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28 lines
703 B
Idris
28 lines
703 B
Idris
module Control.Category
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import Data.Morphisms
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public export
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interface Category (0 cat : obj -> obj -> Type) | cat where
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id : cat a a
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(.) : cat b c -> cat a b -> cat a c
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public export
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Category Morphism where
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id = Mor id
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-- disambiguation needed below, because unification can now get further
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-- here with Category.(.) and it's only interface resolution that fails!
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(Mor f) . (Mor g) = Mor $ Basics.(.) f g
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public export
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Monad m => Category (Kleislimorphism m) where
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id = Kleisli (pure . id)
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(Kleisli f) . (Kleisli g) = Kleisli $ \a => g a >>= f
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infixr 1 >>>
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public export
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(>>>) : Category cat => cat a b -> cat b c -> cat a c
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f >>> g = g . f
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