A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Partial derivatives of regular expressions and finite automaton constructions
Theoretical Computer Science
ACM Transactions on Programming Languages and Systems (TOPLAS)
Derivatives of Regular Expressions
Journal of the ACM (JACM)
On Hoare logic and Kleene algebra with tests
ACM Transactions on Computational Logic (TOCL)
An axiomatic basis for computer programming
Communications of the ACM
Programming Techniques: Regular expression search algorithm
Communications of the ACM
Introduction to Mathematical Theory of Computation
Introduction to Mathematical Theory of Computation
Certification of Compiler Optimizations Using Kleene Algebra with Tests
CL '00 Proceedings of the First International Conference on Computational Logic
Kleene Algebra with Tests: Completeness and Decidability
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
Kleene Algebra with Tests and Program Schematology
Kleene Algebra with Tests and Program Schematology
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Untyping typed algebraic structures and colouring proof nets of cyclic linear logic
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Partial derivative automata formalized in Coq
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
PLPV '12 Proceedings of the sixth workshop on Programming languages meets program verification
Proving equalities in a commutative ring done right in coq
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
An efficient coq tactic for deciding kleene algebras
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
A decision procedure for regular expression equivalence in type theory
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Proof Pearl: Regular Expression Equivalence and Relation Algebra
Journal of Automated Reasoning
Automated analysis of regular algebra
IJCAR'12 Proceedings of the 6th international joint conference on 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
Deciding regular expressions (in-)equivalence in coq
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
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We present a Coq library about Kleene algebra with tests, including a proof of their completeness over the appropriate notion of languages, a decision procedure for their equational theory, and tools for exploiting hypotheses of a certain kind in such a theory. Kleene algebra with tests make it possible to represent if-then-else statements and while loops in imperative programming languages. They were actually introduced as an alternative to propositional Hoare logic. We show how to exploit the corresponding Coq tools in the context of program verification by proving equivalences of while programs, correctness of some standard compiler optimisations, Hoare rules for partial correctness, and a particularly challenging equivalence of flowchart schemes.