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

Vanessa McHale vanessa.mchale at iohk.io
Tue Dec 11 09:43:37 UTC 2018

```I'd be quite interested in such a book/monograph - less as an
introduction to the language and more as a way of seeing the higher
mathematics one can use in Haskell/functional programming.

On 12/10/18 2:28 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-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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