# Prelude extensions

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<haskell> |
<haskell> |
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instance Num a => Num [[a]] where |
instance Num a => Num [[a]] where |
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− | abs x = map (map abs) x |
+ | negate = map (map negate) |

(+) x y = zipWith (zipWith (+)) x y |
(+) x y = zipWith (zipWith (+)) x y |
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(*) x y = map (matrixXvector x) y |
(*) x y = map (matrixXvector x) y |
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where |
where |
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− | matrixXvector :: [[a]] -> [a] -> [a] |
+ | matrixXvector m v = foldl vectorsum (repeat 0) $ zipWith vectorXnumber m v |

− | matrixXvector m v = foldl vectorsum [] $ zipWith vectorXnumber m v |
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− | vectorXnumber :: [a] -> a -> [a] |
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vectorXnumber v n = map (n*) v |
vectorXnumber v n = map (n*) v |
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− | vectorsum :: [a] -> [a] -> [a] |
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− | vectorsum [] y = y |
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− | vectorsum x [] = x |
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vectorsum x y = zipWith (+) x y |
vectorsum x y = zipWith (+) x y |
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+ | </haskell> |
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+ | |||

+ | Or, as another option: |
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+ | |||

+ | <haskell> |
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+ | import Data.List |
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+ | |||

+ | instance Num a => Num [[a]] where |
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+ | (+) = zipWith (zipWith (+)) |
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+ | (-) = zipWith (zipWith (-)) |
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+ | negate = map (map negate) |
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+ | n * m = [ [ sum $ zipWith (*) v w | w <- transpose n ] | v <- m ] |
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</haskell> |
</haskell> |

## Revision as of 14:24, 22 June 2006

## Contents |

## 1 Sorted lists

The following are versions of standard prelude functions, but intended for sorted lists. The advantage is that they frequently reduce execution time by an O(n). The disadvantage is that the elements have to be members of Ord, and the lists have to be already sorted.

-- Eliminates duplicate entries from the list, where duplication is defined -- by the 'eq' function. The last value is kept. sortedNubBy :: (a -> a -> Bool) -> [a] -> [a] sortedNubBy eq (x1 : xs@(x2 : _)) = if eq x1 x2 then sortedNubBy eq xs else x1 : sortedNubBy eq xs sortedNubBy _ xs = xs sortedNub :: (Eq a) => [a] -> [a] sortedNub = sortedNubBy (==) -- Merge two sorted lists into a new sorted list. Where elements are equal -- the element from the first list is taken first. mergeBy :: (a -> a -> Ordering) -> [a] -> [a] -> [a] mergeBy cmp xs@(x1:xs1) ys@(y1:ys1) = if cmp x1 y1 == GT then y1 : mergeBy cmp xs ys1 else x1 : mergeBy cmp xs1 ys mergeBy _ [] ys = ys mergeBy _ xs [] = xs merge :: (Ord a) => [a] -> [a] -> [a] merge = mergeBy compare

## 2 Tuples

It is often necessary to apply functions to either the first or the second part of a pair. This is often considered a form of mapping (like map from Data.List).

-- | Apply a function to the first element of a pair mapFst :: (a -> c) -> (a, b) -> (c, b) mapFst f (a, b) = (f a, b) -- | Apply a function to the second element of a pair mapSnd :: (b -> c) -> (a, b) -> (c, b) mapSnd f (a, b) = (a, f b) -- | Apply a function to both elements of a pair mapPair :: (a -> c, b -> d) -> (a, b) -> (c, d) mapPair (f, g) (a, b) = (f a, g b)

*Additional Graph Utilities*) contains

mapFst

mapSnd

><

mapPair

first

second

***

See also point-free programming.

## 3 Matrix

Sometimes you just want to multiply 2 matrices, like

[[1,2],[3,4]]*[[1,2],[3,4]]

The following makes it possible, but requires -fglasgow-exts :

instance Num a => Num [[a]] where negate = map (map negate) (+) x y = zipWith (zipWith (+)) x y (*) x y = map (matrixXvector x) y where matrixXvector m v = foldl vectorsum (repeat 0) $ zipWith vectorXnumber m v vectorXnumber v n = map (n*) v vectorsum x y = zipWith (+) x y

Or, as another option:

import Data.List instance Num a => Num [[a]] where (+) = zipWith (zipWith (+)) (-) = zipWith (zipWith (-)) negate = map (map negate) n * m = [ [ sum $ zipWith (*) v w | w <- transpose n ] | v <- m ]