@inproceedings{samoylov-vosoughi-2025-modeling,
    title = "Modeling Tactics as Operators: Effect-Grounded Representations for Lean Theorem Proving",
    author = "Samoylov, Elisaveta  and
      Vosoughi, Soroush",
    editor = "Valentino, Marco  and
      Ferreira, Deborah  and
      Thayaparan, Mokanarangan  and
      Ranaldi, Leonardo  and
      Freitas, Andre",
    booktitle = "Proceedings of The 3rd Workshop on Mathematical Natural Language Processing (MathNLP 2025)",
    month = nov,
    year = "2025",
    address = "Suzhou, China",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-emnlp/2025.mathnlp-main.12/",
    pages = "168--175",
    ISBN = "979-8-89176-348-7",
    abstract = "Interactive theorem provers (ITPs) such as Lean expose proof construction as a sequence of tactics applied to proof states. Existing machine learning approaches typically treat tactics either as surface tokens or as labels conditioned on the current state, eliding their operator-like semantics. This paper introduces a representation learning framework in which tactics are characterized by the changes they induce on proof states. Using a stepwise Lean proof corpus, we construct \textit{delta contexts}{---}token-level additions/removals and typed structural edits{---}and train simple distributional models ($\Delta$-SGNS and CBOW-$\Delta$) to learn tactic embeddings grounded in these state transitions. Experiments on tactic retrieval and operator-style analogy tests show that $\Delta$-supervision yields more interpretable and generalizable embeddings than surface-only baselines. Our findings suggest that capturing the semantics of tactics requires modeling their state-transformational effects, rather than relying on distributional co-occurrence alone."
}