Year: 2025
Type: article
Abstract: Applications like program synthesis sometimes require proving that a property holds for all of the infinitely many programs described by a grammar—i.e., an inductively defined set of programs. Current verification frameworks overapproximate programs’ behavior when sets of programs contain loops, including two Hoare-style logics that fail to be relatively complete when loops are allowed. In this work, we prove that compositionally verifying simple properties for infinite sets of programs requires tracking distinct program behaviors over unboundedly many executions. Tracking this information is both necessary and sufficient for verification. We prove this fact in a general, reusable theory of denotational semantics that can model the expressivity and compositionality of verification techniques over infinite sets of programs. We construct the minimal compositional semantics that captures simple properties of sets of programs and use it to derive the first sound and relatively complete Hoare-style logic for infinite sets of programs. Thus, our methods can be used to design minimally complex, compositional verification techniques for sets of programs.
DOI: 10.1145/3720515
Authors: Jinwoo Kim, Shaan Nagy, Thomas Reps, Loris D'Antoni
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: National Science Foundation
Awards: FMitF: Track I: Formal Methods for Explainable Machine Learning, SaTC: CORE: Medium: SPIPS: Security and Privacy in Programmable Switches, FMitF : Track I: Aligning Code-Generating Models with Formal Specifications, SHF: Medium: Compositional Semantics-Guided Synthesis, Graduate Research Fellowship Program (GRFP), Collaborative Research: SHF: Medium: Semantics-Aware Neural Models of Code, SHF: Medium: Reasoning about Multiplicity in the Machine Learning Pipeline, SHF: Medium: Reasoning about Multiplicity in the Machine Learning Pipeline
OpenAlex ID: W4409311389