{-# LANGUAGE GADTs #-} module Data.Semigroupoid.Product ( Product(..) , distributeDualProduct , factorDualProduct ) where import Data.Semigroupoid import Data.Semigroupoid.Dual import Data.Groupoid data Product j k a b where Pair :: j a b -> k a' b' -> Product j k (a,a') (b,b') instance (Semigroupoid j, Semigroupoid k) => Semigroupoid (Product j k) where Pair w x `o` Pair y z = Pair (w `o` y) (x `o` z) instance (Groupoid j, Groupoid k) => Groupoid (Product j k) where inv (Pair w x) = Pair (inv w) (inv x) distributeDualProduct :: Dual (Product j k) a b -> Product (Dual j) (Dual k) a b distributeDualProduct (Dual (Pair l r)) = Pair (Dual l) (Dual r) factorDualProduct :: Product (Dual j) (Dual k) a b -> Dual (Product j k) a b factorDualProduct (Pair (Dual l) (Dual r)) = Dual (Pair l r)