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

[Siddharth Bhat]

Agreed, having access to the book would be fantastic. :)

On Tue, 11 Dec, 2018, 02:05 MigMit, <migmit at gmail.com> wrote:

> Same here!
>
> Az iPademről küldve
>
> 2018. dec. 10. dátummal, 21:32 időpontban Ara Adkins <me at ara.io> írta:
>
> > 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!
> >>
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-- 
Sending this from my phone, please excuse any typos!
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