On the Fine-Structure of Regular Algebra

Simon Foster, Georg Struth
2014 Journal of automated reasoning  
Regular algebra is the algebra of regular expressions as induced by regular language identity. We use Isabelle/HOL for a detailed systematic study of the regular algebra axioms given by Boffa, Conway, Kozen and Salomaa. We investigate the relationships between these systems, formalise a soundness proof for the smallest class (Salomaa's) and obtain completeness for the largest one (Boffa's) relative to a deep result by Krob. As a case study in formalised mathematics, our investigations also shed
more » ... some light on the power of theorem proving technology for reasoning with algebras and their models, including proof automation and counterexample generation.
doi:10.1007/s10817-014-9318-9 fatcat:tt7toa7wwbdghgymeqowvzxkdu