Unifying Theories of Reactive Design Contracts

TL;DR

This paper introduces a unifying theoretical framework for reactive design contracts that models system evolution and interactions, supporting various computational paradigms and enabling formal verification of complex reactive systems.

Contribution

It presents a comprehensive contract language and calculational theory within UTP, allowing for modular modeling, reasoning, and verification of reactive systems across different time paradigms.

Findings

Supports modeling of state evolution and environment interactions

Enables verification of systems with large or infinite state spaces

Integrates with Isabelle/UTP for practical proof automation

Abstract

Design-by-contract is an important technique for model-based design in which a composite system is specified by a collection of contracts that specify the behavioural assumptions and guarantees of each component. In this paper, we describe a unifying theory for reactive design contracts that provides the basis for modelling and verification of reactive systems. We provide a language for expression and composition of contracts that is supported by a rich calculational theory. In contrast with other semantic models in the literature, our theory of contracts allow us to specify both the evolution of state variables and the permissible interactions with the environment. Moreover, our model of interaction is abstract, and supports, for instance, discrete time, continuous time, and hybrid computational models. Being based in Unifying Theories of Programming (UTP), our theory can be composed with further computational theories to support semantics for multi-paradigm languages. Practical reasoning support is provided via our proof framework, Isabelle/UTP, including a proof tactic that reduces a conjecture about a reactive program to three predicates, symbolically characterising its assumptions and guarantees about intermediate and final observations. This allows us to verify programs with a large or infinite state space. Our work advances the state-of-the-art in semantics for reactive languages, description of their contractual specifications, and compositional verification.