base-4.3.1.0: Basic libraries

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

- id :: a -> a
- const :: a -> b -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- flip :: (a -> b -> c) -> b -> a -> c
- ($) :: (a -> b) -> a -> b
- fix :: (a -> a) -> a
- on :: (b -> b -> c) -> (a -> b) -> a -> a -> c

# Prelude re-exports

id :: a -> a

Identity function.

const :: a -> b -> a

Constant function.

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

Function composition.

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

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

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

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) -> a

``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

`(*) `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)