A calculus and logic of bunched resources and processes

Gabrielle Anderson,David Pym

doi:10.1016/j.tcs.2015.11.035

Abstract

Mathematical modelling and simulation modelling are fundamental tools of engineering, science, and social sciences such as economics, and provide decision-support tools in management. Mathematical models are essentially deployed at all scales, all levels of complexity, and all levels of abstraction. Models are often required to be executable, as a simulation, on a computer. We present some contributions to the process-theoretic and logical foundations of discrete-event modelling with resources and processes. Building on previous work in resource semantics, process calculus, and modal logic, we describe a process calculus with an explicit representation of resources in which processes and resources co-evolve. The calculus is closely connected to a substructural modal logic that may be used as a specification language for properties of models. In contrast to earlier work, we formulate the resource semantics, and its relationship with process calculus, in such a way that we obtain soundness and completeness of bisimulation with respect to logical equivalence for the naturally full range of logical connectives and modalities. We give a range of examples of the use of the process combinators and logical structure to describe system structure and behaviour.

Highlights

Mathematical modelling and simulation modelling are fundamental tools of engineering, science, and social sciences such as economics, and provide decision-support tools in management
This work suggests that the original ideas of resource semantics, though useful and influential in, say, separation logic, may warrant further exploration
We have shown that a technical difficulty present in an earlier formulation of the relationship between resources and processes — that is, the lack of the Hennessy–Milner completeness theorem for the full logic — can be resolved by moving to a version of resource semantics in which there is a closer combinatory match between the structure carried by resources and that carried by processes

Summary

Introduction

Mathematical modelling and simulation modelling are fundamental tools of engineering, science, and social sciences such as economics, and provide decision-support tools in management. The key tract of related work is based around O’Hearn’s concurrent separation logic [29] These ideas have been developed in a range of directions, including the provision of a semantics for Hoare’s Communicating Sequential Processes (CSP) [24] — a calculus of processes that shares some combinatorial properties with our calculus and its relatives — using the structures that support concurrent separation logic. A summary of this work has been presented in [1]

A calculus of bunched resources and processes

Embedding SCRP in CBRP

Algebraic properties

A modal logic of resources and processes

Discussion