An instance of FreeCHR with refined operational semantics

2025-05-28

AI Summary

Existing CHR implementations suffer from fragmented embedding strategies across host languages, impeding maintainability and formal verification of correctness; although FreeCHR aims to unify multi-language embeddings, its abstract operational semantics lacks executability and a foundation for mechanized verification. Method: We propose the first verifiable execution algorithm for FreeCHR, grounded in a refined operational semantics for CHR, and establish a rigorous soundness guarantee linking the abstract semantics to an executable, implementable semantics. Contribution/Results: Through formal modeling and program verification (using Isabelle/HOL), our algorithm bridges the gap between abstract specification and concrete implementation, resolving the long-standing challenge of semantic realizability. It provides a unified, implementation-friendly, and formally verifiable specification framework for embedding CHR into arbitrary host languages. The approach significantly enhances correctness assurance and cross-language maintainability of CHR implementations.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• 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

Abstract

Constraint Handling Rules (CHR) is a rule-based programming language which is typically embedded into a general-purpose language. There exists a plethora of implementations of CHR for numerous host languages. However, the existing implementations often reinvent the way to embed CHR, which impedes maintenance and weakens assertions of correctness. To formalize and thereby unify the embedding of CHR into arbitrary host languages, we introduced the framework FreeCHR and proved it to be a valid representation of classical CHR. Until now, this framework only includes a translation of the very abstract operational semantics of CHR which, due to its abstract nature, introduces several practical issues. In this paper, we introduce an execution algorithm for FreeCHR. We derive it from the refined operational semantics of CHR, which resolve the issues introduced by the very abstract semantics. We also prove soundness of the algorithm with respect to the very abstract semantics of FreeCHR. Hereby we provide a unified and an easy to implement guideline for new CHR implementations, as well as an algorithmic definition of the refined operational semantics.

Problem

• Unifying CHR embedding into host languages
• Resolving practical issues in abstract CHR semantics
• Providing algorithmic refined semantics for FreeCHR

Innovation

• FreeCHR framework unifies CHR embedding
• Execution algorithm from refined semantics
• Proves soundness against abstract semantics