[Haskell-cafe] type metaphysics

Martijn van Steenbergen martijn at van.steenbergen.nl
Mon Feb 2 11:47:23 EST 2009

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?


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