From 25732f4421ac94deb7a3081cc25202d46572bb17 Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Sun, 9 Mar 2014 16:38:27 +0100 Subject: [PATCH] misc --- documents/Programmierparadigmen/Lambda.tex | 49 +++++++++++------- .../Programmierparadigmen.pdf | Bin 640403 -> 653446 bytes documents/Programmierparadigmen/Prolog.tex | 2 +- .../Symbolverzeichnis.tex | 24 +++++++-- documents/Programmierparadigmen/Vorwort.tex | 4 -- documents/Programmierparadigmen/X10.tex | 23 ++++++-- .../scripts/x10/hello-whole-world.x10 | 15 ++++++ .../scripts/x10/hello-world.x10 | 6 +++ 8 files changed, 91 insertions(+), 32 deletions(-) create mode 100644 documents/Programmierparadigmen/scripts/x10/hello-whole-world.x10 create mode 100755 documents/Programmierparadigmen/scripts/x10/hello-world.x10 diff --git a/documents/Programmierparadigmen/Lambda.tex b/documents/Programmierparadigmen/Lambda.tex index e8c041f..739658b 100644 --- a/documents/Programmierparadigmen/Lambda.tex +++ b/documents/Programmierparadigmen/Lambda.tex @@ -101,14 +101,16 @@ Die Funktionsapplikation sei linksassoziativ. Es gilt also: Die Call-By-Name Auswertung wird in Funktionen verwendet. +Haskell verwendet die Call-By-Name Auswertungsreihenfolge zusammen mit \enquote{sharing}. Dies nennt man Lazy Evaluation. +\todo[inline]{Was ist sharing?} + \begin{definition}[Call-By-Value]\xindex{Call-By-Value}% In der Call-By-Value Auswertung wird der linkeste Redex reduziert, der nicht von einem $\lambda$ umgeben ist und dessen Argument ein Wert ist. \end{definition} Die Call-By-Value Auswertungsreihenfolge wird in C und Java verwendet. -Auch in Haskell werden arithmetische Ausdrücke in der Call-By-Name Auswertungsreihenfolge -reduziert. +Auch in Haskell werden arithmetische Ausdrücke in der Call-By-Name Auswertungsreihenfolge reduziert. \section{Church-Zahlen} Im $\lambda$-Kalkül lässt sich jeder mathematische Ausdruck darstellen, also @@ -120,52 +122,63 @@ darstellt. Dafür dürfen wir nur Variablen und $\lambda$ verwenden. Eine Mögli das zu machen sind die sog. \textit{Church-Zahlen}. Dabei ist die Idee, dass die Zahl angibt wie häufig eine Funktion $f$ auf eine -Variable $x$ angewendet wird. Also: +Variable $z$ angewendet wird. Also: \begin{itemize} - \item $0 := \lambda f~x. x$ - \item $1 := \lambda f~x. f x$ - \item $2 := \lambda f~x. f (f x)$ - \item $3 := \lambda f~x. f (f (f x))$ + \item $0 := \lambda f~z. z$ + \item $1 := \lambda f~z. f z$ + \item $2 := \lambda f~z. f (f z)$ + \item $3 := \lambda f~z. f (f (f z))$ \end{itemize} Auch die gewohnten Operationen lassen sich so darstellen. \begin{beispiel}[Nachfolger-Operation] \begin{align*} - \succ :&= \lambda n f z. f (n f x)\\ - &= \lambda n. (\lambda f (\lambda x f (n f x))) + \succ :&= \lambda n f z. f (n f z)\\ + &= \lambda n. (\lambda f (\lambda z f (n f z))) \end{align*} Dabei ist $n$ die Zahl. Will man diese Funktion anwenden, sieht das wie folgt aus: \begin{align*} - \succ 1 &= (\lambda n f x. f(n f x)) 1\\ - &= (\lambda n f x. f(n f x)) \underbrace{(\lambda f~x. f x)}_{n}\\ - &= \lambda f x. f (\lambda f~x. f x) f x\\ - &= \lambda f x. f (f x)\\ - &= 2 + \succ 1&= (\lambda n f z. f(n f z)) 1\\ + &= (\lambda n f z. f(n f z)) \underbrace{(\lambda f~z. f z)}_{n}\\ + &= \lambda f z. f (\lambda f~z. f z) f z\\ + &= \lambda f z. f (f z)\\ + &= 2 \end{align*} \end{beispiel} \begin{beispiel}[Addition] \begin{align*} - \text{+} : &= \lambda m n f x. m f (n f x) + \text{plus} &:= \lambda m n f z. m f (n f z) \end{align*} Dabei ist $m$ der erste Summand und $n$ der zweite Summand. \end{beispiel} \begin{beispiel}[Multiplikation] - %\[\text{\cdot} := \lambda m n.m(n f) \] + \begin{align*} + \text{times} :&= \lambda m n f. m~s~(n~f~z)\\ + &\overset{\eta}{=} \lambda m n f z. n (m s) z + \end{align*} Dabei ist $m$ der erste Faktor und $n$ der zweite Faktor. \end{beispiel} \begin{beispiel}[Potenz] - %\[\text{\cdot} := \text{TODO}\] + \begin{align*} + \text{exp} :&= \lambda b e. eb\\ + &\overset{\eta}{=} \lambda b e f z. e b f z + \end{align*} Dabei ist $b$ die Basis und $e$ der Exponent. \end{beispiel} -\section{Weiteres} +\section{Church-Booleans} +\begin{definition}[Church-Booleans]\xindex{Church-Booleans}% + \texttt{True} wird zu $c_{\text{true}} := \lambda t. \lambda f. t$.\\ + \texttt{False} wird zu $c_{\text{false}} := \lambda t. \lambda f. f$. +\end{definition} +\section{Weiteres} \begin{satz}[Satz von Curch-Rosser] Wenn zwei unterschiedliche Terme $a$ und $b$ äquivalent sind, d.h. mit Reduktionsschritten beliebiger Richtung ineinander transformiert werden können, dann gibt es einen weiteren Term $c$, zu dem sowohl $a$ als auch $b$ reduziert werden können. \end{satz} \ No newline at end of file diff --git a/documents/Programmierparadigmen/Programmierparadigmen.pdf b/documents/Programmierparadigmen/Programmierparadigmen.pdf index 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Es wird eine ausführbare Datei erzeugt. diff --git a/documents/Programmierparadigmen/Symbolverzeichnis.tex b/documents/Programmierparadigmen/Symbolverzeichnis.tex index 02455c5..32c9ef2 100644 --- a/documents/Programmierparadigmen/Symbolverzeichnis.tex +++ b/documents/Programmierparadigmen/Symbolverzeichnis.tex @@ -10,11 +10,25 @@ $\emptyset\;\;\;$ Leere Menge\\ $\epsilon\;\;\;$ Das leere Wort\\ $\alpha, \beta\;\;\;$ Reguläre Ausdrücke\\ $L(\alpha)\;\;\;$ Die durch $\alpha$ beschriebene Sprache\\ -$L(\alpha | \beta) = L(\alpha) \cup L(\beta)$\\ -$L(\alpha \cdot \beta) = L(\alpha) \cdot L(\beta)$\\ -$\alpha^+ = L(\alpha)^+$ TODO: Was ist $L(\alpha)^+$\\ -$\alpha^* = L(\alpha)^*$ TODO: Was ist $L(\alpha)^*$\\ +$\begin{aligned}[t] + L(\alpha | \beta) &= L(\alpha) \cup L(\beta)\\ + L(\alpha \cdot \beta)&= L(\alpha) \cdot L(\beta) +\end{aligned}$\\ +$L^0 := \Set{\varepsilon}\;\;\;$ Die leere Sprache\\ +$L^{n+1} := L^n \circ L \text{ für } n \in \mdn_0\;\;\;$ Potenz einer Sprache\\ +$\begin{aligned}[t] + \alpha^+ &=& L(\alpha)^+ &=& \bigcup_{i \in \mdn} L(\alpha)^i\\ + \alpha^* &=& L(\alpha)^* &=& \bigcup_{i \in \mdn_0} L(\alpha)^i +\end{aligned}$ + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Reguläre Ausdrücke % +% Logik % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section*{Logik} +$\mathcal{M} \models \varphi\;\;\;$ Im Modell $\mathcal{M}$ gilt das Prädikat $\varphi$.\\ +$\psi \vdash \varphi\;\;\;$ Die Formel $\varphi$ kann aus der Menge der Formeln $\psi$ hergeleitet werden.\\ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Weiteres % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section*{Weiteres} $\bot\;\;\;$ Bottom\\ \ No newline at end of file diff --git a/documents/Programmierparadigmen/Vorwort.tex b/documents/Programmierparadigmen/Vorwort.tex index 7fab43e..1bc580a 100644 --- a/documents/Programmierparadigmen/Vorwort.tex +++ b/documents/Programmierparadigmen/Vorwort.tex @@ -24,10 +24,6 @@ Anregungen, Verbesserungsvorschläge und Ergänzungen können per Pull-Request gemacht werden oder mir per Email an info@martin-thoma.de geschickt werden. -\section*{Was ist Programmierparadigmen?} - -TODO - \section*{Erforderliche Vorkenntnisse} Grundlegende Kenntnisse vom Programmieren, insbesondere mit Java, wie sie am KIT in \enquote{Programmieren} vermittelt werden, werden diff --git a/documents/Programmierparadigmen/X10.tex b/documents/Programmierparadigmen/X10.tex index eb7c50d..c05dd65 100644 --- a/documents/Programmierparadigmen/X10.tex +++ b/documents/Programmierparadigmen/X10.tex @@ -1,7 +1,22 @@ -\chapter{X10} -\index{X10|(} +%!TEX root = Programmierparadigmen.tex +\chapter{X10}\index{X10|(}% +X10 ist eine objektorientierte Programmiersprache, die 2004 bei IBM entwickelt +wurde. + +\section{Erste Schritte} +Als erstes sollte man x10 von \url{http://x10-lang.org/x10-development/building-x10-from-source.html?id=248} herunterladen. + +Dann kann man die bin/x10c++ zum erstellen von ausführbaren Dateien nutzen. +Der Befehl \texttt{x10c++ hello-world.x10} erstellt eine ausführbare Datei namens +\texttt{a.out}. + +\inputminted[numbersep=5pt, tabsize=4, frame=lines, label=hello-world.x10]{cpp}{scripts/x10/hello-world.x10} + \section{Syntax} \section{Beispiele} -\index{X10|)} - +\section{Weitere Informationen} +\begin{itemize} + \item \url{http://x10-lang.org/} +\end{itemize} +\index{X10|)} \ No newline at end of file diff --git a/documents/Programmierparadigmen/scripts/x10/hello-whole-world.x10 b/documents/Programmierparadigmen/scripts/x10/hello-whole-world.x10 new file mode 100644 index 0000000..9386b79 --- /dev/null +++ b/documents/Programmierparadigmen/scripts/x10/hello-whole-world.x10 @@ -0,0 +1,15 @@ +import x10.io.Console; + +class HelloWholeWorld { + public static def main(args:Rail[String]):void { + if (args.size < 1) { + Console.OUT.println("Usage: HelloWholeWorld message"); + return; + } + + finish for (p in Place.places()) { + at (p) async Console.OUT.println(here+" says hello and "+args(0)); + } + Console.OUT.println("Goodbye"); + } +} \ No newline at end of file diff --git a/documents/Programmierparadigmen/scripts/x10/hello-world.x10 b/documents/Programmierparadigmen/scripts/x10/hello-world.x10 new file mode 100755 index 0000000..f2a12b6 --- /dev/null +++ b/documents/Programmierparadigmen/scripts/x10/hello-world.x10 @@ -0,0 +1,6 @@ +// file HelloWorld.x10 +public class HelloWorld { + public static def main(args: Array[String](1)){ + x10.io.Console.OUT.println("Hello, World"); + } +} \ No newline at end of file