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Documents authored by Shinnar, Avraham

Document
DOI: 10.4230/LIPIcs.ITP.2022.31
Formalization of a Stochastic Approximation Theorem

Authors: Koundinya Vajjha, Barry Trager, Avraham Shinnar, and Vasily Pestun

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

Abstract
Stochastic approximation algorithms are iterative procedures which are used to approximate a target value in an environment where the target is unknown and direct observations are corrupted by noise. These algorithms are useful, for instance, for root-finding and function minimization when the target function or model is not directly known. Originally introduced in a 1951 paper by Robbins and Monro, the field of Stochastic approximation has grown enormously and has come to influence application domains from adaptive signal processing to artificial intelligence. As an example, the Stochastic Gradient Descent algorithm which is ubiquitous in various subdomains of Machine Learning is based on stochastic approximation theory. In this paper, we give a formal proof (in the Coq proof assistant) of a general convergence theorem due to Aryeh Dvoretzky [Dvoretzky, 1956] (proven in 1956) which implies the convergence of important classical methods such as the Robbins-Monro and the Kiefer-Wolfowitz algorithms. In the process, we build a comprehensive Coq library of measure-theoretic probability theory and stochastic processes.
Cite as

Koundinya Vajjha, Barry Trager, Avraham Shinnar, and Vasily Pestun. Formalization of a Stochastic Approximation Theorem. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 31:1-31:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{vajjha_et_al:LIPIcs.ITP.2022.31,
  author =	{Vajjha, Koundinya and Trager, Barry and Shinnar, Avraham and Pestun, Vasily},
  title =	{{Formalization of a Stochastic Approximation Theorem}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{31:1--31:18},
  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.2022.31},
  URN =		{urn:nbn:de:0030-drops-167402},
  doi =		{10.4230/LIPIcs.ITP.2022.31},
  annote =	{Keywords: Formal Verification, Stochastic Approximation, Stochastic Processes, Probability Theory, Optimization Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SNAPL.2017.6
I Can Parse You: Grammars for Dialogs

Authors: Martin Hirzel, Louis Mandel, Avraham Shinnar, Jerome Simeon, and Mandana Vaziri

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

Abstract
Humans and computers increasingly converse via natural language. Those conversations are moving from today's simple question answering and command-and-control to more complex dialogs. Developers must specify those dialogs. This paper explores how to assist developers in this specification. We map out the staggering variety of applications for human-computer dialogs and distill it into a catalog of flow patterns. Based on that, we articulate the requirements for dialog programming models and offer our vision for satisfying these requirements using grammars. If our approach catches on, computers will soon parse you to better assist you in your daily life.
Cite as

Martin Hirzel, Louis Mandel, Avraham Shinnar, Jerome Simeon, and Mandana Vaziri. I Can Parse You: Grammars for Dialogs. In 2nd Summit on Advances in Programming Languages (SNAPL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 71, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{hirzel_et_al:LIPIcs.SNAPL.2017.6,
  author =	{Hirzel, Martin and Mandel, Louis and Shinnar, Avraham and Simeon, Jerome and Vaziri, Mandana},
  title =	{{I Can Parse You: Grammars for Dialogs}},
  booktitle =	{2nd Summit on Advances in Programming Languages (SNAPL 2017)},
  pages =	{6:1--6:15},
  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.2017.6},
  URN =		{urn:nbn:de:0030-drops-71180},
  doi =		{10.4230/LIPIcs.SNAPL.2017.6},
  annote =	{Keywords: Bots, virtual agents, dialog managers, domain-specific languages}
}
Document
DOI: 10.4230/DARTS.1.1.8
A Pattern Calculus for Rule Languages: Expressiveness, Compilation, and Mechanization (Artifact)

Authors: Avraham Shinnar, Jérôme Siméon, and Martin Hirzel

Published in: DARTS, Volume 1, Issue 1, Special Issue of the 29th European Conference on Object-Oriented Programming (ECOOP 2015)

Abstract
This artifact contains the accompanying code for the ECOOP 2015 paper: "A Pattern Calculus for Rule Languages: Expressiveness, Compilation, and Mechanization". It contains source files for a full mechanization of the three languages presented in the paper: CAMP (Calculus for Aggregating Matching Patterns), NRA (Nested Relational Algebra) and NNRC (Named Nested Relational Calculus). Translations between all three languages and their attendant proofs of correctness are included. Additionally, a mechanization of a type system for the main languages is provided, along with bidirectional proofs of type preservation and proofs of the time complexity of the various compilers.
Cite as

Avraham Shinnar, Jérôme Siméon, and Martin Hirzel. A Pattern Calculus for Rule Languages: Expressiveness, Compilation, and Mechanization (Artifact). In Special Issue of the 29th European Conference on Object-Oriented Programming (ECOOP 2015). Dagstuhl Artifacts Series (DARTS), Volume 1, Issue 1, pp. 8:1-8:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@Article{shinnar_et_al:DARTS.1.1.8,
  author =	{Shinnar, Avraham and Sim\'{e}on, J\'{e}r\^{o}me and Hirzel, Martin},
  title =	{{A Pattern Calculus for Rule Languages: Expressiveness, Compilation, and Mechanization (Artifact)}},
  pages =	{8:1--8:2},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2015},
  volume =	{1},
  number =	{1},
  editor =	{Shinnar, Avraham and Sim\'{e}on, J\'{e}r\^{o}me and Hirzel, Martin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.1.1.8},
  URN =		{urn:nbn:de:0030-drops-55179},
  doi =		{10.4230/DARTS.1.1.8},
  annote =	{Keywords: Rules, Pattern Matching, Aggregation, Nested Queries, Mechanization}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2015.542
A Pattern Calculus for Rule Languages: Expressiveness, Compilation, and Mechanization

Authors: Avraham Shinnar, Jérôme Siméon, and Martin Hirzel

Published in: LIPIcs, Volume 37, 29th European Conference on Object-Oriented Programming (ECOOP 2015)

Abstract
This paper introduces a core calculus for pattern-matching in production rule languages: the Calculus for Aggregating Matching Patterns (CAMP). CAMP is expressive enough to capture modern rule languages such as JRules, including extensions for aggregation. We show how CAMP can be compiled into a nested-relational algebra (NRA), with only minimal extension. This paves the way for applying relational techniques to running rules over large stores. Furthermore, we show that NRA can also be compiled back to CAMP, using named nested-relational calculus (NNRC) as an intermediate step. We mechanize proofs of correctness, program size preservation, and type preservation of the translations using modern theorem-proving techniques. A corollary of the type preservation is that polymorphic type inference for both CAMP and NRA is NP-complete. CAMP and its correspondence to NRA provide the foundations for efficient implementations of rules languages using databases technologies.
Cite as

Avraham Shinnar, Jérôme Siméon, and Martin Hirzel. A Pattern Calculus for Rule Languages: Expressiveness, Compilation, and Mechanization. In 29th European Conference on Object-Oriented Programming (ECOOP 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 37, pp. 542-567, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{shinnar_et_al:LIPIcs.ECOOP.2015.542,
  author =	{Shinnar, Avraham and Sim\'{e}on, J\'{e}r\^{o}me and Hirzel, Martin},
  title =	{{A Pattern Calculus for Rule Languages: Expressiveness, Compilation, and Mechanization}},
  booktitle =	{29th European Conference on Object-Oriented Programming (ECOOP 2015)},
  pages =	{542--567},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-86-6},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{37},
  editor =	{Boyland, John Tang},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2015.542},
  URN =		{urn:nbn:de:0030-drops-52374},
  doi =		{10.4230/LIPIcs.ECOOP.2015.542},
  annote =	{Keywords: Rules, Pattern Matching, Aggregation, Nested Queries, Mechanization}
}
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