7 Search Results for "Carneiro, Mario"

Document
DOI: 10.4230/LIPIcs.SAT.2023.21
Faster LRAT Checking Than Solving with CaDiCaL

Authors: Florian Pollitt, Mathias Fleury, and Armin Biere

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

Abstract
DRAT is the standard proof format used in the SAT Competition. It is easy to generate but checking proofs often takes even more time than solving the problem. An alternative is to use the LRAT proof system. While LRAT is easier and way more efficient to check, it is more complex to generate directly. Due to this complexity LRAT is not supported natively by any state-of-the-art SAT solver. Therefore Carneiro and Heule proposed the mixed proof format FRAT which still suffers from costly intermediate translation. We present an extension to the state-of-the-art solver CaDiCaL which is able to generate LRAT natively for all procedures implemented in CaDiCaL. We further present Lrat-Trim, a tool which not only trims and checks LRAT proofs in both ASCII and binary format but also produces clausal cores and has been tested thoroughly. Our experiments on recent competition benchmarks show that our approach reduces time of proof generation and certification substantially compared to competing approaches using intermediate DRAT or FRAT proofs.
Cite as

Florian Pollitt, Mathias Fleury, and Armin Biere. Faster LRAT Checking Than Solving with CaDiCaL. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 21:1-21:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{pollitt_et_al:LIPIcs.SAT.2023.21,
  author =	{Pollitt, Florian and Fleury, Mathias and Biere, Armin},
  title =	{{Faster LRAT Checking Than Solving with CaDiCaL}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{21:1--21:12},
  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.2023.21},
  URN =		{urn:nbn:de:0030-drops-184837},
  doi =		{10.4230/LIPIcs.SAT.2023.21},
  annote =	{Keywords: SAT solving, Proof Checking, DRAT, LRAT, FRAT}
}
Document
DOI: 10.4230/LIPIcs.ITP.2023.9
Automated Theorem Proving for Metamath

Authors: Mario Carneiro, Chad E. Brown, and Josef Urban

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

Abstract
Metamath is a proof assistant that keeps surprising outsiders by its combination of a very minimalist design with a large library of advanced results, ranking high on the Freek Wiedijk’s 100 list. In this work, we develop several translations of the Metamath logic and its large set-theoretical library into higher-order and first-order TPTP formats for automated theorem provers (ATPs). We show that state-of-the-art ATPs can prove 68% of the Metamath problems automatically when using the premises that were used in the human-written Metamath proofs. Finally, we add proof reconstruction and premise selection methods and combine the components into the first hammer system for Metamath.
Cite as

Mario Carneiro, Chad E. Brown, and Josef Urban. Automated Theorem Proving for Metamath. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 9:1-9:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{carneiro_et_al:LIPIcs.ITP.2023.9,
  author =	{Carneiro, Mario and Brown, Chad E. and Urban, Josef},
  title =	{{Automated Theorem Proving for Metamath}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{9:1--9:19},
  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.2023.9},
  URN =		{urn:nbn:de:0030-drops-183846},
  doi =		{10.4230/LIPIcs.ITP.2023.9},
  annote =	{Keywords: Metamath, Automated theorem proving, Interactive theorem proving, Formal proof assistants, proof discovery}
}
Document
DOI: 10.4230/LIPIcs.ITP.2023.10
Reimplementing Mizar in Rust

Authors: Mario Carneiro

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

Abstract
This paper describes a new open-source proof processing tool, mizar-rs, a wholesale reimplementation of core parts of the Mizar proof system, written in Rust. In particular, the "checker" and "analyzer" of Mizar are implemented, which together form the trusted core of Mizar. This is to our knowledge the first and only external implementation of these components. Thanks to the loose coupling of Mizar’s passes, it is possible to use the checker as a drop-in replacement for the original, and we have used this to verify the entire MML in 11.8 minutes on 8 cores, a 4.8× speedup over the original Pascal implementation. Since Mizar is not designed to have a small trusted core, checking Mizar proofs entails following Mizar closely, so our ability to detect bugs is limited. Nevertheless, we were able to find multiple memory errors, four soundness bugs in the original (which were not being exploited in MML), in addition to one non-critical bug which was being exploited in 46 different MML articles. We hope to use this checker as a base for proof export tooling, as well as revitalizing development of the language.
Cite as

Mario Carneiro. Reimplementing Mizar in Rust. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 10:1-10:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{carneiro:LIPIcs.ITP.2023.10,
  author =	{Carneiro, Mario},
  title =	{{Reimplementing Mizar in Rust}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{10:1--10:18},
  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.2023.10},
  URN =		{urn:nbn:de:0030-drops-183852},
  doi =		{10.4230/LIPIcs.ITP.2023.10},
  annote =	{Keywords: Mizar, proof checker, software, Rust}
}
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}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.12
Formalizing Computability Theory via Partial Recursive Functions

Authors: Mario Carneiro

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

Abstract
We present an extension to the mathlib library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and we use a constructive encoding of partial functions such that they are executable when the programs in question provably halt. Main theorems include the construction of a universal partial recursive function and a proof of the undecidability of the halting problem. Type class inference provides a transparent way to supply Gödel numberings where needed and encapsulate the encoding details.
Cite as

Mario Carneiro. Formalizing Computability Theory via Partial Recursive Functions. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 12:1-12:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{carneiro:LIPIcs.ITP.2019.12,
  author =	{Carneiro, Mario},
  title =	{{Formalizing Computability Theory via Partial Recursive Functions}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{12:1--12:17},
  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.2019.12},
  URN =		{urn:nbn:de:0030-drops-110671},
  doi =		{10.4230/LIPIcs.ITP.2019.12},
  annote =	{Keywords: Lean, computability, halting problem, primitive recursion}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.19
A Formalization of Forcing and the Unprovability of the Continuum Hypothesis

Authors: Jesse Michael Han and Floris van Doorn

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

Abstract
We describe a formalization of forcing using Boolean-valued models in the Lean 3 theorem prover, including the fundamental theorem of forcing and a deep embedding of first-order logic with a Boolean-valued soundness theorem. As an application of our framework, we specialize our construction to the Boolean algebra of regular opens of the Cantor space 2^{omega_2 x omega} and formally verify the failure of the continuum hypothesis in the resulting model.
Cite as

Jesse Michael Han and Floris van Doorn. A Formalization of Forcing and the Unprovability of the Continuum Hypothesis. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 19:1-19:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{han_et_al:LIPIcs.ITP.2019.19,
  author =	{Han, Jesse Michael and van Doorn, Floris},
  title =	{{A Formalization of Forcing and the Unprovability of the Continuum Hypothesis}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{19:1--19:19},
  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.2019.19},
  URN =		{urn:nbn:de:0030-drops-110742},
  doi =		{10.4230/LIPIcs.ITP.2019.19},
  annote =	{Keywords: Interactive theorem proving, formal verification, set theory, forcing, independence proofs, continuum hypothesis, Boolean-valued models, Lean}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.21
Virtualization of HOL4 in Isabelle

Authors: Fabian Immler, Jonas Rädle, and Makarius Wenzel

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

Abstract
We present a novel approach to combine the HOL4 and Isabelle theorem provers: both are implemented in SML and based on distinctive variants of HOL. The design of HOL4 allows to replace its inference kernel modules, and the system infrastructure of Isabelle allows to embed other applications of SML. That is the starting point to provide a virtual instance of HOL4 in the same run-time environment as Isabelle. Moreover, with an implementation of a virtual HOL4 kernel that operates on Isabelle/HOL terms and theorems, we can load substantial HOL4 libraries to make them Isabelle theories, but still disconnected from existing Isabelle content. Finally, we introduce a methodology based on the transfer package of Isabelle to connect the imported HOL4 material to that of Isabelle/HOL.
Cite as

Fabian Immler, Jonas Rädle, and Makarius Wenzel. Virtualization of HOL4 in Isabelle. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 21:1-21:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{immler_et_al:LIPIcs.ITP.2019.21,
  author =	{Immler, Fabian and R\"{a}dle, Jonas and Wenzel, Makarius},
  title =	{{Virtualization of HOL4 in Isabelle}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{21:1--21:18},
  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.2019.21},
  URN =		{urn:nbn:de:0030-drops-110760},
  doi =		{10.4230/LIPIcs.ITP.2019.21},
  annote =	{Keywords: Virtualization, HOL4, Isabelle, Isabelle/HOL, Isabelle/ML}
}
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