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Documents authored by Levy, Paul Blain

Document
DOI: 10.4230/LIPIcs.CALCO.2019.13
Coinductive Resumption Monads: Guarded Iterative and Guarded Elgot

Authors: Paul Blain Levy and Sergey Goncharov

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)

Abstract
We introduce a new notion of "guarded Elgot monad", that is a monad equipped with a form of iteration. It requires every guarded morphism to have a specified fixpoint, and classical equational laws of iteration to be satisfied. This notion includes Elgot monads, but also further examples of partial non-unique iteration, emerging in the semantics of processes under infinite trace equivalence. We recall the construction of the "coinductive resumption monad" from a monad and endofunctor, that is used for modelling programs up to bisimilarity. We characterize this construction via a universal property: if the given monad is guarded Elgot, then the coinductive resumption monad is the guarded Elgot monad that freely extends it by the given endofunctor.
Cite as

Paul Blain Levy and Sergey Goncharov. Coinductive Resumption Monads: Guarded Iterative and Guarded Elgot. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{levy_et_al:LIPIcs.CALCO.2019.13,
  author =	{Levy, Paul Blain and Goncharov, Sergey},
  title =	{{Coinductive Resumption Monads: Guarded Iterative and Guarded Elgot}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.13},
  URN =		{urn:nbn:de:0030-drops-114414},
  doi =		{10.4230/LIPIcs.CALCO.2019.13},
  annote =	{Keywords: Guarded iteration, guarded monads, coalgebraic resumptions}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2015.221
Final Coalgebras from Corecursive Algebras

Authors: Paul Blain Levy

Published in: LIPIcs, Volume 35, 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)

Abstract
We give a technique to construct a final coalgebra in which each element is a set of formulas of modal logic. The technique works for both the finite and the countable powerset functors. Starting with an injectively structured, corecursive algebra, we coinductively obtain a suitable subalgebra called the "co-founded part". We see—first with an example, and then in the general setting of modal logic on a dual adjunction—that modal theories form an injectively structured, corecursive algebra, so that this construction may be applied. We also obtain an initial algebra in a similar way. We generalize the framework beyond Set to categories equipped with a suitable factorization system, and look at the examples of Poset and Set-op .
Cite as

Paul Blain Levy. Final Coalgebras from Corecursive Algebras. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 221-237, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{levy:LIPIcs.CALCO.2015.221,
  author =	{Levy, Paul Blain},
  title =	{{Final Coalgebras from Corecursive Algebras}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{221--237},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Moss, Lawrence S. and Sobocinski, Pawel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2015.221},
  URN =		{urn:nbn:de:0030-drops-55365},
  doi =		{10.4230/LIPIcs.CALCO.2015.221},
  annote =	{Keywords: coalgebra, modal logic, bisimulation, category theory, factorization system}
}
Document
DOI: 10.4230/DagSemProc.10351.4
Limitations of Applicative Bisimulation (Preliminary Report)

Authors: Vasileios Koutavas, Paul Blain Levy, and Eijiro Sumii

Published in: Dagstuhl Seminar Proceedings, Volume 10351, Modelling, Controlling and Reasoning About State (2010)

Abstract
We present a series of examples that illuminate an important aspect of the semantics of higher-order functions with local state. Namely that certain behaviour of such functions can only be observed by pro- viding them with arguments that contain the functions themselves. This provides evidence for the necessity of complex conditions for functions in modern semantics for state, such as logical relations and Kripke-like bisimulations, where related functions are applied to related arguments (that may contain the functions). It also suggests that simpler semantics, such as those based on applicative bisimulations where functions are ap- plied to identical arguments, would not scale to higher-order languages with local state.
Cite as

Vasileios Koutavas, Paul Blain Levy, and Eijiro Sumii. Limitations of Applicative Bisimulation (Preliminary Report). In Modelling, Controlling and Reasoning About State. Dagstuhl Seminar Proceedings, Volume 10351, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{koutavas_et_al:DagSemProc.10351.4,
  author =	{Koutavas, Vasileios and Levy, Paul Blain and Sumii, Eijiro},
  title =	{{Limitations of Applicative Bisimulation (Preliminary Report)}},
  booktitle =	{Modelling, Controlling and Reasoning About State},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10351},
  editor =	{Amal Ahmed and Nick Benton and Lars Birkedal and Martin Hofmann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10351.4},
  URN =		{urn:nbn:de:0030-drops-28074},
  doi =		{10.4230/DagSemProc.10351.4},
  annote =	{Keywords: Imperative languages, higher-order functions, local state}
}
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