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

on b u x y runs the binary function b on the results of applying unary function u to two arguments x and y. From the opposite perspective, it transforms two inputs and combines the outputs.

(op `on` f) x y = f x `op` f y

Examples

>>> sortBy (compare `on` length) [[0, 1, 2], [0, 1], [], [0]]
[[],[0],[0,1],[0,1,2]]

>>> ((+) `on` length) [1, 2, 3] [-1]
4

>>> ((,) `on` (*2)) 2 3
(4,6)

Algebraic properties

• (*) `on` id = (*) -- (if (*) ∉ {⊥, const
  ⊥})

• ((*) `on` f) `on` g = (*) `on` (f . g)

• flip on f . flip on g = flip on (g .
  f)

Known as on in newer versions of the base package.

on b u x y runs the binary function b on the results of applying unary function u to two arguments x and y. From the opposite perspective, it transforms two inputs and combines the outputs.

((+) `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)

Pronounced 'appose'. Synonym for on

(*) `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)