papa-base-export-0.4: Prelude with only useful functions

Papa.Base.Export.Data.Function

Synopsis

• ($) :: (a -> b) -> a -> b • (&) :: a -> (a -> b) -> b • fix :: (a -> a) -> a • on :: (b -> b -> c) -> (a -> b) -> a -> a -> c # Documentation ($) :: (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

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 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)