4 Search Results for "Hoshino, Naohiko"

Document
DOI: 10.4230/LIPIcs.FSCD.2023.20
On the Lattice of Program Metrics

Authors: Ugo Dal Lago, Naohiko Hoshino, and Paolo Pistone

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
In this paper we are concerned with understanding the nature of program metrics for calculi with higher-order types, seen as natural generalizations of program equivalences. Some of the metrics we are interested in are well-known, such as those based on the interpretation of terms in metric spaces and those obtained by generalizing observational equivalence. We also introduce a new one, called the interactive metric, built by applying the well-known Int-Construction to the category of metric complete partial orders. Our aim is then to understand how these metrics relate to each other, i.e., whether and in which cases one such metric refines another, in analogy with corresponding well-studied problems about program equivalences. The results we obtain are twofold. We first show that the metrics of semantic origin, i.e., the denotational and interactive ones, lie in between the observational and equational metrics and that in some cases, these inclusions are strict. Then, we give a result about the relationship between the denotational and interactive metrics, revealing that the former is less discriminating than the latter. All our results are given for a linear lambda-calculus, and some of them can be generalized to calculi with graded comonads, in the style of Fuzz.
Cite as

Ugo Dal Lago, Naohiko Hoshino, and Paolo Pistone. On the Lattice of Program Metrics. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dallago_et_al:LIPIcs.FSCD.2023.20,
  author =	{Dal Lago, Ugo and Hoshino, Naohiko and Pistone, Paolo},
  title =	{{On the Lattice of Program Metrics}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{20:1--20:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.20},
  URN =		{urn:nbn:de:0030-drops-180049},
  doi =		{10.4230/LIPIcs.FSCD.2023.20},
  annote =	{Keywords: Metrics, Lambda Calculus, Linear Types}
}
Document
DOI: 10.4230/LIPIcs.CSL.2022.35
Planar Realizability via Left and Right Applications

Authors: Haruka Tomita

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

Abstract
We introduce a class of applicative structures called bi-BDI-algebras. Bi-BDI-algebras are generalizations of partial combinatory algebras and BCI-algebras, and feature two sorts of applications (left and right applications). Applying the categorical realizability construction to bi-BDI-algebras, we obtain monoidal bi-closed categories of assemblies (as well as of modest sets). We further investigate two kinds of comonadic applicative morphisms on bi-BDI-algebras as non-symmetric analogues of linear combinatory algebras, which induce models of exponential and exchange modalities on non-symmetric linear logics.
Cite as

Haruka Tomita. Planar Realizability via Left and Right Applications. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{tomita:LIPIcs.CSL.2022.35,
  author =	{Tomita, Haruka},
  title =	{{Planar Realizability via Left and Right Applications}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.35},
  URN =		{urn:nbn:de:0030-drops-157558},
  doi =		{10.4230/LIPIcs.CSL.2022.35},
  annote =	{Keywords: Realizability, combinatory algebra, monoidal bi-closed category, exponential modality, exchange modality}
}
Document
DOI: 10.4230/LIPIcs.CSL.2021.38
Realizability Without Symmetry

Authors: Haruka Tomita

Published in: LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)

Abstract
In categorical realizability, it is common to construct categories of assemblies and modest sets from applicative structures. In this paper, we introduce several classes of applicative structures and apply the categorical realizability construction to them. Then we obtain closed multicategories, closed categories and skew closed categories, which are more general categorical structures than Cartesian closed categories and symmetric monoidal closed categories. Moreover, we give the necessary and sufficient conditions for obtaining closed multicategories and closed categories of assemblies.
Cite as

Haruka Tomita. Realizability Without Symmetry. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{tomita:LIPIcs.CSL.2021.38,
  author =	{Tomita, Haruka},
  title =	{{Realizability Without Symmetry}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{38:1--38:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Baier, Christel and Goubault-Larrecq, Jean},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.38},
  URN =		{urn:nbn:de:0030-drops-134729},
  doi =		{10.4230/LIPIcs.CSL.2021.38},
  annote =	{Keywords: Realizability, combinatory algebra, closed multicategory, closed category, skew closed category}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2016.2
Coalgebras and Higher-Order Computation: a GoI Approach

Authors: Ichiro Hasuo

Published in: LIPIcs, Volume 52, 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)

Abstract
Girard's geometry of interaction (GoI) can be seen---in one practical aspect of it---as a compositional compilation method from functional programs to sequential machines. There tokens move around and express interactions between (parts of) programs. Intrigued by the combination of abstract structures and concrete dynamics in GoI, our line of work has aimed at exploiting, in GoI, results from the theory of coalgebra---a categorical abstraction of state-based transition systems that has found its use principally in concurrency theory. Such reinforced connection between higher-order computation and state-based dynamics is made possible thanks to an elegant categorical axiomatization of GoI by Abramsky, Haghverdi and Scott, where traced monoidal categories are identified to be the essential structure behind. In the talk I shall lay out these basic ideas, together with some of our results on: GoI semantics for a quantum programming language; and our ``memoryful'' extension of GoI with algebraic effects. The talk is based on my joint work with my colleague Naohiko Hoshino (RIMS, Kyoto Univer- sity) and my (former) students Koko Muroya (University of Birmingham) and Toshiki Kataoka (University of Tokyo), to whom I owe special thanks.
Cite as

Ichiro Hasuo. Coalgebras and Higher-Order Computation: a GoI Approach. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 2:1-2:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{hasuo:LIPIcs.FSCD.2016.2,
  author =	{Hasuo, Ichiro},
  title =	{{Coalgebras and Higher-Order Computation: a GoI Approach}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{2:1--2:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Kesner, Delia and Pientka, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.2},
  URN =		{urn:nbn:de:0030-drops-59698},
  doi =		{10.4230/LIPIcs.FSCD.2016.2},
  annote =	{Keywords: functional programming, geometry of interaction, categorical semantics, coalgebra}
}
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