On Kleene algebras and closed semirings
MFCS '90 Proceedings on Mathematical foundations of computer science 1990
Action logic and pure induction
JELIA '90 Proceedings of the European workshop on Logics in AI
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
A calculational approach to mathematical induction
Theoretical Computer Science
Two Complete Axiom Systems for the Algebra of Regular Events
Journal of the ACM (JACM)
Local Theory Specifications in Isabelle/Isar
Types for Proofs and Programs
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Packaging Mathematical Structures
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Internal axioms for domain semirings
Science of Computer Programming
Automated engineering of relational and algebraic methods in isabelle/hol
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
A formalisation of the Myhill-Nerode theorem based on regular expressions (proof pearl)
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
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 analysis of regular algebra
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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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We extend a large Isabelle/HOL repository for regular algebras towards higher-order variants based on directed sets and quantales, including reasoning based on general fixpoint properties and Galois connections. In this context we demonstrate that Isabelle's recent integration of automated theorem proving technology effectively supports higher-order reasoning. We present four case studies that underpin this claim: the calculus of Galois connections and fixpoints, action algebras and Galois connections, solvability conditions for regular equations and fixpoint fusion, and the implementation of formal language quantales.