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

[Bhavik Mehta]

I'm happy to do this, I'll aim to put it up over the next few days!

Bhavik Mehta

On Mon, 10 Dec 2018 at 21:05, Olaf Klinke <olf at aatal-apotheke.de> wrote:

> I suggest to use Bhavik Mehta's page
> haskellformathematicians.wordpress.com if we can not find a more official
> place for it on haskell.org. At this point I'd like to thank Haskell Café
> member Sergiu Ivanov for inspiring me to start working on this.
>
> Does anyone know whether literate haskell can be used to generate html?
>
> Olaf
>
> > Am 10.12.2018 um 21:56 schrieb Siddharth Bhat <siddu.druid at gmail.com>:
> >
> > 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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