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

[Ara Adkins]

I’d love to take a read of the current stage of your book!

_ara

> On 10 Dec 2018, at 20:28, Olaf Klinke <olf at aatal-apotheke.de> 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-computer-science/vol/87/
> Pages 21-156, Open access
> 
> [Disclaimer: Martín Escardó was one of my PhD supervisors.]
> 
>> Am 10.12.2018 um 13:38 schrieb Siddharth Bhat <siddu.druid at gmail.com>:
>> 
>> 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!
> 
> _______________________________________________
> Haskell-Cafe mailing list
> To (un)subscribe, modify options or view archives go to:
> http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe
> Only members subscribed via the mailman list are allowed to post.