From 8e73ed0910244bf1653ef1ab7c3228a3d2cf3452 Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Tue, 18 Mar 2014 19:31:04 +0100 Subject: [PATCH] =?UTF-8?q?Haskell-Beispiele=20hinzugef=C3=BCgt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- documents/Programmierparadigmen/Haskell.tex | 17 ++++++++++++-- .../Programmierparadigmen.pdf | Bin 719434 -> 724758 bytes .../scripts/haskell/hirsch-index.hs | 12 ++++++++++ .../scripts/haskell/lauflaengencodierung.hs | 21 ++++++++++++++++++ .../scripts/haskell/let-where-bindung.hs | 5 +++++ .../scripts/haskell/polynome.hs | 16 +++++++++++++ 6 files changed, 69 insertions(+), 2 deletions(-) create mode 100644 documents/Programmierparadigmen/scripts/haskell/hirsch-index.hs create mode 100644 documents/Programmierparadigmen/scripts/haskell/lauflaengencodierung.hs create mode 100644 documents/Programmierparadigmen/scripts/haskell/let-where-bindung.hs create mode 100644 documents/Programmierparadigmen/scripts/haskell/polynome.hs diff --git a/documents/Programmierparadigmen/Haskell.tex b/documents/Programmierparadigmen/Haskell.tex index 0ea4527..0d87b18 100644 --- a/documents/Programmierparadigmen/Haskell.tex +++ b/documents/Programmierparadigmen/Haskell.tex @@ -122,6 +122,9 @@ in etwa folgendem Haskell-Code: \texttt{tail "ABCDEF"} gibt \texttt{"BCDEF"} zurück. \end{itemize} +\subsection{Let und where}\xindex{let}\xindex{where}% +\inputminted[numbersep=5pt, tabsize=4]{haskell}{scripts/haskell/let-where-bindung.hs} + \section{Typen} \subsection{Standard-Typen} Haskell kennt einige Basis-Typen: @@ -206,8 +209,18 @@ sich das ganze sogar noch kürzer schreiben: \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} -\subsection{Quicksort} -TODO +\subsection{Polynome}\xindex{Polynome}\xindex{zipWith}\xindex{foldr}\xindex{tail}% +\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}% +\textbf{Parameter}: Eine Liste $L$ von Zahlen aus $\mdn$\\ +\textbf{Rückgabe}: $\max \Set{n \in \mdn | n \leq \|\Set{i \in L | i \geq n}\|}$ + +\inputminted[linenos, numbersep=5pt, tabsize=4, frame=lines, label=hirsch-index.hs]{haskell}{scripts/haskell/hirsch-index.hs} + +\subsection{Lauflängencodierung}\xindex{Lauflängencodierung}\xindex{splitWhen}\xindex{group}\xindex{concat}% + +\inputminted[linenos, numbersep=5pt, tabsize=4, frame=lines, label=lauflaengencodierung.hs]{haskell}{scripts/haskell/lauflaengencodierung.hs} \subsection{Funktionen höherer Ordnung}\xindex{Folds}\xindex{foldl}\xindex{foldr}\label{bsp:foldl-und-foldr} \inputminted[linenos, numbersep=5pt, tabsize=4, 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L*x6Ne)d>Cr14w!Q diff --git a/documents/Programmierparadigmen/scripts/haskell/hirsch-index.hs b/documents/Programmierparadigmen/scripts/haskell/hirsch-index.hs new file mode 100644 index 0000000..10416d9 --- /dev/null +++ b/documents/Programmierparadigmen/scripts/haskell/hirsch-index.hs @@ -0,0 +1,12 @@ +import Data.List --sort und reverse + +hIndex :: (Num a, Ord a) => [a] -> a +hIndex l = helper (reverse (sort l)) 0 + where helper [] acc = acc + helper (z:ls) acc + | z > acc = helper ls (acc + 1) + | otherwise = acc + +-- Alternativ +hindex1 = length . takeWhile id . zipWith (<=) [1..] . reverse . sort +hindex2 = length . takeWhile (\(i, n) -> n >= i) . zip [1..] . reverse . sort \ No newline at end of file diff --git a/documents/Programmierparadigmen/scripts/haskell/lauflaengencodierung.hs b/documents/Programmierparadigmen/scripts/haskell/lauflaengencodierung.hs new file mode 100644 index 0000000..a3c9c99 --- /dev/null +++ b/documents/Programmierparadigmen/scripts/haskell/lauflaengencodierung.hs @@ -0,0 +1,21 @@ +splitWhen :: (a -> Bool) -> [a] -> ([a], [a]) +splitWhen _ [] = ([], []) +splitWhen p (x:xs) + | p x = ([], x:xs) + | otherwise = let (ys, zs) = splitWhen p xs + in (x:ys, zs) +-- >>> splitWhen even [1,2,3] +-- ([1],[2,3]) + +group :: Eq a => [a] -> [[a]] +group [] = [] +group (x:xs) = let (group1, rest) = splitWhen (/=x) xs + in (x:group1) : group rest + +encode :: Eq a => [a] -> [(a, Int)] +encode xs = map (\x -> (head x, length x)) (group xs) + +decode [] = [] +decode ((x,n):xs) = replicate n x ++ decode xs +-- alternativ +decode = concat . (map (\(x,n)->replicate n x)) diff --git a/documents/Programmierparadigmen/scripts/haskell/let-where-bindung.hs b/documents/Programmierparadigmen/scripts/haskell/let-where-bindung.hs new file mode 100644 index 0000000..c905c62 --- /dev/null +++ b/documents/Programmierparadigmen/scripts/haskell/let-where-bindung.hs @@ -0,0 +1,5 @@ +>>> let f = 3; g = f where f = 7 +>>> f +3 +>>> g +7 \ No newline at end of file diff --git a/documents/Programmierparadigmen/scripts/haskell/polynome.hs b/documents/Programmierparadigmen/scripts/haskell/polynome.hs new file mode 100644 index 0000000..3be9da0 --- /dev/null +++ b/documents/Programmierparadigmen/scripts/haskell/polynome.hs @@ -0,0 +1,16 @@ +type Polynom = [Double] + +add :: Polynom -> Polynom -> Polynom +add a [] = a +add [] a = a +add (x:xs) (y:ys) = (x+y) : add xs ys + +eval :: Polynom -> Double -> Double +eval [] x = 0 +eval (p:ps) x = p + x * (eval ps x) +-- alternativ: +eval p x = foldr (\element rest ->element+x*rest) 0 p + +deriv :: Polynom -> Polynom +deriv [] = [] +deriv p = zipWith (*) [1..] (tail p) \ No newline at end of file