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Documents authored by Tasson, Christine

Document
DOI: 10.4230/LIPIcs.CSL.2020.16
Taylor expansion for Call-By-Push-Value

Authors: Jules Chouquet and Christine Tasson

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

Abstract
The connection between the Call-By-Push-Value lambda-calculus introduced by Levy and Linear Logic introduced by Girard has been widely explored through a denotational view reflecting the precise ruling of resources in this language. We take a further step in this direction and apply Taylor expansion introduced by Ehrhard and Regnier. We define a resource lambda-calculus in whose terms can be used to approximate terms of Call-By-Push-Value. We show that this approximation is coherent with reduction and with the translations of Call-By-Name and Call-By-Value strategies into Call-By-Push-Value.
Cite as

Jules Chouquet and Christine Tasson. Taylor expansion for Call-By-Push-Value. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chouquet_et_al:LIPIcs.CSL.2020.16,
  author =	{Chouquet, Jules and Tasson, Christine},
  title =	{{Taylor expansion for Call-By-Push-Value}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{16:1--16:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.16},
  URN =		{urn:nbn:de:0030-drops-116594},
  doi =		{10.4230/LIPIcs.CSL.2020.16},
  annote =	{Keywords: Call-By-Push-Value, Quantitative semantics, Taylor expansion, Linear Logic}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.35
Local Validity for Circular Proofs in Linear Logic with Fixed Points

Authors: Rémi Nollet, Alexis Saurin, and Christine Tasson

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Circular (ie. non-wellfounded but regular) proofs have received increasing interest in recent years with the simultaneous development of their applications and meta-theory: infinitary proof theory is now well-established in several proof-theoretical frameworks such as Martin Löf's inductive predicates, linear logic with fixed points, etc. In the setting of non-wellfounded proofs, a validity criterion is necessary to distinguish, among all infinite derivation trees (aka. pre-proofs), those which are logically valid proofs. A standard approach is to consider a pre-proof to be valid if every infinite branch is supported by an infinitely progressing thread. The paper focuses on circular proofs for MALL with fixed points. Among all representations of valid circular proofs, a new fragment is described, based on a stronger validity criterion. This new criterion is based on a labelling of formulas and proofs, whose validity is purely local. This allows this fragment to be easily handled, while being expressive enough to still contain all circular embeddings of Baelde's muMALL finite proofs with (co)inductive invariants: in particular deciding validity and computing a certifying labelling can be done efficiently. Moreover the Brotherston-Simpson conjecture holds for this fragment: every labelled representation of a circular proof in the fragment is translated into a standard finitary proof. Finally we explore how to extend these results to a bigger fragment, by relaxing the labelling discipline while retaining (i) the ability to locally certify the validity and (ii) to some extent, the ability to finitize circular proofs.
Cite as

Rémi Nollet, Alexis Saurin, and Christine Tasson. Local Validity for Circular Proofs in Linear Logic with Fixed Points. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 35:1-35:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{nollet_et_al:LIPIcs.CSL.2018.35,
  author =	{Nollet, R\'{e}mi and Saurin, Alexis and Tasson, Christine},
  title =	{{Local Validity for Circular Proofs in Linear Logic with Fixed Points}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{35:1--35:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.35},
  URN =		{urn:nbn:de:0030-drops-97025},
  doi =		{10.4230/LIPIcs.CSL.2018.35},
  annote =	{Keywords: sequent calculus, non-wellfounded proofs, circular proofs, induction, coinduction, fixed points, proof-search, linear logic, muMALL, finitization, infinite descent}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2017.4
Quantitative Semantics for Probabilistic Programming (Invited Talk)

Authors: Christine Tasson

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
Probabilistic programming has many applications in statistics, physics, ... so that all programming languages have been equipped with probabilistic library. However, there is a need in developing semantical tools in order to formalize higher order and recursive probabilistic languages. Indeed, it is well known that categories of measurable spaces are not Cartesian closed. We have been studying quantitative semantics of probabilistic spaces to fill this gap. A first step has been to focus on probabilistic programming languages with discrete types such as integers and booleans. In this setting, probabilistic programs can be seen as linear combinations of deterministic programs. Probabilistic Coherent Spaces constitute a Cartesian closed category that is fully abstract with respect to probabilistic Call-By-Push-Value. Moreover, this toy language is endowed with a memorization operator that allow to encode most discrete probabilistic programs. The second step is to move on probabilistic programming with continuous types representing for instance reals endowed with Lebesgue measurable sets. We introduce the category of cones and stable functions which is Cartesian closed. The trick is to enlarge the category of measurable spaces to gain closeness and to embrace measurable spaces. Besides, the category of cones is a sound and adequate model of a higher order and recursive probabilistic language in which most classical distributions and probabilistic tools can be encoded. This is joint work with Thomas Ehrhard and Michele Pagani.
Cite as

Christine Tasson. Quantitative Semantics for Probabilistic Programming (Invited Talk). In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{tasson:LIPIcs.FSCD.2017.4,
  author =	{Tasson, Christine},
  title =	{{Quantitative Semantics for Probabilistic Programming}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{4:1--4:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.4},
  URN =		{urn:nbn:de:0030-drops-77456},
  doi =		{10.4230/LIPIcs.FSCD.2017.4},
  annote =	{Keywords: denotational semantics, probabilistic programming, programming language, probability}
}
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