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

MigMit migmit at gmail.com
Mon Dec 10 20:35:18 UTC 2018

```Same here!

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!
>>
>> _______________________________________________