Constraint Logic Programming over Infinite Domains with an Application to Proof

TL;DR

This paper introduces a constraint logic programming solver over infinite domains that guarantees soundness through a novel enumeration detection technique, applicable to data validation and proof tasks.

Contribution

It presents a new CLP(FD) solver capable of handling unbounded domains with soundness guarantees and support for nested quantifiers, extending the applicability of constraint programming.

Findings

Guarantees soundness when solutions are found or enumeration is complete.

Handles nested universal and existential quantifiers effectively.

Applicable to data validation and formal proof applications.

Abstract

We present a CLP(FD)-based constraint solver able to deal with unbounded domains. It is based on constraint propagation, resorting to enumeration if all other methods fail. An important aspect is detecting when enumeration was complete and if this has an impact on the soundness of the result. We present a technique which guarantees soundness in the following way: if the constraint solver finds a solution it is guaranteed to be correct; if the constraint solver fails to find a solution it can either return the result "definitely false" in case it knows enumeration was exhaustive, or "unknown" in case it was aborted. The technique can deal with nested universal and existential quantifiers. It can easily be extended to set comprehensions and other operators introducing new quantified variables. We show applications in data validation and proof.