Useful high order functions in Haskell

p0.md

Useful high order functions in Haskell

flip

• Header:

  flip :: (a -> b -> c) -> (b -> a -> c)

• Description:

  flip f returns the f function but with its two parameters inverted. It is defined by

  flip f x y = f y x

• Examples:

  half = flip div 2
  
  half 10
  👉 5

composition (.)

• Header:

  (.) :: (b -> c) -> (a -> b) -> a -> c

• Description:

  f . g is the composition of functions f i g.

• Examples:

  bigger3 = take 3 . reverse . sort
  
  bigger3 [3, 1, 2, 6, 7]
  👉 [7, 6, 3]

   ```

aplication ($)

• Header:

  ($) :: (a -> b) -> a -> b

• Description:

  f $ xis the same as f x. Looks like unnecessay, but because of its low priority, it can save us from closing lots of parameters!

• Examples:

  tail (tail (tail (tail "Jordi")))
  👉 "i"
  tail $ tail $ tail $ tail "Jordi"
  👉 "i"

map

• Header:

  map :: (a -> b) -> [a] -> [b]

• Description:

  map f xs is the list obtained when applying f to each element of the xs list, so that map f [x1, x2, ..., xn] és [f x1, f x2, ..., f xn].

• Examples:

  map even [2, 4, 6, 7]
  👉 [True, True, True, False]
  
  map (*2) [2, 4, 6, 7]
  👉 [4, 8, 12, 14]

filter

• Header:

  filter :: (a -> Bool) -> [a] -> [a]

• Description:

  filter p xs is the sublist of elements from xs that satisfy the p predicate.

• Examples:

  filter even [2, 1, 4, 6, 7]
  👉 [2, 4, 6]

zipWith

• Header:

  zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

• Description:

  zipWith op xs ys is the list obtained operating each element of xs with each elements of ys via the op function, from left to right, as long as there are elements.

• Examples:

  zipWith (+) [1, 2, 3] [5, 1, 8, 9]
  👉 [6, 3, 11]

all

• Header:

  all :: (a -> Bool) -> [a] -> Bool

• Description:

  all p xs tells whether all elements in xs satisfy the p predicate.

• Examples:

  all even [2, 1, 4, 6, 7]
  👉 False
  all even [2, 4, 6]
  👉 True

any

• Header:

  any :: (a -> Bool) -> [a] -> Bool

• Description:

  any p xs tells whether some element in xs satisfies the p predicate.

• Examples:

  any even [2, 1, 4, 6, 7]
  👉 True
  all odd [2, 4, 6]
  👉 False

dropWhile

• Header:

  dropWhile :: (a -> Bool) -> [a] -> [a]

• Description:

  dropWhile p xs és la subllista de xs que elimina els primers elements de xs que compleixen el predicat p (fins al final o al primer qua no la compleix).

• Examples:

  dropWhile even [2, 4, 6, 7, 8]
  👉 [7, 8]
  dropWhile even [2, 4]
  👉 []

takeWhile

• Header:

  takeWhile :: (a -> Bool) -> [a] -> [a]

• Description:

  takeWhile p xs is the sublist of xs that contains the first elements of xs that satisfy the p predicate.

• Examples:

  takeWhile even [2, 4, 6, 7, 8]
  👉 [2, 4, 6]
  takeWhile even [1, 3]
  👉 []

iterate

• Header:

  iterate :: (a -> a) -> a -> [a]

• Description:

  iterate f x returns the infinite list [x, f x, f (f x), f (f (f x)), ...].

• Examples:

  iterate (*2) 1
  👉 [1, 2, 4, 8, 16, ...]

foldl

• Header:

  foldl :: (b -> a -> b) -> b -> [a] -> b

• Description:

  foldl ⊕ x0 xs folds an operator ⊕ from the left, so that foldl ⊕ x0 [x1, x2, ..., xn] és (((x0 ⊕ x1) ⊕ x2) ⊕ ...) ⊕ xn.

• Examples:

  foldl (+) 0 [3, 2, (-1)]
  👉 4

foldr

• Header:

  foldr :: (a -> b -> b) -> b -> [a] -> b

• Description:

  foldr ⊕ x0 xs folds an operator ⊕ from the right, so that foldr ⊕ x0 [x1, x2, ..., xn] és x1 ⊕ (x2 ... ⊕ (xn ⊕ x0))).

• Examples:

  foldr (+) 0 [3, 2, (-1)]
  👉 4

scanl

• Header:

  scanl :: (b -> a -> b) -> b -> [a] -> [b]

• Description:

  scanl f z xs is just like foldl f z xs but rather than returning the final results, it returns the list with all the partial results.

• Examples:

  scanl (+) 0 [3, 2, (-1)]
  👉 [0, 3, 5, 4]

scanr

• Header:

  scanr :: (a -> b -> b) -> b -> [a] -> [b]

• Description:

  scanr f z xs is just like foldr f z xs but rather than returning the final results, it returns the list with all the partial results.

• Examples:

  scanr (+) 0 [3, 2, (-1)]
  👉 [4, 1, -1, 0]

const

• Header:

  const :: a -> b -> a

• Description:

   const x is the function tha always returns x, independently of what is applied to it.

• Examples:

  map (const 42) [1 .. 5]
  👉 [42, 42, 42, 42, 42]

id

• Header:

  id :: a -> a

• Description:

   id és the identity function. Looks unnecessary but may be useful at some point.

• Examples:

  map id [1 .. 5]
  👉 [1, 2, 3, 4, 5]

A la signatura i a la descripció de takeWhile posa dropWhile

@felixarpa: Arreglat, gràcies! 👍

good set of functions