Search Result for "generic type variable":
```
The Free On-line Dictionary of Computing (26 July 2010):generic type variable
schematic type variable

(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.
```