Automated Reasoning with Nested Datatypes

2026-06-29

AI Summary

This work addresses the challenge that unrestricted combinations of nested data types and arrays often give rise to non-standard models, thereby undermining the reliability of automated reasoning. To resolve this issue, the paper proposes a carefully restricted yet sufficiently expressive theory of nested data types, which systematically eliminates non-standard models by constraining how such types may interact with arrays. Building upon this theoretical foundation, the authors design and implement a decision procedure that integrates SMT-solving techniques. The effectiveness and practicality of the approach are demonstrated through evaluations on both real-world and synthetic benchmarks, establishing a robust basis for verifying programs involving complex nested structures.

Abstract

We introduce a theory of nested datatypes. The theory is obtained by restricting the naive combination of datatypes and arrays, so as to prevent non-standard models from emerging. A decision procedure for the theory is given and proven correct. Finally, we describe an implementation of the procedure, as well as an evaluation over both real-world and crafted benchmarks.

Problem

• nested datatypes
• automated reasoning
• non-standard models
• decision procedure

Innovation

• nested datatypes
• decision procedure
• non-standard models
• automated reasoning
• formal verification