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Data.Function

Portability | portable
Stability | experimental
Maintainer | libraries@haskell.org

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)

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