Idris2/tests/idris2/interface006/Biapplicative.idr
2020-09-30 10:51:07 +01:00

70 lines
1.8 KiB
Idris

module Biapplicative
import Apply
infixl 4 <<*>>, <<*, *>>, <<**>>
||| Biapplicatives
||| @p the action of the Biapplicative on pairs of objects
public export
interface Bifunctor p => Biapplicative p where -- (p : Type -> Type -> Type) where
||| Lifts two values into a Biapplicative
|||
||| ````idris example
||| bipure 1 "hello" = (1, "hello")
||| ````
|||
bipure : a -> b -> p a b
||| Applies a Biapplicative of functions to a second Biapplicative
|||
||| ````idris example
||| ( (\x => x + 1), reverse ) <<*>> (1, "hello") == (2, "olleh")
||| ````
|||
(<<*>>) : p (a -> b) (c -> d) -> p a c -> p b d
||| Sequences two Biapplicatives rightwards
|||
||| ````idris example
||| (1, "hello") *>> (2, "goodbye") = (2, "goodbye")
||| ````
|||
(*>>) : p a b -> p c d -> p c d
a *>> b = bimap (const id) (const id) <<$>> a <<*>> b
||| Sequences two Biapplicatives leftwards
|||
||| ````idris example
||| (1, "hello") <<* (2, "goodbye") = (1, "hello")
||| ````
|||
(<<*) : p a b -> p c d -> p a b
a <<* b = bimap const const <<$>> a <<*>> b
||| Applies the second of two Biapplicatives to the first
|||
||| ````idris example
||| (1, "hello") <<**>> ( (\x => x + 1), reverse ) == (2, "olleh")
||| ````
|||
export
(<<**>>) : Biapplicative p => p a c -> p (a -> b) (c -> d) -> p b d
(<<**>>) = flip (<<*>>)
export
biliftA2 : Biapplicative p => (a -> b -> c) ->
(d -> e -> f) -> p a d -> p b e -> p c f
biliftA2 f g a b = bimap f g <<$>> a <<*>> b
export
biliftA3 : Biapplicative p =>
(a -> b -> c -> d) -> (e -> f -> g -> h) -> p a e -> p b f -> p c g -> p d h
biliftA3 f g a b c = bimap f g <<$>> a <<*>> b <<*>> c
public export
implementation Biapplicative Pair where
bipure a b = (a, b)
(f, g) <<*>> (a, b) = (f a, g b)