Basic proof theory
Coinductive axiomatization of recursive type equality and subtyping
Fundamenta Informaticae - Special issue: typed lambda-calculi and applications, selected papers
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Two Complete Axiom Systems for the Algebra of Regular Events
Journal of the ACM (JACM)
Automata and Coinduction (An Exercise in Coalgebra)
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
Regular expression containment: coinductive axiomatization and computational interpretation
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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In the specific situation of formal reasoning concerned with “regular expression equivalence” we address instances of more general questions such as: how can coinductive argumentation be formalised logically and be applied effectively, as well as how is it linked to traditional forms of proof. For statements expressing that two regular expressions are language equivalent, we demonstrate that proofs by coinduction can be formulated in a proof system based on equational logic, where effective proof-search is possible. And we describe a proof-theoretic method for translating derivations in this proof system into a “traditional” axiom system: namely, into a “reverse form” of the axiomatisation of “regular expression equivalence” due to Salomaa. Hereby we obtain a coinductive completeness proof for the traditional proof system.