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