Verifying Solutions to Semantics-Guided Synthesis Problems

Semantics-Guided Synthesis (SemGuS) provides a framework to specify synthesis problems in a solver-agnostic and domain-agnostic way, by allowing a user to provide both the syntax and semantics of the language in which the desired program should be synthesized. Because synthesis and verification are...

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Vydáno v:Proceedings of ACM on programming languages Ročník 9; číslo PLDI; s. 1741 - 1765
Hlavní autoři: Murphy, Charlie, Johnson, Keith J.C., Reps, Thomas, D'Antoni, Loris
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY, USA ACM 10.06.2025
Témata:
Automated reasoning
Constraint and logic programming
Logic and verification
Operational semantics
Semantics
Software and its engineering
Theory of computation
Program Verification
SMT
Semantics
SemGuS
CHC
Program Synthesis
ISSN:2475-1421, 2475-1421
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Shrnutí:Semantics-Guided Synthesis (SemGuS) provides a framework to specify synthesis problems in a solver-agnostic and domain-agnostic way, by allowing a user to provide both the syntax and semantics of the language in which the desired program should be synthesized. Because synthesis and verification are closely intertwined, the SemGuS framework raises the following question: how does one verify that a user-given program satisfies a given specification when interpreted according to a user-given semantics? In this paper, we prove that this form of language-agnostic verification (specifically that verifying whether a program is a valid solution to a SemGuS problem) can be reduced to proving validity of a query in the µCLP calculus, a fixed-point logic that is capable of expressing alternating least and greatest fixed-points. Our encoding into µCLP allows us to further classify the SemGuS verification problems into ones that are reducible to satisfiability of (i) first-order-logic formulas, (ii) Constrained Horn Clauses, and (iii) µCLP queries. Furthermore, our encoding shines light on some limitations of the SemGuS framework, such as its inability to model nondeterminism and reactive synthesis. We thus propose a modification to SemGuS that makes it more expressive, and for which verifying solutions is exactly equivalent to proving validity of a query in the µCLP calculus. Our implementation of SemGuS verifiers based on the above encoding can verify instances that were not even encodable in previous work. Furthermore, we use our SemGuS verifiers within an enumeration-based SemGuS solver to correctly synthesize solutions to SemGuS problems that no previous SemGuS synthesizer could solve.
ISSN:2475-1421
2475-1421
DOI:10.1145/3729320