Le 29 janv. 10 à 02:56, o...@okmij.org a écrit :
Here is a bit more simplified version of the example. The example has
no value level recursion and no overt recursive types, and no
impredicative
polymorphism. The key is the observation, made earlier, that two types
c (c ()) and R (c ())
unify when c = R. Although the GADTs R c below is not recursive, when
we instantiate c = R, it becomes recursive, with the negative
occurrence. The trouble is imminent.
We reach the conclusion that an instance of a non-recursive GADT
can be a recursive type. GADT may harbor recursion, so to speak.
The code below, when loaded into GHCi 6.10.4, diverges on
type-checking. It type-checks when we comment-out absurd.
{-# LANGUAGE GADTs, EmptyDataDecls #-}
data False -- No constructors
data R c where -- Not recursive
R :: (c (c ()) -> False) -> R (c ())
Thanks Oleg,
that's a bit simpler indeed. However, I'm skeptical on
the scoping of c here. Correct me if I'm wrong but in R's
constructor [c] is applied to () so it has to be a type
constructor variable of kind :: * -> s. But [c] is also
applied to [c ()] so we must have s = * and c :: * -> *.
Now given the application [R (c ())] we must have
[R :: * -> *]. Then in [data R c] we must have [c :: *],
hence a contradiction?
My intuition would be that the declaration is informally
equivalent to the impredicative:
data R (c :: *) where
R :: forall c' :: * -> *, (c' (c' ()) -> False) -> R (c' ()).
-- Matthieu_______________________________________________
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