module Control.Category.Tensor where

import Data.Semigroupoid.Dual
import Prelude

-- could use data-lens:Control.Category.Product(Tensor)
class Tensor cc where
    tensorUnit :: cc () ()
    tensorPair :: cc a1 b1 -> cc a2 b2 -> cc (a1, a2) (b1, b2)

instance Tensor (->) where
    tensorUnit = id
    tensorPair ab1 ab2 (a1, a2) = (ab1 a1, ab2 a2)

instance (Tensor cc) => Tensor (Dual cc) where
    tensorUnit = Dual tensorUnit
    tensorPair (Dual ab1) (Dual ab2) = Dual (tensorPair ab1 ab2)