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    • simonpj@microsoft.com's avatar
      Simon's big boxy-type commit · ac10f840
      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 stage-2 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 higher-rank types and
         impredicativity" paper
      
      b) GHC handles GADTs in the new simplified (and very sligtly less
         epxrssive) way described in the
         "Simple unification-based type inference for GADTs" paper
      
        
      But there are lots of smaller changes, and since it was pre-Darcs
      they are not individually recorded.
        
      Some things to watch out for:
        
      c)   The story on lexically-scoped 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 pattern-bound 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 eta-expand 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 eta-expand function arguments when
           using higher-rank 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
         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 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 lexically-scoped 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 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 
         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) 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.
      
      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.
      ac10f840
    • Simon Marlow's avatar
    • simonpj@microsoft.com's avatar
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