search

ekmett / profunctors

Haskell 98 Profunctors
http://hackage.haskell.org/package/profunctors
Other
70 stars 43 forks source link

Add a real Cotambara and Copastro construction. #33

Closed ekmett closed 8 years ago

ekmett commented 8 years ago

If we look at the forgetful functor U from the category LPro of costrong profunctors to the category Pro of profunctors, we can find its adjoints by using the usual Kan extension trick.

Ran U 1 -| U -| Lan U 1

Composing the parts of this adjoint triple yields a "real" Cotambara and Copastro construction.

Using Lan U 1:

data Cotambara q a b where
    Cotambara :: Costrong r => (r :-> q) -> r a b -> Cotambara q a b

Using Ran U 1:

newtype Copastro p a b = Copastro { runCopastro :: forall r. Costrong r => (p :-> r) -> r a b }

Copastro -| Cotambara

and now they freely/cofreely generate costrength. They should also have the profunctor comonad/monad structure we find in the usual Pastro and Tambara constructions.