Abstraction Logic: The Marriage of Contextual Refinement and Separation Logic

TL;DR

This paper introduces abstraction logic (AL), a novel verification framework that combines the strengths of contextual refinement and separation logic, enabling modular, high-level reasoning about programs with formal guarantees.

Contribution

AL is a new formal verification technique that unifies contextual refinement and separation logic, formalized in Coq, supporting advanced reasoning and integration with CompCert for end-to-end correctness.

Findings

Verified ownership and purity properties using AL

Demonstrated reasoning about mutual recursion and function pointers

Established behavioral refinement from high-level programs to assembly

Abstract

Contextual refinement and separation logics are successful verification techniques that are very different in nature. First, the former guarantees behavioral refinement between a concrete program and an abstract program while the latter guarantees safety of a concrete program under certain conditions (expressed in terms of pre and post conditions). Second, the former does not allow any assumption about the context when locally reasoning about a module while the latter allows rich assumptions. In this paper, we present a new verification technique, called abstraction logic (AL), that inherently combines contextual refinement and separation logics such as Iris and VST, thereby taking the advantages of both. Specifically, AL allows us to locally verify a concrete module against an abstract module under separation-logic-style pre and post conditions about external modules. AL are fully formalized in Coq and provides a proof mode that supports a combination of simulation-style reasoning using our own tactics and SL-style reasoning using IPM (Iris Proof Mode). Using the proof mode, we verified various examples to demonstrate reasoning about ownership (based on partial commutative monoids) and purity ($i.e.$, termination with no system call), cyclic and higher-order reasoning about mutual recursion and function pointers, and reusable and gradual verification via intermediate abstractions. Also, the verification results are combined with CompCert, so that we formally establish behavioral refinement from top-level abstract programs, all the way down to their assembly code.