base-4.10.1.0: Basic libraries

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
• ($) :: (a -> b) -> a -> b • (&) :: a -> (a -> b) -> b • fix :: (a -> a) -> a • on :: (b -> b -> c) -> (a -> b) -> a -> a -> c Prelude re-exports id :: a -> a Source # Identity function. const :: a -> b -> a Source # const x is a unary function which evaluates to x for all inputs. For instance, >>> map (const 42) [0..3] [42,42,42,42]  (.) :: (b -> c) -> (a -> b) -> a -> c infixr 9 Source # Function composition. flip :: (a -> b -> c) -> b -> a -> c Source # flip f takes its (first) two arguments in the reverse order of f. ($) :: (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.

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 $.

Since: 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.

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

(*) 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)