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{-# LANGUAGE | |
DeriveGeneric, | |
FlexibleInstances, | |
FlexibleContexts, | |
AllowAmbiguousTypes, | |
ScopedTypeVariables, | |
TypeApplications, | |
TypeFamilies, | |
TypeOperators, | |
PartialTypeSignatures, | |
UndecidableInstances #-} | |
import Data.Kind (Type) | |
import Data.Coerce | |
import GHC.Generics | |
-- Example | |
data Foo | |
= Foo1 | |
| Foo2 Foo | |
| Foo3 Foo Foo | |
deriving Generic | |
data T3 a b c = T3 a b c | |
deriving Generic | |
foo1 :: _ | |
foo2 :: _ | |
foo3 :: _ | |
(T3 foo1 foo2 foo3) = magic @Foo @(T3 _ _ _) | |
example :: [Foo] | |
example = [foo1, foo2 Foo1, foo3 Foo1 Foo1] | |
-- Implementation | |
type family Productify (a :: Type) (f :: Type -> Type) :: Type -> Type where | |
Productify a (M1 D c f) = M1 D c (Productify a f) | |
Productify a (f :+: g) = Productify a f :*: Productify a g | |
Productify a (M1 C c f) = M1 S c (K1 R (Arrowify f a)) | |
type family Arrowify (f :: Type -> Type) (a :: Type) :: Type where | |
Arrowify (f :*: g) a = Arrowify f (Arrowify g a) | |
Arrowify U1 a = a | |
Arrowify (M1 S c (K1 i t)) a = t -> a | |
class GProductify f where | |
gproductify :: (f p -> a) -> Productify a f p | |
instance GProductify f => GProductify (M1 D c f) where | |
gproductify f = M1 (gproductify (f . M1)) | |
instance (GProductify f, GProductify g) => GProductify (f :+: g) where | |
gproductify f = gproductify (f . L1) :*: gproductify (f . R1) | |
instance GArrowify f => GProductify (M1 C c f) where | |
gproductify f = M1 (K1 (garrowify (f . M1))) | |
class GArrowify f where | |
garrowify :: (f p -> a) -> Arrowify f a | |
instance (GArrowify f, GArrowify g) => GArrowify (f :*: g) where | |
garrowify f = garrowify (\x -> garrowify (\y -> f (x :*: y))) | |
instance GArrowify (M1 S c (K1 i t)) where | |
garrowify = coerce | |
instance GArrowify U1 where | |
garrowify f = f U1 | |
type family Fields (f :: Type -> Type) :: Type where | |
Fields (M1 i c f) = Fields f | |
Fields (f :*: g) = (Fields f, Fields g) | |
Fields (K1 i a) = a | |
productify_ :: forall a p. (Generic a, GProductify (Rep a)) => Productify a (Rep a) () | |
productify_ = gproductify @(Rep a) @() @a (to @a) | |
magic :: forall a b. | |
( Generic a, GProductify (Rep a) | |
, Generic b, Coercible (Productify a (Rep a)) (Rep b), Fields (Productify a (Rep a)) ~ Fields (Rep b)) => | |
b | |
magic = to (coerce' (productify_ @a @())) where | |
coerce' :: Productify a (Rep a) () -> Rep b () | |
coerce' = coerce |
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