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{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE TypeOperators #-}
module Data.Profunctor.Strong where
import Control.Arrow
import Control.Category
import Data.Tuple
import Prelude hiding (id,(.))
infixr 0 :->
type p :-> q = forall a b. p a b -> q a b
class Profunctor p where
dimap :: (a -> b) -> (c -> d) -> p b c -> p a d
class ProfunctorFunctor t where
promap :: Profunctor p => (p :-> q) -> t p :-> t q
class ProfunctorFunctor t => ProfunctorMonad t where
proreturn :: Profunctor p => p :-> t p
projoin :: Profunctor p => t (t p) :-> t p
class ProfunctorFunctor t => ProfunctorComonad t where
proextract :: Profunctor p => t p :-> p
produplicate :: Profunctor p => t p :-> t (t p)
class Profunctor p => Strong p where
first' :: p a b -> p (a, c) (b, c)
first' = dimap swap swap . second'
second' :: p a b -> p (c, a) (c, b)
second' = dimap swap swap . first'
----------------------------------------------------------------------------
newtype Tambara p a b = Tambara { runTambara :: forall c. p (a, c) (b, c) }
instance Profunctor p => Profunctor (Tambara p) where
dimap f g (Tambara p) = Tambara $ dimap (first f) (first g) p
instance ProfunctorFunctor Tambara where
promap f (Tambara p) = Tambara (f p)
instance ProfunctorComonad Tambara where
proextract (Tambara p) = dimap (\a -> (a,())) fst p
produplicate (Tambara p) = Tambara (Tambara $ dimap hither yon p)
where
hither :: ((a, b), c) -> (a, (b, c))
hither ~(~(x,y),z) = (x,(y,z))
yon :: (a, (b, c)) -> ((a, b), c)
yon ~(x,~(y,z)) = ((x,y),z)
instance Profunctor p => Strong (Tambara p) where
first' = (\x -> runTambara x) . produplicate
-- Simple subsumption (#17775) requires eta expansion here
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