From bb674b307b1d118e05083cc2fac686d5d48958d9 Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Tue, 25 Mar 2014 19:48:20 +0100 Subject: [PATCH] Funktionsapplikation --- documents/Programmierparadigmen/Haskell.tex | 31 ++++++++++++++++++ .../Programmierparadigmen.pdf | Bin 849459 -> 851589 bytes documents/Programmierparadigmen/Prolog.tex | 2 +- .../scripts/haskell/binary-tree.hs | 2 ++ .../scripts/haskell/function-composition.hs | 4 +++ .../scripts/haskell/general-tree.hs | 1 + .../scripts/haskell/mapt.hs | 5 +++ 7 files changed, 44 insertions(+), 1 deletion(-) create mode 100644 documents/Programmierparadigmen/scripts/haskell/binary-tree.hs create mode 100644 documents/Programmierparadigmen/scripts/haskell/function-composition.hs create mode 100644 documents/Programmierparadigmen/scripts/haskell/general-tree.hs create mode 100644 documents/Programmierparadigmen/scripts/haskell/mapt.hs diff --git a/documents/Programmierparadigmen/Haskell.tex b/documents/Programmierparadigmen/Haskell.tex index a0c5523..f7c6ae5 100644 --- a/documents/Programmierparadigmen/Haskell.tex +++ b/documents/Programmierparadigmen/Haskell.tex @@ -133,6 +133,18 @@ in etwa folgendem Haskell-Code: \subsection{Let und where}\xindex{let}\xindex{where}% \inputminted[numbersep=5pt, tabsize=4]{haskell}{scripts/haskell/let-where-bindung.hs} +\subsection{Funktionskomposition}\xindex{.}\xindex{Funktionskomposition}% +In Haskell funktioniert Funktionskomposition mit einem Punkt: + +\inputminted[numbersep=5pt, tabsize=4]{haskell}{scripts/haskell/function-composition.hs} + +Dabei ergibt \texttt{h (-3)} in der mathematischen Notation +\[(g \circ f) (-3) = f(g(-3)) = f(-4) = 16\] +und \texttt{i (-3)} ergibt +\[(f \circ g) (-3) = g(f(-3)) = g(9) = 8\] +Es ist also anzumerken, dass die Reihenfolge \underline{nicht} der mathematischen +konvention entspricht. + \section{Typen} \subsection{Standard-Typen} Haskell kennt einige Basis-Typen: @@ -245,6 +257,25 @@ wird wie folgt erzeugt: \subsection{Chruch-Zahlen} \inputminted[linenos, numbersep=5pt, tabsize=4, frame=lines, label=church.hs]{haskell}{scripts/haskell/church.hs} +\subsection{Trees}\xindex{tree}\xindex{map!tree}% +Einen Binärbaum kann man in Haskell so definieren: + +\inputminted[numbersep=5pt, tabsize=4]{haskell}{scripts/haskell/binary-tree.hs} + +Einen allgemeinen Baum so: + +\inputminted[numbersep=5pt, tabsize=4]{haskell}{scripts/haskell/general-tree.hs} + +Hier ist \texttt{t} der polymorphe Typ des Baumes. \texttt{t} gibt also an welche +Elemente der Baum enthält. + +Man kann auf einem solchen Baum auch eine Variante von \texttt{map} und +\texttt{reduce} definieren, +also eine Funktion \texttt{mapT}, die eine weitere Funktion \texttt{f} auf jeden +Knoten anwendet: + +\inputminted[numbersep=5pt, tabsize=4]{haskell}{scripts/haskell/mapt.hs} + \subsection{Standard Prelude} Hier sind die Definitionen eininger wichtiger Funktionen: \xindex{zipWith}\xindex{zip} diff --git 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