparallelität: Ausnutzung inhärenter Parallelität durch simultane Ausführung unabhängiger Aufgaben + \item Datenparallelität: Gemeinsame Operation auf homogener Datenmenge; Zerlegung eines Datensatzes in kleinere Abschnitte + \end{itemize*} + \end{itemize*} + + \subsubsection{The free launch is over} + Taktfrequenz wächst nur noch langsam + \begin{itemize*} + \item Physikalische Gründe: Wärmeentwicklung, Energiebedarf, Kriechströme,… + \end{itemize*} + Auswege + \begin{itemize*} + \item Hyperthreading: + \begin{itemize*} + \item Abarbeitung mehrerer Threads auf einer CPU (5-15 \% Performancegewinn) + \item Einfache Hardwareunterstützung (einige Register) + \end{itemize*} + \item Multicore: + \begin{itemize*} + \item Mehrere CPUs auf einem Chip + \item Billiger als echte Mehrprozessorsysteme + \end{itemize*} + \item Caching: + \begin{itemize*} + \item Vergrößerung L1, L2, L3 Cache + \item Speicherzugriff 10-50 $\cdot$ teurer als Cachezugriff + \end{itemize*} + \end{itemize*} + + \subsubsection{Konsequenzen und Trends} + \begin{itemize*} + \item Applikationen müssen nebenläufig programmiert werden um CPU auszunutzen $\rightarrow$ Many-Core-Systeme + \item CPU-Begrenzung von Applikationen + \item Effizienz und Performanceoptimierung werden immer wichtiger + \item Unterstützung von Nebenläufigkeit/Parallelität durch Programmiersprachen + \end{itemize*} + + \begin{figure}[!tbp] + \centering + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=1.0\linewidth]{Assets/Programmierparadigmen-einordnung-programmierung} + \caption{Einordnung} + \end{minipage} + \hfill + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=1.0\linewidth]{Assets/Programmierparadigmen-Architekturen} + \caption{Architekturen: SIMD, SMP, NUMA, Cluster, Grid} + \end{minipage} + \vfill + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=1.0\linewidth]{Assets/Programmierparadigmen-Multiprozessorsysteme} + \caption{Multiprozessorsysteme} + \begin{itemize*} + \item Zugriff über Bus auf gemeinsamen Speicher + \item jeder Prozessor mit eigenen Caches + \end{itemize*} + \end{minipage} + \hfill + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=1.0\linewidth]{Assets/Programmierparadigmen-Multicore-Systeme} + \caption{Multicore-Systeme} + \begin{itemize*} + \item mehrere Prozessorkerne auf einem Chip + \item Kerne typischerweise mit eigenen L1/L2-Caches und gemeinsamen L3-Cache + \end{itemize*} + \end{minipage} + \vfill + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=1.0\linewidth]{Assets/Programmierparadigmen-SMP} + \caption{SMP (Symmetric Multi Processing)} + \begin{itemize*} + \item Speicherbandbreite begrenzt und von allen Prozessoren gemeinsam genutzt + \item Skalierbarkeit begrenzt + \item Single Socket Lösung + \end{itemize*} + \end{minipage} + \hfill + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=1.0\linewidth]{Assets/Programmierparadigmen-NUMA} + \caption{NUMA (Non-Uniform Memory Access)} + \begin{itemize*} + \item jedem Prozessor sind Teile des Speichers zugeordnet + \item lokaler Zugriff ist schneller als entfernter + \item Typisch für Multi-Socket Systeme + \end{itemize*} + \end{minipage} + \end{figure} + + \subsubsection{Symmetrisch vs. Nicht-symmetrisch} + \begin{tabular}{c | c} + SMP (Symmetric Multi Processing) & NUMA (Non-Uniform Memory-Access) \\ + Speicherbandbreite begrenzt und von allen Prozessoren gemeinsam genutzt & jedem Prozessor sind Teile des Speichers zugeordnet \\ + Skalierbarkeit begrenzt & lokaler Zugriff ist schneller als entfernter \\ + Single Socket-Lösung & Mehr-Socket-Board \\ + \end{tabular} + + \subsubsection{CPU vs. GPU} + \begin{itemize*} + \item GPU = Graphics Processing Units + \item Hochparallele Prozessorarchitekturen (nicht nur) für Grafikrendering + \end{itemize*} + \begin{center} + \includegraphics[width=0.95\linewidth]{Assets/Programmierparadigmen-CPU-vs-GPU} + \end{center} + + \subsubsection{Flynn's Architekturklassifikation} + \begin{center} + \includegraphics[width=0.95\linewidth]{Assets/Programmierparadigmen-flynn-architekturklassifikation} + \end{center} + + \subsubsection{Maße zur Leistungsbewertung} + \begin{itemize*} + \item Maße für Laufzeitgewinn durch Parallelisierung + \item $T_n$ = Laufzeit des Programms mit n Prozessoren/Kernen + \item Speedup $Speedup = {{T_1} \over {T_n}}$ + \item Effizienz $Effizienz = {Speedup \over n}$ + \end{itemize*} + + \subsubsection{Amdahlsches Gesetz} + \begin{itemize*} + \item Berücksichtigung parallelisierbarer und serieller Anteile im Programmablauf + \item p = paralleler Anteil + \item s = serieller Anteil + \item n Prozessoren + \item $p+s = 1$ + \item Maximaler Speedup $Speedup_{max} = {T_1 \over T_n} = {{s+p}\over{s+{p \over n}}} = {1 \over {s+{p \over n}}} = \frac{1}{s+\frac{p}{n}}$ + \end{itemize*} + \begin{center} + \includegraphics[width=0.35\linewidth]{Assets/Programmierparadigmen-parallelisierung} + \includegraphics[width=0.35\linewidth]{Assets/Programmierparadigmen-amdahlsches-gesetz} + \end{center} + + \subsubsection{Prozesse und Threads} + Prozess := Programm in Ausführung; Ausführungsumgebung für ein Programm + \begin{itemize*} + \item hat eigenen Adressraum + \item Prozessor kann immer nur einen Prozess ausführen + \end{itemize*} + Thread ("Faden") := leichtgewichtige Ausführungsreinheit oder Kontrollfluss (Folge von Anweisungen) innerhalb eines sich in Ausführung befindlichen Programms + \begin{itemize*} + \item leichtgewichtig im Vergleich zu Betriebssystemprozess + \item Threads eines Prozesses teilen sich den Adressraum + \item Thread kann von einer CPU oder einem Core ausgeführt werden + \end{itemize*} + + \subsubsection{Shared Memory vs Message Passing} + Art der Kommunikation zwischen Prozessen oder Threads + \paragraph{Shared Memory} + \begin{itemize*} + \item Kommunikation (über Variable im) gemeinsamen Speicher + \item Prozess kann direkt auf Speicher eines anderen Prozesses zugreifen + \item erfordert explizite Synchronisation, z.B. über zeitkritische Abschnitte + \end{itemize*} + \paragraph{Message Passing} + \begin{itemize*} + \item Prozesse mit getrennten Adressräumen; Zugriff nur auf eigenen Speicher + \item Kommunikation durch explizites Senden/Empfangen von Nachrichten + \end{itemize*} + + \begin{figure}[!tbp] + \centering + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-Shared-Memory-vs-Message-Passing} + \caption{Shared Memory vs Message Passing} + \end{minipage} + \hfill + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-Programmiermodelle} + \caption{Programmiermodelle} + \end{minipage} + \end{figure} + + \subsubsection{Parallelisierungsarten} + Instruktionsparallelität: + \begin{description*} + \item[parallele Ausführung] mehrerer Operationen durch eine CPU-Instruktion + \item[explizit] Vektorinstruktionen, SIMD + \item[implizit] Pipelining von Instruktionen + \item[Taskparallelität] Ausnutzung inhärenter Parallelität durch simultane Ausführung unabhängiger Aufgaben + \item[Datenparalelität] \hfill + \begin{itemize*} + \item Gemeinsame Operation auf homogener Datenmenge + \item Zerlegung eines Datensatzes in kleinere Abschnitte + \end{itemize*} + \end{description*} + + \begin{figure}[!tbp] + \centering + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-Instruktionsparallelität} + \caption{Instruktionsparallelität: SIMD} + \begin{itemize*} + \item Autovektorisierung durch Compiler + \item explizite Instruktionen + \item Beispiel: Addition zweier Vektoren + \end{itemize*} + \end{minipage} + \hfill + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-Taskparallelität} + \caption{Taskparallelität} + \begin{itemize*} + \item Unabhängikeit von Teilprozessen $\rightarrow$ Desequentialisierung + \item Beispiel: Quicksort + \end{itemize*} + \end{minipage} + \vfill + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-Datenparallelität} + \caption{Datenparallelität} + \begin{itemize*} + \item homogene Datenmenge: Felder, Listen, Dokumentenmenge,… + \item Verteilung der Daten + \item alle Prozessoren führen gleiches Programm auf jeweils eigenen Daten aus + \item Beispiel: Matrixaddition S = A + B + \end{itemize*} + \end{minipage} + \end{figure} + + \subsubsection{Herausforderungen} + \begin{itemize*} + \item Zerlegung eines Problems in parallel verarbeitbare Teile + \begin{itemize*} + \item Beispiel: Suche in einer Datenbank mit 1 TB Größe + \item Annahme: 100 MB/Sekunde mit einem Prozessor = 175 Minuten + \item bei paralleler Suche durch 10 Prozessoren = 17.5 Minuten + \item Übertragbar auf andere Probleme, z.B. Sortieren, Suche in Graphen? + \end{itemize*} + \item Synchronisation konkurrierender Zugriffe auf gemeinsame Ressourcen + \begin{itemize*} + \item Beispiel: Produzent-Konsument-Beziehung + \item Annahme: Datenaustausch über gemeinsame Liste + \item Fragestellungen: Benachrichtigung über neues Element in der Liste, Konsument entnimmt Element während Produzent einfügt + \item Wechselseitiger Ausschluss + \end{itemize*} + \item außerdem: Fehlersuche, Optimierung + \end{itemize*} + + \subsubsection{Zusammenfassung} + \begin{itemize*} + \item Parallele Verarbeitung als wichtiges Paradigma moderner Software + \item verschiedene parallele + \begin{itemize*} + \item Hardwarearchitekturen und + \item Programmiermodelle + \end{itemize*} + \item Herausforderungen + \begin{itemize*} + \item Problemzerlegung + \item Synchronisation + \item … + \end{itemize*} + \item im Weiteren: konkrete Methoden und Techniken in Erlang und C++ + \end{itemize*} + + \subsection{Parallele Programmierung in Erlang} + \subsubsection{Unterstützung paralleler Programmierung in Erlang} + \begin{itemize*} + \item Leichtgewichtige Prozesse und Message Passing + \item SMP-Support (Symmetric Multi Processing) + \item Ziele für effiziente Parallelisierung + \begin{itemize*} + \item Problem in viele Prozesse zerlegen (aber nicht zu viele …) + \item Seiteneffekte vermeiden (würde Synchronisation erfordern …) + \item Sequentiellen Flaschenhals vermeiden (Zugriff auf gemeinsame Ressourcen: IO, Registrierung von Prozessen, …) -> Small Messages, Big Computation! + \end{itemize*} + \end{itemize*} + + \subsubsection{Prozesse in Erlang} + \begin{itemize*} + \item Erlang VM = Betriebssystemprozess + \item Erlang-Prozess = Thread innerhalb der Erlang VM + \begin{itemize*} + \item kein Zugriff auf gemeinsame Daten, daher "Prozess" + \end{itemize*} + \item jede Erlang-Funktion kann einen Prozess bilden + \item Funktion spawn erzeugt einen Prozess, der die Funktion Fun ausführt + \begin{lstlisting} + Pid = spawn(fun Fun/0) + \end{lstlisting} + \item Resultat = Prozessidentifikation Pid, mittels der man dem Prozess Nachrichten schicken kann. + \item über self() kann man die eigene Pid ermitteln + \item Übergabe von Arghumenten an den Prozess bei der Erzeugung + \begin{lstlisting} + Pid = spawn(fun() $\rightarrow$ any_func(Arg1, Arg2, ...) end) + \end{lstlisting} + \end{itemize*} + + \begin{figure}[!tbp] + \centering + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-erlang-Beispiele} + \caption{Beispiele} + \end{minipage} + \hfill + \begin{minipage}[b]{0.45\textwidth} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-SMP Erlang} + \caption{SMP Erlang} + \end{minipage} + \end{figure} + + \begin{itemize*} + \item 4 Betriebssystemthreads (hier 2 Kerne mit Hyperthreading) + \item kann mit -smp [disable $\mid$ enable $\mid$ auto] beeinflusst werden + \item +S [Anzahl] bestimmt Anzahl der Scheduler + \begin{itemize*} + \item sollte nicht größer als Anzahl der Kerne/Prozessoren sein + \end{itemize*} + \end{itemize*} + + \subsubsection{Scheduler in Erlang} + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-erlang-scheduler} + \end{center} + + \subsubsection{Message Passing in Erlang: Senden einer Nachricht} + \begin{lstlisting} + Pid ! Message + \end{lstlisting} + \begin{itemize*} + \item an Prozess Pid wird die Nachricht Message gesendet + \item der Prozess muss eine Empfangsoperation ausführen. damit ihn die Nachricht erreichen kann + \begin{lstlisting}[language=erlang] + receive + Pattern1 [when Guard1] -> Expressions1; + Pattern2 [when Guard2] -> Expressions2; + ... + end + \end{lstlisting} + \item trifft eine Nachricht ein, wird versucht, diese mit einem Pattern und ggf. vorhandenen Guard zu "matchen" + \item erstes zutreffendes Pattern (inkl. Guard) bestimmt, welcher Ausdruck ausgewertet wird + \item trifft kein Pattern zu, wird die Nachricht für spätere Verwendung aufgehoben und Prozess wartet auf die nächste Nachricht ($\rightarrow$ selective receive) + \end{itemize*} + + + \subsubsection{Ein einfacher Echo-Server} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-code-snippet-02} + \end{center} + + Erklärungen + \begin{itemize*} + \item Funktion loop() realisiert einen (nur bedingt nützlichen) Echo-Dienst, der jede empfangene Nachricht unverändert an den Absender zurückschickt, bis er nach Empfang von stop endet + \item Funktion run() + \begin{enumerate*} + \item startet den Echoserver (Zeile 4) + \item schickt ihm als nächstes eine Nachricht (Zeile 5) + \item wartet auf eine Antwort (Zeile 6) + \item gibt diese aus (Zeile 7) + \item schickt dann stop an den Echoserver (Zeile 9) + \end{enumerate*} + \item Aufruf in der Funktion loop() erfolgt endrekursiv, daher wird kein wachsender Aufrufstapel angelegt (Hinweis: grundsätzlich zu beachten, da sonst der Speicherbedarf stetig wächst) + \end{itemize*} + + \subsubsection{Ansätze zur Parallelisierung} + \begin{itemize*} + \item Beispiel: Berechnung einer (zufällig generierten) Liste von Fibonaccizahlen \item Sequentielle Lösung über lists:map/2 \end{itemize*} -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-036} -\end{center} - - -\subsubsection{pmap: Parallele Funktionen höherer Ordnung} -\begin{itemize*} - \item[] Parallele Variante von lists:map(Fun, list) + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-03} + \end{center} + + \subsubsection{pmap: Parallele Funktionen höherer Ordnung} \begin{itemize*} - \item für jedes Listenelement einen Prozess erzeugen - \item Ergebnisse einsammeln + \item Parallele Variante von lists:map(Fun, list) + \item für jedes Listenelement einen Prozess erzeugen + \item Ergebnisse einsammeln \end{itemize*} -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-035} -\end{center} - -\paragraph{pmap: Hilfsfunktionen} -\color{orange} Eigentliche Verarbeitungsfunktion ausführen \color{black} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-034} -\end{center} - -\begin{itemize*} - \item Funktion F aufrufen, catch sorgt für korrekte Behandlung von Fehlern in F - \item Ergebnis zusammen mit eigener Pid (self()) an Elternprozess senden -\end{itemize*} - -\color{orange} Einsammeln der Ergebnisse \color{black} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-037} -\end{center} -\begin{itemize*} - \item Zeile 5: Warten bis Paar (Pid, Ergebniswert) eintrifft - \item Zeile 7: Tail ist leer $\rightarrow$ alle Ergebnisse eingetroffen -\end{itemize*} - -\paragraph{Parallele Berechnung der Fibonacci-Zahlen} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-038} -\end{center} - -\paragraph{Diskussion} -\begin{itemize*} - \item Passende Abstraktion wählen + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-04} + \end{center} + + \paragraph{pmap: Hilfsfunktionen} + + \color{orange} Eigentliche Verarbeitungsfunktion ausführen \color{black} + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-05} + \end{center} \begin{itemize*} - \item Ist Ordnung der Ergebnisse notwendig? - \item Werden Ergebnisse benötigt? + \item Funktion F aufrufen, catch sorgt für korrekte Behandlung von Fehlern in F + \item Ergebnis zusammen mit eigener Pid (self()) an Elternprozess senden \end{itemize*} - \item Anzahl der parallelen Prozesse + + \color{orange} Einsammeln der Ergebnisse \color{black} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-code-snippet-06} + \end{center} \begin{itemize*} - \item Abhängig von Berechnungsmodell, Hardware etc. - \item evtl. pmap mit max. Anzahl gleichzeitiger Prozesse + \item Zeile 5: Warten bis Paar (Pid, Ergebniswert) eintrifft + \item Zeile 7: Tail ist leer $\rightarrow$ alle Ergebnisse eingetroffen \end{itemize*} - \item Berechnungsaufwand der Prozesse + + \paragraph{Parallele Berechnung der Fibonacci-Zahlen} + + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-07} + \end{center} + + \paragraph{Diskussion} + \begin{itemize*} - \item Berechnung vs. Daten/Ergebnisse senden - \end{itemize*} -\end{itemize*} - -\paragraph{pmap: Alternative Implementierung} -\begin{itemize*} - \item ohne Berücksichtigung der Ordnung der Ergebnismenge - \item Zählen für die bereits eingetroffenen Ergebnisse -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-039} -\end{center} - -\subsubsection{Speedup} -Bestimmung des Speedups erfordert -\begin{itemize*} - \item Zeitmessung - \item Kontrolle der genutzten Prozessoren/Cores -\end{itemize*} -\color{orange} Welchen Einfluss hat die Zahl der erzeugten Prozesse. \color{black} - -\paragraph{Speedup: Zeitmessung} -Nutzung der Funktion timer:tc/3 -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-040} -\end{center} -Für bessere Aussagekraft: mehrfache Ausführung -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-041} -\end{center} - -\paragraph{Bestimmung: Speedup} -ch4\_6:benchmark(ch4\_4, run, 1000). -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-042} -\end{center} -\color{orange} Achtung: \color{black} -\begin{itemize*} - \item Aufwand für Berechnung einer Fibonaccizahl ist nicht konstant - \item Zufallszahlen als Eingabe -\end{itemize*} - -\paragraph{Diskussion: Speedup} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-043} -\end{center} - -\subsubsection{Datenparallelität: Das Map-Reduce-Paradigma} -\begin{itemize*} - \item Parallelisierungsmuster inspiriert von Konzepten funktionaler Programmiersprachen (map,reduce/fold) - \item Basis von Big-Data-plattformen wie Hadoop, Spark,… - \item Grundidee: - \begin{itemize*} - \item map(F, Seq) ? wende Funktion F (als Argument übergeben) auf alle Elemente einer Folge Seq an, + \item Passende Abstraktion wählen \begin{itemize*} - \item Funktion F kann unabhängig (=parallel) auf jedes Element angewendet werden - \item Partitionieren und Verteilen der Elemente der Folge - \item z.B. multipliziere jedes Element mit 2 + \item Ist Ordnung der Ergebnisse notwendig? + \item Werden Ergebnisse benötigt? \end{itemize*} - \item reduce(F, Seq) = wende eine Funktion F schrittweise auf die Elemente einer Folge Seq an und produziere einen einzelnen Wert, + \item Anzahl der parallelen Prozesse \begin{itemize*} - \item prinzipiell ähnlich zu map(F, Seq), d.h. Funktion F kann auf Paare unabhängig angewendet werden - \item z.B. die Summe aller Elemente der Folge + \item Abhängig von Berechnungsmodell, Hardware etc. + \item evtl. pmap mit max. Anzahl gleichzeitiger Prozesse + \end{itemize*} + \item Berechnungsaufwand der Prozesse + \begin{itemize*} + \item Berechnung vs. Daten/Ergebnisse senden \end{itemize*} \end{itemize*} -\end{itemize*} - -\paragraph{map in Erlang} -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-044} -\end{center} - -\paragraph{reduce in Erlang} -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-045} -\end{center} - -\paragraph{Parallelisierung von map und reduce} -\color{orange} map \color{black} -\begin{itemize*} - \item Funktion F kann unabhängig (=parallel) auf jedes Element angewendet werden - \item Partitionieren und Verteilen der Elemente der Folge - \item siehe pmap -\end{itemize*} -\color{orange} reduce \color{black} -\begin{itemize*} - \item prinzipiell ähnlich, d.h. Funktion F kann auf Paare unabhängig angewandt werden -\end{itemize*} - -\paragraph{Parallelisierung von reduce} -\begin{center} - \includegraphics[width=0.5\linewidth]{Assets/Programmierparadigmen-046} -\end{center} - -\subsubsection{Taskparallelität: Sortieren} -\color{orange} Quicksort in Erlang \color{black} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-047} -\end{center} - -\begin{itemize*} - \item typische funktionale Notation von Quicksort mit List Comprehensions - \item Zeile 2: H dient als Pivotelement -\end{itemize*} \ \newline -Idee: -\begin{itemize*} - \item Prozess für das Sortieren der einen Hälfte starten - \item Elternprozess kann andere Hälfte sortieren - \item rekursive Zerlegung… -\end{itemize*} - -\subsubsection{Parallel Quicksort} -\paragraph{Version 1} -Quicksort in Erlang -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-048} -\end{center} - -Erläuterungen -\begin{itemize*} - \item Zeile 4: Erzeugen eines neuen Prozesses zur Sortierung der "oberen" Hälfte - \item Zeile 6-7: Wie bisher - \item Zeile 8: Warten auf Empfang der sortierten anderen Hälfte -\end{itemize*} -Zeitmessung: -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-049} -\end{center} - -Bewertung -\begin{itemize*} - \item parallele Version 1 ist langsamer! - \item mögliche Erklärung: Prozess-Start ist aufwändiger als Sortieren kleiner Teilfolgen - \item bessere Variante nach John Hughes: Parallel Programming in Erlang + + \paragraph{pmap: Alternative Implementierung} + \begin{itemize*} - \item Kontrolle der Granularität für parallele Ausführungen - \item danach Sortieren mit sequenzieller Variante - \item einfache Idee: Anzahl der parallelen Zerlegung begrenzen + \item ohne Berücksichtigung der Ordnung der Ergebnismenge + \item Zählen für die bereits eingetroffenen Ergebnisse \end{itemize*} -\end{itemize*} -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-050} -\end{center} - -\paragraph{Version 2} -\begin{center} - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-051} -\end{center} - -\subsubsection{Fazit} -\begin{itemize*} - \item \color{orange} leichtgewichtige Prozesse \color{black} als Baustein der Parallelisierung in Erlang - \item Prozesskommunikation ausschließlich über \color{orange} Message Passing \color{black} - \item \color{orange} funktionaler Charakter \color{black} (u.a. Vermeidung von Seiteneffekten) vereinfacht Parallelisierung deutlich - \item \color{orange} Daten- und Taskparallelität \color{black} möglich - \item hoher Abstraktionsgrad, aber auch wenig Einflussmöglichkeiten -\end{itemize*} - -\subsection{Parallele Programmierung in C++} -\subsubsection{Threads in C++} -\color{orange} Thread (Faden) \color{black} = leichtgewichtige Ausführungseinheit oder Kontrollfluss (Folge von Anweisungen) innerhalb eines sich in Ausführung befindlichen Programms -\begin{itemize*} - \item Threads teilen sich den Adressraum ihres Prozesses - \item in C++: Instanzen der Klasse std::thread - \item führen eine (initiale) Funktion aus -\end{itemize*} -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -\#include -\#include - -void say_hello() { -std::cout << "Hello Concurrent C++\n"; -} - -int main() { -std::thread t(say_hello); -t.join(); -} -\end{lstlisting} - -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-052} -\end{center} - -\paragraph{Alternative Erzeugung von Threads} -\color{orange} über Lambda-Ausdruck \color{black} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-053} -\end{center}\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily -] -std::thread t([]() { do_something(); }); -\end{lstlisting} - -\color{orange} mit Instanzen einer Klasse \color{black} - erfordert Überladen von operator() -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-054} -\end{center}\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily -] -struct my_task { -void operator()() const { do_something(); } -}; - -my_task tsk; -std::thread t1(tsk); // mit Objekt -std::thread t2{ my_task() }; // über Konstruktor -\end{lstlisting} - -\paragraph{Parameterübergabe bei Threaderzeugung} -\begin{itemize*} - \item über zusätzliche Argumente des thread-Konstruktors - \item Vorsicht bei Übergabe von Referenzen, wenn Elternthread vor dem erzeugten Thread beendet wird -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-056} -\end{center} -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -void fun(int n, const std::string\& s) { - for (auto i = 0; i < n; i++) - std::cout << s << " "; - std::cout << std::endl; -} -std::thread t(fun, 2, "Hello"); -t.join(); -\end{lstlisting} - -\paragraph{Warten auf Threads} -\begin{itemize*} - \item t.join() wartet auf Beendigung des Threads t - \item blockiert aktuellen Thread - \item ohne join() keine Garantie, dass t zur Ausführung kommt - \item Freigabe der Ressourcen des Threads -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-057} -\end{center} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-058} -\end{center} -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -std::thread t([]() { do_something(); }); -t.join(); -\end{lstlisting} - -\paragraph{Hintergrundthreads} -\begin{itemize*} - \item Threads können auch im Hintergrund laufen, ohne, dass auf Ende gewartet werden muss - \item "abkoppeln" durch detach() - \item Thread läuft danach unter Kontrolle des C++-Laufzeitsystems, join nicht mehr möglich -\end{itemize*} - -\paragraph{Threadidentifikation} -\begin{itemize*} - \item Threadidentifikator vom Typ std::thread::id - \item Ermittlung über Methode get\_id() -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-059} -\end{center} -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] -void fun() { -std::cout << "Hello from " - << std::this_thread::get_id() - << std::endl; -} -std::thread t(fun); -t.join(); -\end{lstlisting} - -\paragraph{Beispiel: Berechnung von Fibonacci-Zahlen in C++} -\begin{itemize*} - \item rekursive und nichtrekursive Variante möglich -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-060} -\end{center} - -Parallele Berechnung von Fibonacci-Zahlen -\begin{itemize*} - \item einfachste Lösung (ähnlich zu Erlang): pro Zahl ein Thread -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-061} -\end{center} - -Erläuterungen -\begin{itemize*} - \item Zeile 1: Feld der Threads - \item Zeile 2: Feld für Ergebniswerte - \item Zeile 5: Zufallszahl erzeugen - \item Zeilen 6-7 Thread zur Berechnung der Fibonacci-Zahl erzeugen und Ergebnis im Feld speichern - \item Zeile 10-11: Warten auf Beendigung der Threads (std::mem\_fn = Wrapper für Zeiger auf Member-Funktion) - \item \color{orange} aber: \color{black} + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-08} + \end{center} + + \subsubsection{Speedup} + Bestimmung des Speedups erfordert \begin{itemize*} - \item Zugriff auf gemeinsame Ressource (results)! - \item Anzahl Fibonaccizahlen = Anzahl Threads + \item Zeitmessung + \item Kontrolle der genutzten Prozessoren/Cores \end{itemize*} -\end{itemize*} + \color{orange} Welchen Einfluss hat die Zahl der erzeugten Prozesse. \color{black} + + \paragraph{Speedup: Zeitmessung} + + Nutzung der Funktion timer:tc/3 + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-09} + \end{center} + Für bessere Aussagekraft: mehrfache Ausführung + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-10} + \end{center} + + \paragraph{Bestimmung: Speedup} + + ch4\_6:benchmark(ch4\_4, run, 1000). + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-Speedup-Bestimmung} + \end{center} + \color{orange} Achtung: \color{black} + \begin{itemize*} + \item Aufwand für Berechnung einer Fibonaccizahl ist nicht konstant + \item Zufallszahlen als Eingabe + \end{itemize*} + + \paragraph{Diskussion: Speedup} + + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-Speedup-Diskussion} + \end{center} + + \subsubsection{Datenparallelität: Das Map-Reduce-Paradigma} + \begin{itemize*} + \item Parallelisierungsmuster inspiriert von Konzepten funktionaler Programmiersprachen (map,reduce/fold) + \item Basis von Big-Data-plattformen wie Hadoop, Spark,… + \item Grundidee: + \begin{itemize*} + \item map(F, Seq) ? wende Funktion F (als Argument übergeben) auf alle Elemente einer Folge Seq an, + \begin{itemize*} + \item Funktion F kann unabhängig (=parallel) auf jedes Element angewendet werden + \item Partitionieren und Verteilen der Elemente der Folge + \item z.B. multipliziere jedes Element mit 2 + \end{itemize*} + \item reduce(F, Seq) = wende eine Funktion F schrittweise auf die Elemente einer Folge Seq an und produziere einen einzelnen Wert, + \begin{itemize*} + \item prinzipiell ähnlich zu map(F, Seq), d.h. Funktion F kann auf Paare unabhängig angewendet werden + \item z.B. die Summe aller Elemente der Folge + \end{itemize*} + \end{itemize*} + \end{itemize*} + + \paragraph{map in Erlang} + + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-erlang-map} + \end{center} + + \paragraph{reduce in Erlang} + + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-erlang-reduce} + \end{center} + + \paragraph{Parallelisierung von map und reduce} + + \color{orange} map \color{black} + \begin{itemize*} + \item Funktion F kann unabhängig (=parallel) auf jedes Element angewendet werden + \item Partitionieren und Verteilen der Elemente der Folge + \item siehe pmap + \end{itemize*} + \color{orange} reduce \color{black} + \begin{itemize*} + \item prinzipiell ähnlich, d.h. Funktion F kann auf Paare unabhängig angewandt werden + \end{itemize*} + + \paragraph{Parallelisierung von reduce} + + \begin{center} + \includegraphics[width=0.5\linewidth]{Assets/Programmierparadigmen-erlang-reduce-parallel} + \end{center} + + \subsubsection{Taskparallelität: Sortieren} + \color{orange} Quicksort in Erlang \color{black} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-code-snippet-11} + \end{center} + + \begin{itemize*} + \item typische funktionale Notation von Quicksort mit List Comprehensions + \item Zeile 2: H dient als Pivotelement + \end{itemize*} + Idee: + \begin{itemize*} + \item Prozess für das Sortieren der einen Hälfte starten + \item Elternprozess kann andere Hälfte sortieren + \item rekursive Zerlegung… + \end{itemize*} + + \subsubsection{Parallel Quicksort} + \paragraph{Version 1} + + Quicksort in Erlang + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-12} + \end{center} + + Erläuterungen + \begin{itemize*} + \item Zeile 4: Erzeugen eines neuen Prozesses zur Sortierung der "oberen" Hälfte + \item Zeile 6-7: Wie bisher + \item Zeile 8: Warten auf Empfang der sortierten anderen Hälfte + \end{itemize*} + Zeitmessung: + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-13} + \end{center} + + Bewertung + \begin{itemize*} + \item parallele Version 1 ist langsamer! + \item mögliche Erklärung: Prozess-Start ist aufwändiger als Sortieren kleiner Teilfolgen + \item bessere Variante nach John Hughes: Parallel Programming in Erlang + \begin{itemize*} + \item Kontrolle der Granularität für parallele Ausführungen + \item danach Sortieren mit sequenzieller Variante + \item einfache Idee: Anzahl der parallelen Zerlegung begrenzen + \end{itemize*} + \end{itemize*} + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-14} + \end{center} + + \paragraph{Version 2} + + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-15} + \end{center} + + \subsubsection{Fazit} + \begin{itemize*} + \item \color{orange} leichtgewichtige Prozesse \color{black} als Baustein der Parallelisierung in Erlang + \item Prozesskommunikation ausschließlich über \color{orange} Message Passing \color{black} + \item \color{orange} funktionaler Charakter \color{black} (u.a. Vermeidung von Seiteneffekten) vereinfacht Parallelisierung deutlich + \item \color{orange} Daten- und Taskparallelität \color{black} möglich + \item hoher Abstraktionsgrad, aber auch wenig Einflussmöglichkeiten + \end{itemize*} + + \subsection{Parallele Programmierung in C++} + \subsubsection{Threads in C++} + \color{orange} Thread (Faden) \color{black} = leichtgewichtige Ausführungseinheit oder Kontrollfluss (Folge von Anweisungen) innerhalb eines sich in Ausführung befindlichen Programms + \begin{itemize*} + \item Threads teilen sich den Adressraum ihres Prozesses + \item in C++: Instanzen der Klasse std::thread + \item führen eine (initiale) Funktion aus + \end{itemize*} + \begin{lstlisting}[language=C++] + #include + #include -\paragraph{parallel-for in C++} -\begin{itemize*} - \item Unterstützung durch Higher-Level-APIs und Frameworks -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-062} -\end{center} + void say_hello() { + std::cout << "Hello Concurrent C++\n"; + } -\paragraph{Kontrolle der Anzahl der Threads} -\begin{itemize*} - \item Erzeugung von Threads ist mit Kosten verbunden - \item begrenzte Anzahl von Hardwarethreads (Anzahl Cores, Hyperthreading) - \item Ermittlung der Anzahl der unterstützten Hardwarethreads -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-063} -\end{center} -\begin{itemize*} - \item Nutzung für Implementierung von Threadpools, Task Libraries, … -\end{itemize*} + int main() { + std::thread t(say_hello); + t.join(); + } + \end{lstlisting} + + \paragraph{Alternative Erzeugung von Threads} + + \color{orange} über Lambda-Ausdruck \color{black} + \begin{lstlisting}[language=C++] + std::thread t([]() { do_something(); }); + \end{lstlisting} + + \color{orange} mit Instanzen einer Klasse \color{black} - erfordert Überladen von operator() + \begin{lstlisting}[language=C++] + struct my_task { + void operator()() const { do_something(); } + }; -\subsubsection{Probleme nebenläufiger Ausführung} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-064} -\end{center} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-065} -\end{center} -Ausgabe: -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-066} -\end{center} -\color{orange} Race Conditions \color{black}(Wettlaufsituationen) := Ergebnis nebenläufiger Ausführung auf gemeinsamen Zustand (hier: Ausgabekanal) hängt vom zeitlichen Verhalten der Einzeloperationen ab - - -\begin{itemize*} - \item Race Conditions (Wettlaufsituation) := Ergebnis nebenläufiger Ausführung auf gemeinsamen Zustand (hier: Ausgabekanal) hängt vom zeitlichen Verhalten der Einzeloperationen ab - \item kritischer Abschnitt: Programmabschnitt in einem Thread, in dem auf eine gemeinsame Ressource (Speicher etc.) zugegriffen wird und der nicht parallel (oder zeitlich verzahnt) zu einem anderen Thread ausgeführt werden darf - \item Lösung durch wechselseitigen Ausschluss (engl. mutual exclusion = mutex) + my_task tsk; + std::thread t1(tsk); // mit Objekt + std::thread t2{ my_task() }; // über Konstruktor + \end{lstlisting} + + \paragraph{Parameterübergabe bei Threaderzeugung} + + \begin{itemize*} + \item über zusätzliche Argumente des thread-Konstruktors + \item Vorsicht bei Übergabe von Referenzen, wenn Elternthread vor dem erzeugten Thread beendet wird + \end{itemize*} + \begin{lstlisting}[language=C++] + void fun(int n, const std::string\& s) { + for (auto i = 0; i < n; i++) + std::cout << s << " "; + std::cout << std::endl; + } + std::thread t(fun, 2, "Hello"); + t.join(); + \end{lstlisting} + + \paragraph{Warten auf Threads} + + \begin{itemize*} + \item t.join() wartet auf Beendigung des Threads t + \item blockiert aktuellen Thread + \item ohne join() keine Garantie, dass t zur Ausführung kommt + \item Freigabe der Ressourcen des Threads + \end{itemize*} + \begin{lstlisting}[language=C++] + std::thread t([]() { do_something(); }); + t.join(); + \end{lstlisting} + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-16} + \end{center} + + \paragraph{Hintergrundthreads} + + \begin{itemize*} + \item Threads können auch im Hintergrund laufen, ohne, dass auf Ende gewartet werden muss + \item "abkoppeln" durch detach() + \item Thread läuft danach unter Kontrolle des C++-Laufzeitsystems, join nicht mehr möglich + \end{itemize*} + + \paragraph{Threadidentifikation} + + \begin{itemize*} + \item Threadidentifikator vom Typ std::thread::id + \item Ermittlung über Methode get\_id() + \end{itemize*} + \begin{lstlisting}[language=C++] + void fun() { + std::cout << "Hello from " + << std::this_thread::get_id() + << std::endl; + } + std::thread t(fun); + t.join(); + \end{lstlisting} + + \paragraph{Beispiel: Berechnung von Fibonacci-Zahlen in C++} + + \begin{itemize*} + \item rekursive und nichtrekursive Variante möglich + \end{itemize*} + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-17} + \end{center} + + Parallele Berechnung von Fibonacci-Zahlen + \begin{itemize*} + \item einfachste Lösung (ähnlich zu Erlang): pro Zahl ein Thread + \end{itemize*} + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-18} + \end{center} + + Erläuterungen + \begin{itemize*} + \item Zeile 1: Feld der Threads + \item Zeile 2: Feld für Ergebniswerte + \item Zeile 5: Zufallszahl erzeugen + \item Zeilen 6-7 Thread zur Berechnung der Fibonacci-Zahl erzeugen und Ergebnis im Feld speichern + \item Zeile 10-11: Warten auf Beendigung der Threads (std::mem\_fn = Wrapper für Zeiger auf Member-Funktion) + \item \color{orange} aber: \color{black} + \begin{itemize*} + \item Zugriff auf gemeinsame Ressource (results)! + \item Anzahl Fibonaccizahlen = Anzahl Threads + \end{itemize*} + \end{itemize*} + + \paragraph{parallel-for in C++} + + \begin{itemize*} + \item Unterstützung durch Higher-Level-APIs und Frameworks + \end{itemize*} + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-19} + \end{center} + + \paragraph{Kontrolle der Anzahl der Threads} + + \begin{itemize*} + \item Erzeugung von Threads ist mit Kosten verbunden + \item begrenzte Anzahl von Hardwarethreads (Anzahl Cores, Hyperthreading) + \item Ermittlung der Anzahl der unterstützten Hardwarethreads + \end{itemize*} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-code-snippet-20} + \end{center} + \begin{itemize*} + \item Nutzung für Implementierung von Threadpools, Task Libraries, … + \end{itemize*} + + \subsubsection{Probleme nebenläufiger Ausführung} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-code-snippet-21} + \end{center} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-code-snippet-22} + \end{center} + Ausgabe: + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-code-snippet-23} + \end{center} + \color{orange} Race Conditions \color{black}(Wettlaufsituationen) := Ergebnis nebenläufiger Ausführung auf gemeinsamen Zustand (hier: Ausgabekanal) hängt vom zeitlichen Verhalten der Einzeloperationen ab + + + \begin{itemize*} + \item Race Conditions (Wettlaufsituation) := Ergebnis nebenläufiger Ausführung auf gemeinsamen Zustand (hier: Ausgabekanal) hängt vom zeitlichen Verhalten der Einzeloperationen ab + \item kritischer Abschnitt: Programmabschnitt in einem Thread, in dem auf eine gemeinsame Ressource (Speicher etc.) zugegriffen wird und der nicht parallel (oder zeitlich verzahnt) zu einem anderen Thread ausgeführt werden darf + \item Lösung durch wechselseitigen Ausschluss (engl. mutual exclusion = mutex) + \begin{itemize*} + \item Instanz der Klasse std::mutex + \item Methoden zum Sperren ( lock ) und Freigeben ( unlock ) + \item 'mutex' : Standard-Mutex für exklusiven Zugriff + \item 'timed\_mutex' : Mutex mit Timeout für Warten ( try\_lock\_for() ) + \item 'recursive\_mutex' : rekursives Mutex - erlaubt mehrfaches Sperren durch einen Thread, z.B. für rekursive Aufrufe + \item 'recursive\_timed\_mutex' : rekursives Mutex mit Timeout + \item 'shared\_mutex' : Mutex, das gemeinsamen Zugriff ( lock\_shared() ) mehrerer Threads oder exklusiven Zugriff ( lock() ) ermöglicht + \item 'shared\_timed\_mutex' : Mutex mit Timeout und gemeinsamen Zugriff + \end{itemize*} + \item Lock Guards + \begin{itemize*} + \item Vereinfachung der Nutzung von Mutexen durch RAII ("Ressourcenbelegung ist Initialisierung") + \item Konstruktor = lock + \item Destruktor = unlock + \item std::unique\_lock erweiterte Variante von lock\_guard, vermeidet aber sofortiges Sperren + \item std::lock : erlaubt gleichzeitiges deadlock-freies Sperren von 2 Mutexen + \item Sperrstrategien: u.a. + \begin{itemize*} + \item std::try\_to\_lock versucht Sperre ohne Blockierung zu setzen + \item std::adopt\_lock versucht nicht, ein zweites Mal zu sperren, wenn bereits durch den aktuellen Thread gesperrt + \end{itemize*} + \end{itemize*} + \end{itemize*} + + \subsubsection{Wechselseitiger Ausschluss} + \begin{itemize*} + \item \color{orange} kritischer Abschnitt\color{black}: Programmabschnitt in einem Thread, in dem auf eine gemeinsame Ressource (Speicher etc.) zugegriffen wird und der nicht parallel (oder zeitlich verzahnt) zu einem anderen Thread ausgeführt werden darf + \item Lösung durch \color{orange} wechselseitigen Ausschluss \color{black} (engl. mutual exclusion = mutex) + \end{itemize*} + + \paragraph{Mutex in C++} + \begin{itemize*} \item Instanz der Klasse std::mutex - \item Methoden zum Sperren ( lock ) und Freigeben ( unlock ) - \item 'mutex' : Standard-Mutex für exklusiven Zugriff - \item 'timed\_mutex' : Mutex mit Timeout für Warten ( try\_lock\_for() ) - \item 'recursive\_mutex' : rekursives Mutex - erlaubt mehrfaches Sperren durch einen Thread, z.B. für rekursive Aufrufe - \item 'recursive\_timed\_mutex' : rekursives Mutex mit Timeout - \item 'shared\_mutex' : Mutex, das gemeinsamen Zugriff ( lock\_shared() ) mehrerer Threads oder exklusiven Zugriff ( lock() ) ermöglicht - \item 'shared\_timed\_mutex' : Mutex mit Timeout und gemeinsamen Zugriff + \item Methoden zum Sperren (lock) und Freigeben (unlock) \end{itemize*} - \item Lock Guards + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-mutex-c} + \end{center} + + \paragraph{Mutex-Varianten} + + \begin{itemize*} + \item mutex: Standard-Mutex für exklusiven Zugriff + \item timed\_mutex: Mutex mit Timeout für Warten (try\_lock\_for()) + \item recursive\_mutex:rekursives Mutex - erlaubt mehrfaches Sperren durch einen Thread, z.B. für rekursive Aufrufe + \item recursive\_timed\_mutex: rekursives Mutex mit Timeout + \item shared\_mutex: Mutex, das gemeinsamen Zugriff (lock\_shared()) mehrerer Threads oder exklusiven Zugriff (lock()) ermöglicht + \item shared\_timed\_mutex: Mutex mit Timeout und gemeinsamen Zugriff + \end{itemize*} + + \paragraph{Lock Guards} + \begin{itemize*} \item Vereinfachung der Nutzung von Mutexen durch RAII ("Ressourcenbelegung ist Initialisierung") \item Konstruktor = lock \item Destruktor = unlock - \item std::unique\_lock erweiterte Variante von lock\_guard, vermeidet aber sofortiges Sperren - \item std::lock : erlaubt gleichzeitiges deadlock-freies Sperren von 2 Mutexen + \end{itemize*} + + \begin{lstlisting}[language=C++] + std::vector data; + std::mutex my_mtx; + + void add(int val) { + std::lock_guard guard(my_mtx); + data.push_back(val); + } + + int get() { + std::lock_guard guard(my_mtx); + return data.front(); + } + \end{lstlisting} + + \paragraph{Lock Gurads und Locks} + + \begin{itemize*} + \item std::unique\_lock erweiterte Variante von lock\_guards, vermeidet aber sofortiges Sperren + \item std::lock erlaubt gleichzeitiges deadlock-freies Sperren von 2 Mutexen \item Sperrstrategien: u.a. \begin{itemize*} \item std::try\_to\_lock versucht Sperre ohne Blockierung zu setzen \item std::adopt\_lock versucht nicht, ein zweites Mal zu sperren, wenn bereits durch den aktuellen Thread gesperrt \end{itemize*} \end{itemize*} -\end{itemize*} -\begin{lstlisting}[ -language=C++, -showspaces=false, -basicstyle=\ttfamily -] -std::vector data; -std::mutex my_mtx; - -void add(int val) { -std::lock_guard guard(my_mtx); -data.push_back(val); -} - -int get() { -std::lock_guard guard(my_mtx); -return data.front(); -} -\end{lstlisting} - - -\subsubsection{Wechselseitiger Ausschluss} -\begin{itemize*} - \item \color{orange} kritischer Abschnitt\color{black}: Programmabschnitt in einem Thread, in dem auf eine gemeinsame Ressource (Speicher etc.) zugegriffen wird und der nicht parallel (oder zeitlich verzahnt) zu einem anderen Thread ausgeführt werden darf - \item Lösung durch \color{orange} wechselseitigen Ausschluss \color{black} (engl. mutual exclusion = mutex) -\end{itemize*} - -\paragraph{Mutex in C++} -\begin{itemize*} - \item Instanz der Klasse std::mutex - \item Methoden zum Sperren (lock) und Freigeben (unlock) -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-067} -\end{center} - -\paragraph{Mutex-Varianten} -\begin{itemize*} - \item mutex: Standard-Mutex für exklusiven Zugriff - \item timed\_mutex: Mutex mit Timeout für Warten (try\_lock\_for()) - \item recursive\_mutex:rekursives Mutex - erlaubt mehrfaches Sperren durch einen Thread, z.B. für rekursive Aufrufe - \item recursive\_timed\_mutex: rekursives Mutex mit Timeout - \item shared\_mutex: Mutex, das gemeinsamen Zugriff (lock\_shared()) mehrerer Threads oder exklusiven Zugriff (lock()) ermöglicht - \item shared\_timed\_mutex: Mutex mit Timeout und gemeinsamen Zugriff -\end{itemize*} - -\paragraph{Lock Guards} -\begin{itemize*} - \item Vereinfachung der Nutzung von Mutexen durch RAII ("Ressourcenbelegung ist Initialisierung") - \item Konstruktor = lock - \item Destruktor = unlock -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-068} -\end{center} - -\paragraph{Lock Gurads und Locks} -\begin{itemize*} - \item std::unique\_lock erweiterte Variante von lock\_guards, vermeidet aber sofortiges Sperren - \item std::lock erlaubt gleichzeitiges deadlock-freies Sperren von 2 Mutexen - \item Sperrstrategien: u.a. + + \paragraph{Atomare Datentypen} + \begin{itemize*} - \item std::try\_to\_lock versucht Sperre ohne Blockierung zu setzen - \item std::adopt\_lock versucht nicht, ein zweites Mal zu sperren, wenn bereits durch den aktuellen Thread gesperrt + \item std::atomic\_flag = sperrfreier, atomarer Datentyp: + \begin{itemize*} + \item clear() setzt den Wert auf false + \item test\_and\_set() setzt den Wert atomar auf true und liefert den vorherigen Wert + \end{itemize*} + \item std::atomic = mächtigere Variante, erlaubt explizites Setzen + \begin{itemize*} + \item operator= atomare Wertzuweisung + \item load() liefert den aktuellen Wert + \item read-modify-write-Operation (siehe später) + \end{itemize*} + \item std::atomic = generische Variante für weitere Datentypen \end{itemize*} -\end{itemize*} - -\paragraph{Atomare Datentypen} -\begin{itemize*} - \item std::atomic\_flag = sperrfreier, atomarer Datentyp: + + + \paragraph{Synchronisation über atomare Variable} + + \begin{center} + \includegraphics[width=0.4\linewidth]{Assets/Programmierparadigmen-code-snippet-24} + \end{center} + Erläuterungen \begin{itemize*} - \item clear() setzt den Wert auf false - \item test\_and\_set() setzt den Wert atomar auf true und liefert den vorherigen Wert + \item Zeile 1: gemeinsam genutzte Liste - erfordert synchronisierten Zugriff + \item Zeile 2: atomare boolsche Variable ready + \item Zeile 4/12: Konsument/Produzent-Threads + \item Zeile 5: atomares prüfen der ready-Variablen + \item Zeile 6-7 kurz warten und neu versuchen + \item Zeile 8-9/13 Zugriff auf gemeinsame Liste + \item Zeile 14: atomares Setzen der Variablen ready \end{itemize*} - \item std::atomic = mächtigere Variante, erlaubt explizites Setzen + + \subsubsection{Taskparallelität: Die 5 speisenden Philosophen} \begin{itemize*} - \item operator= atomare Wertzuweisung - \item load() liefert den aktuellen Wert - \item read-modify-write-Operation (siehe später) + \item fünf Philosophen teilen sich eine Schüssel Sphagetti + \item fünf Gabeln, je eine zwischen zwei Philosophen + \item Philosoph kann nur mit zwei benachbarten Gabeln essen + \item Gabeln werden nur nach dem Essen zurückgelegt + \item Philosoph durchläuft Zyklus von Zuständen: denken $\rightarrow$ hungrig $\rightarrow$ essen $\rightarrow$ denken $\rightarrow$ etc. \end{itemize*} - \item std::atomic = generische Variante für weitere Datentypen -\end{itemize*} - - -\paragraph{Synchronisation über atomare Variable} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-069} -\end{center} -Erläuterungen -\begin{itemize*} - \item Zeile 1: gemeinsam genutzte Liste - erfordert synchronisierten Zugriff - \item Zeile 2: atomare boolsche Variable ready - \item Zeile 4/12: Konsument/Produzent-Threads - \item Zeile 5: atomares prüfen der ready-Variablen - \item Zeile 6-7 kurz warten und neu versuchen - \item Zeile 8-9/13 Zugriff auf gemeinsame Liste - \item Zeile 14: atomares Setzen der Variablen ready -\end{itemize*} - -\subsubsection{Taskparallelität: Die 5 speisenden Philosophen} -\begin{itemize*} - \item fünf Philosophen teilen sich eine Schüssel Sphagetti - \item fünf Gabeln, je eine zwischen zwei Philosophen - \item Philosoph kann nur mit zwei benachbarten Gabeln essen - \item Gabeln werden nur nach dem Essen zurückgelegt - \item Philosoph durchläuft Zyklus von Zuständen: denken $\rightarrow$ hungrig $\rightarrow$ essen $\rightarrow$ denken $\rightarrow$ etc. -\end{itemize*} - -\paragraph{Das Problem mit den Philosophen} -\begin{itemize*} - \item Jeder greift die linke Gabel - \item und wartet auf die rechte Gabel - \item … und wartet … -\end{itemize*} -\begin{center} - \includegraphics[width=0.3\linewidth]{Assets/Programmierparadigmen-070} -\end{center} -\color{orange} \textbf{Verklemmung!} \color{black} - -\paragraph{Lösungsidee} -\begin{itemize*} - \item immer beide Gabeln aufnehmen, dh. wenn nur eine Gabel verfügbar ist: liegen lassen und warten - \item synchronisierter Zugriff auf Gablen, dh. in einem kritischen Abschnitt unter gegenseitige Ausschluss - \item Wecken von wartenden Philosophen -\end{itemize*} - -\paragraph{Verklemmungsfreies Sperren} - -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily -] -std::lock(mtx1, mtx2); -std::lock_guard lk1(mtx1, std::adopt_lock); -std::lock_guard lk2(mtx2, std::adopt_lock); -\end{lstlisting} -Führt zu Verklemmung; Alternative Lösung -\begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily -] -std::unique_lock lk1(mtx1, std::defer_lock); -std::unique_lock lk2(mtx2, std::defer_lock); -std::lock(lk1, lk2); -\end{lstlisting} - -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-071} -\end{center} -Alternative Lösung -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-072} -\end{center} - -\paragraph{Gabeln und Spaghetti-Teller} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-073} -\end{center} - -\paragraph{Die Philosophen-Klasse} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-074} -\end{center} - -\paragraph{Die Philosophen-Klasse: Hilfsmethoden} -Textausgabe erfordert synchronisierten Zugriff auf cout über globalen Mutex -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-075} -\end{center} \ \\ -Hilfsmethode für zufällige Wartezeit in Millisekunden -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-076} -\end{center} - -\paragraph{Die Philosophen-Klasse: Essen} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-077} -\end{center} - -\paragraph{Die Philosophen-Klasse: Denken} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-078} -\end{center} - -\paragraph{Das Leben eines Philosophen} -\begin{itemize*} - \item Zur Erinnerung: überladener ()-Operator eines Objekts definiert auszuführende Funktion eines Threads -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-079} -\end{center} - -\paragraph{Das Dinner: Initialisierung} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-080} -\end{center} - -\paragraph{Das Dinner beginnt} -\begin{itemize*} - \item Beginn (und Ende) des Dinners über atomare Variable signalisieren - \item Philosophen-Threads arbeiten ihre operator()()-Methode ab -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-081} -\end{center} - -\paragraph{Fazit} -\begin{itemize*} - \item Philosophenproblem: klassisches Problem der Informatik zur Demonstration von Nebenläufigkeit und Verklemmung - \item von Edsger W. Dijkstra formuliert - \item betrachte C++ Lösung illustriert + + \paragraph{Das Problem mit den Philosophen} + \begin{itemize*} - \item Nebenläufigkeit durch Threads - \item Synchronisation über Mutexe - \item verklemmungsfreies Sperren + \item Jeder greift die linke Gabel + \item und wartet auf die rechte Gabel + \item … und wartet … \end{itemize*} - \item moderene C++ Sprachversion vereinfacht Programmierung gegenüber Low-Level-API auf Betriebssystemebene (z.B. pthreads) -\end{itemize*} - -\subsubsection{Weitere Möglichkeiten der Thread-Interaktion} -\begin{itemize*} - \item bisher: + \begin{center} + \includegraphics[width=0.3\linewidth]{Assets/Programmierparadigmen-philosophen} + \end{center} + \color{orange} \textbf{Verklemmung!} \color{black} + + \paragraph{Lösungsidee} + \begin{itemize*} - \item Mutexe und Locks - \item atomare Variablen + \item immer beide Gabeln aufnehmen, dh. wenn nur eine Gabel verfügbar ist: liegen lassen und warten + \item synchronisierter Zugriff auf Gablen, dh. in einem kritischen Abschnitt unter gegenseitige Ausschluss + \item Wecken von wartenden Philosophen \end{itemize*} - \item typischer Anwendungsfall: Warten auf Ereignis / Setzen eines Flags -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-082} -\end{center} + + \paragraph{Verklemmungsfreies Sperren} + + \begin{lstlisting}[language=C++] + std::lock(mtx1, mtx2); + std::lock_guard lk1(mtx1, std::adopt_lock); + std::lock_guard lk2(mtx2, std::adopt_lock); + \end{lstlisting} + Führt zu Verklemmung; Alternative Lösung + \begin{lstlisting}[language=C++] + std::unique_lock lk1(mtx1, std::defer_lock); + std::unique_lock lk2(mtx2, std::defer_lock); + std::lock(lk1, lk2); + \end{lstlisting} + + \paragraph{Gabeln und Spaghetti-Teller} + + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-073} + \end{center} + + \paragraph{Die Philosophen-Klasse} + + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-074} + \end{center} + + \paragraph{Die Philosophen-Klasse: Hilfsmethoden} + + Textausgabe erfordert synchronisierten Zugriff auf cout über globalen Mutex + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-075} + \end{center} -\subsubsection{Bedingungsvariablen} -\begin{itemize*} - \item Thread wartet, bis Bedingung erfüllt ist - \item Erfüllung der Bedingung wird durch anderen Thread angezeigt (notify) $\rightarrowtail$ "Aufwecken" des wartenden Threads - \item notwendig: synchronisierter Zugriff über Mutex -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-083} -\end{center} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-084} -\end{center} - -\subsubsection{Thread-sichere Datenstrukturen} -\begin{itemize*} - \item Thread-Sicherheit := eine Komponente kann gleichzeitig von verschiedenen Programmbereichen (Threads) mehrfach ausgeführt werden, ohne dass diese sich gegenseitig behindern - \item verschiedene Varianten: + Hilfsmethode für zufällige Wartezeit in Millisekunden + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-076} + \end{center} + + \paragraph{Die Philosophen-Klasse: Essen} + + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-077} + \end{center} + + \paragraph{Die Philosophen-Klasse: Denken} + + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-078} + \end{center} + + \paragraph{Das Leben eines Philosophen} + \begin{itemize*} - \item Standard-Datenstruktur + über Mutexe/Sperren synchronisierte Zugriffe - \item Integration der Sperren in die Datenstruktur - \item Sperr-freie Datenstrukturen: nicht-blockierend, Vermeidung von Sperren, z.B. durch Compare/Exchange-Operationen + \item Zur Erinnerung: überladener ()-Operator eines Objekts definiert auszuführende Funktion eines Threads \end{itemize*} - \item async , future und promise - \item std::future - Resultat einer asynchronen Berechnung, d.h. einer Berechnung die erst noch stattfindet - \item std::async() - asynchrones Starten eines Tasks - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-079} + \end{center} + + \paragraph{Das Dinner: Initialisierung} + + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-080} + \end{center} + + \paragraph{Das Dinner beginnt} + + \begin{itemize*} + \item Beginn (und Ende) des Dinners über atomare Variable signalisieren + \item Philosophen-Threads arbeiten ihre operator()()-Methode ab + \end{itemize*} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-081} + \end{center} + + \paragraph{Fazit} + + \begin{itemize*} + \item Philosophenproblem: klassisches Problem der Informatik zur Demonstration von Nebenläufigkeit und Verklemmung + \item von Edsger W. Dijkstra formuliert + \item betrachte C++ Lösung illustriert + \begin{itemize*} + \item Nebenläufigkeit durch Threads + \item Synchronisation über Mutexe + \item verklemmungsfreies Sperren + \end{itemize*} + \item moderene C++ Sprachversion vereinfacht Programmierung gegenüber Low-Level-API auf Betriebssystemebene (z.B. pthreads) + \end{itemize*} + + \subsubsection{Weitere Möglichkeiten der Thread-Interaktion} + \begin{itemize*} + \item bisher: + \begin{itemize*} + \item Mutexe und Locks + \item atomare Variablen + \end{itemize*} + \item typischer Anwendungsfall: Warten auf Ereignis / Setzen eines Flags + \end{itemize*} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-082} + \end{center} + + \subsubsection{Bedingungsvariablen} + \begin{itemize*} + \item Thread wartet, bis Bedingung erfüllt ist + \item Erfüllung der Bedingung wird durch anderen Thread angezeigt (notify) $\rightarrowtail$ "Aufwecken" des wartenden Threads + \item notwendig: synchronisierter Zugriff über Mutex + \end{itemize*} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-083} + \end{center} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-084} + \end{center} + + \subsubsection{Thread-sichere Datenstrukturen} + \begin{itemize*} + \item Thread-Sicherheit := eine Komponente kann gleichzeitig von verschiedenen Programmbereichen (Threads) mehrfach ausgeführt werden, ohne dass diese sich gegenseitig behindern + \item verschiedene Varianten: + \begin{itemize*} + \item Standard-Datenstruktur + über Mutexe/Sperren synchronisierte Zugriffe + \item Integration der Sperren in die Datenstruktur + \item Sperr-freie Datenstrukturen: nicht-blockierend, Vermeidung von Sperren, z.B. durch Compare/Exchange-Operationen + \end{itemize*} + \item async , future und promise + \item std::future - Resultat einer asynchronen Berechnung, d.h. einer Berechnung die erst noch stattfindet + \item std::async() - asynchrones Starten eines Tasks + \begin{lstlisting}[language=C++] int long_calculation() { ... } std::future result = std::async(long_calculation); // Fortsetzung der Berechnung ... result.wait(); std::cout << result.get() << std::endl; \end{lstlisting} - \item std::promise - erlaubt Wert zu setzen, wenn der aktuelle Thread beendet ist; oft in Kombination mit std::future eingesetzt - \item future = Ergebnisobjekt, promise = Ergebnisproduzent - \begin{itemize*} - \item Warten auf Ende des Tasks (wait(), wait\_for()) - \item Ergebnis lesen (get()) + \item std::promise - erlaubt Wert zu setzen, wenn der aktuelle Thread beendet ist; oft in Kombination mit std::future eingesetzt + \item future = Ergebnisobjekt, promise = Ergebnisproduzent + \begin{itemize*} + \item Warten auf Ende des Tasks (wait(), wait\_for()) + \item Ergebnis lesen (get()) + \end{itemize*} \end{itemize*} -\end{itemize*} - - -\subsubsection{Anforderungen} -\begin{itemize*} - \item mehrere Threads können gleichzeitig auf die Datenstruktur zugreifen - \item kein Thread sieht (Zwischen-)Zustand, bei dem Invarianten der Datenstruktur durch einen anderen Thread (kurzzeitig) verletzt ist - \item Vermeidung von Wettlaufsituationen - \item Vermeidung von Verklemmungen - \item korrekte Behandlung von Ausnahmen (Fehlern) -\end{itemize*} - -\subsubsection{Thread-sichere Queue} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-085} -\end{center} -\begin{itemize*} - \item Zeilen 1,2,6: Kapselung der std::queue-Klasse - \item Zeile 4: Mutex für exklusiven Zugriff - \item Zeile 5: Bedingungsvariable für Warten -\end{itemize*} - -\paragraph{Thread-sichere Queue: Methode push} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-086} -\end{center} -\begin{itemize*} - \item Zeile 2: Lock Guard sichert exklusiven Zugriff - \item Zeile 3: Element an die Queue anhängen - \item Zeile 4: Aufwecken von eventuell wartenden Threads -\end{itemize*} - -\paragraph{Thread-sichere Queue: Methode waiting\_pop} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-087} -\end{center} -\begin{itemize*} - \item Zeile 2: Lock Guard sichert exklusiven Zugriff - \item Zeile 3: Warten bis Queue nicht mehr leer ist - \item Zeilen 4,5: erstes Element aus der Queue entnehmen -\end{itemize*} - -\subsubsection{async, future und promise} -\begin{itemize*} - \item std::future - Resultat einer asynchronen Berechnung, d.h. einer Berechnung die erst noch stattfindet - \item std::async() - asynchrones Starten eines Tasks + + + \subsubsection{Anforderungen} + \begin{itemize*} + \item mehrere Threads können gleichzeitig auf die Datenstruktur zugreifen + \item kein Thread sieht (Zwischen-)Zustand, bei dem Invarianten der Datenstruktur durch einen anderen Thread (kurzzeitig) verletzt ist + \item Vermeidung von Wettlaufsituationen + \item Vermeidung von Verklemmungen + \item korrekte Behandlung von Ausnahmen (Fehlern) + \end{itemize*} + + \subsubsection{Thread-sichere Queue} \begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-088} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-085} \end{center} - \item std::promise - erlaubt Wert zu setzen, wenn der aktuelle Thread beendet ist, of in Kombination mit std::future eingesetzt - \item future = Ergbenisobjekt, promise = Ergebnisproduzent -\end{itemize*} - -\paragraph{Future} -\begin{itemize*} - \item Methoden zum \begin{itemize*} - \item Warten auf das Ende des Tasks (wait(), wait\_for()) - \item Ergebnis lesen (get()) + \item Zeilen 1,2,6: Kapselung der std::queue-Klasse + \item Zeile 4: Mutex für exklusiven Zugriff + \item Zeile 5: Bedingungsvariable für Warten \end{itemize*} -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-089} -\end{center} - -\paragraph{Beispiel} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-090} -\end{center} - -\subsubsection{Deklarative Parallelisierung mit OpenMP} -\begin{itemize*} - \item Programmierschnittstelle für Parallelisierung in C/C++/Fortran - \item Programmiersprachenerweiterung durch Direktiven - \item in C/C++: \#pragma omp … - \item zusätzliche Bibliotheksfunktionen: \#include - \item aktuelle Version 5.0 - \item Unterstützung in gcc und clang + + \paragraph{Thread-sichere Queue: Methode push} + + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-086} + \end{center} \begin{itemize*} - \item vollständig 4.5, partiell 5.0 - \item Nutzung über Compilerflag - fopenmp + \item Zeile 2: Lock Guard sichert exklusiven Zugriff + \item Zeile 3: Element an die Queue anhängen + \item Zeile 4: Aufwecken von eventuell wartenden Threads \end{itemize*} - \item beschränkt auf Architekturen mit gemeinsamen Speicher -\end{itemize*} - -\subsubsection{Programmiermodell} -\begin{itemize*} - \item Master-Thread und mehrere Worker-Threads (Anzahl typischerweise durch OpenMP-Laufzeitsystem bestimmt) - \item über parallel-Direktive kann Arbeit in einem Programmabschnitt auf Worker-Threads aufgeteilt werden - \item Ende des parallelen Abschnitts $\rightarrowtail$ implizite Synchronisation - \item Fortsetzung des Master-Threads -\end{itemize*} -\begin{center} - \includegraphics[width=0.2\linewidth]{Assets/Programmierparadigmen-091} -\end{center} - - -\begin{itemize*} - \item Master-Thread und mehrere Worker-Threads (Anzahl typischerweise durch OpenMP-Laufzeitsystem bestimmt) - \item über parallel -Direktive kann Arbeit in einem Programmabschnitt auf Worker-Threads aufgeteilt werden - \item Ende des parallelen Abschnitts $\rightarrow$ implizite Synchronisation $\rightarrow$ Fortsetzung des Master-Threads - \item der dem 'pragma' folgende Block wird parallel von allen Threads ausgeführt - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] + + \paragraph{Thread-sichere Queue: Methode waiting\_pop} + + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-087} + \end{center} + \begin{itemize*} + \item Zeile 2: Lock Guard sichert exklusiven Zugriff + \item Zeile 3: Warten bis Queue nicht mehr leer ist + \item Zeilen 4,5: erstes Element aus der Queue entnehmen + \end{itemize*} + + \subsubsection{async, future und promise} + \begin{itemize*} + \item std::future - Resultat einer asynchronen Berechnung, d.h. einer Berechnung die erst noch stattfindet + \item std::async() - asynchrones Starten eines Tasks + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-088} + \end{center} + \item std::promise - erlaubt Wert zu setzen, wenn der aktuelle Thread beendet ist, of in Kombination mit std::future eingesetzt + \item future = Ergbenisobjekt, promise = Ergebnisproduzent + \end{itemize*} + + \paragraph{Future} + + \begin{itemize*} + \item Methoden zum + \begin{itemize*} + \item Warten auf das Ende des Tasks (wait(), wait\_for()) + \item Ergebnis lesen (get()) + \end{itemize*} + \end{itemize*} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-089} + \end{center} + + \paragraph{Beispiel} + + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-090} + \end{center} + + \subsubsection{Deklarative Parallelisierung mit OpenMP} + \begin{itemize*} + \item Programmierschnittstelle für Parallelisierung in C/C++/Fortran + \item Programmiersprachenerweiterung durch Direktiven + \item in C/C++: \#pragma omp … + \item zusätzliche Bibliotheksfunktionen: \#include + \item aktuelle Version 5.0 + \item Unterstützung in gcc und clang + \begin{itemize*} + \item vollständig 4.5, partiell 5.0 + \item Nutzung über Compilerflag - fopenmp + \end{itemize*} + \item beschränkt auf Architekturen mit gemeinsamen Speicher + \end{itemize*} + + \subsubsection{Programmiermodell} + \begin{itemize*} + \item Master-Thread und mehrere Worker-Threads (Anzahl typischerweise durch OpenMP-Laufzeitsystem bestimmt) + \item über parallel-Direktive kann Arbeit in einem Programmabschnitt auf Worker-Threads aufgeteilt werden + \item Ende des parallelen Abschnitts $\rightarrowtail$ implizite Synchronisation + \item Fortsetzung des Master-Threads + \end{itemize*} + \begin{center} + \includegraphics[width=0.2\linewidth]{Assets/Programmierparadigmen-091} + \end{center} + + + \begin{itemize*} + \item Master-Thread und mehrere Worker-Threads (Anzahl typischerweise durch OpenMP-Laufzeitsystem bestimmt) + \item über parallel -Direktive kann Arbeit in einem Programmabschnitt auf Worker-Threads aufgeteilt werden + \item Ende des parallelen Abschnitts $\rightarrow$ implizite Synchronisation $\rightarrow$ Fortsetzung des Master-Threads + \item der dem 'pragma' folgende Block wird parallel von allen Threads ausgeführt + \begin{lstlisting}[language=C++] \#include \#include int main() { @@ -4823,60 +4127,52 @@ Hilfsmethode für zufällige Wartezeit in Millisekunden return 0; } \end{lstlisting} - \item Schleifenparallelisierung: jedem Thread wird ein Teil der Iteration zugewiesen (beeinflusst nur äußere Schleife) - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] + \item Schleifenparallelisierung: jedem Thread wird ein Teil der Iteration zugewiesen (beeinflusst nur äußere Schleife) + \begin{lstlisting}[language=C++] ... \#pragma omp parallel for for (int i = 0; i < 20; i++) {... \end{lstlisting} - \begin{itemize*} - \item collapse(n) gibt an, dass n Schleifen in einem gemeinsamen Iterationsbereich zusammengefasst und auf die Threads verteilt werden sollen - \begin{lstlisting} + \begin{itemize*} + \item collapse(n) gibt an, dass n Schleifen in einem gemeinsamen Iterationsbereich zusammengefasst und auf die Threads verteilt werden sollen + \begin{lstlisting} #pragma omp parallel for collapse(3) \end{lstlisting} - \end{itemize*} - \item Beeinflussung der Thread Anzahl - \begin{itemize*} - \item maximale Anzahl: - \begin{lstlisting} + \end{itemize*} + \item Beeinflussung der Thread Anzahl + \begin{itemize*} + \item maximale Anzahl: + \begin{lstlisting} #pragma omp parallel for num_threads(8) \end{lstlisting} - \item bedingte Parallelisierung: - \begin{lstlisting} + \item bedingte Parallelisierung: + \begin{lstlisting} #pragma omp parallel for if(i>50) \end{lstlisting} - \end{itemize*} - \item Aufteilung des Iterationsbereichs; Beeinflussung durch schedule -Direktive - \begin{itemize*} - \item schedule(auto): Default - implementierungsspezifisch - \item schedule(static, n): statische Round-Robin-Verteilung - Bereiche der Größe n (Angabe von n ist optional) - \item schedule(dynamic, n): dynamische Verteilung nach Bedarf - \item schedule(guided, n): Verteilung nach Bedarf und proportional zur Restarbeit - \end{itemize*} - \item Direktiven für parallele Ausführung - \begin{itemize*} - \item '\#pragma omp single/master' Abschnitt wird nur durch einen/den Master-Thread ausgeführt - \item '\#pragma omp critical' kritischer Abschnitt - \item '\#pragma omp barrier' Warten auf alle Worker-Threads - \item '\#pragma omp atomic' kritischer Abschnitt \item Zugriff auf gemeinsame Variable (z.B. Zähler) - \end{itemize*} - \item Speicherklauseln für Variablen - \begin{itemize*} - \item 'shared' für alle Threads sichtbar/änderbar - \item 'private' jeder Thread hat eigene Kopie der Daten, wird nicht außerhalb initialisiert - \item 'reduction' private Daten, die am Ende des Abschnitts zu globalem Wert zusammengefasst werden - \item 'firstprivate / lastprivate' privat - initialisiert mit letztem Wert vor dem Abschnitt / Wert des letzten Threads der Iteration wird zurückgegeben - \end{itemize*} - \item zuweisung von Programmabschnitten zu Threads $\rightarrow$ statische Parallelität (geeignet für rekursive Abschnitte) - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] + \end{itemize*} + \item Aufteilung des Iterationsbereichs; Beeinflussung durch schedule -Direktive + \begin{itemize*} + \item schedule(auto): Default - implementierungsspezifisch + \item schedule(static, n): statische Round-Robin-Verteilung - Bereiche der Größe n (Angabe von n ist optional) + \item schedule(dynamic, n): dynamische Verteilung nach Bedarf + \item schedule(guided, n): Verteilung nach Bedarf und proportional zur Restarbeit + \end{itemize*} + \item Direktiven für parallele Ausführung + \begin{itemize*} + \item '\#pragma omp single/master' Abschnitt wird nur durch einen/den Master-Thread ausgeführt + \item '\#pragma omp critical' kritischer Abschnitt + \item '\#pragma omp barrier' Warten auf alle Worker-Threads + \item '\#pragma omp atomic' kritischer Abschnitt \item Zugriff auf gemeinsame Variable (z.B. Zähler) + \end{itemize*} + \item Speicherklauseln für Variablen + \begin{itemize*} + \item 'shared' für alle Threads sichtbar/änderbar + \item 'private' jeder Thread hat eigene Kopie der Daten, wird nicht außerhalb initialisiert + \item 'reduction' private Daten, die am Ende des Abschnitts zu globalem Wert zusammengefasst werden + \item 'firstprivate / lastprivate' privat - initialisiert mit letztem Wert vor dem Abschnitt / Wert des letzten Threads der Iteration wird zurückgegeben + \end{itemize*} + \item zuweisung von Programmabschnitten zu Threads $\rightarrow$ statische Parallelität (geeignet für rekursive Abschnitte) + \begin{lstlisting}[language=C++] \#pragma omp parallel sections { \#pragma omp section @@ -4885,17 +4181,13 @@ Hilfsmethode für zufällige Wartezeit in Millisekunden qsort(data, p + 1, right); } \end{lstlisting} - \item Task Programmierung - \begin{itemize*} - \item reihum Threads zugewiesen werden - \item an beliebiger Stelle definiert werden können - \item von beliebigem Thread definiert werden kann - \end{itemize*} - \begin{lstlisting}[ - language=C++, - showspaces=false, - basicstyle=\ttfamily - ] + \item Task Programmierung + \begin{itemize*} + \item reihum Threads zugewiesen werden + \item an beliebiger Stelle definiert werden können + \item von beliebigem Thread definiert werden kann + \end{itemize*} + \begin{lstlisting}[language=C++] unsigned int f1, f2; \#pragma omp task shared(f1) f1 = fib(f \item 1); @@ -4904,111 +4196,111 @@ Hilfsmethode für zufällige Wartezeit in Millisekunden \#pragma omp taskwait return f1 + f2; \end{lstlisting} -\end{itemize*} - -\subsubsection{Hello World! mit OpenMP} -\begin{itemize*} - \item der dem pragma folgende Block wird parallel von allen Threads ausgeführt -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-092} -\end{center} - -\subsubsection{Schleifenparallelisierung} -\begin{itemize*} - \item parallele Ausführung einer Schleife: jedem Thread wird ein Teil der Iterationen zugewiesen - \item für for-Schleifgen mit eingeschränkter Syntax (ganzzahlige Schleifenvariablen, Operatoren auf Schleifenvariablen) und für STL-Iteratoren -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-093} -\end{center} -\subsubsection{Beeinflussung der Thread-Anzahl} -maximale Anzahl -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-094} -\end{center} -\noindent -bedingte Parallelisierung -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-095} -\end{center} - -\subsubsection{Aufteilung des Iterationsbereichs} -\begin{itemize*} - \item Iterationsbereich kann auf verschiedene Weise auf Threads aufgeteilt werden - \item Beeinflussung durch schedule-Direktive - \begin{itemize*} - \item schedule(auto): Default - implementierungsspezifisch - \item schedule(static,n): statische Round-Robin-Verteilung - Bereiche der Größe n (Angabe von n ist optional) - \item schedule(dynamic, n): dynamische Verteilung nach Bedarf - \item schedule(guided, n): Verteilung nach Bedarf und proportional zur Restarbeit - \item … \end{itemize*} -\end{itemize*} - -\subsubsection{Geschachtelte Schleifen} -\begin{itemize*} - \item Parallelisierung mit \textbf{parallel for} beeinflusst nur äußere Schleife - \item collapse(n) gibt an, dass n Schleifen in einem gemeinsamen Iterationsbereich zusammengefasst, und auf die Threads verteilt werden sollen - \item Beispiel: Matrizenmultiplikation -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-096} -\end{center} - -\subsubsection{Synchronisation} -\begin{itemize*} - \item Direktiven für parallele Ausführung + + \subsubsection{Hello World! mit OpenMP} \begin{itemize*} - \item \textbf{\#pragma omp single/master} Abschnitt wird nur durch einen/den Master-Thread ausgeführt - \item \textbf{\#pragma omp critical} kritischer Abschnitt - \item \textbf{\#pragma omp barrier} Warten auf alle Worker-Threads - \item \textbf{\#pragma omp atomic} kritischer Abschnitt - ZUgriff auf gemeinsame Variable (z.B. Zähler) + \item der dem pragma folgende Block wird parallel von allen Threads ausgeführt \end{itemize*} - \item Speicherklauseln für Variablen + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-092} + \end{center} + + \subsubsection{Schleifenparallelisierung} \begin{itemize*} - \item \textbf{shared} für alle Threads sichtbar/änderbar - \item \textbf{private} jeder Thread hat eigene Kopie der Daten, wird nicht außerhalb initialisiert - \item \textbf{reduction} private Daten, die am Ende des Abschnitts zu globalem Wert zusammengefasst werden - \item \textbf{firstprivate/lastprivate} privat - initialisiert mit letztem Wert vor dem Abschnitt / Wert des letzten Threads der Iteration wird zurückgegeben + \item parallele Ausführung einer Schleife: jedem Thread wird ein Teil der Iterationen zugewiesen + \item für for-Schleifgen mit eingeschränkter Syntax (ganzzahlige Schleifenvariablen, Operatoren auf Schleifenvariablen) und für STL-Iteratoren \end{itemize*} -\end{itemize*} - -\subsubsection{Parallele Abschnitte} -\begin{itemize*} - \item Zuweisung von Programmabschnitten zu Threads $\rightarrowtail$ statische Parallelität - \item geeignet z.B. für rekursive Aufrufe -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-097} -\end{center} - -\subsubsection{Task-Programmierung mit OpenMP} -\begin{itemize*} - \item seit OpenMP 3.0 Unterstützung von Tasks, die + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-093} + \end{center} + \subsubsection{Beeinflussung der Thread-Anzahl} + maximale Anzahl + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-094} + \end{center} + \noindent + bedingte Parallelisierung + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-095} + \end{center} + + \subsubsection{Aufteilung des Iterationsbereichs} \begin{itemize*} - \item reihum Threads zugewiesen werden - \item an beliebiger Stelle definiert werden können - \item von beliebigem Thread definiert werden kann + \item Iterationsbereich kann auf verschiedene Weise auf Threads aufgeteilt werden + \item Beeinflussung durch schedule-Direktive + \begin{itemize*} + \item schedule(auto): Default - implementierungsspezifisch + \item schedule(static,n): statische Round-Robin-Verteilung - Bereiche der Größe n (Angabe von n ist optional) + \item schedule(dynamic, n): dynamische Verteilung nach Bedarf + \item schedule(guided, n): Verteilung nach Bedarf und proportional zur Restarbeit + \item … + \end{itemize*} \end{itemize*} -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-098} -\end{center} - -\subsubsection{Fazit} -\begin{itemize*} - \item C++ bietet weitreichende und mächtige Konzepte zur Parallelisierung + + \subsubsection{Geschachtelte Schleifen} \begin{itemize*} - \item von Basiskontrolle wie Threads und Synchronisationsprimitiven (u.a. Mutexe) - \item …über höherwertige Abstraktionen wie async, Features und Promises - \item bis hin zu deklarativen Ansätzen wie OpenMP + \item Parallelisierung mit \textbf{parallel for} beeinflusst nur äußere Schleife + \item collapse(n) gibt an, dass n Schleifen in einem gemeinsamen Iterationsbereich zusammengefasst, und auf die Threads verteilt werden sollen + \item Beispiel: Matrizenmultiplikation \end{itemize*} - \item alle Formen von Parallelität (Instruktions-, Daten-, und Taskparallelität) möglich - \item aber anspruchsvolle Programmierung - \item erleichtert durch zusätzliche Bibliotheken und Frameworks wie Parallel STL, TBB, … -\end{itemize*} -\begin{lstlisting}[ + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-096} + \end{center} + + \subsubsection{Synchronisation} + \begin{itemize*} + \item Direktiven für parallele Ausführung + \begin{itemize*} + \item \textbf{\#pragma omp single/master} Abschnitt wird nur durch einen/den Master-Thread ausgeführt + \item \textbf{\#pragma omp critical} kritischer Abschnitt + \item \textbf{\#pragma omp barrier} Warten auf alle Worker-Threads + \item \textbf{\#pragma omp atomic} kritischer Abschnitt - ZUgriff auf gemeinsame Variable (z.B. Zähler) + \end{itemize*} + \item Speicherklauseln für Variablen + \begin{itemize*} + \item \textbf{shared} für alle Threads sichtbar/änderbar + \item \textbf{private} jeder Thread hat eigene Kopie der Daten, wird nicht außerhalb initialisiert + \item \textbf{reduction} private Daten, die am Ende des Abschnitts zu globalem Wert zusammengefasst werden + \item \textbf{firstprivate/lastprivate} privat - initialisiert mit letztem Wert vor dem Abschnitt / Wert des letzten Threads der Iteration wird zurückgegeben + \end{itemize*} + \end{itemize*} + + \subsubsection{Parallele Abschnitte} + \begin{itemize*} + \item Zuweisung von Programmabschnitten zu Threads $\rightarrowtail$ statische Parallelität + \item geeignet z.B. für rekursive Aufrufe + \end{itemize*} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-097} + \end{center} + + \subsubsection{Task-Programmierung mit OpenMP} + \begin{itemize*} + \item seit OpenMP 3.0 Unterstützung von Tasks, die + \begin{itemize*} + \item reihum Threads zugewiesen werden + \item an beliebiger Stelle definiert werden können + \item von beliebigem Thread definiert werden kann + \end{itemize*} + \end{itemize*} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-098} + \end{center} + + \subsubsection{Fazit} + \begin{itemize*} + \item C++ bietet weitreichende und mächtige Konzepte zur Parallelisierung + \begin{itemize*} + \item von Basiskontrolle wie Threads und Synchronisationsprimitiven (u.a. Mutexe) + \item …über höherwertige Abstraktionen wie async, Features und Promises + \item bis hin zu deklarativen Ansätzen wie OpenMP + \end{itemize*} + \item alle Formen von Parallelität (Instruktions-, Daten-, und Taskparallelität) möglich + \item aber anspruchsvolle Programmierung + \item erleichtert durch zusätzliche Bibliotheken und Frameworks wie Parallel STL, TBB, … + \end{itemize*} + \begin{lstlisting}[ language=java, showspaces=false, basicstyle=\ttfamily @@ -5031,13 +4323,13 @@ public class Hello { public static void main(String[] args) { Thread t = new Thread(new Heartbeat(2)); //Thread Objekt mit runnable erzeugen - t.start(); //methode start() aufrufen -> ruft run() auf + t.start(); //methode start() aufrufen $\rightarrow$ ruft run() auf } } \end{lstlisting} -\hfill - -\begin{lstlisting}[ + \hfill + + \begin{lstlisting}[ language=C++, showspaces=false, basicstyle=\ttfamily @@ -5075,9 +4367,9 @@ int main(int argc, char* argv[]){ return 0; } \end{lstlisting} -\hfill - -\begin{lstlisting}[ + \hfill + + \begin{lstlisting}[ language=erlang, showspaces=false, basicstyle=\ttfamily @@ -5092,71 +4384,68 @@ basicstyle=\ttfamily %% Variables begin with an upper-case letter %% Start defining a function with the most specific case first -countdown(0) -> +countdown(0) $\rightarrow$ io:format("Zero!~n"); % function clauses end with a semicolon %% Another clause of the same function, with a guard expression -countdown(Bogus) when Bogus < 0 -> +countdown(Bogus) when Bogus < 0 $\rightarrow$ io:format("Bad value: ~B~n", [Bogus]), % normal lines end with a comma error; % return value (io:format returns 'ok') %% Last clause matches any single parameter -countdown(Start) -> +countdown(Start) $\rightarrow$ %% case and if statements return values! Type = case Start rem 2 of - 1 -> "odd"; % case and if clauses end with semicolons - 0 -> "even" % except the last one + 1 $\rightarrow$ "odd"; % case and if clauses end with semicolons + 0 $\rightarrow$ "even" % except the last one end, % end with comma, like a normal line io:format("~B is ~s~n", [Start, Type]), countdown(Start - 1). % When the function is all done, end with a period %% This is a different function because it has a different number of parameters. -countdown() -> +countdown() $\rightarrow$ countdown(10). \end{lstlisting} - - -\subsection{Parallele Programmierung in Java} -Unterstützung durch -\begin{itemize*} - \item Thread-Konzept - \item eingebaute Mechanismen zur Synchronisation nebenläufiger Prozesse - \item spezielle High-Level-Klassen im Package - \newline \textbf{java.util.concurrent} -\end{itemize*} - -\subsubsection{Threads in Java} -\begin{itemize*} - \item Repräsentiert durch Klasse \textbf{java.lang.Thread} - \item Implementierung eines eigenen Kontrollflusses - \item Eigene Klasse muss Runnable implementieren + + + \subsection{Parallele Programmierung in Java} + Unterstützung durch \begin{itemize*} - \item Implementierung des Interface \textbf{java.lang.Runnable} + \item Thread-Konzept + \item eingebaute Mechanismen zur Synchronisation nebenläufiger Prozesse + \item spezielle High-Level-Klassen im Package + \newline \textbf{java.util.concurrent} + \end{itemize*} + + \subsubsection{Threads in Java} + \begin{itemize*} + \item Repräsentiert durch Klasse \textbf{java.lang.Thread} + \item Implementierung eines eigenen Kontrollflusses + \item Eigene Klasse muss Runnable implementieren \begin{itemize*} - \item keine weitere Beeinflussung des Threads über zusätzliche Methoden notwendig - \item soll von anderer Klasse als Thread abgeleitet werden - \end{itemize*} - \item Subklasse von \textbf{java.lang.Thread} - \begin{itemize*} - \item zusätzliche Methoden zur Steuerung des Ablaufs benötigt - \item keine andere Superklasse notwendig + \item Implementierung des Interface \textbf{java.lang.Runnable} + \begin{itemize*} + \item keine weitere Beeinflussung des Threads über zusätzliche Methoden notwendig + \item soll von anderer Klasse als Thread abgeleitet werden + \end{itemize*} + \item Subklasse von \textbf{java.lang.Thread} + \begin{itemize*} + \item zusätzliche Methoden zur Steuerung des Ablaufs benötigt + \item keine andere Superklasse notwendig + \end{itemize*} \end{itemize*} \end{itemize*} -\end{itemize*} - -\paragraph{Threads: Runnable-Schnittstelle} -Eigene Klasse muss \textbf{Runnable} implementieren -\begin{itemize*} - \item Methode \textbf{public void run()} - wird beim Start des Threads aufgerufen -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-099} -\end{center} -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily -] + + \paragraph{Threads: Runnable-Schnittstelle} + Eigene Klasse muss \textbf{Runnable} implementieren + \begin{itemize*} + \item Methode \textbf{public void run()} - wird beim Start des Threads aufgerufen + \end{itemize*} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-099} + \end{center} + \begin{lstlisting}[ + language=java] public class Heartbeat implements Runnable { int pulse; public Heartbeat(int p) { pulse = p * 1000; } @@ -5174,167 +4463,167 @@ Eigene Klasse muss \textbf{Runnable} implementieren t.start(); //methode start() aufrufen $\rightarrow$ ruft run() auf } \end{lstlisting} - -\paragraph{Thread-Erzeugung} -\begin{itemize*} - \item Thread-Objekt mit Runnable-Objekt erzeugen - \item Methode \textbf{start()} aufrufen + + \paragraph{Thread-Erzeugung} + \begin{itemize*} - \item Ruft \textbf{run()} auf - \end{itemize*} -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-100} -\end{center} - -\paragraph{Subklasse von Thread} -\begin{itemize*} - \item Klasse muss von Thread abgeleitet werden - \item Methode run() muss überschrieben werden -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-101} -\end{center} - -\begin{itemize*} - \item Objekt der eigenen Thread-Klasse erzeugen - \item Methode \textbf{start()} aufrufen - \begin{itemize*} - \item Ruft \textbf{run()} auf + \item Thread-Objekt mit Runnable-Objekt erzeugen + \item Methode \textbf{start()} aufrufen + \begin{itemize*} + \item Ruft \textbf{run()} auf + \end{itemize*} \end{itemize*} \begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-102} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-100} \end{center} - \item Spätere Beeinflussung durch andere Threads möglich + + \paragraph{Subklasse von Thread} + + \begin{itemize*} + \item Klasse muss von Thread abgeleitet werden + \item Methode run() muss überschrieben werden + \end{itemize*} \begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-103} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-101} \end{center} -\end{itemize*} - - -\paragraph{Threads: Wichtige Methoden} -\begin{itemize*} - \item void start(): initiiert Ausführung des Threads durch Aufruf der Methode run - \item void run(): die eigentliche Arbeitsmethode - \item static void sleep(int millis): hält die Ausführung des aktuellen Threads für 'millis' Millisekunden an; Keinen Einfluss auf andere Threads! - \item void join(): blockiert den aufrufenden Thread so lange, bis der aufgerufene Thread beendet ist -\end{itemize*} - -\begin{itemize*} - \item \textbf{void start()} + \begin{itemize*} - \item initiiert Ausführung des Threads durch Aufruf der Methode run + \item Objekt der eigenen Thread-Klasse erzeugen + \item Methode \textbf{start()} aufrufen + \begin{itemize*} + \item Ruft \textbf{run()} auf + \end{itemize*} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-102} + \end{center} + \item Spätere Beeinflussung durch andere Threads möglich + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-103} + \end{center} \end{itemize*} - \item \textbf{void run()} + + + \paragraph{Threads: Wichtige Methoden} + \begin{itemize*} - \item die eigentliche Arbeitsmethode + \item void start(): initiiert Ausführung des Threads durch Aufruf der Methode run + \item void run(): die eigentliche Arbeitsmethode + \item static void sleep(int millis): hält die Ausführung des aktuellen Threads für 'millis' Millisekunden an; Keinen Einfluss auf andere Threads! + \item void join(): blockiert den aufrufenden Thread so lange, bis der aufgerufene Thread beendet ist \end{itemize*} - \item \textbf{static void sleep(int millisec)} + \begin{itemize*} - \item hält die Ausführung des aktuellen Threads für millisec Millisekunden an - \item Hat keinen Einfluss auf andere Threads! + \item \textbf{void start()} + \begin{itemize*} + \item initiiert Ausführung des Threads durch Aufruf der Methode run + \end{itemize*} + \item \textbf{void run()} + \begin{itemize*} + \item die eigentliche Arbeitsmethode + \end{itemize*} + \item \textbf{static void sleep(int millisec)} + \begin{itemize*} + \item hält die Ausführung des aktuellen Threads für millisec Millisekunden an + \item Hat keinen Einfluss auf andere Threads! + \end{itemize*} + \item \textbf{void join()} + \begin{itemize*} + \item blockiert den aufrufenden Thread so lange, bis der aufgerufene Thread beendet ist + \end{itemize*} \end{itemize*} - \item \textbf{void join()} + + \subsubsection{Parallele Berechnung von Fibonacci-Zahlen} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-104} + \end{center} + Thread-Erzeugung und Ausführung + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-105} + \end{center} + + \subsubsection{Wechselseitiger Ausschluss in Java} + Schlüsselwort \textbf{synchronized} \begin{itemize*} - \item blockiert den aufrufenden Thread so lange, bis der aufgerufene Thread beendet ist - \end{itemize*} -\end{itemize*} - -\subsubsection{Parallele Berechnung von Fibonacci-Zahlen} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-104} -\end{center} -Thread-Erzeugung und Ausführung -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-105} -\end{center} - -\subsubsection{Wechselseitiger Ausschluss in Java} -Schlüsselwort \textbf{synchronized} -\begin{itemize*} - \item Implementierung von sogenannten Monitoren bzw. locks (exklusiven Sperren) - \begin{itemize*} - \item nur ein Thread darf den kritischen Abschnitt betreten - \item alle anderen Threads, die darauf zugrifen wollen, müssen auf Freigabe warten - \end{itemize*} - \item für Methoden: \textbf{public synchronized void doSomething()} - \begin{itemize*} - \item nur ein Thread darf diese Methode auf einem Objekt zur gleichen Zeit ausführen - \end{itemize*} - \item für Anweisungen: \textbf{synchronized(anObject)\{…\}} - \begin{itemize*} - \item nur ein Thread darf den Block betreten - \item Sperre wird durch das Objekt \textbf{anObject} verwaltet (jedem Java-Objekt ist eine Sperre zugeordnet) - \end{itemize*} -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-106} -\end{center} -\begin{itemize*} - \item Schlüsselwort synchronized - \begin{itemize*} - \item Implementierung von sogenannten Monitoren bzw. locks (exklusiven Sperren); nur ein Thread darf den kritischen Abschnitt betreten; alle anderen Threads, die darauf zugreifen wollen, müssen auf Freigabe warten - \item für Methoden: - \begin{lstlisting} - public synchronized void doSomething() - \end{lstlisting} + \item Implementierung von sogenannten Monitoren bzw. locks (exklusiven Sperren) + \begin{itemize*} + \item nur ein Thread darf den kritischen Abschnitt betreten + \item alle anderen Threads, die darauf zugrifen wollen, müssen auf Freigabe warten + \end{itemize*} + \item für Methoden: \textbf{public synchronized void doSomething()} \begin{itemize*} \item nur ein Thread darf diese Methode auf einem Objekt zur gleichen Zeit ausführen \end{itemize*} - \item für Anweisungen: synchronized(anObject) { ... } + \item für Anweisungen: \textbf{synchronized(anObject)\{…\}} \begin{itemize*} \item nur ein Thread darf den Block betreten - \item Sperre wird durch das Objekt anObject verwaltet (jedem Java-Objekt ist ein Sperre zugeordnet) + \item Sperre wird durch das Objekt \textbf{anObject} verwaltet (jedem Java-Objekt ist eine Sperre zugeordnet) \end{itemize*} \end{itemize*} -\end{itemize*} - -\subsubsection{wait \& notify} -\begin{itemize*} - \item Signalisierung zwischen Threads in Java - \item Basismethoden der Klasse \textbf{java.lang.Object} - \item \textbf{wait()}: der aktive Thread wartet an diesem Objekt, Sperren werden ggf. freigegeben. - \item \textbf{notify()}: wekct an diesem Objekt wartenden Thread auf - \item \textbf{notifyAll()}: weckt alle an diesem Objekt wartenden Threads auf - \item \textbf{wait() \& notify()} dürfen nur in einem \textbf{synchronized}-Block aufgerufen werden -\end{itemize*} - -\begin{itemize*} - \item Signalisierung zwischen Threads in Java - \item Basismethoden der Klasse java.lang.Object - \item wait() : der aktive Thread wartet an diesem Objekt, Sperren werden ggf. freigegeben! - \item notify() : weckt an diesem Objekt wartenden Thread auf - \item notifyAll() : weckt alle an diesem Objekt wartenden Threads auf - \item wait() \& notify() dürfen nur in einem synchronized -Block aufgerufen werden -\end{itemize*} - -\subsubsection{Java: High-Level-Klassen} -\begin{itemize*} - \item Paket \textbf{java.util.concurrent} seit Java Version 1.5 - \item Abstraktionsschicht versteckt Details über Thread-Erzeugung - \item Übernimmt Erstellung und Überwachung von parallelen Tasks, u.a. + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-106} + \end{center} \begin{itemize*} - \item \textbf{ExecutorService} zum erzeugen asynchroner Tasks - \item \textbf{Future}: Referenz auf diesen Task bzw. dessen Ergebnis - \item \textbf{ForkJoinPool \& RecursiveAction}: rekursives Aufteilen eines großen Problems + \item Schlüsselwort synchronized + \begin{itemize*} + \item Implementierung von sogenannten Monitoren bzw. locks (exklusiven Sperren); nur ein Thread darf den kritischen Abschnitt betreten; alle anderen Threads, die darauf zugreifen wollen, müssen auf Freigabe warten + \item für Methoden: + \begin{lstlisting} + public synchronized void doSomething() + \end{lstlisting} + \begin{itemize*} + \item nur ein Thread darf diese Methode auf einem Objekt zur gleichen Zeit ausführen + \end{itemize*} + \item für Anweisungen: synchronized(anObject) { ... } + \begin{itemize*} + \item nur ein Thread darf den Block betreten + \item Sperre wird durch das Objekt anObject verwaltet (jedem Java-Objekt ist ein Sperre zugeordnet) + \end{itemize*} + \end{itemize*} \end{itemize*} -\end{itemize*} - -\subsubsection{Tasks und Futures in Java} -\begin{itemize*} - \item Task = logische Ausführungseinheit - \item Thread = Mechanismus zur asynchronen/parallelen Ausführung von Tasks -\end{itemize*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-107} -\end{center} -\begin{lstlisting}[ - language=java, - showspaces=false, - basicstyle=\ttfamily -] + + \subsubsection{wait \& notify} + \begin{itemize*} + \item Signalisierung zwischen Threads in Java + \item Basismethoden der Klasse \textbf{java.lang.Object} + \item \textbf{wait()}: der aktive Thread wartet an diesem Objekt, Sperren werden ggf. freigegeben. + \item \textbf{notify()}: wekct an diesem Objekt wartenden Thread auf + \item \textbf{notifyAll()}: weckt alle an diesem Objekt wartenden Threads auf + \item \textbf{wait() \& notify()} dürfen nur in einem \textbf{synchronized}-Block aufgerufen werden + \end{itemize*} + + \begin{itemize*} + \item Signalisierung zwischen Threads in Java + \item Basismethoden der Klasse java.lang.Object + \item wait() : der aktive Thread wartet an diesem Objekt, Sperren werden ggf. freigegeben! + \item notify() : weckt an diesem Objekt wartenden Thread auf + \item notifyAll() : weckt alle an diesem Objekt wartenden Threads auf + \item wait() \& notify() dürfen nur in einem synchronized -Block aufgerufen werden + \end{itemize*} + + \subsubsection{Java: High-Level-Klassen} + \begin{itemize*} + \item Paket \textbf{java.util.concurrent} seit Java Version 1.5 + \item Abstraktionsschicht versteckt Details über Thread-Erzeugung + \item Übernimmt Erstellung und Überwachung von parallelen Tasks, u.a. + \begin{itemize*} + \item \textbf{ExecutorService} zum erzeugen asynchroner Tasks + \item \textbf{Future}: Referenz auf diesen Task bzw. dessen Ergebnis + \item \textbf{ForkJoinPool \& RecursiveAction}: rekursives Aufteilen eines großen Problems + \end{itemize*} + \end{itemize*} + + \subsubsection{Tasks und Futures in Java} + \begin{itemize*} + \item Task = logische Ausführungseinheit + \item Thread = Mechanismus zur asynchronen/parallelen Ausführung von Tasks + \end{itemize*} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-107} + \end{center} + \begin{lstlisting}[ + language=java] Runnable task = () $\rightarrow$ { String me = Thread.currentThread().getName(); System.out.println("Hallo " + me); @@ -5343,282 +4632,283 @@ task.run(); Thread thread = new Thread(task); thread.start(); \end{lstlisting} - -\subsubsection{Future \& ExecutorService} -\begin{itemize*} - \item \textbf{ExecutorService} stellt Methoden zum Starten/Beenden/Steuern von parallelen Aufgaben bereit - \item implementiert \textbf{Executor}-Interface + + \subsubsection{Future \& ExecutorService} \begin{itemize*} - \item definiert Methode \textbf{void execute(Runnable r)} + \item \textbf{ExecutorService} stellt Methoden zum Starten/Beenden/Steuern von parallelen Aufgaben bereit + \item implementiert \textbf{Executor}-Interface + \begin{itemize*} + \item definiert Methode \textbf{void execute(Runnable r)} + \end{itemize*} + \item Starten einer Aufgabe mit \textbf{submit} + \begin{itemize*} + \item \textbf{Future submit(Callable c)} + \item \textbf{Future submit(Runnable r)} + \end{itemize*} + \item Zugriff auf das Ergebnis mit \textbf{get} + \begin{itemize*} + \item \textbf{T get(long timeout, TimeUnit unit)} + \item \textbf{T get()} + \end{itemize*} \end{itemize*} - \item Starten einer Aufgabe mit \textbf{submit} + + \paragraph{Future \& ExecutorService: Beispiel} + + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-108} + \end{center} + + \subsubsection{RecursiveAction \& Fork/Join} \begin{itemize*} - \item \textbf{Future submit(Callable c)} - \item \textbf{Future submit(Runnable r)} + \item Rekursives Zerlegen eines großen Problems in kleinere Probleme + \item Solange bis Problem klein genug um direkt ausgeführt werden zu können + \item Task erstellt zwei oder mehr Teiltasks von sich selbst $\rightarrowtail$ Datenparallelität + \item ForkJoinPool zum Ausführen $\rightarrow$ implementiert Executor Interface + \item \textbf{ForkJoinPool} zum Ausführen + \begin{itemize*} + \item implementiert \textbf{Executor} Interface + \end{itemize*} + \item Fazit + \begin{itemize*} + \item Parallelprogrammierung in Java sehr ähnlich zu C++ + \item Konzepte: Threads, kritische Abschnitte über synchronized + \item mächtige Abstraktionen in java.util.concurrent + \begin{itemize*} + \item Tasks und Futures, Executor und ThreadPool + \item thread-sichere Datenstrukturen + \item Synchronisation: Barrieren, Semaphoren, ... + \end{itemize*} + \end{itemize*} \end{itemize*} - \item Zugriff auf das Ergebnis mit \textbf{get} - \begin{itemize*} - \item \textbf{T get(long timeout, TimeUnit unit)} - \item \textbf{T get()} - \end{itemize*} -\end{itemize*} - -\paragraph{Future \& ExecutorService: Beispiel} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-108} -\end{center} - -\subsubsection{RecursiveAction \& Fork/Join} -\begin{itemize*} - \item Rekursives Zerlegen eines großen Problems in kleinere Probleme - \item Solange bis Problem klein genug um direkt ausgeführt werden zu können - \item Task erstellt zwei oder mehr Teiltasks von sich selbst $\rightarrowtail$ Datenparallelität - \item ForkJoinPool zum Ausführen $\rightarrow$ implementiert Executor Interface - \item \textbf{ForkJoinPool} zum Ausführen - \begin{itemize*} - \item implementiert \textbf{Executor} Interface - \end{itemize*} - \item Fazit + + \paragraph{Beispiel} + + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-109} + \end{center} + Starten der Verarbeitung: + \begin{enumerate*} + \item (große) Gesamtaufgabe erstellen + \item ForkJoinPool erstellen + \item Aufgabe vom Pool ausführen lassen + \end{enumerate*} + \begin{center} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-110} + \end{center} + + \subsubsection{Fazit} \begin{itemize*} \item Parallelprogrammierung in Java sehr ähnlich zu C++ - \item Konzepte: Threads, kritische Abschnitte über synchronized - \item mächtige Abstraktionen in java.util.concurrent + \item Konzepte: Threads, kritische Abschnitte über \textbf{synchronized} + \item mächtige Abstraktionen in \textbf{java.util.concurrent} \begin{itemize*} - \item Tasks und Futures, Executor und ThreadPool + \item Tasks und Futures, Executor und Threadpool \item thread-sichere Datenstrukturen - \item Synchronisation: Barrieren, Semaphoren, ... + \item Synchronisation: Barrieren, Semaphoren,… \end{itemize*} \end{itemize*} -\end{itemize*} - -\paragraph{Beispiel} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-109} -\end{center} -Starten der Verarbeitung: -\begin{enumerate*} - \item (große) Gesamtaufgabe erstellen - \item ForkJoinPool erstellen - \item Aufgabe vom Pool ausführen lassen -\end{enumerate*} -\begin{center} - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-110} -\end{center} - -\subsubsection{Fazit} -\begin{itemize*} - \item Parallelprogrammierung in Java sehr ähnlich zu C++ - \item Konzepte: Threads, kritische Abschnitte über \textbf{synchronized} - \item mächtige Abstraktionen in \textbf{java.util.concurrent} + + \subsection{Zusammenfassung} \begin{itemize*} - \item Tasks und Futures, Executor und Threadpool - \item thread-sichere Datenstrukturen - \item Synchronisation: Barrieren, Semaphoren,… + \item Parallelprogrammierung als wichtige Technik zur Nutzung moderner Hardware (Multicore, GPU, …) + \item verschiedene Architekturen und Programmiermodelle + \item Instruktions-, Daten- und Taskparallelität + \item Message Passing vs. gemeinsamer Speicher + \item Konzepte in Erlang, C++, Java + \item hoher Abstraktionsgrad funktionaler Sprachen + \item C++/Java: Thread-Modell und Synchronisation mit vielen weiteren Konzepten + \item höherwertige Abstraktion durch zusätzliche Bibliotheken und Programmierschnittstellen \end{itemize*} -\end{itemize*} - -\subsection{Zusammenfassung} -\begin{itemize*} - \item Parallelprogrammierung als wichtige Technik zur Nutzung moderner Hardware (Multicore, GPU, …) - \item verschiedene Architekturen und Programmiermodelle - \item Instruktions-, Daten- und Taskparallelität - \item Message Passing vs. gemeinsamer Speicher - \item Konzepte in Erlang, C++, Java - \item hoher Abstraktionsgrad funktionaler Sprachen - \item C++/Java: Thread-Modell und Synchronisation mit vielen weiteren Konzepten - \item höherwertige Abstraktion durch zusätzliche Bibliotheken und Programmierschnittstellen -\end{itemize*} - -\section{Verteilte Programmierung} - -\paragraph{Aktormodell} -\begin{itemize*} - \item formales Modell für Nebenläufigkeit und Verteilung - \item Basis für verschiedene Programmiersprachen/Frameworks: Erlang, Akka (Scala/Java) - \item Prinzipien: + + \newpage + \section{Verteilte Programmierung} + + \paragraph{Aktormodell} + \begin{itemize*} - \item Aktor kapselt Zustand und Verhalten - \item Aktoren sind aktiv - \item Aktoren kommunizieren durch Nachrichtenaustausch + \item formales Modell für Nebenläufigkeit und Verteilung + \item Basis für verschiedene Programmiersprachen/Frameworks: Erlang, Akka (Scala/Java) + \item Prinzipien: \begin{itemize*} - \item Nichtblockierendes Senden - \item Blockierendes Empfangen + \item Aktor kapselt Zustand und Verhalten + \item Aktoren sind aktiv + \item Aktoren kommunizieren durch Nachrichtenaustausch + \begin{itemize*} + \item Nichtblockierendes Senden + \item Blockierendes Empfangen + \end{itemize*} \end{itemize*} \end{itemize*} -\end{itemize*} - -Aktormodell in Erlang -\begin{itemize*} - \item Aktormodell in Erlang nativ umgesetzt + + Aktormodell in Erlang \begin{itemize*} - \item Sende- und Empfangsoperationen schon für parallele Programmierung benutzt - \item bisher aber nur auf einem Knoten + \item Aktormodell in Erlang nativ umgesetzt + \begin{itemize*} + \item Sende- und Empfangsoperationen schon für parallele Programmierung benutzt + \item bisher aber nur auf einem Knoten + \end{itemize*} + \item Programmbestandteile im Aktormodell + \begin{itemize*} + \item Verhaltensdefinition $\Rightarrow$ f() $\rightarrow$ ... end. + \item Erzeugen neuer Aktoren $\Rightarrow$ Pid = spawn(fun ... ) . + \item Empfangen von Nachrichten $\Rightarrow$ receive ... end . + \item Senden $\Rightarrow$ Pid ! Request . + \end{itemize*} + \item kein globaler Zustand \end{itemize*} - \item Programmbestandteile im Aktormodell + + Cookie-System \begin{itemize*} - \item Verhaltensdefinition $\Rightarrow$ f() $\rightarrow$ ... end. - \item Erzeugen neuer Aktoren $\Rightarrow$ Pid = spawn(fun ... ) . - \item Empfangen von Nachrichten $\Rightarrow$ receive ... end . - \item Senden $\Rightarrow$ Pid ! Request . - \end{itemize*} - \item kein globaler Zustand -\end{itemize*} - -Cookie-System -\begin{itemize*} - \item erteilte Erlang-Knoten benötigen zur Kommunikation gemeinsames Magic Cookie (Passwort) - \item Mehrere Varianten - \begin{itemize*} - \item Datei \~/.erlang.cookie - \item Erlang-Funktion - \begin{lstlisting}[ + \item erteilte Erlang-Knoten benötigen zur Kommunikation gemeinsames Magic Cookie (Passwort) + \item Mehrere Varianten + \begin{itemize*} + \item Datei \~/.erlang.cookie + \item Erlang-Funktion + \begin{lstlisting}[ language=erlang, - showspaces=false, - basicstyle=\ttfamily ]:set_cookie(node(), Cookie). \end{lstlisting} - \item Option - \begin{lstlisting} + \item Option + \begin{lstlisting} erl -setcookie Cookie \end{lstlisting} - \end{itemize*} - \item Verbindungsaufbau mittels Funktion - \begin{lstlisting} + \end{itemize*} + \item Verbindungsaufbau mittels Funktion + \begin{lstlisting} net_adm:ping(adress) \end{lstlisting} -\end{itemize*} - -Das Alternating Bit Protokoll - Übersicht -\begin{itemize*} - \item ermöglicht es, Nachrichten über einen verlustbehafteten Kommunikationskanal vollständig zu übertragen, sofern Verluste nur gelegentlich auftreten (transiente Fehler) - \item Empfänger quittiert jedes erhaltene Paket (Ackknowledgement, kurz: Ack) - \item Achtung: Kanal kann Nachrichten und Acks verlieren - \begin{itemize*} - \item $\Rightarrow$ benötigen je zwei unterschiedliche Sequenznummern und Acks \end{itemize*} - \item Empfänger liefert eine Nachricht nur beim ersten Empfang aus (keine Duplikate) - \item bei Timeout: Nachricht erneut senden - \item bei Erhalt eines unerwarteten Ack: aktuelle Nachricht erneut senden -\end{itemize*} - -\subsection{Grundlagen} -\subsubsection{Lernziele} -\begin{itemize*} - \item Verständnis von Techniken verteilter Programmierung als Paradigma + + Das Alternating Bit Protokoll - Übersicht \begin{itemize*} - \item Modelle und Konzepte unabhängig von Programmiersprache und Betriebssystem - \item Herausforderungen und Besonderheiten verteilter Programme + \item ermöglicht es, Nachrichten über einen verlustbehafteten Kommunikationskanal vollständig zu übertragen, sofern Verluste nur gelegentlich auftreten (transiente Fehler) + \item Empfänger quittiert jedes erhaltene Paket (Ackknowledgement, kurz: Ack) + \item Achtung: Kanal kann Nachrichten und Acks verlieren + \begin{itemize*} + \item $\Rightarrow$ benötigen je zwei unterschiedliche Sequenznummern und Acks + \end{itemize*} + \item Empfänger liefert eine Nachricht nur beim ersten Empfang aus (keine Duplikate) + \item bei Timeout: Nachricht erneut senden + \item bei Erhalt eines unerwarteten Ack: aktuelle Nachricht erneut senden \end{itemize*} - \item Kennenlernen konkreter Konzepte und Mechanismen + + \subsection{Grundlagen} + \subsubsection{Lernziele} \begin{itemize*} - \item praktische Beispiele in Java, Erlang und C++ - \item Bewertung und Vergleich verschiedener Plattformen + \item Verständnis von Techniken verteilter Programmierung als Paradigma + \begin{itemize*} + \item Modelle und Konzepte unabhängig von Programmiersprache und Betriebssystem + \item Herausforderungen und Besonderheiten verteilter Programme + \end{itemize*} + \item Kennenlernen konkreter Konzepte und Mechanismen + \begin{itemize*} + \item praktische Beispiele in Java, Erlang und C++ + \item Bewertung und Vergleich verschiedener Plattformen + \end{itemize*} \end{itemize*} -\end{itemize*} - -\subsubsection{Einordnung} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-001} -\end{center} -\begin{itemize*} - \item mehrere Rechner - \item Prozesse auf verschiedenen Rechnern - \item Kommunikation über Knotengrenzen hinweg - \item Behandlung von Knoten- oder Netzwerkausfällen -\end{itemize*} - -\subsubsection{Ziele} -\begin{itemize*} - \item Bisher: - \begin{itemize*} - \item eine Maschine - \item Prozesse kommunizieren nur innerhalb dieser Maschine (shared Memory vs. Message Passing) - \end{itemize*} - \item Jetzt: + + \subsubsection{Einordnung} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-001} + \end{center} \begin{itemize*} \item mehrere Rechner \item Prozesse auf verschiedenen Rechnern - \end{itemize*} - \item Erfordert: - \begin{itemize*} \item Kommunikation über Knotengrenzen hinweg \item Behandlung von Knoten- oder Netzwerkausfällen \end{itemize*} -\end{itemize*} - -\subsubsection{Motivation} -\begin{itemize*} - \item viele verschiedene Systeme (Knoten) zur Verfügung + + \subsubsection{Ziele} \begin{itemize*} - \item PC, Server, virtuelle Maschinen - \item Lastverteilung, Spezialisierung auf bestimmte Probleme + \item Bisher: + \begin{itemize*} + \item eine Maschine + \item Prozesse kommunizieren nur innerhalb dieser Maschine (shared Memory vs. Message Passing) + \end{itemize*} + \item Jetzt: + \begin{itemize*} + \item mehrere Rechner + \item Prozesse auf verschiedenen Rechnern + \end{itemize*} + \item Erfordert: + \begin{itemize*} + \item Kommunikation über Knotengrenzen hinweg + \item Behandlung von Knoten- oder Netzwerkausfällen + \end{itemize*} \end{itemize*} - \item Knoten sind über Netzwerke verbunden + + \subsubsection{Motivation} \begin{itemize*} - \item LAN(Wohnräume, Büros,…): bis zu 10 Gbit/s - \item MAN(Metropolitan Area Network, Behördennetze, dicht besiedelte Regionen): bis zu 10 Gbit/s - \item WAN(Wide Area Network, weltweite Vernetzung): hohe Kapazitäten zwischen den ISPs + \item viele verschiedene Systeme (Knoten) zur Verfügung + \begin{itemize*} + \item PC, Server, virtuelle Maschinen + \item Lastverteilung, Spezialisierung auf bestimmte Probleme + \end{itemize*} + \item Knoten sind über Netzwerke verbunden + \begin{itemize*} + \item LAN(Wohnräume, Büros,…): bis zu 10 Gbit/s + \item MAN(Metropolitan Area Network, Behördennetze, dicht besiedelte Regionen): bis zu 10 Gbit/s + \item WAN(Wide Area Network, weltweite Vernetzung): hohe Kapazitäten zwischen den ISPs + \end{itemize*} \end{itemize*} -\end{itemize*} - -Wofür werden verteilte Systeme eingesetzt? -\begin{itemize*} - \item Gemeinsame Nutzung von Ressourcen + + Wofür werden verteilte Systeme eingesetzt? \begin{itemize*} - \item Cloud-Umgebungen - \item verteilte Datenbanksysteme + \item Gemeinsame Nutzung von Ressourcen + \begin{itemize*} + \item Cloud-Umgebungen + \item verteilte Datenbanksysteme + \end{itemize*} + \item Teilaufgaben in großen Anwendungen + \begin{itemize*} + \item parallele Ausführung + \item getrennte Teilaufgaben (Micro-Services) + \end{itemize*} + \item Informationsaustausch + \begin{itemize*} + \item Email, Messenger + \item verteilte Algorithmen + \end{itemize*} \end{itemize*} - \item Teilaufgaben in großen Anwendungen + + \subsubsection{Software Architekturen} + \begin{enumerate*} + \item Früher: Hardware, Betriebssystem, Anwendung + \begin{itemize*} + \item Virtualisierung von Prozessor, Speicher, E/A Systemen + \item Interprozesskommunikation (IPC) + \end{itemize*} + \item Middlewaresysteme: Hardware, OS, Middleware, Anwendung + \begin{itemize*} + \item verteilte Dienste + \item Programmierparadigmen: RPC, Client/Server,… + \item Java, CORBA, … + \end{itemize*} + \item Heute: Virtualisierung + \begin{itemize*} + \item VM Hypervisor: verstecken Hardware vor dem Betriebssystem + \item Docker: eine Anwendung pro Container + \end{itemize*} + \end{enumerate*} + + \subsubsection{Herausforderungen} \begin{itemize*} - \item parallele Ausführung - \item getrennte Teilaufgaben (Micro-Services) + \item viele verschiedene Computer/Server + \begin{itemize*} + \item verschiedene Betriebssysteme + \item unterschiedliche Leistungsfähigkeit + \end{itemize*} + \item Systemkomponenten müssen miteinander kommunizieren + \item verteilte Algorithmen: Nachrichten senden, empfangen, bestätigen, Synchronisation + \item Knotenausfälle behandeln \end{itemize*} - \item Informationsaustausch - \begin{itemize*} - \item Email, Messenger - \item verteilte Algorithmen - \end{itemize*} -\end{itemize*} - -\subsubsection{Software Architekturen} -\begin{enumerate*} - \item Früher: Hardware, Betriebssystem, Anwendung - \begin{itemize*} - \item Virtualisierung von Prozessor, Speicher, E/A Systemen - \item Interprozesskommunikation (IPC) - \end{itemize*} - \item Middlewaresysteme: Hardware, OS, Middleware, Anwendung - \begin{itemize*} - \item verteilte Dienste - \item Programmierparadigmen: RPC, Client/Server,… - \item Java, CORBA, … - \end{itemize*} - \item Heute: Virtualisierung - \begin{itemize*} - \item VM Hypervisor: verstecken Hardware vor dem Betriebssystem - \item Docker: eine Anwendung pro Container - \end{itemize*} -\end{enumerate*} - -\subsubsection{Herausforderungen} -\begin{itemize*} - \item viele verschiedene Computer/Server - \begin{itemize*} - \item verschiedene Betriebssysteme - \item unterschiedliche Leistungsfähigkeit - \end{itemize*} - \item Systemkomponenten müssen miteinander kommunizieren - \item verteilte Algorithmen: Nachrichten senden, empfangen, bestätigen, Synchronisation - \item Knotenausfälle behandeln -\end{itemize*} -\color{orange} $\Rightarrow$ brauchen Modelle zur Beschreibung der Kommunikation \color{black} - -\subsubsection{Anforderungen} -\color{orange} Anforderungen an Kommunikationsmodelle in … \color{black} -\newline -… verteilten Systemen\newline \newline -\begin{minipage}[h]{0.5\linewidth} + \color{orange} $\Rightarrow$ brauchen Modelle zur Beschreibung der Kommunikation \color{black} + + \subsubsection{Anforderungen} + \color{orange} Anforderungen an Kommunikationsmodelle in … \color{black} + \newline + … verteilten Systemen\newline \newline \begin{itemize*} \item Korrektheit \item Sicherheit @@ -5626,422 +4916,456 @@ Wofür werden verteilte Systeme eingesetzt? \item Skalierbarkeit \item Heterogenität \end{itemize*} -\end{minipage} -\begin{minipage}[h]{0.4\linewidth} - \includegraphics[width=1.0\linewidth]{Assets/Programmierparadigmen-002} -\end{minipage} - -…verteilten Verkehrsmanagementsystemen\newline \newline -\begin{minipage}[h]{0.5\linewidth} + + …verteilten Verkehrsmanagementsystemen\newline \newline \begin{itemize*} \item Echtzeitfähigkeit \item Offenheit \item Korrektheit, \newline Sicherheit \item Skalierbarkeit, \newline Verfügbarkeit \end{itemize*} -\end{minipage} -\begin{minipage}[h]{0.4\linewidth} - \includegraphics[width=1.0\linewidth]{Assets/Programmierparadigmen-003} -\end{minipage} -\newline \newline \newline \newline -\color{orange} Anforderungen \color{black} an den Betrieb eines (großen) verteilten Systems -\begin{itemize*} - \item (Last-)Skalierbarkeit (Scale-out): + + \color{orange} Anforderungen \color{black} an den Betrieb eines (großen) verteilten Systems \begin{itemize*} - \item viele kleine Server - statt eines großen - \item neue Server nach Bedarf hinzuzufügen - \end{itemize*} - \item Funktionssicherheit (Safety) / IT-Sicherheit (Security) - \item Fehlertoleranz / Verfügbarkeit - \begin{itemize*} - \item Ausfälle von einzelnen Knoten kompensieren - \item Redundante Verarbeitung - \end{itemize*} - \item Offenheit / Interoperabilität - \begin{itemize*} - \item neue Knoten und Systeme einfach integrieren - \end{itemize*} - \item Transparenz - \begin{itemize*} - \item verstecke die vielen Server vor den Nutzern - \end{itemize*} -\end{itemize*} - -\subsection{Grundlagen verteilter Programmierung in Java und Erlang} -\subsubsection{Sockets} -\begin{itemize*} - \item Verteilte Programmierung: Wir müssen einen entfernten Computer ansprechen - \item benötigen: Adresse $\rightarrow$ IP-Adresse - \item da mehrere Dienste auf demselben Computer laufen lauscht jeder Dienst auf einem Port (Nummer) - \begin{itemize*} - \item Wichtige Ports: 80 WWW, 20 (FTP), 25 (SMTP) - \end{itemize*} - \item \textbf{Socket} beschreibt einen Endpunkt, dh. Adresse und Port in einem TCP (oder UDP) Netzwerk - \item \textbf{Server-Socket} wartet auf Verbindungen - \item \textbf{Client} initiiert Verbindung, ebenfalls über einen (Client-Socket) -\end{itemize*} - -\subsubsection{Sockets in Java} -Socket in dem package ''java.net.Socket'' -\begin{itemize*} - \item einen \textbf{ServerSocket} auf Port 4242 erstellen - \begin{center} - ServerSocket serverSocket = new ServerSocket(4242); - \end{center} - \item Warte \color{orange}blockierend \color{black} auf Verbindungen - \begin{center} - Socket client = serverSocket.accept(); - \end{center} - \item Client Socket erstellen und zum Server verbinden - \begin{center} - Socket client = new Socket("localhost",4242); - \end{center} - \item Sockets in ähnlicher Form in C++ -\end{itemize*} - -\paragraph{Sockets in Java - Beispiel} -Echo Server (Serverseite) -\begin{center} - \centering - \includegraphics[width=0.8\linewidth]{Assets/Programmierparadigmen-004} -\end{center} - -Echo Server (Clientseite) -\begin{center} - \centering - \includegraphics[width=0.8\linewidth]{Assets/Programmierparadigmen-005} -\end{center} - -\subsection{Aktormodell in Erlang} -\begin{itemize*} - \item formales Modell für Nebenläufigkeit und Verteilung - \item Basis für verschiedene Programmiersprachen/Frameworks: Erlang, Akka (Scala/Java) - \item Prinzipien: - \begin{itemize*} - \item Aktor kapselt Zustand und Verhalten - \item Aktoren sind aktiv - \item Aktoren kommunizieren durch Nachrichtenaustausch + \item (Last-)Skalierbarkeit (Scale-out): \begin{itemize*} - \item Nichtblockierendes Senden - \item Blockierendes Empfangen + \item viele kleine Server - statt eines großen + \item neue Server nach Bedarf hinzuzufügen + \end{itemize*} + \item Funktionssicherheit (Safety) / IT-Sicherheit (Security) + \item Fehlertoleranz / Verfügbarkeit + \begin{itemize*} + \item Ausfälle von einzelnen Knoten kompensieren + \item Redundante Verarbeitung + \end{itemize*} + \item Offenheit / Interoperabilität + \begin{itemize*} + \item neue Knoten und Systeme einfach integrieren + \end{itemize*} + \item Transparenz + \begin{itemize*} + \item verstecke die vielen Server vor den Nutzern \end{itemize*} \end{itemize*} -\end{itemize*} - -\subsubsection{Übersicht} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-006} -\end{center} - -\begin{itemize*} - \item Aktormodell in Erlang nativ umgesetzt + + \subsection{Grundlagen verteilter Programmierung in Java und Erlang} + \subsubsection{Sockets} \begin{itemize*} - \item Sende- und Empfangsoperationen schon für parallele Programmierung benutzt - \item bisher aber nur auf einem Knoten + \item Verteilte Programmierung: Wir müssen einen entfernten Computer ansprechen + \item benötigen: Adresse $\rightarrow$ IP-Adresse + \item da mehrere Dienste auf demselben Computer laufen lauscht jeder Dienst auf einem Port (Nummer) + \begin{itemize*} + \item Wichtige Ports: 80 WWW, 20 (FTP), 25 (SMTP) + \end{itemize*} + \item \textbf{Socket} beschreibt einen Endpunkt, dh. Adresse und Port in einem TCP (oder UDP) Netzwerk + \item \textbf{Server-Socket} wartet auf Verbindungen + \item \textbf{Client} initiiert Verbindung, ebenfalls über einen (Client-Socket) \end{itemize*} - \item Programmbestandteile im Aktormodell + + \subsubsection{Sockets in Java} + Socket in dem package ''java.net.Socket'' \begin{itemize*} - \item Verhaltensdefinition $\Rightarrow$ f() $\rightarrow$ … end. - \item Erzeugen neuer Aktoren $\Rightarrow$ Pid = spwan(fun …). - \item Empfangen von Nachrichten $\Rightarrow$ receive … end. - \item Senden $\Rightarrow$ Pid ! Request. + \item einen \textbf{ServerSocket} auf Port 4242 erstellen + \begin{center} + ServerSocket serverSocket = new ServerSocket(4242); + \end{center} + \item Warte \color{orange}blockierend \color{black} auf Verbindungen + \begin{center} + Socket client = serverSocket.accept(); + \end{center} + \item Client Socket erstellen und zum Server verbinden + \begin{center} + Socket client = new Socket("localhost",4242); + \end{center} + \item Sockets in ähnlicher Form in C++ \end{itemize*} - \item kein globaler Zustand -\end{itemize*} - -\subsubsection{Kommunikation zwischen Erlangknoten} -Erlangknoten starten (sname = short name) -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-008} -\end{center} - -Weiteren Erlangknoten starten (selber oder anderer PC) -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-009} -\end{center} - -Liste der verbundenen Knoten -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-010} -\end{center} -\subsubsection{Cookie-System} -\begin{itemize*} - \item verteilte Erlangknoten benötigen zur Kommunikation gemeinsames \color{orange} Magic Cookie \color{black} (Passwort) - \item Mehrere Varianten + + \paragraph{Sockets in Java - Beispiel} + + Echo Server (Serverseite) + \begin{lstlisting}[language=C++] + ServerSocket server = new ServerSocket(4242); + while(true){ + try(Socket client = server.accept(); ){ + Scanner in = new Scanner(client.getInputStream()); + PrintWriter out = new PrintWriter(client.getOutputStream(), true); + String line = in.readLine(); + out.println(line); + } + catch ( Exception e) { e.printStackTrace(); } + } +\end{lstlisting} + + Echo Server (Clientseite) + \begin{lstlisting}[language=C++] + try(Socket server = new Socket("localhost", 4242); ){ + Scanner in = new Scanner(client.getInputStream() ); + PrintWriter out = new PrintWriter(server.getOutputStream(), true); + out.println("Hello World"); + System.out.println(in.nextLine()); + } + catch ( Exception e) { e.printStackTrace(); } +\end{lstlisting} + + \subsection{Aktormodell in Erlang} \begin{itemize*} - \item Datei {\raise.17ex\hbox{$\scriptstyle\mathtt{\sim}$}}/.erlang.cookie - \item Erlang Funktion \newline - \color{blue} erlang:\color{OliveGreen}set\_cookie(node(), \color{blue}Cookie)\color{black} - \item Option: erl - setcookie Cookie + \item formales Modell für Nebenläufigkeit und Verteilung + \item Basis für verschiedene Programmiersprachen/Frameworks: Erlang, Akka (Scala/Java) + \item Prinzipien: + \begin{itemize*} + \item Aktor kapselt Zustand und Verhalten + \item Aktoren sind aktiv + \item Aktoren kommunizieren durch Nachrichtenaustausch + \begin{itemize*} + \item Nichtblockierendes Senden + \item Blockierendes Empfangen + \end{itemize*} + \end{itemize*} \end{itemize*} -\end{itemize*} -\subsubsection{Verbindungsaufbau zwischen Erlangknoten} -Verbindungsaufbau mittels \color{blue} net\_adm:\color{black}ping Funktion -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-011} -\end{center} -\subsubsection{Kommunikation zwischen Erlangknoten} -Starten eines Prozesses auf einem entfernten Host -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-012} -\end{center} -\subsection{Alternating Bit Protokoll} -\subsubsection{Übersicht} -\begin{itemize*} - \item ermöglicht es, Nachrichten über einen verlustbehafteten Kommunikationskanal vollständig zu übertragen, sofern Verluste nur gelegentlich auftreten (transiente Fehler) - \item Empfänger quittiert jedes erhaltene Paket (Achnowledgement, kurz ACK) - \item \textbf{Achtung} Kanal kann Nachrichten und ACKs verlieren + + \subsubsection{Übersicht} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-Aktormodell.png} + \end{center} + \begin{itemize*} - \item benötigen je zwei unterschiedliche Sequenznummern und ACKs + \item Aktormodell in Erlang nativ umgesetzt + \begin{itemize*} + \item Sende- und Empfangsoperationen schon für parallele Programmierung benutzt + \item bisher aber nur auf einem Knoten + \end{itemize*} + \item Programmbestandteile im Aktormodell + \begin{itemize*} + \item Verhaltensdefinition $\Rightarrow$ f() $\rightarrow$ … end. + \item Erzeugen neuer Aktoren $\Rightarrow$ Pid = spwan(fun …). + \item Empfangen von Nachrichten $\Rightarrow$ receive … end. + \item Senden $\Rightarrow$ Pid ! Request. + \end{itemize*} + \item kein globaler Zustand \end{itemize*} - \item Empfänger liefert eine Nachricht nur beim ersten Empfang aus (keine Duplikate) - \item bei Timeout: Nachricht erneut senden - \item bei Erhalt eines unerwarteten ACKs: \textbf{aktuelle Nachricht erneut senden} -\end{itemize*} -\subsubsection{Zustände} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-013} -\end{center} -\subsubsection{Das Alternating Bit Protokoll} -Wir implementieren eine Variante, bei welcher: -\begin{itemize*} - \item der Sender zu Beginn eine Liste mit sämtlichen zu sendenden Nachrichten erhält, und - \item der Empfänger die erstmals empfangenen Nachrichten einfach auf dem Bildschirm ausgibt - \item alle Aktoren Statusmeldungen ausgeben - \item Verluste über einen Zufallszahlengenerator ausgelöst werden -\end{itemize*} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0014} -\end{center} -drei Prozesse mit \textbf{initialize(ErrorRate, NumberOfMessages, ReceiverPid, SenderPid, ChannelPid)} initialisieren und starten -\begin{itemize*} - \item Sender hat vier Zustandsfunktionen; Startet mit senderReady0(List): Liste mit Zahlen 1,…,NumberOfMessages - \item Kanal: Nachricht "verlieren", wenn Zufallszahl $\ngeq$ ErrorRate - \item Empfänger hat zwei Zustandsfunktionen; zu Beginn wird receiverWait0 gestartet - \item initialize wartet auf eine ready-Nachricht; sendet danach stop-Nachrichten an alle -\end{itemize*} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0015} -\end{center} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0016} -\end{center} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0017} -\end{center} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0018} -\end{center} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0019} -\end{center} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0020} -\end{center} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0021} -\end{center} + + \subsubsection{Kommunikation zwischen Erlangknoten} + Erlangknoten starten (sname = short name) + \begin{lstlisting}[language=erlang] + #erl -sname node1 -setcookie 1234 + Eshell V11.0 (abort with ^G) + (node1@localhost)1> +\end{lstlisting} + + Weiteren Erlangknoten starten (selber oder anderer PC) + \begin{lstlisting}[language=erlang] + #erl -sname node2 -setcookie 1234 + Eshell V11.0 (abort with ^G) + (node2@localhost)1> +\end{lstlisting} + + Liste der verbundenen Knoten + \begin{lstlisting}[language=erlang] + (node@localhost)1> nodes(). + [] +\end{lstlisting} + + \subsubsection{Cookie-System} + \begin{itemize*} + \item verteilte Erlangknoten benötigen zur Kommunikation gemeinsames \color{orange} Magic Cookie \color{black} (Passwort) + \item Mehrere Varianten + \begin{itemize*} + \item Datei {\raise.17ex\hbox{$\scriptstyle\mathtt{\sim}$}}/.erlang.cookie + \item Erlang Funktion \newline + \color{blue} erlang:\color{OliveGreen}set\_cookie(node(), \color{blue}Cookie)\color{black} + \item Option: erl - setcookie Cookie + \end{itemize*} + \end{itemize*} + + \subsubsection{Verbindungsaufbau zwischen Erlangknoten} + Verbindungsaufbau mittels \color{blue} net\_adm:\color{black}ping Funktion + + \begin{lstlisting}[language=erlang] +(node1@localhost)2> net_adm:ping("node2@localhost"). +pong +(node1@localhost)3> nodes(). +["node2@localhost"] -\subsection{Kommunikationsmodelle \& Implementierungen} -\subsubsection{Kommunikationsmodelle} -Frage: Wie sollen Knoten miteinander kommunizieren? -\begin{itemize*} - \item Sprechen die Teilnehmer direkt miteinander oder über einen Vermittler? - \item Kann jeder jedem eine Nachricht schicken? - \item Wartet ein Teilnehmer darauf, dass seine Nachricht angekommen ist? - \item Wartet ein Teilnehmer darauf, dass eine Nachricht ankommt? - \item Muss ein Teilnehmer auf eine Nachricht antworten? -\end{itemize*} +(node2@localhost)1> nodes(). +["node1@localhost"] +\end{lstlisting} + + \subsubsection{Kommunikation zwischen Erlangknoten} + Starten eines Prozesses auf einem entfernten Host + + \begin{lstlisting}[language=erlang] +complicated() -> + receive + {Sender, I} -> Sender ! I*I + end. + +sender(Num, Pid) -> + Pid ! {self(), Num}, + receive + Res -> io:format("Result = ~p~n", [Res]) +(node1@localhost)4> N2Pid = spawn("node2@localhost", fun ch5_1:complicated/0) +(node1@localhost)5> ch5_1:sender(25, N2Pid). +Result = 625 +ok +\end{lstlisting} + + \subsection{Alternating Bit Protokoll} + \subsubsection{Übersicht} + \begin{itemize*} + \item ermöglicht es, Nachrichten über einen verlustbehafteten Kommunikationskanal vollständig zu übertragen, sofern Verluste nur gelegentlich auftreten (transiente Fehler) + \item Empfänger quittiert jedes erhaltene Paket (Achnowledgement, kurz ACK) + \item \textbf{Achtung} Kanal kann Nachrichten und ACKs verlieren + \begin{itemize*} + \item benötigen je zwei unterschiedliche Sequenznummern und ACKs + \end{itemize*} + \item Empfänger liefert eine Nachricht nur beim ersten Empfang aus (keine Duplikate) + \item bei Timeout: Nachricht erneut senden + \item bei Erhalt eines unerwarteten ACKs: \textbf{aktuelle Nachricht erneut senden} + \end{itemize*} + + \subsubsection{Zustände} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-zustände-bit-protokoll.png} + \end{center} + + \subsubsection{Das Alternating Bit Protokoll} + Wir implementieren eine Variante, bei welcher: + \begin{itemize*} + \item der Sender zu Beginn eine Liste mit sämtlichen zu sendenden Nachrichten erhält, und + \item der Empfänger die erstmals empfangenen Nachrichten einfach auf dem Bildschirm ausgibt + \item alle Aktoren Statusmeldungen ausgeben + \item Verluste über einen Zufallszahlengenerator ausgelöst werden + \end{itemize*} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-alternate-bit-protokoll.png} + \end{center} + drei Prozesse mit \textbf{initialize(ErrorRate, NumberOfMessages, ReceiverPid, SenderPid, ChannelPid)} initialisieren und starten + \begin{itemize*} + \item Sender hat vier Zustandsfunktionen; Startet mit senderReady0(List): Liste mit Zahlen 1,…,NumberOfMessages + \item Kanal: Nachricht "verlieren", wenn Zufallszahl $\ngeq$ ErrorRate + \item Empfänger hat zwei Zustandsfunktionen; zu Beginn wird receiverWait0 gestartet + \item initialize wartet auf eine ready-Nachricht; sendet danach stop-Nachrichten an alle + \end{itemize*} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20015} + \end{center} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20016} + \end{center} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20017} + \end{center} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20018} + \end{center} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20019} + \end{center} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20020} + \end{center} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20021} + \end{center} + + \subsection{Kommunikationsmodelle \& Implementierungen} + \subsubsection{Kommunikationsmodelle} + Frage: Wie sollen Knoten miteinander kommunizieren? + \begin{itemize*} + \item Sprechen die Teilnehmer direkt miteinander oder über einen Vermittler? + \item Kann jeder jedem eine Nachricht schicken? + \item Wartet ein Teilnehmer darauf, dass seine Nachricht angekommen ist? + \item Wartet ein Teilnehmer darauf, dass eine Nachricht ankommt? + \item Muss ein Teilnehmer auf eine Nachricht antworten? + \end{itemize*} $\Rightarrow$ das Verhalten der Teilnehmer ist in \color{orange} Kommunikationsmodellen \color{black} beschrieben - -\subsubsection{Arten von Kommunikationsmodellen} -Es gibt viele verschiedene Modelle, z.B. für \color{orange} Botschaftenbasierte Modelle \color{black} -\begin{itemize*} - \item Auftragsorientierte Modelle - \item Funktionsaufrufbasierte Modelle - \item Blackboards - \item Ereignisbasierte Modelle - \item Strombasierte Modelle - \item Wissensbasierte Modelle -\end{itemize*} -Kommunikationspartner sind für uns: -\begin{itemize*} - \item Threads/Prozesse innerhalb verteilter Anwendungen - \item Komponenten verteilter Systeme (Browser $\Leftrightarrow$ Webserver, DB Client $\Leftrightarrow$ DB-Server) -\end{itemize*} - -\subsubsection{Modellbestandteile} -\begin{itemize*} - \item \color{orange} Rollenmodell: \color{black} + + \subsubsection{Arten von Kommunikationsmodellen} + Es gibt viele verschiedene Modelle, z.B. für \color{orange} Botschaftenbasierte Modelle \color{black} \begin{itemize*} - \item gemeinsames Handlungsmuster festlegen - \item z.B. Anrufer/Angerufener, Clinet/Server, Quelle/Senke + \item Auftragsorientierte Modelle + \item Funktionsaufrufbasierte Modelle + \item Blackboards + \item Ereignisbasierte Modelle + \item Strombasierte Modelle + \item Wissensbasierte Modelle \end{itemize*} - \item \color{orange} Datenmodell: \color{black} + Kommunikationspartner sind für uns: \begin{itemize*} - \item einheitliche Interpretation der ausgetauschten Daten - \item z.B. Dateiformate (XML/JSON), Kodierungen (MPEG4/H.264) + \item Threads/Prozesse innerhalb verteilter Anwendungen + \item Komponenten verteilter Systeme (Browser $\Leftrightarrow$ Webserver, DB Client $\Leftrightarrow$ DB-Server) \end{itemize*} - \item \color{orange} Fehlersemantiken \color{black} + + \subsubsection{Modellbestandteile} \begin{itemize*} - \item Einvernehmen über Wirkungen von Ausfällen - \item Eigenschaften von Kommunikationsoperationen müssen bei Ausfällen garantiert werden - \end{itemize*} - \item \color{orange} Terminierungssemantik \color{black} - \begin{itemize*} - \item Einvernehmen über das Ende der Kommunikation - \item Garantien über das Ende von Kommunikationsoperationen (auch bei Ausfällen) - \end{itemize*} -\end{itemize*} - -\subsubsection{Kommunikationsarten} -\begin{itemize*} - \item Wann ist eine Kommunikationsoperation abgeschlossen? - \item entspricht Terminierungssemantik - \item zwei grundlegende Arten: - \begin{itemize*} - \item \color{orange} synchron \color{black} + \item \color{orange} Rollenmodell: \color{black} \begin{itemize*} - \item blockierend - \item Teilnehmer wartet bis die Gegenseite bereit ist - \item kann lange dauern, Sender kann nicht weiter arbeiten - \item Senden: Botschaftenankunft garantiert, einfache Implementierung synchroner Aktivitäten - \item Empfangen: Botschaftenankunft einfach und präzise feststellbar + \item gemeinsames Handlungsmuster festlegen + \item z.B. Anrufer/Angerufener, Clinet/Server, Quelle/Senke \end{itemize*} - \item \color{orange} asynchron \color{black} + \item \color{orange} Datenmodell: \color{black} \begin{itemize*} - \item nicht-blockierend - \item Der Teilnehmer wartet nicht auf die Gegenseite (”fire and forget”) - \item unklar ob Botschaft angekommen - \item Senden: einfache Implementierung von Nebenläufigkeit - \item Empfangen: unklar wann Botschaft ankommt, einfache Implementierung von Nebenläufigkeit + \item einheitliche Interpretation der ausgetauschten Daten + \item z.B. Dateiformate (XML/JSON), Kodierungen (MPEG4/H.264) \end{itemize*} - \item gilt sowohl für das Senden als auch das Empfangen - \end{itemize*} -\end{itemize*} - -\paragraph{Kommunikationsarten: Senden} -\color{orange} synchrones Senden: \color{black} Der Sender wartet bis der Empfänger die Botschaft annimmt -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0024} -\end{center} -\noindent \color{orange} asynchrones Senden: \color{black} Der Sender wartet nicht bis der Empfänger die Botschaft annimmt ("fire and forget" Prinzip) -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0025} -\end{center} - -\paragraph{Synchrones vs. asynchrones Senden} -\begin{itemize*} - \item synchrones Senden - \begin{itemize*} - \item kann lange dauern, der Sender kann währenddessen nicht weiterarbeiten - \item die Botschaftenankunft ist garantiert, eine einfache Implementierung synchroner Aktivitäten - \end{itemize*} - \item asynchrones Senden - \begin{itemize*} - \item unklar ob die Botschaft angekommen ist - \item einfache Implementierung von Nebenläufigkeit - \end{itemize*} -\end{itemize*} - -\paragraph{Kommunikationsarten: Empfangen} -\color{orange} synchrones Empfangen: \color{black} Der Empfänger wartet bis die Botschaft eintrifft -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0026} -\end{center} -\color{orange} asynchrones Empfangen: \color{black} Der Empfänger macht weiter, falls keine Nachricht eingetroffen ist -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0027} -\end{center} - -\paragraph{Synchrones vs. asynchrones Empfangen} -\begin{itemize*} - \item synchrones Empfangen: - \begin{itemize*} - \item kann lange dauern, der Sender kann nicht weiterarbeiten - \item Botschaftenankunft ist einfach und präzise feststellbar - \end{itemize*} - \item asynchrones Empfangen: - \begin{itemize*} - \item unklar wann die Botschaft ankommt; - \newline Benachrichtigungstechniken + \item \color{orange} Fehlersemantiken \color{black} \begin{itemize*} - \item Nachfragen (Polling) - \item ankommende Botschaft erzeugt neuen Thread beim Empfänger - \item weitere Techniken möglich + \item Einvernehmen über Wirkungen von Ausfällen + \item Eigenschaften von Kommunikationsoperationen müssen bei Ausfällen garantiert werden + \end{itemize*} + \item \color{orange} Terminierungssemantik \color{black} + \begin{itemize*} + \item Einvernehmen über das Ende der Kommunikation + \item Garantien über das Ende von Kommunikationsoperationen (auch bei Ausfällen) \end{itemize*} - \item einfache Implementierung von Nebenläufigkeit \end{itemize*} -\end{itemize*} - -\subsubsection{Fehlerbehandlung} -\begin{itemize*} - \item unverlässliches vs. verlässliches Senden + + \subsubsection{Kommunikationsarten} \begin{itemize*} - \item "Brief vs. Einschreiben" + \item Wann ist eine Kommunikationsoperation abgeschlossen? + \item entspricht Terminierungssemantik + \item zwei grundlegende Arten: + \begin{itemize*} + \item \color{orange} synchron \color{black} + \begin{itemize*} + \item blockierend + \item Teilnehmer wartet bis die Gegenseite bereit ist + \item kann lange dauern, Sender kann nicht weiter arbeiten + \item Senden: Botschaftenankunft garantiert, einfache Implementierung synchroner Aktivitäten + \item Empfangen: Botschaftenankunft einfach und präzise feststellbar + \end{itemize*} + \item \color{orange} asynchron \color{black} + \begin{itemize*} + \item nicht-blockierend + \item Der Teilnehmer wartet nicht auf die Gegenseite (”fire and forget”) + \item unklar ob Botschaft angekommen + \item Senden: einfache Implementierung von Nebenläufigkeit + \item Empfangen: unklar wann Botschaft ankommt, einfache Implementierung von Nebenläufigkeit + \end{itemize*} + \item gilt sowohl für das Senden als auch das Empfangen + \end{itemize*} \end{itemize*} - \item verlässliche Kommunikation erfordert + + \paragraph{Kommunikationsarten: Senden} + + \color{orange} synchrones Senden: \color{black} Der Sender wartet bis der Empfänger die Botschaft annimmt + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20024} + \end{center} + \noindent \color{orange} asynchrones Senden: \color{black} Der Sender wartet nicht bis der Empfänger die Botschaft annimmt ("fire and forget" Prinzip) + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20025} + \end{center} + + \paragraph{Synchrones vs. asynchrones Senden} + \begin{itemize*} - \item Quittierungen (Acknowledgements) $\rightarrow$ mehr Daten senden - \item Timeouts $\rightarrow$ Zeitverwaltung, langes Warten + \item synchrones Senden + \begin{itemize*} + \item kann lange dauern, der Sender kann währenddessen nicht weiterarbeiten + \item die Botschaftenankunft ist garantiert, eine einfache Implementierung synchroner Aktivitäten + \end{itemize*} + \item asynchrones Senden + \begin{itemize*} + \item unklar ob die Botschaft angekommen ist + \item einfache Implementierung von Nebenläufigkeit + \end{itemize*} \end{itemize*} - \item vielfältige Fehlermöglichkeiten in verteilten Anwendungen: + + \paragraph{Kommunikationsarten: Empfangen} + + \color{orange} synchrones Empfangen: \color{black} Der Empfänger wartet bis die Botschaft eintrifft + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20026} + \end{center} + \color{orange} asynchrones Empfangen: \color{black} Der Empfänger macht weiter, falls keine Nachricht eingetroffen ist + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20027} + \end{center} + + \paragraph{Synchrones vs. asynchrones Empfangen} + \begin{itemize*} - \item Kommunikations-/Netzwerkfehler: $\rightarrow$ Nachricht/Antwort gar nicht oder verzögert zugestellt + \item synchrones Empfangen: + \begin{itemize*} + \item kann lange dauern, der Sender kann nicht weiterarbeiten + \item Botschaftenankunft ist einfach und präzise feststellbar + \end{itemize*} + \item asynchrones Empfangen: + \begin{itemize*} + \item unklar wann die Botschaft ankommt; + \newline Benachrichtigungstechniken + \begin{itemize*} + \item Nachfragen (Polling) + \item ankommende Botschaft erzeugt neuen Thread beim Empfänger + \item weitere Techniken möglich + \end{itemize*} + \item einfache Implementierung von Nebenläufigkeit + \end{itemize*} + \end{itemize*} + + \subsubsection{Fehlerbehandlung} + \begin{itemize*} + \item unverlässliches vs. verlässliches Senden + \begin{itemize*} + \item "Brief vs. Einschreiben" + \end{itemize*} + \item verlässliche Kommunikation erfordert + \begin{itemize*} + \item Quittierungen (Acknowledgements) $\rightarrow$ mehr Daten senden + \item Timeouts $\rightarrow$ Zeitverwaltung, langes Warten + \end{itemize*} + \item vielfältige Fehlermöglichkeiten in verteilten Anwendungen: + \begin{itemize*} + \item Kommunikations-/Netzwerkfehler: $\rightarrow$ Nachricht/Antwort gar nicht oder verzögert zugestellt + \item Serverausfall: Nachricht empfangen? Operation ausgeführt? + \item Clientausfall: Aufruf gültig? Bestätigung erhalten? + \end{itemize*} + \end{itemize*} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20028} + \end{center} + + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20029} + \end{center} + + vielfältige Fehlermöglichkeiten in verteilten Anwendungen: + \begin{itemize*} + \item Kommunikations-/Netzwerkfehler: $\rightarrow$ Nachricht/Antwort gar nicht oder nur verzögert zugestellt \item Serverausfall: Nachricht empfangen? Operation ausgeführt? \item Clientausfall: Aufruf gültig? Bestätigung erhalten? + \item Beispiel: Reisebuchung + \begin{itemize*} + \item Buchung durchgeführt? Bestätigung erhalten? + \item Bei wiederholter Ausführung: wirklich neue Buchung? + \end{itemize*} \end{itemize*} -\end{itemize*} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-0028} -\end{center} - -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-029} -\end{center} - -vielfältige Fehlermöglichkeiten in verteilten Anwendungen: -\begin{itemize*} - \item Kommunikations-/Netzwerkfehler: $\rightarrow$ Nachricht/Antwort gar nicht oder nur verzögert zugestellt - \item Serverausfall: Nachricht empfangen? Operation ausgeführt? - \item Clientausfall: Aufruf gültig? Bestätigung erhalten? - \item Beispiel: Reisebuchung + + \paragraph{Fehlerbehandlung in Erlang} + \begin{itemize*} - \item Buchung durchgeführt? Bestätigung erhalten? - \item Bei wiederholter Ausführung: wirklich neue Buchung? + \item Timeout beim Warten auf Nachrichten + \item Wenn keine passende Nachricht innerhalb \textbf{Time} msecs empfangen wird, dann wird der Rückgabewert des \textbf{after}-Ausdrucks verwendet. \end{itemize*} -\end{itemize*} - -\paragraph{Fehlerbehandlung in Erlang} -\begin{itemize*} - \item Timeout beim Warten auf Nachrichten - \item Wenn keine passende Nachricht innerhalb \textbf{Time} msecs empfangen wird, dann wird der Rückgabewert des \textbf{after}-Ausdrucks verwendet. -\end{itemize*} -\begin{lstlisting}[ + \begin{lstlisting}[ language=erlang, - showspaces=false, - basicstyle=\ttfamily ] receive {ok, Resp} $\rightarrow$ Resp; @@ -6049,378 +5373,394 @@ receive after Time $\rightarrow$ timeout end \end{lstlisting} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-030} - - Umgang mit Fehlern (Timeouts, Ausfälle): + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20030} + + Umgang mit Fehlern (Timeouts, Ausfälle): + \begin{itemize*} + \item Maybe: + \begin{itemize*} + \item keine Wiederholung + \item keine Ausführungsgarantie + \end{itemize*} + \item At-least-once: + \begin{itemize*} + \item wiederholte Ausführung, aber keine Erkennung von Nachrichtduplikaten + \item nur für idempotente Operationen (Lesen) + \end{itemize*} + \item At-most-once: + \begin{itemize*} + \item garantiert, dass mehrfache Aufrufe nur zu einziger Ausführung führen + \item z.B. durch Sequenznummern (erfordert Protokollierung zur Duplikateliminierung) + \item für nicht-idempotente Operationen (schreibend, z.B. Einfügen, Löschen) + \end{itemize*} + \end{itemize*} + + \end{center} + \subsubsection{Überwachung von Erlang-Prozessen} \begin{itemize*} - \item Maybe: + \item Linking von Prozessen: \color{green}link\color{blue}(Pid) \color{black} + \item M überwacht S; S bricht durch Fehler ab + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20031} + \end{center} + \item M wartet auf EXIT Nachricht von S $\rightarrow$ asynchroner Handler nötig + \end{itemize*} + + \subsubsection{on\_exit-Handler} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20032} + \end{center} + + \begin{itemize*} + \item überwacht den Prozess \textbf{Pid} auf Abbruch + \item Anwendungsspezifische Reaktionen möglich + \begin{itemize*} + \item Fehlermeldung + \item Neustart des Prozesses + \end{itemize*} + \item auch über Erlang-Knotengrenzen hinweg! + \end{itemize*} + + \paragraph{Anwendung des on\_exit-Handlers} + + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20033} + \end{center} + + \begin{itemize*} + \item Funktion anlegen (Liste in Atom konvertieren) + \item Prozess erzeugen + \item \textbf{on\_exit}-Handler definieren + \item Fehler verursachen (Nachricht ist keine Liste) + \end{itemize*} + + \subsubsection{Fehlersemantiken} + Umgang mit Fehlern (Timeouts, Ausfälle) + \begin{itemize*} + \item \color{orange} Maybe: \color{black} \begin{itemize*} \item keine Wiederholung \item keine Ausführungsgarantie \end{itemize*} - \item At-least-once: + \item \color{orange} At-least-once: \color{black} \begin{itemize*} - \item wiederholte Ausführung, aber keine Erkennung von Nachrichtduplikaten - \item nur für idempotente Operationen (Lesen) + \item wiederholte Ausführung, aber keine Erkennung von Nachrichtenduplikaten + \item nur für idempotente Optionen (Lesen) \end{itemize*} - \item At-most-once: + \item \color{orange} At-most-once: \color{black} \begin{itemize*} \item garantiert, dass mehrfache Aufrufe nur zu einziger Ausführung führen - \item z.B. durch Sequenznummern (erfordert Protokollierung zur Duplikateliminierung) + \item z.B. durch Sequenznummern (erfordert Protokollierung zur Duplikatelliminierung) \item für nicht-idempotente Operationen (schreibend, z.B. Einfügen, Löschen) \end{itemize*} \end{itemize*} -\end{center} -\subsubsection{Überwachung von Erlang-Prozessen} -\begin{itemize*} - \item Linking von Prozessen: \color{green}link\color{blue}(Pid) \color{black} - \item M überwacht S; S bricht durch Fehler ab + \subsubsection{Auftragsorientierte Modelle} + \begin{itemize*} + \item klassische Modell serviceorientierten Systemdesigns + \item in verteilten Systemen: + \begin{itemize*} + \item Menge von Dienstanbietern (Server) + \item Menge von Clients, die diese Dienste nutzen wollen + \end{itemize*} + \end{itemize*} + Typische Anwendungsszenarien + \begin{itemize*} + \item \textbf{DB-Server}: verwalten Datenbestände, verarbeiten SQL Anfragen + \begin{itemize*} + \item Clients: "Gib mir alle Personen, die älter als 18 Jahre alt sind" + \end{itemize*} + \item \textbf{Web}: Webserver stellt HTML Dokumente bereit, Brwoser ruft URLs für Dokumente auf + \item \textbf{E-Mail}: Mailserver verwalten Postfächer, leiten Mails weiter, Outlook/Thunderbird/…senden/lesen von Emails + \item Namensdienste (DNS), Fileserver, Zeitserver (NTP) + \end{itemize*} + + \paragraph{Auftragsorientierte Modelle: Modellsicht} + + \begin{itemize*} + \item Rollenmodell: Clients erteilen Aufträge an Server + \item Datenmodell: Notschaften mit vereinbarter Struktur (Protokoll) + \end{itemize*} \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-031} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20034} \end{center} - \item M wartet auf EXIT Nachricht von S $\rightarrow$ asynchroner Handler nötig -\end{itemize*} - -\subsubsection{on\_exit-Handler} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-032} -\end{center} - -\begin{itemize*} - \item überwacht den Prozess \textbf{Pid} auf Abbruch - \item Anwendungsspezifische Reaktionen möglich \begin{itemize*} - \item Fehlermeldung - \item Neustart des Prozesses - \end{itemize*} - \item auch über Erlang-Knotengrenzen hinweg! -\end{itemize*} - -\paragraph{Anwendung des on\_exit-Handlers} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-033} -\end{center} - -\begin{itemize*} - \item Funktion anlegen (Liste in Atom konvertieren) - \item Prozess erzeugen - \item \textbf{on\_exit}-Handler definieren - \item Fehler verursachen (Nachricht ist keine Liste) -\end{itemize*} - -\subsubsection{Fehlersemantiken} -Umgang mit Fehlern (Timeouts, Ausfälle) -\begin{itemize*} - \item \color{orange} Maybe: \color{black} - \begin{itemize*} - \item keine Wiederholung - \item keine Ausführungsgarantie - \end{itemize*} - \item \color{orange} At-least-once: \color{black} - \begin{itemize*} - \item wiederholte Ausführung, aber keine Erkennung von Nachrichtenduplikaten - \item nur für idempotente Optionen (Lesen) - \end{itemize*} - \item \color{orange} At-most-once: \color{black} - \begin{itemize*} - \item garantiert, dass mehrfache Aufrufe nur zu einziger Ausführung führen - \item z.B. durch Sequenznummern (erfordert Protokollierung zur Duplikatelliminierung) - \item für nicht-idempotente Operationen (schreibend, z.B. Einfügen, Löschen) - \end{itemize*} -\end{itemize*} - -\subsubsection{Auftragsorientierte Modelle} -\begin{itemize*} - \item klassische Modell serviceorientierten Systemdesigns - \item in verteilten Systemen: - \begin{itemize*} - \item Menge von Dienstanbietern (Server) - \item Menge von Clients, die diese Dienste nutzen wollen - \end{itemize*} -\end{itemize*} -Typische Anwendungsszenarien -\begin{itemize*} - \item \textbf{DB-Server}: verwalten Datenbestände, verarbeiten SQL Anfragen - \begin{itemize*} - \item Clients: "Gib mir alle Personen, die älter als 18 Jahre alt sind" - \end{itemize*} - \item \textbf{Web}: Webserver stellt HTML Dokumente bereit, Brwoser ruft URLs für Dokumente auf - \item \textbf{E-Mail}: Mailserver verwalten Postfächer, leiten Mails weiter, Outlook/Thunderbird/…senden/lesen von Emails - \item Namensdienste (DNS), Fileserver, Zeitserver (NTP) -\end{itemize*} - -\paragraph{Auftragsorientierte Modelle: Modellsicht} -\begin{itemize*} - \item Rollenmodell: Clients erteilen Aufträge an Server - \item Datenmodell: Notschaften mit vereinbarter Struktur (Protokoll) -\end{itemize*} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-034} -\end{center} -\begin{itemize*} - \item Fehlersemantiken: Was ist der Grund, wenn ich keine Antwort erhalte? - \begin{itemize*} - \item Auftrag angekommen? Vollständig bearbeitet? - \item Was passiert wenn ein Auftrag wiederholt wird? - \end{itemize*} - \item Terminierungssemantiken: - \begin{itemize*} - \item Auftragserteilung in der Regel synchron - \item es existieren aber auch asynchrone Aufträge - \end{itemize*} -\end{itemize*} - -\paragraph{Auftragsorientierte Modelle: Implementierung} -\begin{itemize*} - \item Implementierung aufbauend auf send/receive -\end{itemize*} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-035} -\end{center} \ \linebreak - -\paragraph{Ein Fileserver in Java} -Server -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-036} -\end{center} -Erläuterungen zum Server -\begin{itemize*} - \item Zeile 1 \& 2: Serversocket erstellen, lauscht auf Port 4242, wartet blockierend bis sich ein Client verbindet - \item Zeile 6: lies eine Zeile vom Client - \item Zeile 7: unser Nachrichtenformat: \textbf{Operation $<$Leerzeichen$>$ Dateipfad} - \item Zeile 8ff: unterscheide Operationen und führe Aktionen aus; antworte dem Client entsprechend -\end{itemize*} - -Client -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-037} -\end{center} -\begin{itemize*} - \item Zeile 1: erstelle Clientsocket, d.h. Verbindungsaufbau zum Server auf localhost auf Port 4242 - \item Zeile 2: lese Befehl und Dateipfad - \item Zeile 4: sende Befehl als String an den Server - \item Zeile 6ff: lese alle Antwortzeilen vom Server; Ausgabe auf dem Bildschirm -\end{itemize*} - -\paragraph{Auftragsorientierte Modelle} -\begin{itemize*} - \item Können benutzt werden, um einfache Protokolle zu implementieren - \item Binär oder ASCII - \begin{itemize*} - \item auch Übertragung komplexer Objekte möglich - \end{itemize*} - \item gesendeter Befehl könnte einer Methode/Funktion auf dem Server entsprechen - \begin{itemize*} - \item es erfolgt eine Art entfernter Funktionsaufruf - \item RPC wird im nächsten Abschnitt behandelt - \end{itemize*} - \item Funktionalität kann über das Internet angeboten werden - \begin{itemize*} - \item[$\Rightarrow$] Implementierung eines Webservices - \end{itemize*} -\end{itemize*} - -\subsubsection{Webservices - Allgemein} -\begin{itemize*} - \item WebService: Dienst, der über das Internet/WWW von Clients angesprochen werden kann - \item typischerweise über HTTP - \item Früher \textbf{SOAP}: Simple Object Access Protocol - \begin{itemize*} - \item Protokoll zum Austausch von Informationen in XML - \item Verzeichnisdienste zum Finden von Diensten, z.B. UDDI - \end{itemize*} - \item Heute \textbf{REST} -\end{itemize*} - -\subsubsection{REST} -\begin{itemize*} - \item Die Grundidee von REST: - \begin{itemize*} - \item \textbf{REST}: Representional State Transfer - \item oftmals existiert ein HTTP Server / Anwendungsserver schon - \item Idee: Jede Ressource die vom Server angeboten wird, ist durch eine URI beschrieben/identifiziert + \item Fehlersemantiken: Was ist der Grund, wenn ich keine Antwort erhalte? \begin{itemize*} - \item Datei, ein Eintrag in einer Datenbank, Tweet,… + \item Auftrag angekommen? Vollständig bearbeitet? + \item Was passiert wenn ein Auftrag wiederholt wird? \end{itemize*} - \item Anlegen, Lesen, Verändern, Löschen (CRUD) + \item Terminierungssemantiken: \begin{itemize*} - \item Art der Operation über HTTP Request-Typ festlegen (POST, GET, PUT, DELETE) + \item Auftragserteilung in der Regel synchron + \item es existieren aber auch asynchrone Aufträge \end{itemize*} - \item Unabhängigkeit von verwendeter Programmiersprache in Client und Server durch HTTP und Textformate \end{itemize*} -\end{itemize*} - -\paragraph{Anforderungen an Ressourcen} -Anforderungen an Ressourcen nach Fielding: -\begin{enumerate*} - \item Adressierbarkeit: jede Ressource muss über URI adressierbar sein (Achtung: URI != URL, Identifier vs. Locator) - \item Zustandslosigkeit: Kommunikation zwischen Client und Server hat keinen Zustand (Session/Cookie) + + \paragraph{Auftragsorientierte Modelle: Implementierung} + \begin{itemize*} - \item bei jeder Anfrage werden alle Informationen gesendet + \item Implementierung aufbauend auf send/receive \end{itemize*} - \item Einheitliche Schnittstelle: über HTTP Standardmethoden auf Ressourcen zugreifen - \item Entkopplung von Ressource und Repräsentation: Ressourcen können in verschiedenen Formaten angeboten werden (JSON, XML,…) -\end{enumerate*} - -\paragraph{HTTP Methoden für REST} -\begin{itemize*} - \item selbe URL mit verschiedenen Methoden aufrufbar - \item Methode bestimmt ausgeführte Aktion auf dem Server -\end{itemize*} -\begin{itemize*} - \item[GET:] eine Ressource lese, Daten sollten nicht verändert werden - \item[POST:] neue Ressource erstellen - \begin{itemize*} - \item Die URI ist dem Anrufer zunächst unbekannt - \item Der Server kann dem Anrufer die erzeugte URI in der Antwort mitteilen - \end{itemize*} - \item[PUT:] neue Ressource erstellen, oder existierende bearbeiten - \item[DELETE:] zum Löschen von Ressourcen -\end{itemize*} - -\paragraph{REST - Beispiel} -Spotify API -\begin{itemize*} - \item \textbf{Authorization}-Header benötigt - \item \textbf{id}: Spotify-ID eines Künstlers -\end{itemize*} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-038} -\end{center} - -\paragraph{Implementierung von RESTful Webservices} -\begin{itemize*} - \item manuelle Implementierung recht aufwändig - \begin{itemize*} - \item unterscheiden von HTTP Methoden (GET, POST,…) - \item parsen/prüfen von URL Pfaden und Parametern - \item setzen von Antwortheadern \& Kodierung in XML/JSON - \end{itemize*} - \item REST Frameworks erleichtern die Arbeit deutlich - \begin{itemize*} - \item JAX-RS Spezifikation für Java zur Erstellung von RESTful Services - \begin{itemize*} - \item Implementierung: Jersey: https://eclipse-ee4j.github.io/jersey/ - \item Implementierung: Spring: - https://spring.io/guides/gs/rest-service/ - \end{itemize*} - \item Microsofts \textbf{cpprestsdk} für C++ als Client-Bibliothek: - https://github.com/Microsoft/cpprestsdk - \end{itemize*} -\end{itemize*} -\begin{itemize*} - \item Beispiel: Jersey - \item Definition einer einfachen Klasse - \begin{itemize*} - \item Einstellungen über Annotationen - \item Klasse muss als Servlet in einem Applicationserver ausgeführt werden - \end{itemize*} -\end{itemize*} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-039} -\end{center} - -\paragraph{Restful Webservice - Erläuterungen} -\begin{itemize*} - \item Zeile 1: dieser Dienst ist über den Pfad files erreichbar, - z.B. http://localhost/files - \item Zeile 3: die nachfolgende Methode soll HTTP GET Anfragen - verarbeiten - \item Zeile 4: die URL enthält den Dateinamen als - Pfad-Bestandteil, z.B. - http://localhost/files/myfile.txt - \item Zeile 5: Hinweis an das Jersey-Framework das Ergebnis - automatisch ins JSON Format umzuwandeln - \item Zeile 6: normale Definition einer Methode \& Mapping des - Eingabeparameters auf den URL-Parameter - \item Zeile 8: das infos Objekt vom Typ FileInfo wird - automatisch als JSON repräsentiert -\end{itemize*} - -\paragraph{Aufruf von REST-Services} -https://reques.in kostenloser Dienst zum Testen von REST-Clients -\begin{itemize*} - \item Variante 1: telnet reques.in 80 … - \item Variante 2: Auf der Kommandozeile \newline - \$ curl https://reqres.in/api/users/1 \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-040} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20035} + \end{center} \ \linebreak + + \paragraph{Ein Fileserver in Java} + + Server + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20036} \end{center} - \item Variante 3: Aufruf in einem Programm -\end{itemize*} - -\paragraph{HTTP GET Aufrufe in Java} -In Java ab Version 11 eingebauter HTTP Client -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-041} -\end{center} - -\paragraph{HTTP POST in Java} -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-042} -\end{center} -Antwort: -\begin{center} - \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-043} -\end{center} -Eigentlich: JSON Ergebnis mit geeigneten Frameworks parsen und weiterverarbeiten - -\paragraph{Zusammenfassung} -\begin{itemize*} - \item Auftragsorientierte Modelle nach dem Client-Server Prinzip - \item WebServices bieten Dienste über das WWW an - \item RESTful WebServices + Erläuterungen zum Server \begin{itemize*} - \item jede Ressource hat eine URI - \item HTTP Methoden für Aktionen auf Ressourcen - \item unabhängig von Programmiersprachen + \item Zeile 1 \& 2: Serversocket erstellen, lauscht auf Port 4242, wartet blockierend bis sich ein Client verbindet + \item Zeile 6: lies eine Zeile vom Client + \item Zeile 7: unser Nachrichtenformat: \textbf{Operation $<$Leerzeichen$>$ Dateipfad} + \item Zeile 8ff: unterscheide Operationen und führe Aktionen aus; antworte dem Client entsprechend \end{itemize*} -\end{itemize*} - -\subsubsection{Funktionsaufrufbasierte Protokolle} -\begin{itemize*} - \item Grundidee: Adaption von anwendungsnahen und unkomplizierten Kommunikationsparadigmen an Eigenschaften verteilter Systeme - \item d.h., aus Aufrufen auf lokalen Prozeduren und Methoden werden Aufrufe entfernter Prozeduren und Methoden - \item bekannt als: + + Client + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20037} + \end{center} \begin{itemize*} - \item RPC: Remote Procedure Calls - \item oder Java RMI: Remote Method Invocation + \item Zeile 1: erstelle Clientsocket, d.h. Verbindungsaufbau zum Server auf localhost auf Port 4242 + \item Zeile 2: lese Befehl und Dateipfad + \item Zeile 4: sende Befehl als String an den Server + \item Zeile 6ff: lese alle Antwortzeilen vom Server; Ausgabe auf dem Bildschirm \end{itemize*} - \item Erlang und Java haben die Konzepte nativ implementiert, in C++ nur über zusätzliche Bibliotheken -\end{itemize*} - -\paragraph{Eigenschaften von Prozedurfernaufrufen} -Aufruf und Ausführung in unterschiedlichen Umgebungen/Kontexten -\begin{itemize*} - \item Programmiersprachen - \item Namens- und Adressräume - \item Betriebssystemkontext - \item Hardwarekontext -\end{itemize*} -Woher kennt der Aufrufer die Signatur der Prozedur auf dem Server? $\Rightarrow$ \color{orange} Stubs \color{black} + + \paragraph{Auftragsorientierte Modelle} + + \begin{itemize*} + \item Können benutzt werden, um einfache Protokolle zu implementieren + \item Binär oder ASCII + \begin{itemize*} + \item auch Übertragung komplexer Objekte möglich + \end{itemize*} + \item gesendeter Befehl könnte einer Methode/Funktion auf dem Server entsprechen + \begin{itemize*} + \item es erfolgt eine Art entfernter Funktionsaufruf + \item RPC wird im nächsten Abschnitt behandelt + \end{itemize*} + \item Funktionalität kann über das Internet angeboten werden + \begin{itemize*} + \item[$\Rightarrow$] Implementierung eines Webservices + \end{itemize*} + \end{itemize*} + + \subsubsection{Webservices - Allgemein} + \begin{itemize*} + \item WebService: Dienst, der über das Internet/WWW von Clients angesprochen werden kann + \item typischerweise über HTTP + \item Früher \textbf{SOAP}: Simple Object Access Protocol + \begin{itemize*} + \item Protokoll zum Austausch von Informationen in XML + \item Verzeichnisdienste zum Finden von Diensten, z.B. UDDI + \end{itemize*} + \item Heute \textbf{REST} + \end{itemize*} + + \subsubsection{REST} + \begin{itemize*} + \item Die Grundidee von REST: + \begin{itemize*} + \item \textbf{REST}: Representional State Transfer + \item oftmals existiert ein HTTP Server / Anwendungsserver schon + \item Idee: Jede Ressource die vom Server angeboten wird, ist durch eine URI beschrieben/identifiziert + \begin{itemize*} + \item Datei, ein Eintrag in einer Datenbank, Tweet,… + \end{itemize*} + \item Anlegen, Lesen, Verändern, Löschen (CRUD) + \begin{itemize*} + \item Art der Operation über HTTP Request-Typ festlegen (POST, GET, PUT, DELETE) + \end{itemize*} + \item Unabhängigkeit von verwendeter Programmiersprache in Client und Server durch HTTP und Textformate + \end{itemize*} + \end{itemize*} + + \paragraph{Anforderungen an Ressourcen} + + Anforderungen an Ressourcen nach Fielding: + \begin{enumerate*} + \item Adressierbarkeit: jede Ressource muss über URI adressierbar sein (Achtung: URI != URL, Identifier vs. Locator) + \item Zustandslosigkeit: Kommunikation zwischen Client und Server hat keinen Zustand (Session/Cookie) + \begin{itemize*} + \item bei jeder Anfrage werden alle Informationen gesendet + \end{itemize*} + \item Einheitliche Schnittstelle: über HTTP Standardmethoden auf Ressourcen zugreifen + \item Entkopplung von Ressource und Repräsentation: Ressourcen können in verschiedenen Formaten angeboten werden (JSON, XML,…) + \end{enumerate*} + + \paragraph{HTTP Methoden für REST} + + \begin{itemize*} + \item selbe URL mit verschiedenen Methoden aufrufbar + \item Methode bestimmt ausgeführte Aktion auf dem Server + \end{itemize*} + \begin{itemize*} + \item[GET:] eine Ressource lese, Daten sollten nicht verändert werden + \item[POST:] neue Ressource erstellen + \begin{itemize*} + \item Die URI ist dem Anrufer zunächst unbekannt + \item Der Server kann dem Anrufer die erzeugte URI in der Antwort mitteilen + \end{itemize*} + \item[PUT:] neue Ressource erstellen, oder existierende bearbeiten + \item[DELETE:] zum Löschen von Ressourcen + \end{itemize*} + + \paragraph{REST - Beispiel} + + Spotify API + \begin{itemize*} + \item \textbf{Authorization}-Header benötigt + \item \textbf{id}: Spotify-ID eines Künstlers + \end{itemize*} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20038} + \end{center} + + \paragraph{Implementierung von RESTful Webservices} + + \begin{itemize*} + \item manuelle Implementierung recht aufwändig + \begin{itemize*} + \item unterscheiden von HTTP Methoden (GET, POST,…) + \item parsen/prüfen von URL Pfaden und Parametern + \item setzen von Antwortheadern \& Kodierung in XML/JSON + \end{itemize*} + \item REST Frameworks erleichtern die Arbeit deutlich + \begin{itemize*} + \item JAX-RS Spezifikation für Java zur Erstellung von RESTful Services + \begin{itemize*} + \item Implementierung: Jersey: https://eclipse-ee4j.github.io/jersey/ + \item Implementierung: Spring: + https://spring.io/guides/gs/rest-service/ + \end{itemize*} + \item Microsofts \textbf{cpprestsdk} für C++ als Client-Bibliothek: + https://github.com/Microsoft/cpprestsdk + \end{itemize*} + \end{itemize*} + \begin{itemize*} + \item Beispiel: Jersey + \item Definition einer einfachen Klasse + \begin{itemize*} + \item Einstellungen über Annotationen + \item Klasse muss als Servlet in einem Applicationserver ausgeführt werden + \end{itemize*} + \end{itemize*} + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20039} + \end{center} + + \paragraph{Restful Webservice - Erläuterungen} + + \begin{itemize*} + \item Zeile 1: dieser Dienst ist über den Pfad files erreichbar, + z.B. http://localhost/files + \item Zeile 3: die nachfolgende Methode soll HTTP GET Anfragen + verarbeiten + \item Zeile 4: die URL enthält den Dateinamen als + Pfad-Bestandteil, z.B. + http://localhost/files/myfile.txt + \item Zeile 5: Hinweis an das Jersey-Framework das Ergebnis + automatisch ins JSON Format umzuwandeln + \item Zeile 6: normale Definition einer Methode \& Mapping des + Eingabeparameters auf den URL-Parameter + \item Zeile 8: das infos Objekt vom Typ FileInfo wird + automatisch als JSON repräsentiert + \end{itemize*} + + \paragraph{Aufruf von REST-Services} + + https://reques.in kostenloser Dienst zum Testen von REST-Clients + \begin{itemize*} + \item Variante 1: telnet reques.in 80 … + \item Variante 2: Auf der Kommandozeile \newline + \$ curl https://reqres.in/api/users/1 + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20040} + \end{center} + \item Variante 3: Aufruf in einem Programm + \end{itemize*} + + \paragraph{HTTP GET Aufrufe in Java} + + In Java ab Version 11 eingebauter HTTP Client + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20041} + \end{center} + + \paragraph{HTTP POST in Java} + + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20042} + \end{center} + Antwort: + \begin{center} + \centering + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20043} + \end{center} + Eigentlich: JSON Ergebnis mit geeigneten Frameworks parsen und weiterverarbeiten + + \paragraph{Zusammenfassung} + + \begin{itemize*} + \item Auftragsorientierte Modelle nach dem Client-Server Prinzip + \item WebServices bieten Dienste über das WWW an + \item RESTful WebServices + \begin{itemize*} + \item jede Ressource hat eine URI + \item HTTP Methoden für Aktionen auf Ressourcen + \item unabhängig von Programmiersprachen + \end{itemize*} + \end{itemize*} + + \subsubsection{Funktionsaufrufbasierte Protokolle} + \begin{itemize*} + \item Grundidee: Adaption von anwendungsnahen und unkomplizierten Kommunikationsparadigmen an Eigenschaften verteilter Systeme + \item d.h., aus Aufrufen auf lokalen Prozeduren und Methoden werden Aufrufe entfernter Prozeduren und Methoden + \item bekannt als: + \begin{itemize*} + \item RPC: Remote Procedure Calls + \item oder Java RMI: Remote Method Invocation + \end{itemize*} + \item Erlang und Java haben die Konzepte nativ implementiert, in C++ nur über zusätzliche Bibliotheken + \end{itemize*} + + \paragraph{Eigenschaften von Prozedurfernaufrufen} + + Aufruf und Ausführung in unterschiedlichen Umgebungen/Kontexten + \begin{itemize*} + \item Programmiersprachen + \item Namens- und Adressräume + \item Betriebssystemkontext + \item Hardwarekontext + \end{itemize*} + Woher kennt der Aufrufer die Signatur der Prozedur auf dem Server? $\Rightarrow$ \color{orange} Stubs \color{black} \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-044} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20044} \end{center} \subsubsection{Remote Procedure Calls (RPC)} \paragraph{Stubs} + Ein Stub hat verschiedene Aufgaben: \begin{itemize*} \item wandelt lokalen Prozeduraufruf in Netzwerkfunktion um @@ -6435,11 +5775,12 @@ Der Server-Stub/Skeleton \end{itemize*} \paragraph{RPC in Erlang} + \begin{itemize*} \item Vordefiniertes Erlang-Modul für RPC \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-045} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20045} \end{center} \item führt \textbf{Module:Func(Args)} auf \textbf{Node} aus \begin{itemize*} @@ -6447,7 +5788,7 @@ Der Server-Stub/Skeleton \end{itemize*} \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-046} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20046} \end{center} \item andere Möglichkeit: eigene Funktionen über \textbf{register} anmelden (siehe Alternating Bit Protokoll) \item mit \textbf{whereis} PID von registrierten Erlang-Prozessen finden @@ -6468,12 +5809,14 @@ Der Server-Stub/Skeleton \end{itemize*} \paragraph{RMI - Schnittstelle für entfernte Objekte} + \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-047} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20047} \end{center} \paragraph{RMI: Server} + Server-Objekt muss: \begin{itemize*} \item Remote-Schnittstelle implementieren @@ -6483,16 +5826,18 @@ Server-Objekt muss: Server-Objekt anlegen: \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-048} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20048} \end{center} \paragraph{RMI: Serverobjekt registrieren} + \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-049} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20049} \end{center} \paragraph{RMI - Client} + \begin{itemize*} \item über Namensdienst Server-Objekt finden \item Stub erzeugen (erfolgt automatisch von JVM) @@ -6500,16 +5845,18 @@ Server-Objekt anlegen: \end{itemize*} \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-050} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20050} \end{center} \paragraph{RMI - Ablauf} + \begin{center} \centering - \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-051} + \includegraphics[width=0.9\linewidth]{Assets/Programmierparadigmen-20051} \end{center} \paragraph{Interoperabilität von RPC} + Problem von Erlang, Java RMI, etc.: \begin{itemize*} \item an Programmiersprache gebunden $\rightarrow$ verschiedene Systeme können nicht miteinander verbunden werden @@ -6519,13 +5866,14 @@ Lösungsansätze: \item \textbf{XML-RPC, JSON-RPC}: kodiere alle zum Aufruf nötigen Informationen als XML bzw. JSON \begin{itemize*} \item HTTP zur Übertragung - \item \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-052} + \item \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20052} \item \textbf{id} für die Zuordnung von Antworten zu Anfragen \end{itemize*} \item \textbf{gRPC}: Code-Generierung für Server, Stubs und ausgetauschte Daten \end{itemize*} \paragraph{gRPC} + \begin{itemize*} \item initiiert von Google im Jahr 2015 \item plattformunabhängige Beschreibung von Daten und Diensten @@ -6537,17 +5885,19 @@ Lösungsansätze: \end{itemize*} \begin{center} \centering - \includegraphics[width=0.45\linewidth]{Assets/Programmierparadigmen-053} + \includegraphics[width=0.45\linewidth]{Assets/Programmierparadigmen-20053} \end{center} \paragraph{gRPC: Dienstbeschreibung} + fileservice.proto \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-054} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20054} \end{center} \paragraph{gRPC: Dienstbeschreibung - Erläuterungen} + \begin{itemize*} \item Datenklasse \textbf{FileInfo} mit drei Attributen, Zahlen geben Reihenfolge bei Serialisierung an \item \textbf{Request:} Service darf nur eine Eingabe- und Ausgabe-Message haben @@ -6558,32 +5908,36 @@ fileservice.proto \end{itemize*} \paragraph{gRPC: Dienstbeschreibung} + \begin{itemize*} \item *.proto Dateien werden mittels protoc Compiler in die Zielsprache übersetzt \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-055} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20055} \end{center} \item erzuegt C++ Dateien für messages sowie Service-Klassen (FileService) \item Klasse \textbf{FileService} enthält generierten Stub und Methoden für den Server zum überschreiben \end{itemize*} \paragraph{gRPC: Server erzeugen} + \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-056} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20056} \end{center} \paragraph{gRPC: Server starten} + \begin{center} \centering - \includegraphics[width=0.65\linewidth]{Assets/Programmierparadigmen-057} + \includegraphics[width=0.65\linewidth]{Assets/Programmierparadigmen-20057} \end{center} \paragraph{gRPC: Client} + \begin{center} \centering - \includegraphics[width=0.65\linewidth]{Assets/Programmierparadigmen-058} + \includegraphics[width=0.65\linewidth]{Assets/Programmierparadigmen-20058} \end{center} \subsubsection{Zusammenfassung} @@ -6609,10 +5963,11 @@ fileservice.proto \end{itemize*} \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-059} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20059} \end{center} \paragraph{Blackboards: Modell-Sicht} + \begin{itemize*} \item Rollenmodell: \begin{itemize*} @@ -6637,6 +5992,7 @@ fileservice.proto \end{itemize*} \paragraph{Blackboards: Vor- und Nachteile} + \begin{itemize*} \item Vorteile \begin{itemize*} @@ -6672,10 +6028,11 @@ fileservice.proto \end{itemize*} \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-060} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20060} \end{center} \paragraph{Ereignisbasierte Modelle: Modell-Sicht} + \begin{itemize*} \item Rollenmodell: \begin{itemize*} @@ -6698,6 +6055,7 @@ fileservice.proto \end{itemize*} \paragraph{Ereignisbasierte Modelle: Vor- und Nachteile} + \begin{itemize*} \item Vorteile: \begin{itemize*} @@ -6729,13 +6087,14 @@ RabbitMQ \end{itemize*} \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-061} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20061} \end{center} \paragraph{RabbitMQ Publish} + \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-062} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20062} \end{center} \begin{itemize*} \item Zeilen 7,8: \textbf{ConnectionFactory} zum Handling von Verbindungen, im Beispiel nur auf dem lokalen Host @@ -6748,9 +6107,10 @@ RabbitMQ \end{itemize*} \paragraph{RabbitMQ Subscribe} + \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-063} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20063} \end{center} \begin{itemize*} \item Zeilen 1\&2: Connection und Channel erstellen, siehe vorherige Bilder @@ -6815,13 +6175,13 @@ Cloud Computing als Geschäftsmodell: \subsubsection{Architekturen} \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-064} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20064} \end{center} \subsubsection{Amazon AWS Produkte} \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-065} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20065} \end{center} Hinweis: Bei AWS, Google, Azure viele Dienste auch (dauerhaft) kostenlos nutzbar! @@ -6839,7 +6199,7 @@ Hinweis: Bei AWS, Google, Azure viele Dienste auch (dauerhaft) kostenlos nutzbar \end{itemize*} \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-066} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20066} \end{center} \subsubsection{Serverless Computing} \begin{itemize*} @@ -6867,7 +6227,7 @@ Aufgaben des Entwicklers \end{itemize*} \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-067} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20067} \end{center} AWS Lambda Designer: HTTP Trigger, auszuführende Funktion und Nachfolgefunktion. @@ -6893,7 +6253,7 @@ Mittlerweile auch Serverless Microservice: Microservice nicht immer ausführen, \subsubsection{AWS Lambda: Java Beispiel} \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-068} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20068} \end{center} \begin{itemize*} \item \textbf{RequestHandler} als Einstiegspunkt für Lambda-Funktionen @@ -6912,16 +6272,18 @@ Mittlerweile auch Serverless Microservice: Microservice nicht immer ausführen, \end{itemize*} \paragraph{Spring Cloud Function: Projekt anlegen} + \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-069} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20069} \end{center} Projekt generieren, herunterladen und entpacken \paragraph{Spring Cloud Functions: Beispiel} + \begin{center} \centering - \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-070} + \includegraphics[width=0.7\linewidth]{Assets/Programmierparadigmen-20070} \end{center} \begin{itemize*} \item Zeile 1: für Spring Boot, diese Klasse enthält Definitionen für Dienste @@ -6939,6 +6301,7 @@ Projekt generieren, herunterladen und entpacken \end{itemize*} \paragraph{Aufruf der Spring Cloud Funktion} + \begin{enumerate*} \item Projekt kompilieren \newline ./mvnw clean install \item Starten \newline diff --git a/README.md b/README.md index 723d06f..9a0734c 100644 --- a/README.md +++ b/README.md @@ -22,7 +22,7 @@ Unterlagen zu Informatik Vorlesungen der TU Ilmenau - [Neurobiologische Informationsverarbeitung](Neurobiologische%20Informationsverarbeitung.md) - [Neuroinformatik](Neuroinformatik.md) (letzte 2 Kapitel fehlen) - [Programmierparadigmen](Programmierparadigmen.md) - - [LaTex Version](Programmierparadigmen.pdf) + - [LaTex Version](Programmierparadigmen.pdf) (work in progress) - [Rechnerarchitekturen 1](Rechnerarchitekturen%201.md) - [Praktikum A1](Rechnerarchitekturen%201%20-%20Praktikum%20A1.pdf) - [Praktikum A2](Rechnerarchitekturen%201%20-%20Praktikum%20A2.pdf)

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