Principles for Verification Tools: Separation Logic

TL;DR

This paper presents a principled framework for designing program verification tools using separation logic, modeling control flow with power series and convolution, and ensuring correctness through formal proofs in Isabelle/HOL.

Contribution

It introduces a generic construction that lifts resource monoids to assertion and predicate transformer quantales, enabling automatic and correct verification tool implementation.

Findings

The framework simplifies implementation in Isabelle/HOL.

Verification conditions are derived through equational reasoning.

The approach is demonstrated with linked list reversal example.

Abstract

A principled approach to the design of program verification and con- struction tools is applied to separation logic. The control flow is modelled by power series with convolution as separating conjunction. A generic construction lifts resource monoids to assertion and predicate transformer quantales. The data flow is captured by concrete store/heap models. These are linked to the separation algebra by soundness proofs. Verification conditions and transformation laws are derived by equational reasoning within the predicate transformer quantale. This separation of concerns makes an implementation in the Isabelle/HOL proof as- sistant simple and highly automatic. The resulting tool is correct by construction; it is explained on the classical linked list reversal example.