Date of Award

Spring 6-3-2026

Document Type

Thesis (Undergraduate)

Department

Computer Science

First Advisor

Soroush Vosoughi

Abstract

In neural theorem proving for interactive proof assistants such as Lean, tactic prediction models score proof steps by surface likelihood, missing whether a move actually advances the proof. This thesis proposes representing each step by the symbolic edit it induces on the proof state rather than by its token-level surface form, and shows that this effect-grounded view yields better tactic embeddings, reveals structured geometry in complete proofs, and enables a practical proof search prior.

We introduce Delta Tokens — token-level state edits augmented with structural indicators — and show they outperform surface-only representations on tactic retrieval and operator-analogy benchmarks. Embedding proof steps with a Transformer language model trained on these tokens, we find that longer proofs trace increasingly indirect paths in the learned space, with geometric patterns corresponding to recognizable styles of mathematical argument. Finally, we aggregate the trajectories of solved proofs into local direction fields and use them to rerank candidate next steps during proof search. On 76,855 held-out tactic transitions, the trajectory field achieves mean cosine alignment of 0.583 versus 0.165 for a surface baseline, recovering the correct next tactic family in 83.2% of cases.

Download

Share

COinS