Dependently Typed Model Composition for Matching Logic

2026-09-24

Electronic Proceedings in Theoretical Computer Science

AI Summary

This study addresses the challenge in matching logic where model composition fails to preserve satisfiability proofs, preventing composite models from inheriting the verified properties of their submodels. To overcome this limitation, this work proposes a dependently typed model composition framework grounded in polymorphically sorted matching logic. By leveraging dependent type definitions to precisely characterize compositional semantics, the framework provides a direct blueprint for formalization within the Rocq proof assistant. The primary contribution lies in establishing a mechanizable theoretical foundation for model composition, ensuring that verification properties of submodels rigorously hold within composite models and thereby fundamentally guaranteeing semantic consistency.

Abstract

This paper investigates model composition—often referred to as"gluing"—within the framework of matching logic. Specifically, we examine the systematic combination of existing signatures, variable valuations, theories, and their corresponding models. Our primary objective is to ensure that this composition preserves satisfaction proofs; that is, any theory validated by the individual constituent models is also validated by the resulting composite model. Our definitions are based on a polyadic, sorted variant of matching logic, which has also been expressed in the Rocq proof assistant. Therefore, we outline our definitions with dependent types for this work to serve as a direct blueprint for the mechanization in the short-term future.

Problem

• Matching Logic
• Model Composition
• Gluing
• Dependent Types
• Satisfaction Preservation

Innovation

• Matching Logic
• Model Composition
• Dependent Types
• Mechanization
• Satisfaction Proofs