From 338b7a2b45a8cb64b5c8ab94bbd3d03fc56fd54b Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Sat, 13 Sep 2014 17:28:03 +0200 Subject: [PATCH] =?UTF-8?q?Index=20verbessert;=20Inhalte=20zum=20Lambda-Ka?= =?UTF-8?q?lk=C3=BCl=20hinzugef=C3=BCgt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- documents/Programmierparadigmen/Haskell.tex | 17 +++--- documents/Programmierparadigmen/Lambda.tex | 21 ++++++- .../Programmierparadigmen/Parallelitaet.tex | 6 +- .../Programmierparadigmen.pdf | Bin 906233 -> 912213 bytes .../Programmierparadigmen.tex | 31 +++++++++- documents/Programmierparadigmen/Prolog.tex | 56 ++++++++++-------- .../Symbolverzeichnis.tex | 14 +++++ .../Programmierparadigmen/Typinferenz.tex | 35 +++++++---- documents/Programmierparadigmen/X10.tex | 8 +-- 9 files changed, 138 insertions(+), 50 deletions(-) diff --git a/documents/Programmierparadigmen/Haskell.tex b/documents/Programmierparadigmen/Haskell.tex index 34d5329..338f103 100644 --- a/documents/Programmierparadigmen/Haskell.tex +++ b/documents/Programmierparadigmen/Haskell.tex @@ -87,6 +87,9 @@ hat einen Speicherverbrauch von $\mathcal{O}(n)$. Durch einen \inputminted[numbersep=5pt, tabsize=4]{haskell}{scripts/haskell/fakultaet-akkumulator.hs} \subsection{Listen} +Listen sind in Haskell 0-indiziert, d.~h. das erste Element jeder Liste hat +den Index 0. + \begin{itemize} \item \texttt{[]} erzeugt die leere Liste, \item \texttt{[1,2,3]} erzeugt eine Liste mit den Elementen $1, 2, 3$ @@ -148,7 +151,7 @@ in etwa folgendem Haskell-Code: \texttt{tail "ABCDEF"} gibt \texttt{"BCDEF"} zurück. \end{itemize} -\subsection{Let und where}\xindex{let}\xindex{where}% +\subsection{Let und where}\xindex{let (Haskell)@\texttt{let} (Haskell)}\xindex{where (Haskell)@\texttt{where} (Haskell)}% \inputminted[numbersep=5pt, tabsize=4]{haskell}{scripts/haskell/let-where-bindung.hs} \subsection{Funktionskomposition}\xindex{. (Haskell)}\xindex{Funktionskomposition}% @@ -223,12 +226,12 @@ Ein paar Beispiele zur Typinferenz: \label{fig:haskell-type-hierarchy} \end{figure} -\subsection{type}\xindex{type}% +\subsection{type}\xindex{type (Haskell)@\texttt{type} (Haskell)}% Mit \texttt{type} können Typsynonyme erstellt werden: \inputminted[numbersep=5pt, tabsize=4]{haskell}{scripts/haskell/alt-types.hs} -\subsection{data}\xindex{data}% +\subsection{data}\xindex{data (Haskell)@\texttt{data} (Haskell)}% Mit dem Schlüsselwort \texttt{data} können algebraische Datentypen\xindex{Datentyp!algebraischer} erzeugt werden: @@ -267,7 +270,7 @@ sich das ganze sogar noch kürzer schreiben: \subsection{Fibonacci}\xindex{Fibonacci} \inputminted[linenos, numbersep=5pt, tabsize=4, frame=lines, label=fibonacci.hs]{haskell}{scripts/haskell/fibonacci.hs} \inputminted[linenos, numbersep=5pt, tabsize=4, frame=lines, label=fibonacci-akk.hs]{haskell}{scripts/haskell/fibonacci-akk.hs} -\xindex{zipWith} +\xindex{zipWith (Haskell)@\texttt{zipWith} (Haskell)} \inputminted[linenos, numbersep=5pt, tabsize=4, frame=lines, label=fibonacci-zip.hs]{haskell}{scripts/haskell/fibonacci-zip.hs} \inputminted[linenos, numbersep=5pt, tabsize=4, frame=lines, label=fibonacci-pattern-matching.hs]{haskell}{scripts/haskell/fibonacci-pattern-matching.hs} @@ -276,7 +279,7 @@ wird wie folgt erzeugt: \inputminted[linenos, numbersep=5pt, tabsize=4, frame=lines, label=fibonacci-stream.hs]{haskell}{scripts/haskell/fibonacci-stream.hs} -\subsection{Polynome}\xindex{Polynome}\xindex{zipWith}\xindex{foldr}\xindex{tail}% +\subsection{Polynome}\xindex{Polynome}\xindex{zipWith (Haskell)@\texttt{zipWith} (Haskell)}\xindex{Folds!foldr (Haskell)@\texttt{foldr} (Haskell)}\xindex{tail (Haskell)@\texttt{tail} (Haskell)}% \inputminted[linenos, numbersep=5pt, tabsize=4, frame=lines, label=polynome.hs]{haskell}{scripts/haskell/polynome.hs} \subsection{Hirsch-Index}\xindex{Hirsch-Index}\xindex{Ord}\xindex{Num}% @@ -293,7 +296,7 @@ wird wie folgt erzeugt: \inputminted[linenos, numbersep=5pt, tabsize=4, frame=lines, label=intersect.hs]{haskell}{scripts/haskell/intersect.hs} -\subsection{Funktionen höherer Ordnung}\xindex{Folds}\xindex{foldl}\xindex{foldr}\label{bsp:foldl-und-foldr} +\subsection{Funktionen höherer Ordnung}\xindex{Folds}\xindex{Folds!foldl (Haskell)@\texttt{foldl} (Haskell)}\xindex{Folds!foldr (Haskell)@\texttt{foldr} (Haskell)}\label{bsp:foldl-und-foldr} \inputminted[linenos, numbersep=5pt, tabsize=4, frame=lines, label=folds.hs]{haskell}{scripts/haskell/folds.hs} \subsection{Chruch-Zahlen} @@ -320,7 +323,7 @@ Knoten anwendet: \subsection{Standard Prelude} Hier sind die Definitionen eininger wichtiger Funktionen: -\xindex{zipWith}\xindex{zip} +\xindex{zipWith (Haskell)@\texttt{zipWith} (Haskell)}\xindex{zip (Haskell)@\texttt{zip} (Haskell)} \inputminted[numbersep=5pt, tabsize=4]{haskell}{scripts/haskell/standard-definitions.hs} \section{Weitere Informationen} diff --git a/documents/Programmierparadigmen/Lambda.tex b/documents/Programmierparadigmen/Lambda.tex index bbedc69..6ea6125 100644 --- a/documents/Programmierparadigmen/Lambda.tex +++ b/documents/Programmierparadigmen/Lambda.tex @@ -164,7 +164,7 @@ Auch die gewohnten Operationen lassen sich so darstellen. \end{align*} \end{beispiel} -\begin{beispiel}[Vorgänger-Operation] +\begin{beispiel}[Vorgänger-Operation]\xindex{pred}\xindex{pair}\xindex{next}\xindex{fst}\xindex{snd} \begin{align*} \pair&:= \lambda a. \lambda b. \lambda f. f a b\\ \fst &:= \lambda p. p (\lambda a. \lambda b. a)\\ @@ -239,10 +239,25 @@ zurückgibt: \end{definition} \begin{beispiel}[Kombinatoren\footnotemark]% + Folgende $\lambda$-Funktionen sind Beispiele für Kombinatoren: \begin{bspenum} \item $\lambda a.\ a$ \item $\lambda a.\ \lambda b.\ a$ \item $\lambda f.\ \lambda a.\ \lambda b. f\ b\ a$ + \item $\lambda x.\ \lambda y.\ x$\\ + Diese $\lambda$-Funktion hat nur die gebundene Variable $x$, also + ist es ein Kombinator. + \end{bspenum} + + Folgende $\lambda$-Funktionen sind keine Kombinatoren: + \begin{bspenum} + \item $\lambda x.\ y$ + \item $x\ \lambda y.\ y$\\ + Der Gesamtausdruck ist kein $\lambda$-Ausdruck, also ist es auch + kein Kombinator. Außerdem ist $x$ eine freie Variable. + \item $(\lambda x.\ x)\ y$\\ + Der Ausdruck ist kein $\lambda$-Ausdruck, sondern eine + Funktionsanwendung. Also ist es kein Kombinator. \end{bspenum} \end{beispiel} \footnotetext{Quelle: \url{http://www.haskell.org/haskellwiki/Combinator}} @@ -260,6 +275,9 @@ Insbesondere ist also $f \ g$ ein Fixpunkt von $g$. heißt $Y$-Kombinator. \end{definition} +Der Y-Kombinator hat einen Paramter. Er nimmt eine nicht-rekursive Funktion +und gibt eine rekursive zurück. + \begin{behauptung} Der $Y$-Kombinator ist ein Fixpunktkombinator. \end{behauptung} @@ -311,4 +329,5 @@ Insbesondere ist also $f \ g$ ein Fixpunkt von $g$. \begin{itemize} \item \url{http://c2.com/cgi/wiki?FreeVariable} \item \url{http://www.lambda-bound.com/book/lambdacalc/node9.html} + \item \url{http://mvanier.livejournal.com/2897.html} \end{itemize} \ No newline at end of file diff --git a/documents/Programmierparadigmen/Parallelitaet.tex b/documents/Programmierparadigmen/Parallelitaet.tex index 937ebc6..5904f94 100644 --- a/documents/Programmierparadigmen/Parallelitaet.tex +++ b/documents/Programmierparadigmen/Parallelitaet.tex @@ -69,7 +69,11 @@ Dabei wird die Von-Neumann-Architektur als \textit{SISD-Architektur} und die PRAM-Architektur als \textit{SIMD-Architektur} klassifiziert. Es ist so zu verstehen, dass ein einzelner Befehl auf verschiedene Daten angewendet wird. -Bei heutigen Multicore-Rechnern liegt MIMD vor. +Bei heutigen Multicore-Rechnern liegt MIMD vor, da verschiedene Befehle in den +Programmspeichern möglich sind. + +Ein Beispiel für die SIMD sind GPUs. Sie haben einen Befehl im Programmspeicher +der auf verschiedenen Daten (Pixel) angewendet wird. 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