On Eq, was Re: [Haskell-cafe] When to use fancy types [Re: NumberTheory library]

[Jacques Carette]

Lennart Augustsson <lennart at augustsson.net> wrote:
> Jacques Carette wrote:
> > Such people have the nasty habit of also thinking that ALL 
> > functions are continuous!  You might think they were constructivists or 
> > something.
> Why would a constructivist think that all functions are continuous?
> It makes no sense.

That would be a theorem of construtive mathematics!  All *constructible* functions are continuous.  See
http://plato.stanford.edu/entries/mathematics-constructive/
for some of these ideas.  For a lot more details, I recommend the book of Weihrauch, "Computable Analysis".  Others 
have recommended the books of Bishop and of Beeson, but I have not read them (yet).

Jacques