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Documents authored by Avigad, Jeremy

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.
Cite as

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.
Cite as

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.
Cite as

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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