generic type variable

generic type variable
schematic type variable

   <programming> (Also known as a "schematic type variable").
   Different occurrences of a generic type variable in a type
   expression may be instantiated to different types.  Thus, in
   the expression

   	let id x = x in
   	(id True, id 1)

   id's type is (for all a: a -> a).  The universal {quantifier}
   "for all a:" means that a is a generic type variable.  For the
   two uses of id, a is instantiated to Bool and Int.  Compare
   this with

   	let id x = x in
   	let f g = (g True, g 1) in
   	f id

   This looks similar but f has no legal {Hindley-Milner type}.
   If we say

   	f :: (a -> b) -> (b, b)

   this would permit g's type to be any instance of (a -> b)
   rather than requiring it to be at least as general as (a ->
   b).  Furthermore, it constrains both instances of g to have
   the same result type whereas they do not.  The type variables
   a and b in the above are implicitly quantified at the top
   level:

   	f :: for all a: for all b: (a -> b) -> (b, b)

   so instantiating them (removing the {quantifiers}) can only be
   done once, at the top level.  To correctly describe the type
   of f requires that they be locally quantified:

   	f :: ((for all a: a) -> (for all b: b)) -> (c, d)

   which means that each time g is applied, a and b may be
   instantiated differently.  f's actual argument must have a
   type at least as general as ((for all a: a) -> (for all b:
   b)), and may not be some less general instance of this type.
   Type variables c and d are still implicitly quantified at the
   top level and, now that g's result type is a generic type
   variable, any types chosen for c and d are guaranteed to be
   instances of it.

   This type for f does not express the fact that b only needs to
   be at least as general as the types c and d.  For example, if
   c and d were both Bool then any function of type (for all a: a
   -> Bool) would be a suitable argument to f but it would not
   match the above type for f.