A decision procedure for regular expression equivalence in type theory

Authors:
Thierry Coquand;Vincent Siles
Affiliations:
University of Gothenburg, Sweden;University of Gothenburg, Sweden
Venue:
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Year:
2011

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Abstract

We describe and formally verify a procedure to decide regular expressions equivalence: two regular expressions are equivalent if and only if they recognize the same language. Our approach to this problem is inspired by Brzozowski's algorithm using derivatives of regular expressions, with a new definition of finite sets. In this paper, we detail a complete formalization of Brzozowki's derivatives, a new definition of finite sets along with its basic meta-theory, and a decidable equivalence procedure correctly proved using Coq and Ssreflect.