Semantic Prefix Oracles for LLM Decoding: Contracts and Differential Validation

Abstract:Constrained decoding can enforce regular or context-free output formats, but many program-generation failures are semantic: scope, typing, and declaration effects depend on context. We present semantic grammar specifications, a declarative formalism that attaches such constraints to a context-free surface and executes them during Earley descent. Our implementation enforces \emph{safe pruning}: it rejects only prefixes whose semantic contradictions cannot be repaired by any continuation. A separate, grammar-dependent, \emph{dead-end freedom} property guarantees the existence of a realizable witness for each remaining branch. We give simple sufficient conditions based on surface productivity, type coverage, and left-to-right constraint flow. Our finite-lambda, core ML, and C-like fragments satisfy them, while the STLC instance used in our experiments does not: plain STLC can violate type coverage, and we show how restricting its type universe recovers it. A tokenizer-lifting lemma carries character-level witnesses to token sequences under an explicit vocabulary-coverage hypothesis. We validate the implementation differentially against production compilers (\texttt{ocamlc}, \texttt{cc}). Across every prefix of 65 compiler-valid programs we observe zero false prunes. The semantic oracle localizes 25/30 invalid programs mid-stream, against 0/30 for a syntax-only oracle, and agrees on 42/42 recursion probes. A twelve-model generation study, including a matched semantic-versus-syntactic ablation for nine models, finds nonnegative observed semantic-minus-syntactic point estimates for every model-language pair, with maxima of $+15.2$ points on STLC task correctness and $+14.3$ points on ML validity.

Programming Languages (cs.PL); Artificial Intelligence (cs.AI); Computation and Language (cs.CL)

arXiv:2609.35425 [cs.PL]

(or arXiv:2609.35425v1 [cs.PL] for this version)

https://doi.org/10.48550/arXiv.2609.35425 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

https://doi.org/10.1145/3843750.3843841 Focus to learn more DOI(s) linking to related resources

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