Work

Synthesizing Formal Semantics from Executable Interpreters

Year: 2024

Type: article

Abstract: Program verification and synthesis frameworks that allow one to customize the language in which one is interested typically require the user to provide a formally defined semantics for the language. Because writing a formal semantics can be a daunting and error-prone task, this requirement stands in the way of such frameworks being adopted by non-expert users. We present an algorithm that can automatically synthesize inductively defined syntax-directed semantics when given ( i ) a grammar describing the syntax of a language and ( ii ) an executable (closed-box) interpreter for computing the semantics of programs in the language of the grammar. Our algorithm synthesizes the semantics in the form of Constrained-Horn Clauses (CHCs), a natural, extensible, and formal logical framework for specifying inductively defined relations that has recently received widespread adoption in program verification and synthesis. The key innovation of our synthesis algorithm is a Counterexample-Guided Synthesis (CEGIS) approach that breaks the hard problem of synthesizing a set of constrained Horn clauses into small, tractable expression-synthesis problems that can be dispatched to existing SyGuS synthesizers. Our tool SynAntic synthesized inductively-defined formal semantics from 14 interpreters for languages used in program-synthesis applications. When synthesizing formal semantics for one of our benchmarks, Synantic unveiled an inconsistency in the semantics computed by the interpreter for a language of regular expressions; fixing the inconsistency resulted in a more efficient semantics and, for some cases, in a 1.2 x speedup for a synthesizer solving synthesis problems over such a language.

Source: Proceedings of the ACM on Programming Languages

DOI: 10.1145/3689724

Authors: Jiangyi Liu, Charlie Murphy, Anvay Grover, Keith J.C. Johnson, Thomas Reps, Loris D’Antoni

Institutions: University of Wisconsin–Madison, University of California San Diego

Language: English

Topic: Logic, programming, and type systems

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, CAREER: Program Synthesis with Quantitative Guarantees, SHF: Medium: Compositional Semantics-Guided Synthesis, Collaborative Research: SHF: Medium: Semantics-Aware Neural Models of Code