A Coalgebraic Approach to Kleene Algebra with Tests
Abstract
Description
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.
21 pages, 1 figure; preliminary version appeared in Proc. Workshop on Coalgebraic Methods in Computer Science (CMCS'03)
21 pages, 1 figure; preliminary version appeared in Proc. Workshop on Coalgebraic Methods in Computer Science (CMCS'03)