A bug in GHC’s type system

Several days ago, I implemented an experimental type inference system with first-class polymorphism. When comparing it with other systems, I found a possible bug in GHC’s type system regarding universal quantification. The phenomemon was confirmed and reproduced by people at #haskell IRC channel for GHC versions above 7.01. The code that causes trouble is:

gen :: [forall a. a -> a]
gen = [id]
test1 = head gen 1

Obviously this program should typecheck, since:

  • id has the type forall a. a -> a.
  • A list gen containing id should have type [forall a. a -> a](as in the annotation).
  • head has the type forall a. [a] -> a.
  • head gen should have the type forall a. a -> a.
  • head gen should be able to be applied to 1.

But GHC rejected this program for a strange reason.

Couldn't match expected type `t1 -> t0'
with actual type `forall a. a -> a'
Expected type: [t1 -> t0]
Actual type: [forall a. a -> a]
In the first argument of `head', namely `gen'
In the expression: head gen 1

On the other hand, it works if (head gen) is bound at let:

test2 = let hg = head gen in hg 1

It doesn’t break the soundness of the type system since it only rejects some correct programs, but this kind of pecularities of type systems can be painful when they add up. I guess this may be caused by the interaction between GHC’s internal type system with the legacy let-polymorphism.

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