Computer Algebra in the Age of Types

Schedule

Theme

Computer algebra, being one of the oldest computational disciplines, keeps growing rapidly. Most code is available as open source software: Constructive code tends to be written in very weakly typed systems like Python (notably Sage), GAP, C, or C++. Formal systems naturally carry strong typing and formal proof tools.

There is still, somewhat surprisingly, very little connection between the two disciplines, though many attempts have been made to bridge the gap by devising new systems that incorporate strong typing, proof assistants, and powerful (bespoke) programming languages.

This workshop advocates a slightly different approach: For modern computational mathematics to thrive we want to promote the use of types to

• compose existing constructive and formal systems with a low initial overhead, and a strong incentive towards eventual formal checkability and correctness,
• enable development of domain specific tools that make computations and algorithms in mathematical domains more natural, concise, and avoid large classes of common errors and cognitive overhead.
• provide access to machine verified proofs for use in computation and algorithm development
• provide access to efficient computations for use in proofs
• enable effective automated testing a-la Haskell's Quickcheck

Topics of Interest

• Type systems in computer algebra software
• (Computer) algebra in type systems
• Interfacing mathematics software using types
• Mathematical challenges for contemporary computer algebra
• Tools for using types in algorithm development and implementation
• Work in progress
• Real world applications

Invited speakers

• Michael Kohlhase, FAU Erlangen-Nürnberg
• Edwin Brady, University of St Andrews, author of Idris
• Dennis Müller, FAU Erlangen-Nürnberg

Submissions

Submissions are welcome for papers, software presentations, and posters. Contributors should submit a short abstract (no more than 4 pages) through EasyChair. It is expected that at least one author of each accepted submission is present at the workshop to give a presentation.

Important dates

Programme Committee (TBC)

• Markus Pfeiffer, University of St Andrews
• Gabriel Dos Reis, Microsoft Research