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Invited Talk

DOI: 10.4230/LIPIcs.FSCD.2024.1

Meaningfulness and Genericity in a Subsuming Framework (Invited Talk)

Authors: Delia Kesner, Victor Arrial, and Giulio Guerrieri

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

This paper studies the notion of meaningfulness for a unifying framework called dBang-calculus, which subsumes both call-by-name (dCBN) and call-by-value (dCBV). We first define meaningfulness in dBang and then characterize it by means of typability and inhabitation in an associated non-idempotent intersection type system previously appearing in the literature. We validate the proposed notion of meaningfulness by showing two properties: (1) consistency of the smallest theory, called ℋ, equating all meaningless terms, and (2) genericity, stating that meaningless subterms have no bearing on the significance of meaningful terms. The theory ℋ is also shown to have a unique consistent and maximal extension ℋ*, which coincides with a well-known notion of observational equivalence. Last but not least, we show that the notions of meaningfulness and genericity in the literature for dCBN and dCBV are subsumed by the corresponding ones proposed here for the dBang-calculus.

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Delia Kesner, Victor Arrial, and Giulio Guerrieri. Meaningfulness and Genericity in a Subsuming Framework (Invited Talk). In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kesner_et_al:LIPIcs.FSCD.2024.1,
  author =	{Kesner, Delia and Arrial, Victor and Guerrieri, Giulio},
  title =	{{Meaningfulness and Genericity in a Subsuming Framework}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{1:1--1:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.1},
  URN =		{urn:nbn:de:0030-drops-203305},
  doi =		{10.4230/LIPIcs.FSCD.2024.1},
  annote =	{Keywords: Lambda calculus, Solvability, Meaningfulness, Inhabitation, Genericity}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2024.23

Mirroring Call-By-Need, or Values Acting Silly

Authors: Beniamino Accattoli and Adrienne Lancelot

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

Call-by-need evaluation for the λ-calculus can be seen as merging the best of call-by-name and call-by-value, namely the wise erasing behaviour of the former and the wise duplicating behaviour of the latter. To better understand how duplication and erasure can be combined, we design a degenerated calculus, dubbed call-by-silly, that is symmetric to call-by-need in that it merges the worst of call-by-name and call-by-value, namely silly duplications by-name and silly erasures by-value. We validate the design of the call-by-silly calculus via rewriting properties and multi types. In particular, we mirror the main theorem about call-by-need - that is, its operational equivalence with call-by-name - showing that call-by-silly and call-by-value induce the same contextual equivalence. This fact shows the blindness with respect to efficiency of call-by-value contextual equivalence. We also define a call-by-silly strategy and measure its length via tight multi types. Lastly, we prove that the call-by-silly strategy computes evaluation sequences of maximal length in the calculus.

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Beniamino Accattoli and Adrienne Lancelot. Mirroring Call-By-Need, or Values Acting Silly. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 23:1-23:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{accattoli_et_al:LIPIcs.FSCD.2024.23,
  author =	{Accattoli, Beniamino and Lancelot, Adrienne},
  title =	{{Mirroring Call-By-Need, or Values Acting Silly}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{23:1--23:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.23},
  URN =		{urn:nbn:de:0030-drops-203527},
  doi =		{10.4230/LIPIcs.FSCD.2024.23},
  annote =	{Keywords: Lambda calculus, intersection types, call-by-value, call-by-need}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2024.29

Böhm and Taylor for All!

Authors: Aloÿs Dufour and Damiano Mazza

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

Böhm approximations, used in the definition of Böhm trees, are a staple of the semantics of the lambda-calculus. Introduced more recently by Ehrhard and Regnier, Taylor approximations provide a quantitative account of the behavior of programs and are well-known to be connected to intersection types. The key relation between these two notions of approximations is a commutation theorem, roughly stating that Taylor approximations of Böhm trees are the same as Böhm trees of Taylor approximations. Böhm and Taylor approximations are available for several variants or extensions of the lambda-calculus and, in some cases, commutation theorems are known. In this paper, we define Böhm and Taylor approximations and prove the commutation theorem in a very general setting. We also introduce (non-idempotent) intersection types at this level of generality. From this, we show how the commutation theorem and intersection types may be applied to any calculus embedding in a sufficiently nice way into our general calculus. All known Böhm-Taylor commutation theorems, as well as new ones, follow by this uniform construction.

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Aloÿs Dufour and Damiano Mazza. Böhm and Taylor for All!. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dufour_et_al:LIPIcs.FSCD.2024.29,
  author =	{Dufour, Alo\"{y}s and Mazza, Damiano},
  title =	{{B\"{o}hm and Taylor for All!}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.29},
  URN =		{urn:nbn:de:0030-drops-203582},
  doi =		{10.4230/LIPIcs.FSCD.2024.29},
  annote =	{Keywords: Linear logic, Differential linear logic, Taylor expansion of lambda-terms, B\"{o}hm trees, Process calculi}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2023.8

The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic

Authors: Thomas Ehrhard, Claudia Faggian, and Michele Pagani

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

Abstract

We consider an extension of multiplicative linear logic which encompasses bayesian networks and expresses samples sharing and marginalisation with the polarised rules of contraction and weakening. We introduce the necessary formalism to import exact inference algorithms from bayesian networks, giving the sum-product algorithm as an example of calculating the weighted relational semantics of a multiplicative proof-net improving runtime performance by storing intermediate results.

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Thomas Ehrhard, Claudia Faggian, and Michele Pagani. The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ehrhard_et_al:LIPIcs.FSCD.2023.8,
  author =	{Ehrhard, Thomas and Faggian, Claudia and Pagani, Michele},
  title =	{{The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{8:1--8:18},
  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.2023.8},
  URN =		{urn:nbn:de:0030-drops-179926},
  doi =		{10.4230/LIPIcs.FSCD.2023.8},
  annote =	{Keywords: Linear Logic, Proof-Nets, Denotational Semantics, Probabilistic Programming}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2022.21

Linear Lambda-Calculus is Linear

Authors: Alejandro Díaz-Caro and Gilles Dowek

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract

We prove a linearity theorem for an extension of linear logic with addition and multiplication by a scalar: the proofs of some propositions in this logic are linear in the algebraic sense. This work is part of a wider research program that aims at defining a logic whose proof language is a quantum programming language.

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Alejandro Díaz-Caro and Gilles Dowek. Linear Lambda-Calculus is Linear. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{diazcaro_et_al:LIPIcs.FSCD.2022.21,
  author =	{D{\'\i}az-Caro, Alejandro and Dowek, Gilles},
  title =	{{Linear Lambda-Calculus is Linear}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.21},
  URN =		{urn:nbn:de:0030-drops-163024},
  doi =		{10.4230/LIPIcs.FSCD.2022.21},
  annote =	{Keywords: Proof theory, Lambda calculus, Linear logic, Quantum computing}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2021.143

Analytical Differential Calculus with Integration

Authors: Han Xu and Zhenjiang Hu

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract

Differential lambda-calculus was first introduced by Thomas Ehrhard and Laurent Regnier in 2003. Despite more than 15 years of history, little work has been done on a differential calculus with integration. In this paper, we shall propose a differential calculus with integration from a programming point of view. We show its good correspondence with mathematics, which is manifested by how we construct these reduction rules and how we preserve important mathematical theorems in our calculus. Moreover, we highlight applications of the calculus in incremental computation, automatic differentiation, and computation approximation.

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Han Xu and Zhenjiang Hu. Analytical Differential Calculus with Integration. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 143:1-143:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{xu_et_al:LIPIcs.ICALP.2021.143,
  author =	{Xu, Han and Hu, Zhenjiang},
  title =	{{Analytical Differential Calculus with Integration}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{143:1--143:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.143},
  URN =		{urn:nbn:de:0030-drops-142127},
  doi =		{10.4230/LIPIcs.ICALP.2021.143},
  annote =	{Keywords: Differential Calculus, Integration, Lambda Calculus, Incremental Computation, Adaptive Computing}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2020.16

A Profunctorial Scott Semantics

Authors: Zeinab Galal

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract

In this paper, we study the bicategory of profunctors with the free finite coproduct pseudo-comonad and show that it constitutes a model of linear logic that generalizes the Scott model. We formalize the connection between the two models as a change of base for enriched categories which induces a pseudo-functor that preserves all the linear logic structure. We prove that morphisms in the co-Kleisli bicategory correspond to the concept of strongly finitary functors (sifted colimits preserving functors) between presheaf categories. We further show that this model provides solutions of recursive type equations which provides 2-dimensional models of the pure lambda calculus and we also exhibit a fixed point operator on terms.

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Zeinab Galal. A Profunctorial Scott Semantics. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{galal:LIPIcs.FSCD.2020.16,
  author =	{Galal, Zeinab},
  title =	{{A Profunctorial Scott Semantics}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.16},
  URN =		{urn:nbn:de:0030-drops-123387},
  doi =		{10.4230/LIPIcs.FSCD.2020.16},
  annote =	{Keywords: Linear Logic, Scott Semantics, Profunctors}
}

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.

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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.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.FSCD.2019.13

On the Taylor Expansion of Probabilistic lambda-terms

Authors: Ugo Dal Lago and Thomas Leventis

Published in: LIPIcs, Volume 131, 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)

Abstract

We generalise Ehrhard and Regnier’s Taylor expansion from pure to probabilistic lambda-terms. We prove that the Taylor expansion is adequate when seen as a way to give semantics to probabilistic lambda-terms, and that there is a precise correspondence with probabilistic Böhm trees, as introduced by the second author. We prove this adequacy through notions of probabilistic resource terms and explicit Taylor expansion.

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Ugo Dal Lago and Thomas Leventis. On the Taylor Expansion of Probabilistic lambda-terms. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{dallago_et_al:LIPIcs.FSCD.2019.13,
  author =	{Dal Lago, Ugo and Leventis, Thomas},
  title =	{{On the Taylor Expansion of Probabilistic lambda-terms}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{13:1--13:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-107-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{131},
  editor =	{Geuvers, Herman},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.13},
  URN =		{urn:nbn:de:0030-drops-105206},
  doi =		{10.4230/LIPIcs.FSCD.2019.13},
  annote =	{Keywords: Probabilistic Lambda-Calculi, Taylor Expansion, Linear Logic}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2019.17

Differentials and Distances in Probabilistic Coherence Spaces

Authors: Thomas Ehrhard

Published in: LIPIcs, Volume 131, 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)

Abstract

In probabilistic coherence spaces, a denotational model of probabilistic functional languages, morphisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives allow to compute the expectation of execution time in the weak head reduction of probabilistic PCF (pPCF). Next we apply a general notion of "local" differential of morphisms to the proof of a Lipschitz property of these morphisms allowing in turn to relate the observational distance on pPCF terms to a distance the model is naturally equipped with. This suggests that extending probabilistic programming languages with derivatives, in the spirit of the differential lambda-calculus, could be quite meaningful.

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Thomas Ehrhard. Differentials and Distances in Probabilistic Coherence Spaces. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ehrhard:LIPIcs.FSCD.2019.17,
  author =	{Ehrhard, Thomas},
  title =	{{Differentials and Distances in Probabilistic Coherence Spaces}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-107-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{131},
  editor =	{Geuvers, Herman},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.17},
  URN =		{urn:nbn:de:0030-drops-105243},
  doi =		{10.4230/LIPIcs.FSCD.2019.17},
  annote =	{Keywords: Denotational semantics, probabilistic coherence spaces, differentials of programs}
}

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.

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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.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}
}

Document

DOI: 10.4230/LIPIcs.CSL.2012.259

Collapsing non-idempotent intersection types

Authors: Thomas Ehrhard

Published in: LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012)

Abstract

We proved recently that the extensional collapse of the relational model of linear logic coincides with its Scott model, whose objects are preorders and morphisms are downwards closed relations. This result is obtained by the construction of a new model whose objects can be understood as preorders equipped with a realizability predicate. We present this model, which features a new duality, and explain how to use it for reducing normalization results in idempotent intersection types (usually proved by reducibility) to purely combinatorial methods. We illustrate this approach in the case of the call-by-value lambda-calculus, for which we introduce a new resource calculus, but it can be applied in the same way to many different calculi.

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Thomas Ehrhard. Collapsing non-idempotent intersection types. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 259-273, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{ehrhard:LIPIcs.CSL.2012.259,
  author =	{Ehrhard, Thomas},
  title =	{{Collapsing non-idempotent intersection types}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{259--273},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{C\'{e}gielski, Patrick and Durand, Arnaud},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.259},
  URN =		{urn:nbn:de:0030-drops-36776},
  doi =		{10.4230/LIPIcs.CSL.2012.259},
  annote =	{Keywords: Linear logic, lambda-calculus, denotational semantics}
}

Document

DOI: 10.4230/LIPIcs.CSL.2011.1

Resource Lambda-Calculus: the Differential Viewpoint

Authors: Thomas Ehrhard

Published in: LIPIcs, Volume 12, Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (2011)

Abstract

We present differential linear logic and its models, the associated resource and differential lambda-calculi, and the Taylor expansion of promotion boxes. We also describe an antiderivative which seems to be available in many models of differential Linear Logic, and we present a very simple categorical axiom for this operation.

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Thomas Ehrhard. Resource Lambda-Calculus: the Differential Viewpoint. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, p. 1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{ehrhard:LIPIcs.CSL.2011.1,
  author =	{Ehrhard, Thomas},
  title =	{{Resource Lambda-Calculus: the Differential Viewpoint}},
  booktitle =	{Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL},
  pages =	{1--1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-32-3},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{12},
  editor =	{Bezem, Marc},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.1},
  URN =		{urn:nbn:de:0030-drops-32152},
  doi =		{10.4230/LIPIcs.CSL.2011.1},
  annote =	{Keywords: proof theory, lambda-calculus, linear logic, denotational semantics}
}

Document

DOI: 10.4230/LIPIcs.CSL.2011.97

Full Abstraction for Resource Calculus with Tests

Authors: Antonio Bucciarelli, Alberto Carraro, Thomas Ehrhard, and Giulio Manzonetto

Published in: LIPIcs, Volume 12, Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (2011)

Abstract

We study the semantics of a resource sensitive extension of the lambda-calculus in a canonical reflexive object of a category of sets and relations, a relational version of the original Scott D infinity model of the pure lambda-calculus. This calculus is related to Boudol's resource calculus and is derived from Ehrhard and Regnier's differential extension of Linear Logic and of the lambda-calculus. We extend it with new constructions, to be understood as implementing a very simple exception mechanism, and with a ``must'' parallel composition. These new operations allow to associate a context of this calculus with any point of the model and to prove full abstraction for the finite sub-calculus where ordinary lambda-calculus application is not allowed. The result is then extended to the full calculus by means of a Taylor Expansion formula.

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Antonio Bucciarelli, Alberto Carraro, Thomas Ehrhard, and Giulio Manzonetto. Full Abstraction for Resource Calculus with Tests. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 97-111, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{bucciarelli_et_al:LIPIcs.CSL.2011.97,
  author =	{Bucciarelli, Antonio and Carraro, Alberto and Ehrhard, Thomas and Manzonetto, Giulio},
  title =	{{Full Abstraction for Resource Calculus with Tests}},
  booktitle =	{Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL},
  pages =	{97--111},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-32-3},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{12},
  editor =	{Bezem, Marc},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.97},
  URN =		{urn:nbn:de:0030-drops-32250},
  doi =		{10.4230/LIPIcs.CSL.2011.97},
  annote =	{Keywords: resource lambda calculus, relational semantics, full abstraction, differential linear logic}
}

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