[Haskell-cafe] Inference for RankNTypes

[Roman Cheplyaka]

* Francesco Mazzoli <f at mazzo.li> [2013-01-02 13:04:36+0100]
> At Wed, 02 Jan 2013 12:32:53 +0100,
> Francesco Mazzoli wrote:
> > 
> > Hi list,
> > 
> > I am a bit puzzled by the behaviour exemplified by this code:
> > 
> >     {-# LANGUAGE RankNTypes #-}
> > 
> >     one :: (forall a. a -> a) -> b -> b
> >     one f = f
> > 
> >     two = let f = flip one in f 'x' id
> >     three = (flip one :: b -> (forall a. a -> a) -> b) 'x' id
> >     four = flip one 'x' id
> > 
> > Try to guess if this code typechecks, and if not what’s the error.
> > 
> > While `two' and `three' are fine, GHC (7.4.1 and 7.6.1) complains about `four':
> > 
> >     Line 8: 1 error(s), 0 warning(s)
> >     
> >     Couldn't match expected type `forall a. a -> a'
> >                 with actual type `a0 -> a0'
> >     In the third argument of `flip', namely `id'
> >     In the expression: flip one 'x' id
> >     In an equation for `four': four = flip one 'x' id
> > 
> > So for some reason the quantified variable in `id' gets instantiated before it
> > should, and I have no idea why.
> > 
> > Any ideas?
> > 
> > Francesco
> 
> OK, I should have looked at the manual first. From
> <http://www.haskell.org/ghc/docs/latest/html/users_guide/other-type-extensions.html#id623016>:
> “For a lambda-bound or case-bound variable, x, either the programmer provides an
> explicit polymorphic type for x, or GHC's type inference will assume that x's
> type has no foralls in it.”.  So there is a difference between let-bound things
> and the rest.

I don't see how this is relevant.

GHC correctly infers the type of "flip one 'x'":

  *Main> :t flip one 'x'
  flip one 'x' :: (forall a. a -> a) -> Char

But then somehow it fails to apply this to id. And there are no bound
variables here that we should need to annotate.

Roman