Hybrid Systems Verification with Isabelle/HOL: Simpler Syntax, Better Models, Faster Proofs

TL;DR

This paper enhances hybrid systems verification in Isabelle/HOL by introducing a new algebraic store model and a user-friendly expression syntax, resulting in more scalable, automated, and intuitive proofs.

Contribution

It presents a novel algebraic store model and a shallow expression model that improve reasoning, automation, and usability in hybrid systems verification within Isabelle/HOL.

Findings

More local inference rules and tactics for hybrid systems

Increased proof automation and scalability

Enhanced syntax and interfaces for real-world modeling

Abstract

We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and domain-specific deductive and calculational support. The new store model yields clean separations and dynamic local views of variables, e.g. discrete/continuous, mutable/immutable, program/logical, and enhanced ways of manipulating them using combinators, projections and framing. This leads to more local inference rules, procedures and tactics for reasoning with invariant sets, certifying solutions of hybrid specifications or calculating derivatives with increased proof automation and scalability. The new expression model provides more user-friendly syntax, better control of name spaces and interfaces connecting the framework with real-world modelling languages.