mirror of
https://github.com/idris-lang/Idris2.git
synced 2024-12-27 05:34:40 +03:00
89 lines
2.4 KiB
Idris
89 lines
2.4 KiB
Idris
module Apply
|
|
|
|
-- These are not Biapplicatives. Those are in Data.Biapplicative
|
|
|
|
infixl 4 <<$>>, <<&>>, <<.>>, <<., .>>, <<..>>
|
|
|
|
||| Primarily used to make the definitions of bilift2 and bilift3 pretty
|
|
|||
|
|
||| ```idris example
|
|
||| bimap const const <<$>> (1, 2) <<.>> (3, 4) == (1, 2)
|
|
||| ```
|
|
|||
|
|
export
|
|
(<<$>>) : (a -> b) -> a -> b
|
|
(<<$>>) = id
|
|
|
|
||| <<$>> with the arguments reversed
|
|
|||
|
|
||| ```idris example
|
|
||| (1, 2) <<&>> bimap const const <<.>> (3, 4) == (1, 2)
|
|
||| ```
|
|
|||
|
|
(<<&>>) : a -> (a -> b) -> b
|
|
(<<&>>) = flip id
|
|
|
|
||| Biapplys (not to be confused with Biapplicatives)
|
|
||| @p The action of the Biapply on pairs of objects
|
|
public export
|
|
interface Bifunctor p => Biapply (0 p : Type -> Type -> Type) where
|
|
|
|
||| Applys a Bifunctor of functions to another Bifunctor of the same type
|
|
|||
|
|
||| ````idris example
|
|
||| (reverse, (\x => x + 1)) <<.>> ("hello", 1) == ("olleh", 2)
|
|
||| ````
|
|
|||
|
|
(<<.>>) : p (a -> b) (c -> d) -> p a c -> p b d
|
|
|
|
||| Given two Bifunctors, sequences them leftwards
|
|
|||
|
|
||| ````idris example
|
|
||| ("hello", 1) <<. ("goodbye", 2) == ("hello", 1)
|
|
||| ````
|
|
|||
|
|
(<<.) : p a b -> p c d -> p a b
|
|
a <<. b = bimap const const <<$>> a <<.>> b
|
|
|
|
||| Given two Bifunctors, sequences them rightwards
|
|
|||
|
|
||| ````idris example
|
|
||| ("hello", 1) <<. ("goodbye", 2) == ("goodbye", 2)
|
|
||| ````
|
|
|||
|
|
(.>>) : p a b -> p c d -> p c d
|
|
a .>> b = bimap (const id) (const id) <<$>> a <<.>> b
|
|
|
|
||| Lifts a pair of binary functions into a Bifunctor
|
|
|||
|
|
||| ````idris example
|
|
||| bilift2 (++) (+) ("hello", 1) ("goodbye", 2) == ("hellogoodbye", 3)
|
|
||| ````
|
|
|||
|
|
bilift2 : Biapply p => (a -> b -> c) -> (d -> e -> f) -> p a d -> p b e -> p c f
|
|
bilift2 f g a b = bimap f g <<$>> a <<.>> b
|
|
|
|
||| Lifts a pair of ternary functions into a Bifunctor
|
|
|||
|
|
||| ````idris example
|
|
||| bilift3 (\x,y,z => x ++ (y ++ z)) (\x,y,z => x + (y + z))
|
|
||| ("hello", 1) ("goodbye", 2) ("hello again", 3) ==
|
|
||| ("hellogoodbyehello again", 6)
|
|
||| ````
|
|
|||
|
|
bilift3 : Biapply p => (a -> b -> c -> d) -> (e -> f -> g -> h)
|
|
-> p a e -> p b f -> p c g -> p d h
|
|
bilift3 f g a b c = bimap f g <<$>> a <<.>> b <<.>> c
|
|
|
|
||| Applies the second of two Bifunctors to the first
|
|
|||
|
|
||| ````idris example
|
|
||| ("hello", 1) <<..>> (reverse, (\x => x + 1)) == ("olleh", 2)
|
|
||| ````
|
|
|||
|
|
(<<..>>): Biapply p => p a c -> p (a -> b) (c -> d) -> p b d
|
|
(<<..>>) = flip (<<.>>)
|
|
|
|
implementation Biapply Pair where
|
|
(f, g) <<.>> (a, b) = (f a, g b)
|