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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 1.2x speedup for a synthesizer solving synthesis problems over such a language. 

Abstract Checking satisfiability of formulae in the theory of linear arithmetic has far reaching applications, including program verification and synthesis. Many satisfiability solvers excel at proving and disproving satisfiability of quantifier-free linear arithmetic formulas and have recently begun to support quantified formulas. Beyond simply checking satisfiability of formulas, fine-grained strategies for satisfiability games enables solving additional program verification and synthesis tasks. Quantified satisfiability games are played between two players—SAT and UNSAT—who take turns instantiating quantifiers and choosing branches of boolean connectives to evaluate the given formula. A winning strategy for SAT (resp. UNSAT) determines the choices of SAT (resp. UNSAT) as a function of UNSAT ’s (resp. SAT ’s) choices such that the given formula evaluates to true (resp. false) no matter what choices UNSAT (resp. SAT) may make. As we are interested in both checking satisfiabilityandsynthesizing winning strategies, we must avoid conversion to normal-forms that alter the game semantics of the formula (e.g. prenex normal form). We present fine-grained strategy improvement and strategy synthesis, the first technique capable of synthesizing winning fine-grained strategies for linear arithmetic satisfiability games, which may be used in higher-level applications. We experimentally evaluate our technique and find it performs favorably compared with state-of-the-art solvers.