Stellis: A Strategy Language for Purifying Separation Logic Entailments

2025-12-04

AI Summary

Automated proof of separation logic entailments remains a core challenge in program verification, as existing rule-based approaches lack explicit formalization of critical memory-structure reasoning techniques—such as structural alignment and elimination. This paper introduces Stellis, a strategy language enabling flexible pattern matching and imperative action specification, which reduces spatial entailments to pure logical entailments. It further proposes the first verifiable strategy framework: soundness conditions are automatically generated and mechanically verified via a theorem prover, ensuring both strategy correctness and system reliability. Evaluated on 229 benchmarks, Stellis successfully discharges 219 entailments (95.6%) using only 98 strategies—demonstrating substantial improvements in automation and practicality for verifying linked-list algorithms and microkernel memory modules.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Machine Learning: Statistical Relational/Logic Learning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Automatically proving separation logic entailments is a fundamental challenge in verification. While rule-based methods rely on separation logic rules (lemmas) for automation, these rule statements are insufficient for describing automation strategies, which usually involve the alignment and elimination of corresponding memory layouts in specific scenarios. To overcome this limitation, we propose Stellis, a strategy language for purifying separation logic entailments, i.e., removing all spatial formulas to reduce the entailment to a simpler pure entailment. Stellis features a powerful matching mechanism and a flexible action description, enabling the straightforward encoding of a wide range of strategies. To ensure strategy soundness, we introduce an algorithm that generates a soundness condition for each strategy, thereby reducing the soundness of each strategy to the correctness of its soundness condition. Furthermore, based on a mechanized reduction soundness theorem, our prototype implementation generates correctness proofs for the overall automation. We evaluate our system on a benchmark of 229 entailments collected from verification of standard linked data structures and the memory module of a microkernel, and the evaluation results demonstrate that, with such flexibility and convenience provided, our system is also highly effective, which automatically purifies 95.6% (219 out of 229) of the entailments using 5 libraries with 98 strategies.

Problem

• Automating separation logic entailment proofs
• Encoding strategies for memory layout alignment
• Generating soundness conditions for verification strategies

Innovation

• Strategy language for purifying separation logic entailments
• Algorithm generates soundness conditions for each strategy
• Prototype generates correctness proofs via mechanized theorem