Unique Solutions of Contractions, CCS, and their HOL Formalisation

TL;DR

This paper formalizes the theory of unique solutions of contractions in CCS within the HOL4 theorem prover, overcoming previous constraints and refining the proof technique for bisimilarity.

Contribution

It provides a comprehensive HOL4 formalisation of CCS core theory focusing on unique solutions of contractions, including removal of summation constraints.

Findings

Refined the theory by removing summation constraints

Developed a formalisation with 20,000 lines of proof scripts

Enhanced the proof technique for bisimilarity

Abstract

The unique solution of contractions is a proof technique for bisimilarity that overcomes certain syntactic constraints of Milner's "unique solution of equations" technique. The paper presents an overview of a rather comprehensive formalisation of the core of the theory of CCS in the HOL theorem prover (HOL4), with a focus towards the theory of unique solutions of contractions. (The formalisation consists of about 20,000 lines of proof scripts in Standard ML.) Some refinements of the theory itself are obtained. In particular we remove the constraints on summation, which must be weakly-guarded, by moving to rooted contraction, that is, the coarsest precongruence contained in the contraction preorder.