Automated Catamorphism Synthesis for Solving Constrained Horn Clauses over Algebraic Data Types

2025-07-28

AI Summary

Existing CHC solvers struggle to model and discover structured inductive models—particularly those involving recursively defined functions (e.g., list summation)—in satisfiability verification of Constraint Horn Clauses over Algebraic Data Types (ADTs). Method: We propose the first demand-driven, fully automatic framework for synthesizing catamorphisms (generalized folds) as inductive abstractions. Our approach dynamically infers and integrates catamorphisms into the CHC solving process, enabling compact representation and efficient reasoning about recursive ADT properties. Contribution/Results: Based on this framework, we design and implement Catalia, a novel CHC solver. Evaluated on the CHC-COMP 2024/2025 benchmarks, Catalia significantly outperforms state-of-the-art tools on satisfiable instances and serves as the core component of ChocoCatalia, which won the ADT-LIA track at CHC-COMP 2025.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

We propose a novel approach to satisfiability checking of Constrained Horn Clauses (CHCs) over Algebraic Data Types (ADTs). CHC-based automated verification has gained considerable attention in recent years, leading to the development of various CHC solvers. However, existing solvers for CHCs over ADTs are not fully satisfactory, due to their limited ability to find and express models involving inductively defined functions/predicates (e.g., those about the sum of list elements). To address this limitation, we consider catamorphisms (generalized fold functions), and present a framework for automatically discovering appropriate catamorphisms on demand and using them to express a model of given CHCs. We have implemented a new CHC solver called Catalia based on the proposed method. Our experimental results for the CHC-COMP 2024 benchmark show that Catalia outperforms state-of-the-art solvers in solving satisfiable CHCs over ADTs. Catalia was also used as a core part of the tool called ChocoCatalia, which won the ADT-LIA category of CHC-COMP 2025.

Problem

• Automated synthesis of catamorphisms for CHCs over ADTs
• Improving model discovery for inductive functions/predicates
• Enhancing solver performance in satisfiable CHC cases

Innovation

• Automated catamorphism synthesis for CHCs
• On-demand discovery of catamorphisms
• Catalia solver outperforms state-of-the-art