Pedro Vasconcelos wrote: >Jim Apple <[EMAIL PROTECTED]> wrote: >>Is there a type we can give to >> >>y f = f . f >> >>y id >>y head >>y fst >> >>are all typeable? > >Using ghci: > >Prelude> let y f = f.f >Prelude> :t y >y :: forall c. (c -> c) -> c -> c > >So it admits principal type (a->a) -> a->a. From this you can see that >(y head) and (y fst) cannot be typed, whereas (y id) can.
I think the OP's point is that all three of his examples make sense, and the resulting functions would have Haskell types, yet there doesn't seem to be a Haskell type which permits all three uses of y. I can come up with types which permit any one of the three:
y :: forall a. (a -> a) -> a -> a y :: forall a f. (forall x. f x -> x) -> f (f a) -> a y :: forall a b c f. (forall x y. f x y -> x) -> f (f a b) c -> a
but I can't find a type which permits more than one. It can probably be done with type classes.
-- Ben
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