[Haskell-cafe] lifting restrictions on defining instances
rendel at cs.au.dk
Mon Jul 27 16:29:50 EDT 2009
wren ng thornton wrote:
>  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).
More information about the Haskell-Cafe