On 2005-02-28 at 23:10EST Jim Apple wrote:
Jon Fairbairn wrote:
If you allow quantification over higher kinds, you can do something like this:
d f = f . f
d:: ∀a::*, b::*→*.(b a → a) → b (b a)→ a
What's the problem with
d :: (forall c . b c -> c) -> b (b a) -> a d f = f . f
to which ghci gives the type
d :: forall a b. (forall c. b c -> c) -> b (b a) -> a
It's too restrictive: it requires that the argument to d be polymorphic, so if f:: [Int]->[Int], d f won't typecheck. It also requires that the type of f have an application on the lhs, so f :: Int->Int won't allow d f to typecheck either. In the imaginary typesystem I was thinking of above, we could instantiate b with (λx.x). As others have pointed out, there are other typesystems that allow different types that also work. Incidentally, I think Ponder would have assigned types to the examples, just not very useful ones; d head would have come out as (μt.[t])->(μt.[t]) (assuming anything came out at all). -- Jón Fairbairn Jon.Fairbairn at cl.cam.ac.uk