[Haskell-cafe] Inference for RankNTypes

[Francesco Mazzoli]

At Wed, 2 Jan 2013 11:20:46 -0500,
Dan Doel wrote:
> Your example doesn't work for the same reason the following doesn't work:
> 
>     id runST (<some st code>)
> 
> It requires the inferencer to instantiate certain variables of id's type to
> polymorphic types based on runST (or flip's based on one), and then use
> that information to check <some st code> (id in your example) as a
> polymorphic type. At various times, GHC has had ad-hoc left-to-right
> behavior that made this work, but it no longer does. Right now, I believe
> it only has an ad-hoc check to make sure that:
> 
>     runST $ <some st code>
> 
> works, and not much else. Note that even left-to-right behavior covers all
> cases, as you might have:
> 
>     f x y
> 
> such that y requires x to be checked polymorphically in the same way. There
> are algorithms that can get this right in general, but it's a little
> tricky, and they're rather different than GHC's algorithm, so I don't know
> whether it's possible to make GHC behave correctly.
> 
> The reason it works when you factor out or annotate "flip one 'x'" is that
> that is the eventual inferred type of the expression, and then it knows to
> expect the id to be polymorphic. But when it's all at once, we just have a
> chain of unifications relating things like: (forall a. a -> a) ~ beta ~
> (alpha -> alpha), where beta is part of type checking flip, and alpha ->
> alpha is the instantiation of id's type with unification variables, because
> we didn't know that it was supposed to be a fully polymorphic use. And that
> unification fails.

Hi Dan,

Thanks a lot for the answer, one forgets that with HM you always replace the
quantified variables immediately.

However I am still confused on how GHC makes it work when I annotate or put
things in separate variables.  In other words, can you provide links or clarify
how this procedure works:

    The reason it works when you factor out or annotate "flip one 'x'" is that
    that is the eventual inferred type of the expression, and then it knows to
    expect the id to be polymorphic.

Thanks,
Francesco