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41 lines
1.0 KiB
Idris
41 lines
1.0 KiB
Idris
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module Bifunctor
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||| Bifunctors
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||| @p The action of the Bifunctor on pairs of objects
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public export
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interface Bifunctor (p : Type -> Type -> Type) where
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||| The action of the Bifunctor on pairs of morphisms
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||| ````idris example
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||| bimap (\x => x + 1) reverse (1, "hello") == (2, "olleh")
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||| ````
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bimap : (a -> b) -> (c -> d) -> p a c -> p b d
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bimap f g = first f . second g
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||| The action of the Bifunctor on morphisms pertaining to the first object
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||| ````idris example
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||| first (\x => x + 1) (1, "hello") == (2, "hello")
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||| ````
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first : (a -> b) -> p a c -> p b c
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first = flip bimap id
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||| The action of the Bifunctor on morphisms pertaining to the second object
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||| ````idris example
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||| second reverse (1, "hello") == (1, "olleh")
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||| ````
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second : (a -> b) -> p c a -> p c b
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second = bimap id
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implementation Bifunctor Either where
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bimap f _ (Left a) = Left $ f a
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bimap _ g (Right b) = Right $ g b
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public export
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implementation Bifunctor Pair where
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bimap f g (a, b) = (f a, g b)
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