Sound State Encodings in Translational Separation Logic Verifiers (Extended Version)

2026-03-20

AI Summary

Existing translational separation logic verifiers lack formal guarantees of semantic correctness for front-end encodings when state models are inconsistent. This work proposes a general formal framework that ensures semantic fidelity of front-end encodings across differing state models by leveraging homomorphic encoding relations and backward satisfiability conditions. Implemented in Isabelle/HOL, the framework enables, for the first time, soundness proofs for translational verifiers employing non-trivial state encodings. It has been successfully applied to verify the correctness of three representative state encodings across multiple combinations of front-end and intermediate verification languages, including Raven, VeriFast, and Viper, thereby significantly enhancing the applicability and reliability of translational verification approaches.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Security and Privacy: Data transparency and provenance
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization

Abstract

Automated program verifiers are often organized into a front-end, which encodes an input program into an intermediate verification language (IVL), and a back-end, which proves that the IVL program is correct. Soundness of such translational verifiers requires that the back-end verification is sound and that correctness of the IVL program implies correctness of the input program. Existing formalizations for translational verifiers based on separation logic target the former, but support the latter only under the strong assumption that there exists a separation logic for the input program with the same state model as the IVL. This assumption is unrealistic in practice, especially since the state model also defines the supported separation logic resources. We present the first formal framework for proving the soundness of translational separation logic verifiers with non-trivial state encodings. To be applicable to various front-ends and IVLs, our framework only assumes the existence of a homomorphic encoding relation between the front-end and IVL state models. At the core of our framework is a novel condition, backward satisfiability, which is crucial to guarantee the soundness of the front-end translation. We formalize our framework for front-end verifiers based on concurrent separation logic and separation logic IVLs, such as Raven, VeriFast, and Viper. We demonstrate its expressiveness by proving soundness for three common state encodings. Our framework and all proofs are formalized in Isabelle/HOL.

Problem

• translational verification
• separation logic
• state encoding
• soundness
• intermediate verification language

Innovation

• translational verification
• separation logic
• state encoding
• backward satisfiability
• soundness