[Haskell-cafe] References for topological arguments of programs?
till at iks.cs.ovgu.de
Mon Dec 10 13:34:07 UTC 2018
Peter G. Hinman: Recursion-Theoretic Hierarchies might contain some
Best, Till Mossakowski
Am 10.12.18 um 13:38 schrieb Siddharth Bhat:
> 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!
> Sending this from my phone, please excuse any typos!
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