Categories in Haskell

Hask(Cat).md

Hask(Cat)

{-# LANGUAGE TypeOperators #-}
 
infix 9 ∘
class Category k where
  ident :: a `k` a
  (∘) :: (b `k` c) -> (a `k` b) -> (a `k` c)
  

instance Category (->) where
  ident = \x -> x
  g ∘ f = \x -> g (f x)

infix 3 Δ
class Category k => Cartesian k where
  (Δ) :: (a `k` c) -> (a `k` d) -> (a `k` (c,d)))
  

instance Category (->) where
  ident = \x -> x
  g ∘ f = \x -> g (f x)

sq x = x * x

main = print $ 
  -- ident sq 2
  (sq ∘ sq) 2