wren ng thornton wrote:
[1] In System F the capital-lambda binder is used for the term-level abstraction of passing type representations. So for example we have,
id :: forall a. a -> a id = /\a. \(x::a). x
Thus, the forall keyword is serving as the type-level abstraction. Perhaps this is suboptimal syntax, but it is the standard. We could, of course, have both a term-level /\ and a type-level /\ where the latter is the type of the former (since the namespaces are separate) though that's also dubious. Capital-pi is the canonical type-level abstraction, though that evokes the idea of dependent types which are much more complex.
What do you mean by "type-level abstraction" here? In a language with type functions and polymorphism, we need three different lambda binders: (1) abstraction over terms in terms (to construct functions) (2) abstraction over types in terms (to construct polymorphic values) (3) abstraction over types in types (to construct type functions) I think only (2) should be written as upper-case lambdas, while (1) and (3) should both be written as lower-case lambdas. Since (1) and (3) belong to different syntactic categories, they can not be confused, and we can reuse the lower-case lambda at the type-level. Furthermore, we need three function types / kinds to describe the three lambdas one level higher: (4) the type of functions (5) the type of polymorphic values (6) the kind of type functions In ghc, we already have "forall" for (5), and arrows for (4) and (6). I would say that (3) is the "type-level abstraction", not (5). Tillmann