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A Coalgebraic Approach to Kleene Algebra with Tests

Hubie Chen·Riccardo Pucella
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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.

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Hubie Chen, Riccardo Pucella. 2004-05-26. A Coalgebraic Approach to Kleene Algebra with Tests. https://arxiv.org/abs/cs/0405097

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