42 Search Results for "Harrison, John"


Volume

LIPIcs, Volume 141

10th International Conference on Interactive Theorem Proving (ITP 2019)

ITP 2019, September 9-12, 2019, Portland, OR, USA

Editors: John Harrison, John O'Leary, and Andrew Tolmach

Document
Fast, Verified Computation for Candle

Authors: Oskar Abrahamsson and Magnus O. Myreen

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


Abstract
This paper describes how we have added an efficient function for computation to the kernel of the Candle interactive theorem prover. Candle is a CakeML port of HOL Light which we have, in prior work, proved sound w.r.t. the inference rules of the higher-order logic. This paper extends the original implementation and soundness proof with a new kernel function for fast computation. Experiments show that the new computation function is able to speed up certain evaluation proofs by several orders of magnitude.

Cite as

Oskar Abrahamsson and Magnus O. Myreen. Fast, Verified Computation for Candle. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{abrahamsson_et_al:LIPIcs.ITP.2023.4,
  author =	{Abrahamsson, Oskar and Myreen, Magnus O.},
  title =	{{Fast, Verified Computation for Candle}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{4:1--4:17},
  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.2023.4},
  URN =		{urn:nbn:de:0030-drops-183797},
  doi =		{10.4230/LIPIcs.ITP.2023.4},
  annote =	{Keywords: Prover soundness, Higher-order logic, Interactive theorem proving}
}
Document
Dandelion: Certified Approximations of Elementary Functions

Authors: Heiko Becker, Mohit Tekriwal, Eva Darulova, Anastasia Volkova, and Jean-Baptiste Jeannin

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)


Abstract
Elementary function operations such as sin and exp cannot in general be computed exactly on today’s digital computers, and thus have to be approximated. The standard approximations in library functions typically provide only a limited set of precisions, and are too inefficient for many applications. Polynomial approximations that are customized to a limited input domain and output accuracy can provide superior performance. In fact, the Remez algorithm computes the best possible approximation for a given polynomial degree, but has so far not been formally verified. This paper presents Dandelion, an automated certificate checker for polynomial approximations of elementary functions computed with Remez-like algorithms that is fully verified in the HOL4 theorem prover. Dandelion checks whether the difference between a polynomial approximation and its target reference elementary function remains below a given error bound for all inputs in a given constraint. By extracting a verified binary with the CakeML compiler, Dandelion can validate certificates within a reasonable time, fully automating previous manually verified approximations.

Cite as

Heiko Becker, Mohit Tekriwal, Eva Darulova, Anastasia Volkova, and Jean-Baptiste Jeannin. Dandelion: Certified Approximations of Elementary Functions. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{becker_et_al:LIPIcs.ITP.2022.6,
  author =	{Becker, Heiko and Tekriwal, Mohit and Darulova, Eva and Volkova, Anastasia and Jeannin, Jean-Baptiste},
  title =	{{Dandelion: Certified Approximations of Elementary Functions}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.6},
  URN =		{urn:nbn:de:0030-drops-167155},
  doi =		{10.4230/LIPIcs.ITP.2022.6},
  annote =	{Keywords: elementary functions, approximation, certificate checking}
}
Document
Complete Volume
LIPIcs, Volume 141, ITP'19, Complete Volume

Authors: John Harrison, John O'Leary, and Andrew Tolmach

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


Abstract
LIPIcs, Volume 141, ITP'19, Complete Volume

Cite as

10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@Proceedings{harrison_et_al:LIPIcs.ITP.2019,
  title =	{{LIPIcs, Volume 141, ITP'19, Complete Volume}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  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},
  URN =		{urn:nbn:de:0030-drops-112972},
  doi =		{10.4230/LIPIcs.ITP.2019},
  annote =	{Keywords: Theory of computation, Logic}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: John Harrison, John O'Leary, and Andrew Tolmach

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


Abstract
Front Matter, Table of Contents, Preface, Conference Organization

Cite as

10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 0:i-0:xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{harrison_et_al:LIPIcs.ITP.2019.0,
  author =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{0:i--0:xiv},
  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.2019.0},
  URN =		{urn:nbn:de:0030-drops-110550},
  doi =		{10.4230/LIPIcs.ITP.2019.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
A Million Lines of Proof About a Moving Target (Invited Talk)

Authors: June Andronick

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


Abstract
In the last ten years, we have been porting, maintaining, and evolving the world’s largest proof base, the formal proof in Isabelle/HOL of the seL4 microkernel. But actually, there is no such thing as "the seL4 proof"; there are a number of proofs (functional correctness, binary translation validation, integrity and confidentiality proofs, etc) about a number of instances of seL4 (depending on the hardware platform it runs on, the features it includes, the extensions it supports). We will give an overview of the current state of these proofs, and, importantly, the challenges we face in keeping to maintain, evolve and extend them, and the processes we have put in place to manage their dependence on the evolving implementation.

Cite as

June Andronick. A Million Lines of Proof About a Moving Target (Invited Talk). In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{andronick:LIPIcs.ITP.2019.1,
  author =	{Andronick, June},
  title =	{{A Million Lines of Proof About a Moving Target}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{1:1--1:1},
  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.2019.1},
  URN =		{urn:nbn:de:0030-drops-110567},
  doi =		{10.4230/LIPIcs.ITP.2019.1},
  annote =	{Keywords: Proof maintentance, proof evolution, seL4, Isabelle/HOL}
}
Document
Invited Talk
What Makes a Mathematician Tick? (Invited Talk)

Authors: Kevin Buzzard

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


Abstract
Formalised mathematics has a serious image problem in mathematics departments. Mathematicians working in "mainstream" areas such as modern algebra, analysis, geometry etc have absolutely no desire to work formally, it slows them down and they cannot see the point. The mathematical community has its own methods for deciding whether a proof (in pdf format) is correct or not; these methods rely on the views of a cabal of experts - our high priests. Our proof of the odd order theorem is "John Thompson got a Fields Medal for the work". This proof is of a rather different nature to the formalised proof of Gonthier et al. Our methods are arcane and mysterious; there is also ample evidence that they are, in general, extremely accurate when it comes to the important stuff. I will talk about my attempts, as a "mainstream mathematician", to introduce formalised mathematics to my community.

Cite as

Kevin Buzzard. What Makes a Mathematician Tick? (Invited Talk). In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{buzzard:LIPIcs.ITP.2019.2,
  author =	{Buzzard, Kevin},
  title =	{{What Makes a Mathematician Tick?}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{2:1--2:1},
  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.2019.2},
  URN =		{urn:nbn:de:0030-drops-110576},
  doi =		{10.4230/LIPIcs.ITP.2019.2},
  annote =	{Keywords: Formalization of mathematics}
}
Document
Invited Talk
An Increasing Need for Formality (Invited Talk)

Authors: Martin Dixon

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


Abstract
The talk will touch on a number of practical opportunities for formal modeling and methods that Intel sees in HW security research including: instruction sets; the proliferation of programmable agents within SoC’s; and negative space testing.

Cite as

Martin Dixon. An Increasing Need for Formality (Invited Talk). In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{dixon:LIPIcs.ITP.2019.3,
  author =	{Dixon, Martin},
  title =	{{An Increasing Need for Formality}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{3:1--3:1},
  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.2019.3},
  URN =		{urn:nbn:de:0030-drops-110588},
  doi =		{10.4230/LIPIcs.ITP.2019.3},
  annote =	{Keywords: Hardware security, formal modeling, instruction sets, SoC’s, negative space testing}
}
Document
A Verified Compositional Algorithm for AI Planning

Authors: Mohammad Abdulaziz, Charles Gretton, and Michael Norrish

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


Abstract
We report on our HOL4 verification of an AI planning algorithm. The algorithm is compositional in the following sense: a planning problem is divided into multiple smaller abstractions, then each of the abstractions is solved, and finally the abstractions' solutions are composed into a solution for the given problem. Formalising the algorithm, which was already quite well understood, revealed nuances in its operation which could lead to computing buggy plans. The formalisation also revealed that the algorithm can be presented more generally, and can be applied to systems with infinite states and actions, instead of only finite ones. Our formalisation extends an earlier model for slightly simpler transition systems, and demonstrates another step towards formal treatments of more and more of the algorithms and reasoning used in AI planning, as well as model checking.

Cite as

Mohammad Abdulaziz, Charles Gretton, and Michael Norrish. A Verified Compositional Algorithm for AI Planning. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{abdulaziz_et_al:LIPIcs.ITP.2019.4,
  author =	{Abdulaziz, Mohammad and Gretton, Charles and Norrish, Michael},
  title =	{{A Verified Compositional Algorithm for AI Planning}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{4:1--4:19},
  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.2019.4},
  URN =		{urn:nbn:de:0030-drops-110596},
  doi =		{10.4230/LIPIcs.ITP.2019.4},
  annote =	{Keywords: AI Planning, Compositional Algorithms, Algorithm Verification, Transition Systems}
}
Document
Proving Tree Algorithms for Succinct Data Structures

Authors: Reynald Affeldt, Jacques Garrigue, Xuanrui Qi, and Kazunari Tanaka

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


Abstract
Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely on cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect of two different tree-based succinct representations and their accompanying algorithms. One is the Level-Order Unary Degree Sequence, which encodes the structure of a tree in breadth-first order as a sequence of bits, where access operations can be defined in terms of Rank and Select, which work in constant time for static bit sequences. The other represents dynamic bit sequences as binary balanced trees, where Rank and Select present a low logarithmic overhead compared to their static versions, and with efficient insertion and deletion. The two can be stacked to provide a dynamic representation of dictionaries for instance. While both representations are well-known, we believe this to be their first formalization and a needed step towards provably-safe implementations of big data.

Cite as

Reynald Affeldt, Jacques Garrigue, Xuanrui Qi, and Kazunari Tanaka. Proving Tree Algorithms for Succinct Data Structures. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{affeldt_et_al:LIPIcs.ITP.2019.5,
  author =	{Affeldt, Reynald and Garrigue, Jacques and Qi, Xuanrui and Tanaka, Kazunari},
  title =	{{Proving Tree Algorithms for Succinct Data Structures}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{5:1--5:19},
  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.2019.5},
  URN =		{urn:nbn:de:0030-drops-110609},
  doi =		{10.4230/LIPIcs.ITP.2019.5},
  annote =	{Keywords: Coq, small-scale reflection, succinct data structures, LOUDS, bit vectors, self balancing trees}
}
Document
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
Primitive Floats in Coq

Authors: Guillaume Bertholon, Érik Martin-Dorel, and Pierre Roux

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


Abstract
Some mathematical proofs involve intensive computations, for instance: the four-color theorem, Hales' theorem on sphere packing (formerly known as the Kepler conjecture) or interval arithmetic. For numerical computations, floating-point arithmetic enjoys widespread usage thanks to its efficiency, despite the introduction of rounding errors. Formal guarantees can be obtained on floating-point algorithms based on the IEEE 754 standard, which precisely specifies floating-point arithmetic and its rounding modes, and a proof assistant such as Coq, that enjoys efficient computation capabilities. Coq offers machine integers, however floating-point arithmetic still needed to be emulated using these integers. A modified version of Coq is presented that enables using the machine floating-point operators. The main obstacles to such an implementation and its soundness are discussed. Benchmarks show potential performance gains of two orders of magnitude.

Cite as

Guillaume Bertholon, Érik Martin-Dorel, and Pierre Roux. Primitive Floats in Coq. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{bertholon_et_al:LIPIcs.ITP.2019.7,
  author =	{Bertholon, Guillaume and Martin-Dorel, \'{E}rik and Roux, Pierre},
  title =	{{Primitive Floats in Coq}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{7:1--7:20},
  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.2019.7},
  URN =		{urn:nbn:de:0030-drops-110629},
  doi =		{10.4230/LIPIcs.ITP.2019.7},
  annote =	{Keywords: Coq formal proofs, floating-point arithmetic, reflexive tactics, Cholesky decomposition}
}
Document
A Certificate-Based Approach to Formally Verified Approximations

Authors: Florent Bréhard, Assia Mahboubi, and Damien Pous

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


Abstract
We present a library to verify rigorous approximations of univariate functions on real numbers, with the Coq proof assistant. Based on interval arithmetic, this library also implements a technique of validation a posteriori based on the Banach fixed-point theorem. We illustrate this technique on the case of operations of division and square root. This library features a collection of abstract structures that organise the specfication of rigorous approximations, and modularise the related proofs. Finally, we provide an implementation of verified Chebyshev approximations, and we discuss a few examples of computations.

Cite as

Florent Bréhard, Assia Mahboubi, and Damien Pous. A Certificate-Based Approach to Formally Verified Approximations. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{brehard_et_al:LIPIcs.ITP.2019.8,
  author =	{Br\'{e}hard, Florent and Mahboubi, Assia and Pous, Damien},
  title =	{{A Certificate-Based Approach to Formally Verified Approximations}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{8:1--8:19},
  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.2019.8},
  URN =		{urn:nbn:de:0030-drops-110638},
  doi =		{10.4230/LIPIcs.ITP.2019.8},
  annote =	{Keywords: approximation theory, Chebyshev polynomials, Banach fixed-point theorem, interval arithmetic, Coq}
}
Document
Higher-Order Tarski Grothendieck as a Foundation for Formal Proof

Authors: Chad E. Brown, Cezary Kaliszyk, and Karol Pąk

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


Abstract
We formally introduce a foundation for computer verified proofs based on higher-order Tarski-Grothendieck set theory. We show that this theory has a model if a 2-inaccessible cardinal exists. This assumption is the same as the one needed for a model of plain Tarski-Grothendieck set theory. The foundation allows the co-existence of proofs based on two major competing foundations for formal proofs: higher-order logic and TG set theory. We align two co-existing Isabelle libraries, Isabelle/HOL and Isabelle/Mizar, in a single foundation in the Isabelle logical framework. We do this by defining isomorphisms between the basic concepts, including integers, functions, lists, and algebraic structures that preserve the important operations. With this we can transfer theorems proved in higher-order logic to TG set theory and vice versa. We practically show this by formally transferring Lagrange’s four-square theorem, Fermat 3-4, and other theorems between the foundations in the Isabelle framework.

Cite as

Chad E. Brown, Cezary Kaliszyk, and Karol Pąk. Higher-Order Tarski Grothendieck as a Foundation for Formal Proof. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{brown_et_al:LIPIcs.ITP.2019.9,
  author =	{Brown, Chad E. and Kaliszyk, Cezary and P\k{a}k, Karol},
  title =	{{Higher-Order Tarski Grothendieck as a Foundation for Formal Proof}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{9:1--9:16},
  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.2019.9},
  URN =		{urn:nbn:de:0030-drops-110643},
  doi =		{10.4230/LIPIcs.ITP.2019.9},
  annote =	{Keywords: model, higher-order, Tarski Grothendieck, proof foundation}
}
Document
Generic Authenticated Data Structures, Formally

Authors: Matthias Brun and Dmitriy Traytel

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


Abstract
Authenticated data structures are a technique for outsourcing data storage and maintenance to an untrusted server. The server is required to produce an efficiently checkable and cryptographically secure proof that it carried out precisely the requested computation. Recently, Miller et al. [https://doi.org/10.1145/2535838.2535851] demonstrated how to support a wide range of such data structures by integrating an authentication construct as a first class citizen in a functional programming language. In this paper, we put this work to the test of formalization in the Isabelle proof assistant. With Isabelle’s help, we uncover and repair several mistakes and modify the small-step semantics to perform call-by-value evaluation rather than requiring terms to be in administrative normal form.

Cite as

Matthias Brun and Dmitriy Traytel. Generic Authenticated Data Structures, Formally. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{brun_et_al:LIPIcs.ITP.2019.10,
  author =	{Brun, Matthias and Traytel, Dmitriy},
  title =	{{Generic Authenticated Data Structures, Formally}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{10:1--10:18},
  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.2019.10},
  URN =		{urn:nbn:de:0030-drops-110657},
  doi =		{10.4230/LIPIcs.ITP.2019.10},
  annote =	{Keywords: Authenticated Data Structures, Verifiable Computation, Isabelle/HOL, Nominal Isabelle}
}
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