2 Search Results for "Andrews, Robert"


Document
Pearl
A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Pearl)

Authors: Jan de Muijnck-Hughes, Edwin Brady, and Wim Vanderbauwhede

Published in: LIPIcs, Volume 166, 34th European Conference on Object-Oriented Programming (ECOOP 2020)


Abstract
Idris' Effects library demonstrates how to embed resource dependent algebraic effect handlers into a dependently typed host language, providing run-time and compile-time based reasoning on type-level resources. Building upon this work, Resources is a framework for realising Embedded Domain Specific Languages (EDSLs) with type systems that contain domain specific substructural properties. Differing from Effects, Resources allows a language’s substructural properties to be encoded within type-level resources that are associated with language variables. Such an association allows for multiple effect instances to be reasoned about autonomically and without explicit type-level declaration. Type-level predicates are used as proof that the language’s substructural properties hold. Several exemplar EDSLs are presented that illustrates our framework’s operation and how dependent types provide correctness-by-construction guarantees that substructural properties of written programs hold.

Cite as

Jan de Muijnck-Hughes, Edwin Brady, and Wim Vanderbauwhede. A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Pearl). In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 20:1-20:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{demuijnckhughes_et_al:LIPIcs.ECOOP.2020.20,
  author =	{de Muijnck-Hughes, Jan and Brady, Edwin and Vanderbauwhede, Wim},
  title =	{{A Framework for Resource Dependent EDSLs in a Dependently Typed Language}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{20:1--20:31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.20},
  URN =		{urn:nbn:de:0030-drops-131773},
  doi =		{10.4230/LIPIcs.ECOOP.2020.20},
  annote =	{Keywords: Dependent Types, Algebraic Effect Handlers, Domain-Specific Languages, Embedded Domain Specific Languages, Idris, Substructural Type-Systems}
}
Document
Algebraic Hardness Versus Randomness in Low Characteristic

Authors: Robert Andrews

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)


Abstract
We show that lower bounds for explicit constant-variate polynomials over fields of characteristic p > 0 are sufficient to derandomize polynomial identity testing over fields of characteristic p. In this setting, existing work on hardness-randomness tradeoffs for polynomial identity testing requires either the characteristic to be sufficiently large or the notion of hardness to be stronger than the standard syntactic notion of hardness used in algebraic complexity. Our results make no restriction on the characteristic of the field and use standard notions of hardness. We do this by combining the Kabanets-Impagliazzo generator with a white-box procedure to take p-th roots of circuits computing a p-th power over fields of characteristic p. When the number of variables appearing in the circuit is bounded by some constant, this procedure turns out to be efficient, which allows us to bypass difficulties related to factoring circuits in characteristic p. We also combine the Kabanets-Impagliazzo generator with recent "bootstrapping" results in polynomial identity testing to show that a sufficiently-hard family of explicit constant-variate polynomials yields a near-complete derandomization of polynomial identity testing. This result holds over fields of both zero and positive characteristic and complements a recent work of Guo, Kumar, Saptharishi, and Solomon, who obtained a slightly stronger statement over fields of characteristic zero.

Cite as

Robert Andrews. Algebraic Hardness Versus Randomness in Low Characteristic. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 37:1-37:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{andrews:LIPIcs.CCC.2020.37,
  author =	{Andrews, Robert},
  title =	{{Algebraic Hardness Versus Randomness in Low Characteristic}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{37:1--37:32},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.37},
  URN =		{urn:nbn:de:0030-drops-125895},
  doi =		{10.4230/LIPIcs.CCC.2020.37},
  annote =	{Keywords: Polynomial identity testing, hardness versus randomness, low characteristic}
}
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