[Agda] decidable equality in algebra
Martin Escardo
m.escardo at cs.bham.ac.uk
Thu Oct 5 23:43:04 CEST 2017
On 05/10/17 19:58, mechvel at botik.ru wrote:
> I wonder of how many nice algorithms are known for real numbers, whether
> they are interesting so that it could be worthy to lift the ≟
> requirement.
There is a huge literature on constructive analysis. You may with to
start with Bishop's Founctions of Constructive Analysis, and Bishop and
Bridges' Constructive Analysis.
Bishop works with setoids, and in particular with a setoid of real
numbers along the lines you describe in your message.
Fred Richman has many interesting papers on constructive analysis, most
of them available on his web page. But he doesn't work with setoids. If
I were to try to formalize his work, I would use univalent type theory
rather than setoids.
As I said, many authors have worked on this vast subject.
Best,
Martin
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