arXiv subjects

Elif Uskuplu

Publications and source records attributed to Elif Uskuplu.

3 recordsLinked to original sources

arXiv2026

KnowTeX: Visualizing Mathematical Dependencies

Dependency graphs that show how definitions, theorems, and proofs relate to each other are valuable for understanding the structure of mathematical texts. Existing tools such as Lean Blueprint and plasTeXdepgraph generate such graphs within formal proof ecosystems, but they require familiarity with proof assistants or specific compilation pipelines. We present KnowTeX, a standalone Python tool that extracts dependency graphs directly from LaTeX sources without requiring any external framework. KnowTeX supports two complementary modes: a manual mode where authors annotate their source with lightweight commands compatible with Lean Blueprint, and an infer mode that automatically discovers dependencies through a layered system of deterministic and heuristic rules. The tool handles multi-file projects, detects cycles, applies transitive reduction, and exports graphs in DOT, TikZ, and PNG formats with an interactive preview. We evaluate KnowTeX on several mathematical texts and discuss how it complements recent tools such as LeanArchitect, which operates from the Lean side, while KnowTeX works entirely on the LaTeX side without requiring any formalization.

cs.HC↗

arXiv2026

FormalProofBench: Can Models Write Graduate Level Math Proofs That Are Formally Verified?

We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level. Each task pairs a natural-language problem with a Lean~4 formal statement, and a model must output a Lean proof accepted by the Lean 4 checker. FormalProofBench targets advanced undergraduate and graduate mathematics, with problems drawn from qualifying exams and standard textbooks across topics including analysis, algebra, probability, and logic. We evaluate a range of frontier models with an agentic harness, and find that the best-performing foundation model achieves 33.5% accuracy, with performance dropping rapidly after that. In addition to the accuracy numbers, we also provide empirical analysis of tool-use, failure modes, cost and latency, thereby providing a thorough evaluation of the formal-theorem proving abilities of frontier models.

cs.AI↗

arXiv2023

Formalizing two-level type theory with cofibrant exo-nat

This study provides some results about two-level type-theoretic notions in a way that the proofs are fully formalizable in a proof assistant implementing two-level type theory such as Agda. The difference from prior works is that these proofs do not assume any abuse of notation, providing us with more direct formalization. Moreover, some new notions, such as function extensionality for cofibrant types, are introduced. The necessity of such notions arises during the task of formalization. In addition, we provide some novel results about inductive types using cofibrant exo-nat, the natural number type at the non-fibrant level. While emphasizing the necessity of this axiom by citing new applications as justifications, we also touch upon the semantic aspect of the theory by presenting various models that satisfy this axiom.

cs.LO↗