Precursor.Function

Documentation

const :: a -> b -> a

const x is a unary function which evaluates to x for all inputs.

For instance,

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

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.

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

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

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

(*) `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)

($) :: (a -> b) -> a -> b infixr 0

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.

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

& 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

applyN :: (a -> a) -> Int -> a -> a

>>> applyN (2+) 2 0
4

converge :: Eq a => (a -> a) -> a -> a

Apply a function until it no longer changes its input.

converge tail xs === []

(.:) :: (c -> d) -> (a -> b -> c) -> a -> b -> d infixr 8

"Blackbird" operator. For example:

aggregate f xs = sum (map f xs)

aggregate = sum .: map