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

Hi Olaf, I think I'd be interested in seeing your work-in-progress. Ryan Reich On Mon, Dec 10, 2018 at 12:29 PM Olaf Klinke wrote:

I highly recommend the So-called "Barbados notes" [1] of Martín Escardó. It is a systematic development of synthetic topology, with program fragments in Haskell. It is to my knowledge the first appearance of the so-called searchable sets and contains many other gems.

I myself have been working on "Haskell for mathematicians", which shall become an entry point to the language for those with a background stronger in mathematics than in other programming languages. It is planned to touch on many areas of mathematics, not only topology. If anyone would like to have a look at the current stage, I'd be happy to share the source.

Olaf

[1] Synthetic Topology: of Data Types and Classical Spaces

https://www.sciencedirect.com/journal/electronic-notes-in-theoretical-comput... Pages 21-156, Open access

[Disclaimer: Martín Escardó was one of my PhD supervisors.]

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Am 10.12.2018 um 13:38 schrieb 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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