Uniform Substitution for Dynamic Logic with Communicating Hybrid Programs

Abstract

AbstractThis paper introduces a uniform substitution calculus for $${\textsf {d{}L}} {}_{\text {CHP}}$$ d L CHP , the dynamic logic of communicating hybrid programs. Uniform substitution enables parsimonious prover kernels by using axioms instead of axiom schemata. Instantiations can be recovered from a single proof rule responsible for soundness-critical instantiation checks rather than being spread across axiom schemata in side conditions. Even though communication and parallelism reasoning are notorious for necessitating subtle soundness-critical side conditions, uniform substitution when generalized to $${\textsf {d{}L}} {}_{\text {CHP}}$$ d L CHP manages to limit and isolate their conceptual overhead. Since uniform substitution has proven to simplify the implementation of hybrid systems provers substantially, uniform substitution for $${\textsf {d{}L}} {}_{\text {CHP}}$$ d L CHP paves the way for a parsimonious implementation of theorem provers for hybrid systems with communication and parallelism.