A coalgebraic approach to Kleene algebra with tests

Authors:
Hubie Chen;Riccardo Pucella
Affiliations:
Department of Computer Science, Cornell University, Ithaca, NY;Department of Computer Science, Cornell University, Ithaca, NY
Venue:
Theoretical Computer Science - Selected papers of CMCS'03
Year:
2004

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Abstract

Kleene algebra with tests is an extension of Kleene algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene algebra with Tests, along the lines of the coalgebraic theory of regular expressions based on deterministic automata. Since the known automata-theoretic presentation of Kleene algebra with tests does not lend itself to a coalgebraic theory, we define a new interpretation of Kleene algebra with tests expressions and a corresponding automata-theoretic presentation. One outcome of the theory is a coinductive proof principle, that can be used to establish equivalence of our Kleene algebra with tests expressions.