Kleene Algebras with Domain

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.