How to allow unification of a type variable with different types?

Question

I have a function with a following type signature

{-# LANGUAGE FlexibleContexts #-}
dataLat :: Load r DIM1 Double
        => (Array r DIM1 Double -> Array U DIM1 Double, Array U DIM1 Double)

Array, U and DIM1 come from Repa library. dataLat creates data that is later passed to other functions as a tuple. At one point r type variable gets unified with type D (this is again from Repa), but at later point r should also unify with type L (this is my type). The problem is that it has already been unified with D and cannot be therefore unified with L. I end up with Couldn't match expected type error. I think this should be solved by some form of higher rank types, but I am unable to figure out how this should be written. Can anyone give me a hand?

Answer 1

Try {-# LANGUAGE NoMonomorphismRestriction #-}

http://www.haskell.org/ghc/docs/7.6.1/html/users_guide/monomorphism.html

Answer 2

You can give dataLat a type saying that it returns a polymorphic function, using Rank2Types.

newtype Unboxer =
  Unboxer {applyUnboxer :: forall repr. Load repr DIM1 Double => Array repr DIM1 Double -> Array U DIM1 Double}

dataLat :: (Unboxer, Array U DIM1 Double)

The body of dataLat must put a polymorphic function into Unboxer. The field accessor, applyUnboxer, returns a polymorphic function that can be used at different types.

It's not clear to me that you really need rank-2 types. Since dataLat takes no arguments, you can probably define the unboxer as a global function with ordinary rank-1 polymorphism.

To be precise, it doesn't make sense to unify a type variable with multiple types. To unify r with U and D would amount to saying that r == U and U == D, which is false. The code above allows a function to be instantiated to multiple types. Think of instantiation as making a copy of the code before assigning types, so you have one instance of the function where r₁ == U and a separate instance where r₂ == D.