module Data.Functor.Invariant where
import Prelude
import Control.Applicative (ZipList)
import Data.Functor.Contravariant
import Data.Functor.Compose
import Data.Functor.Identity
import Data.Functor.Sum
import Data.Functor.Product
import Data.List.NonEmpty (NonEmpty)
class Invariant f where
invmap :: (a -> a') -> (a' -> a) -> f a -> f a'
data Iso a b = Iso (a -> b) (b -> a)
invIso :: Invariant f => Iso a a' -> Iso (f a) (f a')
invIso :: Iso a a' -> Iso (f a) (f a')
invIso (Iso a -> a'
f a' -> a
g) = (f a -> f a') -> (f a' -> f a) -> Iso (f a) (f a')
forall a b. (a -> b) -> (b -> a) -> Iso a b
Iso ((a -> a') -> (a' -> a) -> f a -> f a'
forall (f :: * -> *) a a'.
Invariant f =>
(a -> a') -> (a' -> a) -> f a -> f a'
invmap a -> a'
f a' -> a
g) ((a' -> a) -> (a -> a') -> f a' -> f a
forall (f :: * -> *) a a'.
Invariant f =>
(a -> a') -> (a' -> a) -> f a -> f a'
invmap a' -> a
g a -> a'
f)
newtype FromFunctor f a = FromFunctor { FromFunctor f a -> f a
runBi :: f a }
instance Functor f => Invariant (FromFunctor f) where
invmap :: (a -> a') -> (a' -> a) -> FromFunctor f a -> FromFunctor f a'
invmap :: (a -> a') -> (a' -> a) -> FromFunctor f a -> FromFunctor f a'
invmap a -> a'
f a' -> a
_ = f a' -> FromFunctor f a'
forall (f :: * -> *) a. f a -> FromFunctor f a
FromFunctor (f a' -> FromFunctor f a')
-> (FromFunctor f a -> f a') -> FromFunctor f a -> FromFunctor f a'
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> a') -> f a -> f a'
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> a'
f (f a -> f a')
-> (FromFunctor f a -> f a) -> FromFunctor f a -> f a'
forall b c a. (b -> c) -> (a -> b) -> a -> c
. FromFunctor f a -> f a
forall (f :: * -> *) a. FromFunctor f a -> f a
runBi
newtype FromContra f a = FromContra { FromContra f a -> f a
runContra :: f a }
instance Contravariant f => Invariant (FromContra f) where
invmap :: (a -> a') -> (a' -> a) -> FromContra f a -> FromContra f a'
invmap :: (a -> a') -> (a' -> a) -> FromContra f a -> FromContra f a'
invmap a -> a'
_ a' -> a
g = f a' -> FromContra f a'
forall (f :: * -> *) a. f a -> FromContra f a
FromContra (f a' -> FromContra f a')
-> (FromContra f a -> f a') -> FromContra f a -> FromContra f a'
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a' -> a) -> f a -> f a'
forall (f :: * -> *) a b. Contravariant f => (a -> b) -> f b -> f a
contramap a' -> a
g (f a -> f a') -> (FromContra f a -> f a) -> FromContra f a -> f a'
forall b c a. (b -> c) -> (a -> b) -> a -> c
. FromContra f a -> f a
forall (f :: * -> *) a. FromContra f a -> f a
runContra
deriving via FromFunctor Identity instance Invariant Identity
deriving via FromFunctor (Compose f g) instance (Functor f, Functor g) => Invariant (Compose f g)
deriving via FromFunctor [] instance Invariant []
deriving via FromFunctor ZipList instance Invariant ZipList
deriving via FromFunctor NonEmpty instance Invariant NonEmpty
deriving via FromFunctor Maybe instance Invariant Maybe
deriving via FromFunctor (Either e) instance Invariant (Either e)
deriving via FromFunctor IO instance Invariant IO
deriving via FromFunctor (Sum f g) instance (Functor f, Functor g) => Invariant (Sum f g)
deriving via FromFunctor (Product f g) instance (Functor f, Functor g) => Invariant (Product f g)
deriving via (FromFunctor ((,) x1)) instance Invariant ((,) x1)
deriving via (FromFunctor ((,,) x1 x2)) instance Invariant ((,,) x1 x2)
deriving via (FromFunctor ((,,,) x1 x2 x3)) instance Invariant ((,,,) x1 x2 x3)