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{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE TypeFamilies #-}
module T4903a where
import Data.Kind
class El phi ix where
proof :: phi ix
class Fam phi where
from :: phi ix -> ix -> PF phi I0 ix
type family PF (phi :: Type -> Type) :: (Type -> Type) -> Type -> Type
data I0 a = I0 a
data I xi (r :: Type -> Type) ix = I (r xi)
data (f :*: g) (r :: Type -> Type) ix = f r ix :*: g r ix
class HEq phi f where
heq :: (forall ix. phi ix -> r ix -> Bool)
-> phi ix -> f r ix -> Bool
instance El phi xi => HEq phi (I xi) where
-- Replacing proof by undefined solves the problem
heq eq _ (I x) = eq proof x
instance (HEq phi f, HEq phi g) => HEq phi (f :*: g) where
-- The problem only arises when there are two calls to heq here
heq eq p (x :*: y) = heq eq p x && heq eq p y
{-# INLINABLE eq #-}
eq :: (Fam phi, HEq phi (PF phi)) => phi ix -> ix -> Bool
eq p x = heq (\p (I0 x) -> eq p x) p (from p x)
data Tree = Bin Tree Tree
tree :: Tree
-- The problem only occurs on an inifite (or very large) structure
tree = Bin tree tree
data TreeF :: Type -> Type where Tree :: TreeF Tree
type instance PF TreeF = I Tree :*: I Tree
-- If the representation is only |I Tree| then there is no problem
instance Fam TreeF where
from Tree (Bin l r) = I (I0 l) :*: I (I0 r)
instance El TreeF Tree where proof = Tree
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