base-4.16.0.0: Basic libraries
CopyrightNils Anders Danielsson 2006
Alexander Berntsen 2014
LicenseBSD-style (see the LICENSE file in the distribution)
Maintainerlibraries@haskell.org
Stabilitystable
Portabilityportable
Safe HaskellTrustworthy
LanguageHaskell2010

Data.Function

Contents

Description

Simple combinators working solely on and with functions.

Synopsis
  • id :: a -> a
  • const :: a -> b -> a
  • (.) :: (b -> c) -> (a -> b) -> a -> c
  • flip :: (a -> b -> c) -> b -> a -> c
  • ($) :: forall r a (b :: TYPE r). (a -> b) -> a -> b
  • (&) :: a -> (a -> b) -> b
  • fix :: (a -> a) -> a
  • on :: (b -> b -> c) -> (a -> b) -> a -> a -> c

Prelude re-exports

id :: a -> a Source #

Identity function.

id x = x

const :: a -> b -> a Source #

const x y always evaluates to x, ignoring its second argument.

>>> const 42 "hello"
42
>>> map (const 42) [0..3]
[42,42,42,42]

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9 Source #

Function composition.

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

flip f takes its (first) two arguments in the reverse order of f.

>>> flip (++) "hello" "world"
"worldhello"

($) :: forall r a (b :: TYPE r). (a -> b) -> a -> b infixr 0 Source #

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

Note that ($) is representation-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed.

Other combinators

(&) :: a -> (a -> b) -> b infixl 1 Source #

& is a reverse application operator. This provides notational convenience. Its precedence is one higher than that of the forward application operator $, which allows & to be nested in $.

>>> 5 & (+1) & show
"6"

Since: base-4.8.0.0

fix :: (a -> a) -> a Source #

fix f is the least fixed point of the function f, i.e. the least defined x such that f x = x.

For example, we can write the factorial function using direct recursion as

>>> let fac n = if n <= 1 then 1 else n * fac (n-1) in fac 5
120

This uses the fact that Haskell’s let introduces recursive bindings. We can rewrite this definition using fix,

>>> fix (\rec n -> if n <= 1 then 1 else n * rec (n-1)) 5
120

Instead of making a recursive call, we introduce a dummy parameter rec; when used within fix, this parameter then refers to fix’s argument, hence the recursion is reintroduced.

on :: (b -> b -> c) -> (a -> b) -> a -> a -> c infixl 0 Source #

on b u x y runs the binary function b on the results of applying unary function u to two arguments x and y. From the opposite perspective, it transforms two inputs and combines the outputs.

((+) `on` f) x y = f x + f y

Typical usage: sortBy (compare `on` fst).

Algebraic properties:

  • (*) `on` id = (*) -- (if (*) ∉ {⊥, const ⊥})
  • ((*) `on` f) `on` g = (*) `on` (f . g)
  • flip on f . flip on g = flip on (g . f)