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Add MTL class instances
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Hans Hoeglund
parent
d9c155d717
commit
60c4f37dd5
123
Iso/Deriving.hs
123
Iso/Deriving.hs
@ -30,12 +30,15 @@ import Control.Monad.Reader
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import Control.Monad.State
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import Control.Monad.Writer
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import Data.Bifunctor ()
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import Data.Functor.Classes (Eq1)
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import Data.Kind
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import Data.Profunctor (Profunctor (..))
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import Prelude hiding ((.), id)
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type Iso s t a b = forall p f. (Profunctor p, Functor f) => p a (f b) -> p s (f t)
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type Iso s t a b =
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forall p f.
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(Profunctor p, Functor f) =>
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p a (f b) ->
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p s (f t)
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type Iso' s a = Iso s s a a
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@ -54,13 +57,15 @@ newtype As (a :: Type) b = As b
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-- Like @As@ for kind @k -> Type@.
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--
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-- type As1 :: (k1 -> Type) -> (k1 -> Type) -> k1 -> Type
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newtype As1 (f :: k1 -> Type) (g :: k1 -> Type) (a :: k1) = As1 {getAs1 :: g a}
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newtype As1 (f :: k1 -> Type) (g :: k1 -> Type) (a :: k1)
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= As1 {getAs1 :: g a}
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-- |
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-- Like @As@ for kind @k1 -> k2 -> Type@.
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--
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-- type As2 :: (k1 -> k2 -> Type) -> (k1 -> k2 -> Type) -> k1 -> k2 -> Type
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newtype As2 f g a b = As2 (g a b)
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newtype As2 f g a b
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= As2 (g a b)
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class Inject a b where
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inj :: a -> b
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@ -89,8 +94,6 @@ instance (Project a b, Ord a) => Ord (As a b) where
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instance (Project a b, Show a) => Show (As a b) where
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showsPrec n (As a) = showsPrec n $ prj @a @b a
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-- instance (forall x . Isomorphic (f x) (g x), Eq1 f) => Eq1 (As1 f g) where
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instance (Isomorphic a b, Num a) => Num (As a b) where
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(As a) + (As b) =
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@ -120,31 +123,61 @@ instance (Isomorphic a b, Semigroup a) => Semigroup (As a b) where
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instance (Isomorphic a b, Monoid a) => Monoid (As a b) where
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mempty = As $ inj @a @b mempty
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instance (forall x. Isomorphic (f x) (g x), Functor f) => Functor (As1 f g) where
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instance
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(forall x. Isomorphic (f x) (g x), Functor f) =>
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Functor (As1 f g)
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where
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fmap h (As1 x) = As1 $ inj $ fmap h $ prj @(f _) @(g _) x
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instance (forall x. Isomorphic (f x) (g x), Applicative f) => Applicative (As1 f g) where
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instance
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(forall x. Isomorphic (f x) (g x), Applicative f) =>
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Applicative (As1 f g)
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where
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pure :: forall a. a -> As1 f g a
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pure x = As1 $ inj @(f _) @(g _) $ pure x
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pure x =
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As1 $ inj @(f _) @(g _) $
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pure x
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(<*>) :: forall a b. As1 f g (a -> b) -> As1 f g a -> As1 f g b
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As1 h <*> As1 x = As1 $ inj @(f b) @(g b) $ (prj @(f (a -> b)) @(g (a -> b)) h) <*> (prj @(f a) @(g a) x)
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(<*>) ::
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forall a b.
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As1 f g (a -> b) ->
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As1 f g a ->
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As1 f g b
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As1 h <*> As1 x =
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As1 $ inj @(f b) @(g b) $
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(prj @(f (a -> b)) @(g (a -> b)) h) <*> (prj @(f a) @(g a) x)
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liftA2 :: forall a b c. (a -> b -> c) -> As1 f g a -> As1 f g b -> As1 f g c
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liftA2 ::
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forall a b c.
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(a -> b -> c) ->
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As1 f g a ->
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As1 f g b ->
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As1 f g c
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liftA2 h (As1 x) (As1 y) = As1 $ inj @(f c) @(g c) $ liftA2 h (prj x) (prj y)
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instance (forall x. Isomorphic (f x) (g x), Alternative f) => Alternative (As1 f g) where
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instance
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(forall x. Isomorphic (f x) (g x), Alternative f) =>
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Alternative (As1 f g)
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where
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empty :: forall a. As1 f g a
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empty = As1 $ inj @(f a) @(g a) $ empty
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(<|>) :: forall a. As1 f g a -> As1 f g a -> As1 f g a
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As1 h <|> As1 x = As1 $ inj @(f a) @(g a) $ (prj @(f a) @(g a) h) <|> (prj @(f a) @(g a) x)
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As1 h <|> As1 x =
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As1 $ inj @(f a) @(g a) $
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(prj @(f a) @(g a) h) <|> (prj @(f a) @(g a) x)
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instance (forall x. Isomorphic (f x) (g x), Monad f) => Monad (As1 f g) where
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(>>=) :: forall a b. As1 f g a -> (a -> As1 f g b) -> As1 f g b
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As1 k >>= f = As1 $ inj @(f b) @(g b) $ (prj @(f a) @(g a) k) >>= prj . getAs1 . f
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(>>=) ::
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forall a b.
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As1 f g a ->
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(a -> As1 f g b) ->
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As1 f g b
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As1 k >>= f =
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As1 $ inj @(f b) @(g b) $
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(prj @(f a) @(g a) k) >>= prj . getAs1 . f
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instance
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forall f g s.
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@ -152,28 +185,72 @@ instance
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MonadState s (As1 f g)
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where
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state :: forall a. (s -> (a, s)) -> As1 f g a
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state k = As1 $ inj @(f a) @(g a) (state @s @f k)
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state k =
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As1 $
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inj @(f a) @(g a)
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(state @s @f k)
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instance
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forall f g s.
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(forall x. Isomorphic (f x) (g x), MonadReader s f) =>
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MonadReader s (As1 f g)
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where
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reader :: forall a. (s -> (a)) -> As1 f g a
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reader k = As1 $ inj @(f a) @(g a) (reader @s @f k)
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reader :: forall a. (s -> a) -> As1 f g a
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reader k =
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As1 $
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inj @(f a) @(g a)
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(reader @s @f k)
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local ::
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forall a.
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(s -> s) ->
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As1 f g a ->
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As1 f g a
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local f (As1 k) =
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As1 $
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inj @(f a) @(g a)
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(local f (prj @(f a) @(g a) k))
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instance
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forall f g s.
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(forall x. Isomorphic (f x) (g x), MonadWriter s f) =>
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MonadWriter s (As1 f g)
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where
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writer :: forall a. (a, s) -> As1 f g a
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writer k = As1 $ inj @(f a) @(g a) (writer @s @f k)
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instance (forall x y. Isomorphic (f x y) (g x y), Category f) => Category (As2 f g) where
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writer :: forall a. (a, s) -> As1 f g a
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writer k =
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As1
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$ inj @(f a) @(g a)
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$ (writer @s @f k)
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listen ::
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forall a.
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As1 f g a ->
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As1 f g (a, s)
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listen (As1 k) =
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As1
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$ inj @(f (a, s)) @(g (a, s))
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$ listen (prj @(f a) @(g a) k)
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pass ::
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forall a.
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As1 f g (a, s -> s) ->
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As1 f g a
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pass (As1 k) =
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As1
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$ inj @(f a) @(g a)
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$ pass (prj @(f _) @(g _) k)
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instance
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(forall x y. Isomorphic (f x y) (g x y), Category f) =>
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Category (As2 f g)
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where
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id :: forall a. As2 f g a a
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id = As2 $ inj @(f _ _) @(g _ _) $ Control.Category.id @_ @a
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id =
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As2 $ inj @(f a a) @(g a a) $
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Control.Category.id @_ @a
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(.) :: forall a b c. As2 f g b c -> As2 f g a b -> As2 f g a c
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As2 f . As2 g =
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