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Documents authored by Avigad, Jeremy

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Software
DOI: 10.4230/artifacts.27122
Lean Architect supplementary material

Authors: Thomas Zhu, Pietro Monticone, Sean Welleck, and Jeremy Avigad

Abstract
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Thomas Zhu, Pietro Monticone, Sean Welleck, Jeremy Avigad. Lean Architect supplementary material (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@misc{dagstuhl-artifact-27122,
   title = {{Lean Architect supplementary material}}, 
   author = {Zhu, Thomas and Monticone, Pietro and Welleck, Sean and Avigad, Jeremy},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:b5fd29736a2e6b7dc989266fe19d489e5f7c644d;origin=https://github.com/hanwenzhu/LeanArchitect;visit=swh:1:snp:6673da745f251a6cb39a11ce0fe264fdf4239663;anchor=swh:1:rev:f1c14e1c14290117ffcb017cf2d089a6a5e1523a}{\texttt{swh:1:dir:b5fd29736a2e6b7dc989266fe19d489e5f7c644d}} (visited on 2026-07-16)},
   url = {https://github.com/hanwenzhu/LeanArchitect},
   doi = {10.4230/artifacts.27122},
}
Document
DOI: 10.4230/LIPIcs.ITP.2026.25
LeanArchitect: Automating Blueprint Generation for Humans and AI

Authors: Thomas Zhu, Pietro Monticone, Sean Welleck, and Jeremy Avigad

Published in: LIPIcs, Volume 382, 17th International Conference on Interactive Theorem Proving (ITP 2026)

Abstract
Large-scale formalization projects in Lean rely on blueprints: structured dependency graphs linking informal mathematical exposition to formal declarations. While blueprints are central to human collaboration, existing tooling treats the informal (LaTeX) and formal (Lean) components as largely decoupled artifacts, leading to maintenance overhead and limiting integration with AI automation. We present LeanArchitect, a Lean package for extracting, managing, and exporting blueprint data directly from Lean code. LeanArchitect introduces a declarative annotation mechanism that associates formal declarations with blueprint metadata, automatically infers dependency information, and generates LaTeX blueprint content synchronized with the Lean development. This design eliminates duplication between formal and informal representations and eases fine-grained progress tracking for both human contributors and AI-based theorem provers. We demonstrate the practicality of LeanArchitect through the automated conversion of several large existing blueprint-driven projects, and through a human-AI collaboration case study formalizing a multivariate Taylor theorem. Our results show that LeanArchitect improves maintainability, exposes latent inconsistencies in existing blueprints, and provides an effective interface for integrating AI tools into real-world formalization workflows.
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Thomas Zhu, Pietro Monticone, Sean Welleck, and Jeremy Avigad. LeanArchitect: Automating Blueprint Generation for Humans and AI. In 17th International Conference on Interactive Theorem Proving (ITP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 382, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{zhu_et_al:LIPIcs.ITP.2026.25,
  author =	{Zhu, Thomas and Monticone, Pietro and Welleck, Sean and Avigad, Jeremy},
  title =	{{LeanArchitect: Automating Blueprint Generation for Humans and AI}},
  booktitle =	{17th International Conference on Interactive Theorem Proving (ITP 2026)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-436-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{382},
  editor =	{Komendantskaya, Ekaterina and Nipkow, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.25},
  URN =		{urn:nbn:de:0030-drops-269992},
  doi =		{10.4230/LIPIcs.ITP.2026.25},
  annote =	{Keywords: Lean theorem prover, interactive theorem proving, proof assistants, formal methods, human-computer interface, software development tools}
}
Document
DOI: 10.4230/LIPIcs.ITP.2026.26
An End-To-End Verification of Keller’s Conjecture

Authors: James Gallicchio, Cayden Codel, Jeremy Avigad, and Marijn J. H. Heule

Published in: LIPIcs, Volume 382, 17th International Conference on Interactive Theorem Proving (ITP 2026)

Abstract
In 1930, Keller conjectured that every gap-free tiling of ℝⁿ by n-dimensional unit cubes must contain cubes that fully share an (n - 1)-dimensional face. Keller’s conjecture holds for n ≤ 7 and fails for n ≥ 8. The final case, n = 7, was settled in 2020 using a mix of traditional and automated reasoning. The result was obtained by reducing the conjecture to a set of clique-existence problems, encoding those problems into propositional logic, breaking symmetries, and solving them with a SAT solver. In this paper, we present an end-to-end verification in Lean 4 of Keller’s conjecture for all dimensions. First, we simplify a prior reduction of Keller’s conjecture to the clique-existence problems. We then verify an improved SAT encoding of those problems, as well as some symmetry reasoning on the encoding. Throughout our work, we sought to maximize the synergy between interactive and automated techniques while minimizing human proof burden. In particular, the symmetry reasoning was split between Lean and a mechanically-checkable proof system, since neither was suitable on their own for verifying all of the symmetry reasoning. We discuss how and why we chose to split the reasoning across these systems based on their relative strengths and weaknesses.
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James Gallicchio, Cayden Codel, Jeremy Avigad, and Marijn J. H. Heule. An End-To-End Verification of Keller’s Conjecture. In 17th International Conference on Interactive Theorem Proving (ITP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 382, pp. 26:1-26:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gallicchio_et_al:LIPIcs.ITP.2026.26,
  author =	{Gallicchio, James and Codel, Cayden and Avigad, Jeremy and Heule, Marijn J. H.},
  title =	{{An End-To-End Verification of Keller’s Conjecture}},
  booktitle =	{17th International Conference on Interactive Theorem Proving (ITP 2026)},
  pages =	{26:1--26:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-436-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{382},
  editor =	{Komendantskaya, Ekaterina and Nipkow, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.26},
  URN =		{urn:nbn:de:0030-drops-270008},
  doi =		{10.4230/LIPIcs.ITP.2026.26},
  annote =	{Keywords: Keller’s conjecture, the Lean theorem prover, SAT encodings, SAT solving, Trestle, formal verification}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.14
Canonical for Automated Theorem Proving in Lean

Authors: Chase Norman and Jeremy Avigad

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic supports higher-order and dependently-typed goals, structural recursion over indexed inductive types, and definitional equality. Canonical finds proofs for 84% of Natural Number Game problems in 51 seconds total.
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Chase Norman and Jeremy Avigad. Canonical for Automated Theorem Proving in Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{norman_et_al:LIPIcs.ITP.2025.14,
  author =	{Norman, Chase and Avigad, Jeremy},
  title =	{{Canonical for Automated Theorem Proving in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.14},
  URN =		{urn:nbn:de:0030-drops-246128},
  doi =		{10.4230/LIPIcs.ITP.2025.14},
  annote =	{Keywords: Automated Reasoning, Interactive Theorem Proving, Dependent Type Theory, Inhabitation, Unification, Program Synthesis, Formal Methods}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.10
Duper: A Proof-Producing Superposition Theorem Prover for Dependent Type Theory

Authors: Joshua Clune, Yicheng Qian, Alexander Bentkamp, and Jeremy Avigad

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
We present Duper, a proof-producing theorem prover for Lean based on the superposition calculus. Duper can be called directly as a terminal tactic in interactive Lean proofs, but is also designed with proof reconstruction for a future Lean hammer in mind. In this paper, we describe Duper’s underlying approach to proof search and proof reconstruction with a particular emphasis on the challenges of working in a dependent type theory. We also compare Duper’s performance to Metis' on pre-existing benchmarks to give evidence that Duper is performant enough to be useful for proof reconstruction in a hammer.
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Joshua Clune, Yicheng Qian, Alexander Bentkamp, and Jeremy Avigad. Duper: A Proof-Producing Superposition Theorem Prover for Dependent Type Theory. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{clune_et_al:LIPIcs.ITP.2024.10,
  author =	{Clune, Joshua and Qian, Yicheng and Bentkamp, Alexander and Avigad, Jeremy},
  title =	{{Duper: A Proof-Producing Superposition Theorem Prover for Dependent Type Theory}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.10},
  URN =		{urn:nbn:de:0030-drops-207381},
  doi =		{10.4230/LIPIcs.ITP.2024.10},
  annote =	{Keywords: proof search, automatic theorem proving, interactive theorem proving, Lean, dependent type theory}
}
Document
DOI: 10.4230/LIPIcs.SAT.2023.6
Certified Knowledge Compilation with Application to Verified Model Counting

Authors: Randal E. Bryant, Wojciech Nawrocki, Jeremy Avigad, and Marijn J. H. Heule

Published in: LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

Abstract
Computing many useful properties of Boolean formulas, such as their weighted or unweighted model count, is intractable on general representations. It can become tractable when formulas are expressed in a special form, such as the decision-decomposable, negation normal form (dec-DNNF) . Knowledge compilation is the process of converting a formula into such a form. Unfortunately existing knowledge compilers provide no guarantee that their output correctly represents the original formula, and therefore they cannot validate a model count, or any other computed value. We present Partitioned-Operation Graphs (POGs), a form that can encode all of the representations used by existing knowledge compilers. We have designed CPOG, a framework that can express proofs of equivalence between a POG and a Boolean formula in conjunctive normal form (CNF). We have developed a program that generates POG representations from dec-DNNF graphs produced by the state-of-the-art knowledge compiler D4, as well as checkable CPOG proofs certifying that the output POGs are equivalent to the input CNF formulas. Our toolchain for generating and verifying POGs scales to all but the largest graphs produced by D4 for formulas from a recent model counting competition. Additionally, we have developed a formally verified CPOG checker and model counter for POGs in the Lean 4 proof assistant. In doing so, we proved the soundness of our proof framework. These programs comprise the first formally verified toolchain for weighted and unweighted model counting.
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Randal E. Bryant, Wojciech Nawrocki, Jeremy Avigad, and Marijn J. H. Heule. Certified Knowledge Compilation with Application to Verified Model Counting. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bryant_et_al:LIPIcs.SAT.2023.6,
  author =	{Bryant, Randal E. and Nawrocki, Wojciech and Avigad, Jeremy and Heule, Marijn J. H.},
  title =	{{Certified Knowledge Compilation with Application to Verified Model Counting}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{6:1--6:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.6},
  URN =		{urn:nbn:de:0030-drops-184685},
  doi =		{10.4230/LIPIcs.SAT.2023.6},
  annote =	{Keywords: Propositional model counting, Proof checking}
}
Document
DOI: 10.4230/LIPIcs.ITP.2023.7
A Proof-Producing Compiler for Blockchain Applications

Authors: Jeremy Avigad, Lior Goldberg, David Levit, Yoav Seginer, and Alon Titelman

Published in: LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)

Abstract
Cairo is a programming language for running decentralized applications (dapps) at scale. Programs written in the Cairo language are compiled to machine code for the Cairo CPU architecture, and cryptographic protocols are used to verify the results of the execution traces efficiently on blockchain. We explain how we have extended the Cairo compiler with tooling that enables users to prove, in the Lean 3 proof assistant, that compiled code satisfies high-level functional specifications. We demonstrate the success of our approach by verifying primitives for computations with an elliptic curve over a large finite field, as well as their use in the validation of cryptographic signatures.
Cite as

Jeremy Avigad, Lior Goldberg, David Levit, Yoav Seginer, and Alon Titelman. A Proof-Producing Compiler for Blockchain Applications. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{avigad_et_al:LIPIcs.ITP.2023.7,
  author =	{Avigad, Jeremy and Goldberg, Lior and Levit, David and Seginer, Yoav and Titelman, Alon},
  title =	{{A Proof-Producing Compiler for Blockchain Applications}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{7:1--7:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.7},
  URN =		{urn:nbn:de:0030-drops-183820},
  doi =		{10.4230/LIPIcs.ITP.2023.7},
  annote =	{Keywords: formal verification, smart contracts, interactive proof systems}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.6
Data Types as Quotients of Polynomial Functors

Authors: Jeremy Avigad, Mario Carneiro, and Simon Hudon

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
A broad class of data types, including arbitrary nestings of inductive types, coinductive types, and quotients, can be represented as quotients of polynomial functors. This provides perspicuous ways of constructing them and reasoning about them in an interactive theorem prover.
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Jeremy Avigad, Mario Carneiro, and Simon Hudon. Data Types as Quotients of Polynomial Functors. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{avigad_et_al:LIPIcs.ITP.2019.6,
  author =	{Avigad, Jeremy and Carneiro, Mario and Hudon, Simon},
  title =	{{Data Types as Quotients of Polynomial Functors}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.6},
  URN =		{urn:nbn:de:0030-drops-110612},
  doi =		{10.4230/LIPIcs.ITP.2019.6},
  annote =	{Keywords: data types, polynomial functors, inductive types, coinductive types}
}
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