[Haskell-cafe] References for topological arguments of programs?

[Siddharth Bhat]

Hello,

I was recently intrigued by this style of argument on haskell cafe:


One can write a function
Eq a => ((a -> Bool) -> a) -> [a]
that enumerates the elements of the set. Because we have universal
quantification, this list can not be infinite. Which makes sense,
topologically: These so-called searchable sets are topologically compact,
and the Eq constraint means the space is discrete. Compact subsets of a
discrete space are finite.
-------

I've seen arguments like these "in the wild" during Scott topology
construction and in some other weird places (hyperfunctions), but I've
never seen a systematic treatment of this.


I'd love to have a reference (papers / textbook preferred) to self learn
this stuff!

Thanks
Siddharth
-- 
Sending this from my phone, please excuse any typos!
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