Haskell overlapping instances and type functions

Question

I have the following typeclass which models a SQL-like query optimization:

class OptimizableQuery q where
  type Optimized q :: *
  optimize :: q -> Optimized q

instance Query q => OptimizableQuery q where
  type Optimized q = q
  optimize q = q

instance (Query q, OptimizableQuery q) => OptimizableQuery (Select (Select q p) p) where
  type Optimized (Select (Select q p) p) = Select (Optimized q) p
  optimize (Select (Select q _) p) = Select (optimize q) p

the problem is that I get the error "Conflicting family instance declarations" on the Optimized type function. Why is that and how can I solve it? It would really be nice to have a "fallback instance" instead of having to exhaust all cases (which might be quite many)...

Answer 1

It's illegal to have overlapping instances with type families. See the GHC manual, "Overlap of type synonym instances" for details.

The reason is that having two different possible results for a type function application depending on the available instances can lead to unsoundness.