Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
A mechanical proof of the Church-Rosser theorem
Journal of the ACM (JACM)
Relations and graphs: discrete mathematics for computer scientists
Relations and graphs: discrete mathematics for computer scientists
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Parallel reductions in &lgr;-calculus
Information and Computation
Journal of Symbolic Computation
A calculational approach to mathematical induction
Theoretical Computer Science
The variety of Kleene algebras with conversion is not finitely based
Theoretical Computer Science
Automata, Languages, and Machines
Automata, Languages, and Machines
The Book of Traces
Dynamic Logic
Some Lambda Calculus and Type Theory Formalized
Journal of Automated Reasoning
Journal of Automated Reasoning
Kleene Algebra withTests and Commutativity Conditions
TACAs '96 Proceedings of the Second International Workshop on Tools and Algorithms for Construction and Analysis of Systems
Certification of Compiler Optimizations Using Kleene Algebra with Tests
CL '00 Proceedings of the First International Conference on Computational Logic
MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
Church-Rosser Proofs in Kleene Algebra and Allegories
Church-Rosser Proofs in Kleene Algebra and Allegories
Automated Reasoning in Kleene Algebra
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Diagram Chase in Relational System Development
Electronic Notes in Theoretical Computer Science (ENTCS)
Automated reasoning for hybrid systems: two case studies
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
An efficient coq tactic for deciding kleene algebras
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
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We present simple calculational proofs of Church-Rosser theorems for equational theories, quasiorderings and nonsymmetric transitive relations in Kleene algebra. We also calculate the abstract part of two standard proofs of Church-Rosser theorems in the 驴-calculus and further central statements of rewriting. Since proofs avoid deduction, in particular induction, and large parts are amenable to automata, the approach is suited for mechanization. Since proofs algebraically reconstruct precisely the usual diagrams, they are also very natural for a human. In all considerations, Kleene algebra is an excellent means of abstraction.