GADTs and functional dependencies?

[Conal Elliott]

Do GADTs and functional dependencies get along? I'm wondering why the
following code doesn't type-check under GHC 7.10.3 and 8.1.20160224:

> {-# OPTIONS_GHC -Wall #-}
> {-# LANGUAGE GADTs, KindSignatures, MultiParamTypeClasses,
FunctionalDependencies #-}
>
> module FundepGadt where
>
> class C a b | a -> b
>
> data G :: * -> * where
>   -- ...
>   GC :: C a b => G b -> G a
>
> instance Eq (G a) where
>   -- ...
>   GC b  == GC b' = b == b'

Error message:

    FundepGadt.hs:14:25: error:
        • Couldn't match type 'b1’ with 'b’
          'b1’ is a rigid type variable bound by
            a pattern with constructor: GC :: forall a b. C a b => G b -> G
a,
            in an equation for '==’
            at FundepGadt.hs:14:12
          'b’ is a rigid type variable bound by
            a pattern with constructor: GC :: forall a b. C a b => G b -> G
a,
            in an equation for '==’
            at FundepGadt.hs:14:3
          Expected type: G b
            Actual type: G b1
        • In the second argument of '(==)’, namely 'b'’
          In the expression: b == b'
          In an equation for '==’: (GC b) == (GC b') = b == b'
        • Relevant bindings include
            b' :: G b1 (bound at FundepGadt.hs:14:15)
            b :: G b (bound at FundepGadt.hs:14:6)

I think the functional dependency does ensure that "b == b" is well-typed.

In contrast, the following type-family version does type-check:

>     {-# OPTIONS_GHC -Wall #-}
>     {-# LANGUAGE GADTs, KindSignatures, TypeFamilies #-}
>
>     module TyfamGadt where
>
>     class C a where
>       type B a
>
>     data G :: * -> * where
>       -- ...
>       GC :: C a => G (B a) -> G a
>
>     instance Eq (G a) where
>       -- ...
>       GC b  == GC b' = b == b'

Thanks, - Conal
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