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DOI: 10.4230/LIPIcs.ITP.2022.6

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.

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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

DOI: 10.4230/LIPIcs.SNAPL.2017.5

Fission: Secure Dynamic Code-Splitting for JavaScript

Authors: Arjun Guha, Jean-Baptiste Jeannin, Rachit Nigam, Jane Tangen, and Rian Shambaugh

Published in: LIPIcs, Volume 71, 2nd Summit on Advances in Programming Languages (SNAPL 2017)

Abstract

Traditional web programming involves the creation of two distinct programs: a client-side front-end, a server-side back-end, and a lot of communications boilerplate. An alternative approach is to use a tierless programming model, where a single program describes the behavior of both the client and the server, and the runtime system takes care of communication. Unfortunately, this usually entails adopting a new language and thus abandoning well-worn libraries and web programming tools. In this paper, we present our ongoing work on Fission, a platform that uses dynamic tier-splitting and dynamic information flow control to transparently run a single JavaScript program across the client and server. Although static tier-splitting has been studied before, our focus on dynamic approaches presents several new challenges and opportunities. For example, Fission supports characteristic JavaScript features such as eval and sophisticated JavaScript libraries like React. Therefore, programmers can reason about the integrity and confidentiality of information while continuing to use common libraries and programming patterns. Moreover, by unifying the client and server into a single program, Fission allows language-based tools, like type systems and IDEs, to manipulate complete web applications. To illustrate, we use TypeScript to ensure that client-server communication does not go wrong.

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Arjun Guha, Jean-Baptiste Jeannin, Rachit Nigam, Jane Tangen, and Rian Shambaugh. Fission: Secure Dynamic Code-Splitting for JavaScript. In 2nd Summit on Advances in Programming Languages (SNAPL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 71, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{guha_et_al:LIPIcs.SNAPL.2017.5,
  author =	{Guha, Arjun and Jeannin, Jean-Baptiste and Nigam, Rachit and Tangen, Jane and Shambaugh, Rian},
  title =	{{Fission: Secure Dynamic Code-Splitting for JavaScript}},
  booktitle =	{2nd Summit on Advances in Programming Languages (SNAPL 2017)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-032-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{71},
  editor =	{Lerner, Benjamin S. and Bod{\'\i}k, Rastislav and Krishnamurthi, Shriram},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2017.5},
  URN =		{urn:nbn:de:0030-drops-71247},
  doi =		{10.4230/LIPIcs.SNAPL.2017.5},
  annote =	{Keywords: JavaScript, information flow control}
}

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Documents authored by Jeannin, Jean-Baptiste

Dandelion: Certified Approximations of Elementary Functions

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Fission: Secure Dynamic Code-Splitting for JavaScript

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