{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
module Data.Comp.Multi.Projection (pr, (:<), (:*:)(..), ffst, fsnd) where
import Data.Comp.SubsumeCommon
import Data.Comp.Multi.Ops hiding (Sum, Elem)
type family Elem (f :: * -> *)
(g :: * -> *) :: Emb where
Elem f f = Found Here
Elem (f1 :*: f2) g = Sum' (Elem f1 g) (Elem f2 g)
Elem f (g1 :*: g2) = Choose (Elem f g1) (Elem f g2)
Elem f g = NotFound
class Proj (e :: Emb) (p :: * -> *)
(q :: * -> *) where
pr' :: Proxy e -> q a -> p a
instance Proj (Found Here) f f where
pr' :: Proxy ('Found 'Here) -> f a -> f a
pr' _ = f a -> f a
forall a. a -> a
id
instance Proj (Found p) f g => Proj (Found (Le p)) f (g :*: g') where
pr' :: Proxy ('Found ('Le p)) -> (:*:) g g' a -> f a
pr' _ = Proxy ('Found p) -> g a -> f a
forall (e :: Emb) (p :: * -> *) (q :: * -> *) a.
Proj e p q =>
Proxy e -> q a -> p a
pr' (Proxy ('Found p)
forall k (a :: k). Proxy a
P :: Proxy (Found p)) (g a -> f a) -> ((:*:) g g' a -> g a) -> (:*:) g g' a -> f a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (:*:) g g' a -> g a
forall k (f :: k -> *) (g :: k -> *) (a :: k). (:*:) f g a -> f a
ffst
instance Proj (Found p) f g => Proj (Found (Ri p)) f (g' :*: g) where
pr' :: Proxy ('Found ('Ri p)) -> (:*:) g' g a -> f a
pr' _ = Proxy ('Found p) -> g a -> f a
forall (e :: Emb) (p :: * -> *) (q :: * -> *) a.
Proj e p q =>
Proxy e -> q a -> p a
pr' (Proxy ('Found p)
forall k (a :: k). Proxy a
P :: Proxy (Found p)) (g a -> f a) -> ((:*:) g' g a -> g a) -> (:*:) g' g a -> f a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (:*:) g' g a -> g a
forall k (f :: k -> *) (g :: k -> *) (a :: k). (:*:) f g a -> g a
fsnd
instance (Proj (Found p1) f1 g, Proj (Found p2) f2 g)
=> Proj (Found (Sum p1 p2)) (f1 :*: f2) g where
pr' :: Proxy ('Found ('Sum p1 p2)) -> g a -> (:*:) f1 f2 a
pr' _ x :: g a
x = (Proxy ('Found p1) -> g a -> f1 a
forall (e :: Emb) (p :: * -> *) (q :: * -> *) a.
Proj e p q =>
Proxy e -> q a -> p a
pr' (Proxy ('Found p1)
forall k (a :: k). Proxy a
P :: Proxy (Found p1)) g a
x f1 a -> f2 a -> (:*:) f1 f2 a
forall k (f :: k -> *) (g :: k -> *) (a :: k).
f a -> g a -> (:*:) f g a
:*: Proxy ('Found p2) -> g a -> f2 a
forall (e :: Emb) (p :: * -> *) (q :: * -> *) a.
Proj e p q =>
Proxy e -> q a -> p a
pr' (Proxy ('Found p2)
forall k (a :: k). Proxy a
P :: Proxy (Found p2)) g a
x)
infixl 5 :<
type f :< g = (Proj (ComprEmb (Elem f g)) f g)
pr :: forall p q a . (p :< q) => q a -> p a
pr :: q a -> p a
pr = Proxy (ComprEmb (Elem p q)) -> q a -> p a
forall (e :: Emb) (p :: * -> *) (q :: * -> *) a.
Proj e p q =>
Proxy e -> q a -> p a
pr' (Proxy (ComprEmb (Elem p q))
forall k (a :: k). Proxy a
P :: Proxy (ComprEmb (Elem p q)))