On Wed, 7 Feb 2007, Dan Weston wrote:
A way to categorify elements of objects in a cartesian closed category
(such as that that sufficiently restricted Haskell takes place in) are
to view entities of type A as maps () -> A.Mikael Johansson wrote:
This rather inconveniently clashes with the fact that A and () -> A are two
distinct types in Haskell. A is just the "curried" counterpart to ()
-> A, just as A -> B is the curried counterpart to OneTuple A -> B and A B
-> -> C is the (fully) curried counterpart to (A,B) -> C
I take it by your argument that curried and uncurried functions, being
isomorphic, are represented by the same object in your category?
They probably would be -- which'd end up displaying the category (and thus
the way I think about Haskell) as a quotient category of the Haskell98
category.
I think though, still, that my argument carries content to the discussion:
regardless of whether we handle currying or not (note that any function
has a completely curried normal form) we still end up with the original
argument separating things that doesn't necessarily make sense to separate
-- in the argument 0-ary functions from n-ary functions.
Dan
--
Mikael Johansson | To see the world in a grain of sand
[EMAIL PROTECTED] | And heaven in a wild flower
http://www.mikael.johanssons.org | To hold infinity in the palm of your hand
| And eternity for an hour
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