Complete systems of B -rational identities
Theoretical Computer Science
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Two Complete Axiom Systems for the Algebra of Regular Events
Journal of the ACM (JACM)
Automatic proof and disproof in Isabelle/HOL
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Automating algebraic methods in isabelle
ICFEM'11 Proceedings of the 13th international conference on Formal methods and software engineering
An efficient coq tactic for deciding kleene algebras
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Proof Pearl: Regular Expression Equivalence and Relation Algebra
Journal of Automated Reasoning
Automated reasoning in higher-order regular algebra
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Kleene algebra with tests and coq tools for while programs
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Program analysis and verification based on kleene algebra in Isabelle/HOL
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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Regular algebras axiomatise the equational theory of regular expressions. We use Isabelle/HOL's automated theorem provers and counterexample generators to study the regular algebras of Boffa, Conway, Kozen and Salomaa, formalise their soundness and completeness (relative to a deep result by Krob) and engineer their hierarchy. Proofs range from fully automatic axiomatic and inductive calculations to integrated higher-order reasoning with numbers, sets and monoid submorphisms. In combination with Isabelle's simplifiers and structuring mechanisms, automated deduction provides powerful support to the working mathematician beyond first-order reasoning.