Regular Algebras

Simon Foster 🌐 and Georg Struth 🌐

May 21, 2014

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Regular algebras axiomatise the equational theory of regular expressions as induced by regular language identity. We use Isabelle/HOL for a detailed systematic study of regular algebras given by Boffa, Conway, Kozen and Salomaa. We investigate the relationships between these classes, formalise a soundness proof for the smallest class (Salomaa's) and obtain completeness of the largest one (Boffa's) relative to a deep result by Krob. In addition we provide a large collection of regular identities in the general setting of Boffa's axiom. Our regular algebra hierarchy is orthogonal to the Kleene algebra hierarchy in the Archive of Formal Proofs; we have not aimed at an integration for pragmatic reasons.


BSD License


Session Regular_Algebras

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