Andrew J Bromage
G'day all.
On Wed, Jun 05, 2002 at 08:20:03PM -0500, Jon Cast wrote:
I think you're confused about what the type declarations mean. When you say
sqrt :: Float -> Float
you're promising to operate over /all/ Floats.
That would be true of Haskell functions were constrained to be total functions. They are not. Sqrt takes values of type Float, but it just happens to be a partial function over that type.
That depends on what you mean by ``partial function''. Technically, of course, a function of type (a -> b) is a subset of (a x b) satisfying certain constraints. All Haskell functions f satisfy the property (forall x::a. exists y::b. (x, y) <- f), so you can always get a value of f at any x. In other words, sqrt can take any x and compute with it; it just delivers _|_ at some of them. My point was, (sqrt x) is legal Haskell (and has a value) for all (x :: Float).
Unfortunately, Haskell doesn't allow {x :: Float | x >= 0} as a type, nor does it provide a positive-only floating point type.
One general rule of strongly-typed programming is: A program is type correct if it is accepted by my favourite type checker. A corollary is that what you call a type, I reserve the right to call a precondition.
If I accepted that, I would be un-defining crucial terms. That would destroy the potential for discussion here, no?
Cheers, Andrew Bromage
Jon Cast