ML4PG in Computer Algebra verification

TL;DR

This paper demonstrates how ML4PG, a machine learning extension, can identify proof patterns in CoqEAL library to assist in verifying algorithms for computing inverses of triangular matrices.

Contribution

It introduces the application of ML4PG to find proof patterns in a library dedicated to verifying Computer Algebra algorithms, aiding formalization efforts.

Findings

ML4PG successfully identified proof patterns in CoqEAL.

Assisted in formalizing an efficient matrix inverse algorithm.

Enhanced proof development process with statistical hints.

Abstract

ML4PG is a machine-learning extension that provides statistical proof hints during the process of Coq/SSReflect proof development. In this paper, we use ML4PG to find proof patterns in the CoqEAL library -- a library that was devised to verify the correctness of Computer Algebra algorithms. In particular, we use ML4PG to help us in the formalisation of an efficient algorithm to compute the inverse of triangular matrices.