[Haskell] A question about a possible bug in GHC regarding GADTs and type classes

[Pablo Nogueira]

Hi,

I've been told the following short code is correct but it's GHC's
fault it does not type check.
Is that the case?

--
{-# OPTIONS -fglasgow-exts #-}

-- An expression GADT:

data Exp :: * -> * where
  LitNum  :: Num a => a -> Exp a
  LitBool  :: Bool -> Exp Bool
  Plus      :: Num a => Exp a -> Exp a -> Exp a
  And       :: Exp Bool -> Exp Bool -> Exp Bool
  If           :: Exp Bool -> Exp a -> Exp a -> Exp a

-- An expression evaluator:

evalExp :: Exp a -> a
evalExp (LitNum i)  = i
evalExp (LitBool b) = b
evalExp (Plus x y)  = evalExp x + evalExp y
evalExp (And  x y)  = evalExp x && evalExp y
evalExp (If c t e)  = if (evalExp c) then (evalExp t) else (evalExp e)
--

The type checker complains that evalExp needs a Num constraint on its
type signature.
This can't be right, for Bool is not an instance of Num, right?

Is it the case that the interaction between GADTs and type classes is
not fully worked out yet?

Here is a related problem. I'd like to make the types of expressions
extensible by using a type class:
--
class TyRange a
instance TyRange Int
instance TyRange Bool

  data Exp :: * -> * where
    Lit     :: TyRange a => a -> Exp a
    Plus :: Exp Int  -> Exp Int  -> Exp Int
    And  :: Exp Bool -> Exp Bool -> Exp Bool
    If       :: TyRange a => Exp Bool -> Exp a -> Exp a -> Exp a

But I cannot add the types in other classes into TyRange in modular
fashion, cause the superclass is specified at the moment of
declaration.

I may try to extend TyRange by adding the instances in, say, Num:

--
{-# OPTIONS -fglasgow-exts #-}
{-# OPTIONS -fallow-undecidable-instances #-}

class TyRange a
instance TyRange Bool
instance Num a => TyRange a

data Exp :: * -> * where
  Lit    :: TyRange a => a -> Exp a
  Plus :: Exp Int  -> Exp Int  -> Exp Int
  And  :: Exp Bool -> Exp Bool -> Exp Bool
  If      :: TyRange a => Exp Bool -> Exp a -> Exp a -> Exp a

evalExp :: Exp a -> a
evalExp (Lit i)     = i
evalExp (Plus x y)  = evalExp x + evalExp y
evalExp (And  x y)  = evalExp x && evalExp y
evalExp (If c t e)  = if (evalExp c) then (evalExp t) else (evalExp e)
--

But I get the following error when evaluating   evalExp (If (Lit True)
(Lit 1) (Lit 2))

Overlapping instances for TyRange Bool
      arising from use of `Lit' at <interactive>:1:13-15
    Matching instances:
      /home/pni/Papers/EDT/TyRangeProblem.hs:5:0: instance TyRange Bool
      /home/pni/Papers/EDT/TyRangeProblem.hs:4:0: instance (Num a) => TyRange a
    In the first argument of `If', namely `(Lit True)'
    In the first argument of `evalExp', namely `(If (Lit True) (Lit 1) (Lit 2))

Apologies for being so daft, but why are the instances overlapping if
Bool is not in Num?