A Coalgebraic Approach to Kleene Algebra with Tests

Details A Coalgebraic Approach to Kleene Algebra with Tests A Coalgebraic Approach to Kleene Algebra with Tests

2004-05-26

arxiv.org/abs/cs/0405097v1

Theoretical Computer Science, 327 (1-2), 23-44 (2004)

Computer Science

Logic in Computer Science

21 pages, 1 figure; preliminary version appeared in Proc. Workshop on Coalgebraic Methods in Computer Science (CMCS'03)

Scientific paper

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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