Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Data.Function

Contents

Prelude re-exports
Other combinators

Description

Simple combinators working solely on and with functions.

Synopsis

Prelude re-exports

id :: a -> aSource

Identity function.

const :: a -> b -> aSource

Constant function.

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

Function composition.

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

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

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

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 Data.List.zipWith ($) fs xs.

Other combinators

fix :: (a -> a) -> aSource

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 -> cSource

(*) `on` f = \x y -> f x * f y.

Typical usage: Data.List.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)
```