  Deductive verification of hybrid systems (HSs) increasingly attracts more
attention in recent years because of its power and scalability, where a
powerful specification logic for HSs is the cornerstone. Often, HSs are
naturally modelled by concurrent processes that communicate with each other.
However, existing specification logics cannot easily handle such models. In
this paper, we present a specification logic and proof system for Hybrid
Communicating Sequential Processes (HCSP), that extends CSP with ordinary
differential equations (ODE) and interrupts to model interactions between
continuous and discrete evolution. Because it includes a rich set of algebraic
operators, complicated hybrid systems can be easily modelled in an algebra-like
compositional way in HCSP. Our logic can be seen as a generalization and
simplification of existing hybrid Hoare logics (HHL) based on duration calculus
(DC), as well as a conservative extension of existing Hoare logics for
concurrent programs. Its assertion logic is the first-order theory of
differential equations (FOD), together with assertions about traces recording
communications, readiness, and continuous evolution. We prove continuous
relative completeness of the logic w.r.t. FOD, as well as discrete relative
completeness in the sense that continuous behaviour can be arbitrarily
approximated by discretization. Finally, we implement the above logic in
Isabelle/HOL, and apply it to verify two case studies to illustrate the power
and scalability of our logic.
