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{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE UndecidableInstances #-}
module T14172a where
import Data.Coerce
import Data.Functor.Compose
import Data.Functor.Identity
class Profunctor p where
dimap :: (a -> b) -> (c -> d) -> p b c -> p a d
(#.) :: Coercible c b => (b -> c) -> p a b -> p a c
instance Profunctor (->) where
dimap ab cd bc = cd . bc . ab
{-# INLINE dimap #-}
(#.) _ = coerce (\x -> x :: b) :: forall a b. Coercible b a => a -> b
{-# INLINE (#.) #-}
type Iso s t a b = forall p f. (Profunctor p, Functor f) => p a (f b) -> p s (f t)
type Iso' s a = Iso s s a a
iso :: (s -> a) -> (b -> t) -> Iso s t a b
iso sa bt = dimap sa (fmap bt)
{-# INLINE iso #-}
type AnIso s t a b = Exchange a b a (Identity b) -> Exchange a b s (Identity t)
data Exchange a b s t = Exchange (s -> a) (b -> t)
instance Profunctor (Exchange a b) where
dimap f g (Exchange sa bt) = Exchange (sa . f) (g . bt)
{-# INLINE dimap #-}
(#.) _ = coerce
{-# INLINE ( #. ) #-}
withIso :: AnIso s t a b -> ((s -> a) -> (b -> t) -> r) -> r
withIso ai k = case ai (Exchange id Identity) of
Exchange sa bt -> k sa (runIdentity #. bt)
{-# INLINE withIso #-}
class Wrapped s where
type Unwrapped s :: *
_Wrapped' :: Iso' s (Unwrapped s)
class Wrapped s => Rewrapped (s :: *) (t :: *)
class (Rewrapped s t, Rewrapped t s) => Rewrapping s t
instance (Rewrapped s t, Rewrapped t s) => Rewrapping s t
instance (t ~ Compose f' g' a') => Rewrapped (Compose f g a) t
instance Wrapped (Compose f g a) where
type Unwrapped (Compose f g a) = f (g a)
_Wrapped' = iso getCompose Compose
_Wrapping :: Rewrapping s t => (Unwrapped s -> s) -> Iso s t (Unwrapped s) (Unwrapped t)
_Wrapping _ = _Wrapped
{-# INLINE _Wrapping #-}
_Wrapped :: Rewrapping s t => Iso s t (Unwrapped s) (Unwrapped t)
_Wrapped = withIso _Wrapped' $ \ sa _ -> withIso _Wrapped' $ \ _ bt -> iso sa bt
{-# INLINE _Wrapped #-}
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