Dear GHC users As part of a revision of GHC to make type inference for GADTs simpler and more uniform, I propose to change the way in which lexically- scoped type variables work in GHC. (Indeed, I have done so, and will commit it shortly.) This message explains the new system, highlighting the differences. I'm very interested to know whether you like it or hate it. In the latter case, I'd also like to know whether you also have programs that will be broken by the change. Simon Scoped type variables in GHC ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ January 2006 0) Terminology. A *pattern binding* is of the form pat = rhs A *function binding* is of the form f pat1 .. patn = rhs A binding of the formm var = rhs is treated as a (degenerate) *function binding*. A *declaration type signature* is a separate type signature for a let-bound or where-bound variable: f :: Int -> Int A *pattern type signature* is a signature in a pattern: \(x::a) -> x f (x::a) = x A *result type signature* is a signature on the result of a function definition: f :: forall a. [a] -> a head (x:xs) :: a = x The form x :: a = rhs is treated as a (degnerate) function binding with a result type signature, not as a pattern binding. 1) The main invariants: A) A lexically-scoped type variable always names a rigid type variable (not a wobbly one, and not a non-type-variable type). THIS IS A CHANGE. Previously, a scoped type variable named an arbitrary *type*. B) A type signature always describes a rigid type (since its free (scoped) type variables name rigid type variables). This is also a change, a consequence of (A). C) Distinct lexically-scoped type variables name distinct rigid type variables. This choice is open; This means that you cannot say \(x:: [a]) -> <expr> (where 'a' is not yet in scope) to enforce that x is a list without saying anything about 'a'. (Well, not unless the type of this lambda is known from the "outside".) 1a) Possible extension. We might consider allowing \(x :: [ _ ]) -> <expr> where "_" is a wild card, to mean "x has type list of something", without naming the something. 2) Scoping 2(a) If a declaration type signature has an explicit forall, those type variables are brought into scope in the right hand side of the corresponding binding (plus, for function bindings, the patterns on the LHS). f :: forall a. a -> [a] f (x::a) = [x :: a, x] Both occurences of 'a' in the second line are bound by the 'forall a' in the first line A declaration type signature *without* an explicit top-level forall is implicitly quantified over all the type variables that are mentioned in the type but not already in scope. GHC's current rule is that this implicit quantification does *not* bring into scope any new scoped type variables. f :: a -> a f x = ...('a' is not in scope here)... This gives compatibility with Haskell 98 2(b) A pattern type signature implicitly brings into scope any type variables mentioned in the type that are not already into scope. These are called *pattern-bound type variables*. g :: a -> a -> [a] g (x::a) (y::a) = [y :: a, x] The pattern type signature (x::a) brings 'a' into scope. The 'a' in the pattern (y::a) is bound, as is the occurrence on the RHS. A pattern type siganture is the only way you can bring existentials into scope. data T where MkT :: forall a. a -> (a->Int) -> T f x = case x of MkT (x::a) f -> f (x::a) 2a) QUESTION class C a where op :: forall b. b->a->a instance C (T p q) where op = <rhs> Clearly p,q are in scope in <rhs>, but is 'b'? Not at the moment. Nor can you add a type signature for op in the instance decl. You'd have to say this: instance C (T p q) where op = let op' :: forall b. ... op' = <rhs> in op' 3) A pattern-bound type variable is allowed only if the pattern's expected type is rigid. Otherwise we don't know exactly *which* skolem the scoped type variable should be bound to, and that means we can't do GADT refinement. This is invariant (A), and it is a change from the current situation. f (x::a) = x -- NO g1 :: b -> b g1 (x::b) = x -- YES, because the pattern type is rigid g2 :: b -> b g2 (x::c) = x -- YES, same reason h :: forall b. b -> b h (x::b) = x -- YES, but the inner b is bound k :: forall b. b -> b k (x::c) = x -- NO, it can't be both b and c 3a) You *can* give a different name to the same type variable in different disjoint scopes, just as you can (if you want) give diferent names to the same value parameter f :: a -> Bool -> Maybe a f (x::p) True = Just x :: Maybe p f (y::q) False = Nothing :: Maybe q 3b) Scoped type variables respect alpha renaming. For example, function g from 2(b) above could also be written: g2 :: a -> a -> [a] g2 (x::b) (y::b) = [y :: b, x] where the scoped type variable is called 'b' instead of 'a'. However, you cannot write f :: a -> a -> [a] f (x::b) (y::c) = [y :: b, x] because then two scoped type variables ('b' and 'c') would be bound to the same underlying type variable. (Invariant (C) above.) 4) Result type signatures obey the same rules as pattern types signatures. In particular, they can bind a type variable only if the result type is rigid f x :: a = x -- NO g :: b -> b g x :: b = x -- YES; binds b in rhs 5) A *pattern type signature* in a *pattern binding* cannot bind a scoped type variable (x::a, y) = ... -- Legal only if 'a' is already in scope Reason: in type checking, the "expected type" of the LHS pattern is always wobbly, so we can't bind a rigid type variable. (The exception would be for an existential type variable, but existentials are not allowed in pattern bindings either.) Even this is illegal f :: forall a. a -> a f x = let ((y::b)::a, z) = ... in Here it looks as if 'b' might get a rigid binding; but you can't bind it to the same skolem as a. 6) Explicitly-forall'd type variables in the *declaration type signature(s)* for a *pattern binding* do not scope AT ALL. x :: forall a. a->a -- NO; the forall a does Just (x::a->a) = Just id -- not scope at all y :: forall a. a->a Just y = Just (id :: a->a) -- NO; same reason THIS IS A CHANGE, but one I bet that very few people will notice. Here's why: strange :: forall b. (b->b,b->b) strange = (id,id) x1 :: forall a. a->a y1 :: forall b. b->b (x1,y1) = strange This is legal Haskell 98 (modulo the forall). If both 'a' and 'b' both scoped over the RHS, they'd get unified and so cannot stand for distinct type variables. One could *imagine* allowing this: x2 :: forall a. a->a y2 :: forall a. a->a (x2,y2) = strange using the very same type variable 'a' in both signatures, so that a single 'a' scopes over the RHS. That seems defensible, but odd, because though there are two type signatures, they introduce just *one* scoped type variable, a. Implementation notes ~~~~~~~~~~~~~~~~~~~~ 1) This means that dealing with pattern/result type signatures is simple: - if the signature binds one or more variables, and the pattern type is rigid, *match* the signature against the pattern type to bind the variables - if the signature binds no type variables, *unify* the pattern type against the (necessarily rigid) type signature 2) Skolem constants get introduced by a) Declaration type signatures with explicit foralls b) *Function* declaration type signatures on bindings where there is no explicit forall c) Existential pattern matches d) SKOL rule in subsumption checking A *declaration type signature* for a *pattern-bound* variable does not introduce a skolem, and is never the basis for refinement. Instead we use an ordinary meta type variable, and check after the event that everything is still distinct. That is how the x4/y4 example type-checks.