Dynamic Separation Logic

TL;DR

This paper extends separation logic with dynamic modalities for core instructions, enabling combined reasoning approaches and formal verification within a unified logical framework.

Contribution

It introduces a dynamic logic extension of separation logic with modalities for core instructions, allowing combined reasoning approaches and formal proofs in Coq.

Findings

Formalization of the dynamic logic extension in Coq

Soundness and completeness proofs of the axiomatization

Integration of multiple reasoning approaches within the logic

Abstract

This paper introduces a dynamic logic extension of separation logic. The assertion language of separation logic is extended with modalities for the five types of the basic instructions of separation logic: simple assignment, look-up, mutation, allocation, and de-allocation. The main novelty of the resulting dynamic logic is that it allows to combine different approaches to resolving these modalities. One such approach is based on the standard weakest precondition calculus of separation logic. The other approach introduced in this paper provides a novel alternative formalization in the proposed dynamic logic extension of separation logic. The soundness and completeness of this axiomatization has been formalized in the Coq theorem prover.