On Fri, Jan 29, 2010 at 8:56 AM,
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 ())
-- instantiate c to R, so (c (c ())) and R (c ()) coincide -- and we obtain a recursive type -- mu R. (R (R ()) -> False) -> R (R ())
cond_false :: R (R ()) -> False cond_false x@(R f) = f x
absurd :: False absurd = cond_false (R cond_false)
GHC (the compiler terminates) The following variants terminate, either with GHCi or GHC, absurd1 :: False absurd1 = let x = (R cond_false) in cond_false x absurd2 = R cond_false absurd3 x = cond_false x absurd4 :: False absurd4 = absurd3 absurd2 This suggests there's a bug in the type checker. If i scribble down the type equation, I can't see why the type checker should loop here. -Martin
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