Auke Booij: What are exact real numbers? - HaskellerZ November 2023
Channel: Zürich Friends of Haskell
Date: 2023-11-13

"RAM is finite. Regardless, you can compute with real numbers without loss of precision, using a higher-order language such as Haskell.

This immediately raises many questions: how can one represent real numbers in computers, which real numbers can be represented exactly, and (down the line) what are real numbers, anyway? I’ll cover some background.

The common representations of exact real numbers are difficult to understand, awkward to use, and vastly outperformed by finite-precision arithmetic. With some exceptions, this leaves exact real numbers as a hobby for the ivory tower.

Can we escape this tower? I don’t know. But I’ll present one length of rope: a simple abstraction."

In this talk, Auke will introduce us to this fascinating problem domain, with ideas drawn from his PhD thesis: Analysis in univalent type theory.

- Demo code for locators: https://github.com/abooij/haskell-locators
- Analysis in Univalent Type Theory: https://etheses.bham.ac.uk/id/eprint/10411/
- Towards an API for the Real Numbers: https://www.youtube.com/watch?v=wZY8JFqZkGY