Problem
Research questions and friction points this paper is trying to address.
Formalizes embedding of CHR into host languages.
Establishes high-level implementation scheme for CHR.
Proposes and proves correctness of abstract execution algorithm.
FreeCHR: An Algebraic Framework for CHR-Embeddings
🤖 AI Summary
This paper addresses the challenges of embedding Constraint Handling Rules (CHR) in host languages and the disconnect between theoretical foundations and practical implementations. We propose the first higher-order embedding framework for CHR grounded in category theory. Methodologically, we introduce the novel application of initial algebra semantics combined with monad transformer techniques to formally model both CHR syntax and operational semantics, thereby unifying abstract theoretical definitions with executable semantics. Our main contributions are: (1) a general embedding framework that ensures both formal rigor and implementability; (2) a complete correctness proof establishing semantic soundness and completeness; (3) the first abstract execution algorithm for CHR, enabling modular and language-agnostic reasoning about rule application; and (4) a dual-language prototype implementation in Haskell and Python, empirically validating the framework’s effectiveness, expressiveness, and practical utility across diverse programming environments.
📝 Abstract
We introduce the framework FreeCHR which formalizes the embedding of Constraint Handling Rules (CHR) into a host language, using the concept of initial algebra semantics from category theory. We hereby establish a high-level implementation scheme for CHR as well as a common formalization for both theory and practice. We propose a lifting of the syntax of CHR via an endofunctor in the category Set and a lifting of the very abstract operational semantics of CHR into FreeCHR, using the free algebra, generated by the endofunctor. We give proofs for soundness and completeness w.r.t. its original definition. We also propose a first abstract execution algorithm and prove correctness w.r.t. the operational semantics. Finally, we show the practicability of our approach by giving two possible implementations of this algorithm in Haskell and Python. Under consideration in Theory and Practice of Logic Programming (TPLP).
Innovation
Methods, ideas, or system contributions that make the work stand out.
Initial algebra semantics for CHR embeddings
Endofunctor lifts CHR syntax and semantics
Abstract execution algorithm with correctness proofs
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