The authors introduce Weave of Formal Thought (WoFT), a paradigm combining rigorous syntactic validation with learned structural representations for code generation. The approach utilizes a formal engine and constrained decoder that is sound and complete regarding the full Tree-sitter specification. By augmenting generalized LR parsing with speculative lexing, the system maintains concurrent lexer-state hypotheses to admit valid program prefixes while rejecting invalid ones. Additionally, WoFT employs latent-variable fine-tuning to train models to interleave non-terminal grammar symbols directly into the generation process. This method uses the reweighted wake-sleep algorithm to optimize the importance-weighted evidence lower bound of the surface text. The model learns to selectively retain formal derivations as an adaptive structural scratchpad during inference. Experiments on Python show that fine-tuning StarCoder2-3B with this objective reduces per-token cross-entropy by 14.3% compared to a text-only baseline.