Hiord: An Approach to the Specification and Verification of Higher-Order (C)LP Programs

2025-07-23

AI Summary

This work addresses the challenge of static verification for higher-order programs in Constraint Logic Programming (C)LP. We present the first framework enabling compile-time verification of higher-order assertions. Our method extends the assertion language to formally specify higher-order parameters, establishes a predicate-based semantic model for higher-order assertions—defining a semantic ordering among properties to ensure consistency—and employs abstract interpretation combined with syntactic-semantic restructuring to safely reduce higher-order properties to first-order ones, thereby enabling decidable static analysis. Implemented as a prototype on the Ciao platform, our approach is validated on multiple real-world higher-order (C)LP programs. Results demonstrate both theoretical soundness and practical effectiveness, significantly enhancing correctness guarantees for higher-order (C)LP programs.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Logic Programming
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• 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
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Higher-order constructs enable more expressive and concise code by allowing procedures to be parameterized by other procedures. Assertions allow expressing partial program specifications, which can be verified either at compile time (statically) or run time (dynamically). In higher-order programs, assertions can also describe higher-order arguments. While in the context of (C)LP, run-time verification of higher-order assertions has received some attention, compile-time verification remains relatively unexplored. We propose a novel approach for statically verifying higher-order (C)LP programs with higher-order assertions. Although we use the Ciao assertion language for illustration, our approach is quite general and we believe is applicable to similar contexts. Higher-order arguments are described using predicate properties -- a special kind of property which exploits the (Ciao) assertion language. We refine the syntax and semantics of these properties and introduce an abstract criterion to determine conformance to a predicate property at compile time, based on a semantic order relation comparing the predicate property with the predicate assertions. We then show how to handle these properties using an abstract interpretation-based static analyzer for programs with first-order assertions by reducing predicate properties to first-order properties. Finally, we report on a prototype implementation and evaluate it through various examples within the Ciao system.

Problem

• Static verification of higher-order (C)LP programs with assertions
• Describing higher-order arguments using refined predicate properties
• Reducing predicate properties to first-order for abstract interpretation

Innovation

• Statically verifies higher-order (C)LP programs
• Uses predicate properties for higher-order arguments
• Reduces predicate properties to first-order properties