
simonpj@microsoft.com authored
This very large commit adds impredicativity to GHC, plus numerous other small things. *** WARNING: I have compiled all the libraries, and *** a stage2 compiler, and everything seems *** fine. But don't grab this patch if you *** can't tolerate a hiccup if something is *** broken. The big picture is this: a) GHC handles impredicative polymorphism, as described in the "Boxy types: type inference for higherrank types and impredicativity" paper b) GHC handles GADTs in the new simplified (and very sligtly less epxrssive) way described in the "Simple unificationbased type inference for GADTs" paper But there are lots of smaller changes, and since it was preDarcs they are not individually recorded. Some things to watch out for: c) The story on lexicallyscoped type variables has changed, as per my email. I append the story below for completeness, but I am still not happy with it, and it may change again. In particular, the new story does not allow a patternbound scoped type variable to be wobbly, so (\(x::[a]) > ...) is usually rejected. This is more restrictive than before, and we might loosen up again. d) A consequence of adding impredicativity is that GHC is a bit less gung ho about converting automatically between (ty1 > forall a. ty2) and (forall a. ty1 > ty2) In particular, you may need to etaexpand some functions to make typechecking work again. Furthermore, functions are now invariant in their argument types, rather than being contravariant. Again, the main consequence is that you may occasionally need to etaexpand function arguments when using higherrank polymorphism. Please test, and let me know of any hiccups 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 letbound or wherebound 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 lexicallyscoped type variable always names a (rigid) type variable (not an arbitrary 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 lexicallyscoped type variables name distinct rigid type variables. This choice is open; 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 toplevel 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 *patternbound 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 patternbound 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 big change from the current situation. f (x::a) = x  NO; pattern type is wobbly 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 cannot give different names for the same type variable in the same scope (Invariant (C)): f1 :: p > p > p  NO; because 'a' and 'b' would be f1 (x::a) (y::b) = (x::a)  bound to the same type variable f2 :: p > p > p  OK; 'a' is bound to the type variable f2 (x::a) (y::a) = (x::a)  over which f2 is quantified  NB: 'p' is not lexically scoped f3 :: forall p. p > p > p  NO: 'p' is now scoped, and is bound to f3 (x::a) (y::a) = (x::a)  to the same type varialble as 'a' f4 :: forall p. p > p > p  OK: 'p' is now scoped, and its occurences f4 (x::p) (y::p) = (x::p)  in the patterns are bound by the forall 3b) 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 g :: a > Bool > Maybe a g (x::p) True = Just x :: Maybe p g (y::q) False = Nothing :: Maybe q 3c) Scoped type variables respect alpha renaming. For example, function f2 from (3a) above could also be written: f2' :: p > p > p f2' (x::b) (y::b) = x::b where the scoped type variable is called 'b' instead of 'a'. 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) Explicitlyforall'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. 7) 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.
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