Lennart Augustsson wrote:
The Haskell function space, A->B, is not uncountable. There is only a countable number of Haskell functions you can write, so how could there be more elements in the Haskell function space? :) The explanation is that the Haskell function space is not the same as the functions space in set theory. Most importantly Haskell functions have to be monotonic (in the domain theoretic sense), so that limits the number of possible functions.
I was thinking about a fixed function type A -> B having uncountably many *values* (i.e. implementations). Not about the number of function types of the form A -> B. Is that what you meant? For example, fix the type to Integer -> Bool. I can't enumeratate all possible implementations of this function. Right? Martijn.