# Prelude extensions

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## Contents |

## 1 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.

### 1.1 Treating pairs and lists in the same way

We can define a Pair class which allows us to process both pairs and non-empty lists using the same operator:

import Control.Arrow ((***)) infixl 4 <**> class Pair p x y | p -> x, p -> y where toPair :: p -> (x, y) (<**>) :: (x -> a -> b) -> (y -> a) -> p -> b (<**>) f g = uncurry id . (f *** g) . toPair instance Pair (a, b) a b where toPair = id instance Pair [a] a [a] where toPair l = (head l, tail l)

## 2 Matrices

A simple representation of matrices is as lists of lists of numbers:

newtype Matrix a = Matrix [[a]] deriving (Eq, Show)

Num

abs

signum

instance Num a => Num (Matrix a) where Matrix as + Matrix bs = Matrix (zipWith (zipWith (+)) as bs) Matrix as - Matrix bs = Matrix (zipWith (zipWith (-)) as bs) Matrix as * Matrix bs = Matrix [[sum $ zipWith (*) a b | b <- transpose bs] | a <- as] negate (Matrix as) = Matrix (map (map negate) as) fromInteger x = Matrix (iterate (0:) (fromInteger x : repeat 0)) abs m = m signum _ = 1

fromInteger

Applying the linear transformation defined by a matrix to a vector is

apply :: Num a => Matrix a -> [a] -> [a] apply (Matrix as) b = [sum (zipWith (*) a b) | a <- as]

## 3 Data.Either extensions

import Data.Either either', trigger, trigger_, switch :: (a -> b) -> (a -> b) -> Either a a -> Either b b either' f g (Left x) = Left (f x) either' f g (Right x) = Right (g x) trigger f g (Left x) = Left (f x) trigger f g (Right x) = Left (g x) trigger_ f g (Left x) = Right (f x) trigger_ f g (Right x) = Right (g x) switch f g (Left x) = Right (f x) switch f g (Right x) = Left (g x) sure :: (a->b) -> Either a a -> b sure f = either f f sure' :: (a->b) -> Either a a -> Either b b sure' f = either' f f