Kleene Algebras with Domain

Victor B. F. Gomes ๐ŸŒ, Walter Guttmann ๐ŸŒ, Peter Hรถfner ๐ŸŒ, Georg Struth ๐ŸŒ and Tjark Weber ๐ŸŒ

April 12, 2016

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Abstract

Kleene algebras with domain are Kleene algebras endowed with an operation that maps each element of the algebra to its domain of definition (or its complement) in abstract fashion. They form a simple algebraic basis for Hoare logics, dynamic logics or predicate transformer semantics. We formalise a modular hierarchy of algebras with domain and antidomain (domain complement) operations in Isabelle/HOL that ranges from domain and antidomain semigroups to modal Kleene algebras and divergence Kleene algebras. We link these algebras with models of binary relations and program traces. We include some examples from modal logics, termination and program analysis.

License

BSD License

Topics

Session KAD