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Reactive programs are ubiquitous in modern applications, and so verificationis highly desirable. We present a verification strategy for reactive programswith a large or infinite state space utilising algebraic laws for reactiverelations. We define novel operators to characterise interactions and stateupdates, and an associated equational theory. With this we can calculate areactive program's denotational semantics, and thereby facilitate automatedproof. Of note is our reasoning support for iterative programs with reactiveinvariants, which is supported by Kleene algebra. We illustrate our strategy byverifying a reactive buffer. Our laws and strategy are mechanised inIsabelle/UTP, which provides soundness guarantees, and practical verificationsupport.

Calculational Verification of Reactive Programs with Reactive Relations and Kleene Algebra