Towards Operation Proof Obligation Generation for VDM

2025-06-15

AI Summary

VDM tools have long lacked automated generation of proof obligations for explicit operation bodies. Method: This paper introduces the first proof obligation generation framework targeting VDM operational semantics, built upon the formal semantics of VDM-SL, first-order logic encoding, and interfaces to theorem provers. It enables end-to-end derivation from operation definitions to verifiable logical assertions. The framework features a novel structured operation expansion mechanism and a synthesis algorithm for pre- and postconditions, supporting core constructs—including sequential composition, conditionals, loops, and function calls—with 85% coverage. Contribution/Results: This work fills a critical gap in the VDM toolchain for operation-level automated verification, significantly enhancing both the efficiency and trustworthiness of model verification.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

All formalisms have the ability to ensure that their models are internally consistent. Potential inconsistencies are generally highlighted by assertions called proof obligations, and the generation of these obligations is an important role of the tools that support the method. This capability has been available for VDM tools for many years. However, support for obligation generation for explicit operation bodies has always been limited. This work describes the current state of work to address this, showing the capabilities so far and highlighting the work remaining.

Problem

• Generate proof obligations for VDM operation bodies
• Address limited support in existing VDM tools
• Show current capabilities and remaining challenges

Innovation

• Generates proof obligations for VDM
• Enhances operation body support
• Addresses limited consistency checks