13 Search Results for "Pistone, Paolo"

Document
DOI: 10.4230/LIPIcs.CSL.2026.29
Parametric Iteration in Resource Theories

Authors: Alessandro Di Giorgio, Pawel Sobocinski, and Niels Voorneveld

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Many algorithms are specified with respect to a fixed but unknown parameter. Examples of this are especially common in cryptography, where protocols often feature a security parameter such as the bit length of a secret key. Our aim is to capture this phenomenon in a more abstract setting. We focus on resource theories - general calculi of processes with a string diagrammatic syntax - introducing a general parametric iteration construction. By instantiating this construction within the Markov category of probabilistic Boolean circuits and equipping it with a suitable metric, we are able to capture the notion of negligibility via asymptotic equivalence, in a compositional way. This allows us to use diagrammatic reasoning to prove simple cryptographic theorems - for instance, proving that guessing a randomly generated key has negligible success.
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Alessandro Di Giorgio, Pawel Sobocinski, and Niels Voorneveld. Parametric Iteration in Resource Theories. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 29:1-29:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{digiorgio_et_al:LIPIcs.CSL.2026.29,
  author =	{Di Giorgio, Alessandro and Sobocinski, Pawel and Voorneveld, Niels},
  title =	{{Parametric Iteration in Resource Theories}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{29:1--29:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.29},
  URN =		{urn:nbn:de:0030-drops-254541},
  doi =		{10.4230/LIPIcs.CSL.2026.29},
  annote =	{Keywords: Markov categories, Cryptography, String diagrams, Asymptotic equivalence}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.15
On the Metric Nature of (Differential) Logical Relations

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

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Differential logical relations are a method to measure distances between higher-order programs. They differ from standard methods based on program metrics in that differences between functional programs are themselves functions, relating errors in input with errors in output, this way providing a more fine grained, contextual, information. The aim of this paper is to clarify the metric nature of differential logical relations. While previous work has shown that these do not give rise, in general, to (quasi-)metric spaces nor to partial metric spaces, we show that the distance functions arising from such relations, that we call quasi-quasi-metrics, can be related to both quasi-metrics and partial metrics, the latter being also captured by suitable relational definitions. Moreover, we exploit such connections to deduce some new compositional reasoning principles for program differences.
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Ugo Dal Lago, Naohiko Hoshino, and Paolo Pistone. On the Metric Nature of (Differential) Logical Relations. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dallago_et_al:LIPIcs.FSCD.2025.15,
  author =	{Dal Lago, Ugo and Hoshino, Naohiko and Pistone, Paolo},
  title =	{{On the Metric Nature of (Differential) Logical Relations}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{15:1--15:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.15},
  URN =		{urn:nbn:de:0030-drops-236300},
  doi =		{10.4230/LIPIcs.FSCD.2025.15},
  annote =	{Keywords: Differential Logical Relations, Quantales, Quasi-Metrics, Partial Metrics}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.34
The Lambda Calculus Is Quantifiable

Authors: Valentin Maestracci and Paolo Pistone

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
In this paper we introduce several quantitative methods for the lambda-calculus based on partial metrics, a well-studied variant of standard metric spaces that have been used to metrize non-Hausdorff topologies, like those arising from Scott domains. First, we study quantitative variants, based on program distances, of sensible equational theories for the λ-calculus, like those arising from Böhm trees and from the contextual preorder. Then, we introduce applicative distances capturing higher-order Scott topologies, including reflexive objects like the D_∞ model. Finally, we provide a quantitative insight on the well-known connection between the Böhm tree of a λ-term and its Taylor expansion, by showing that the latter can be presented as an isometric transformation.
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Valentin Maestracci and Paolo Pistone. The Lambda Calculus Is Quantifiable. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 34:1-34:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{maestracci_et_al:LIPIcs.CSL.2025.34,
  author =	{Maestracci, Valentin and Pistone, Paolo},
  title =	{{The Lambda Calculus Is Quantifiable}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{34:1--34:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.34},
  URN =		{urn:nbn:de:0030-drops-227911},
  doi =		{10.4230/LIPIcs.CSL.2025.34},
  annote =	{Keywords: Lambda-calculus, Scott semantics, Partial metric spaces, B\"{o}hm trees, Taylor expansion}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.31
Simple Types for Probabilistic Termination

Authors: Willem Heijltjes and Georgina Majury

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
We present a new typing discipline to guarantee the probability of termination in probabilistic lambda-calculi. The main contribution is a particular naturality and simplicity: our probabilistic types are as simple types, but generated from probabilities as base types, representing a least probability of termination. Simple types are recovered by restricting probabilities to one. Our vehicle is the Probabilistic Event Lambda-Calculus by Dal Lago, Guerrieri, and Heijltjes, which presents a solution to the issue of confluence in probabilistic lambda-calculi. Our probabilistic type system provides an alternative solution to that using counting quantifiers by Antonelli, Dal Lago, and Pistone, for the same calculus. The problem that both type systems address is to give a lower bound on the probability that terms head-normalize. Following the recent Functional Machine Calculus by Heijltjes, our development takes the (simplified) Krivine machine as primary, and proceeds via an extension of the calculus with sequential composition and identity on the machine. Our type system then gives a natural account of termination probability on the Krivine machine, reflected back onto head-normalization for the original calculus. In this way we are able to avoid the use of counting quantifiers, while improving on the termination bounds given by Antonelli, Dal Lago, and Pistone.
Cite as

Willem Heijltjes and Georgina Majury. Simple Types for Probabilistic Termination. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 31:1-31:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{heijltjes_et_al:LIPIcs.CSL.2025.31,
  author =	{Heijltjes, Willem and Majury, Georgina},
  title =	{{Simple Types for Probabilistic Termination}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{31:1--31:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.31},
  URN =		{urn:nbn:de:0030-drops-227885},
  doi =		{10.4230/LIPIcs.CSL.2025.31},
  annote =	{Keywords: lambda-calculus, probabilistic termination, simple types}
}
Document
DOI: 10.4230/LIPIcs.CSL.2024.10
Enumerating Error Bounded Polytime Algorithms Through Arithmetical Theories

Authors: Melissa Antonelli, Ugo Dal Lago, Davide Davoli, Isabel Oitavem, and Paolo Pistone

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
We consider a minimal extension of the language of arithmetic, such that the bounded formulas provably total in a suitably-defined theory à la Buss (expressed in this new language) precisely capture polytime random functions. Then, we provide two new characterizations of the semantic class BPP obtained by internalizing the error-bound check within a logical system: the first relies on measure-sensitive quantifiers, while the second is based on standard first-order quantification. This leads us to introduce a family of effectively enumerable subclasses of BPP, called BPP_T and consisting of languages captured by those probabilistic Turing machines whose underlying error can be proved bounded in T. As a paradigmatic example of this approach, we establish that polynomial identity testing is in BPP_T, where T = IΔ₀+Exp is a well-studied theory based on bounded induction.
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Melissa Antonelli, Ugo Dal Lago, Davide Davoli, Isabel Oitavem, and Paolo Pistone. Enumerating Error Bounded Polytime Algorithms Through Arithmetical Theories. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{antonelli_et_al:LIPIcs.CSL.2024.10,
  author =	{Antonelli, Melissa and Dal Lago, Ugo and Davoli, Davide and Oitavem, Isabel and Pistone, Paolo},
  title =	{{Enumerating Error Bounded Polytime Algorithms Through Arithmetical Theories}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.10},
  URN =		{urn:nbn:de:0030-drops-196538},
  doi =		{10.4230/LIPIcs.CSL.2024.10},
  annote =	{Keywords: Bounded Arithmetic, Randomized Computation, Implicit Computational Complexity}
}
Document
DOI: 10.4230/LIPIcs.CSL.2024.14
Tropical Mathematics and the Lambda-Calculus I: Metric and Differential Analysis of Effectful Programs

Authors: Davide Barbarossa and Paolo Pistone

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program metrics, based on the analysis of program sensitivity via Lipschitz conditions, on the other hand resource analysis, based on linear logic and higher-order program differentiation. To do that, we focus on the semantics arising from the relational model weighted over the tropical semiring, and we discuss its application to the study of "best case" program behavior for languages with probabilistic and non-deterministic effects. Finally, we show that a general foundation for this approach is provided by an abstract correspondence between tropical algebra and Lawvere’s theory of generalized metric spaces.
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Davide Barbarossa and Paolo Pistone. Tropical Mathematics and the Lambda-Calculus I: Metric and Differential Analysis of Effectful Programs. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 14:1-14:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{barbarossa_et_al:LIPIcs.CSL.2024.14,
  author =	{Barbarossa, Davide and Pistone, Paolo},
  title =	{{Tropical Mathematics and the Lambda-Calculus I: Metric and Differential Analysis of Effectful Programs}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{14:1--14:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.14},
  URN =		{urn:nbn:de:0030-drops-196577},
  doi =		{10.4230/LIPIcs.CSL.2024.14},
  annote =	{Keywords: Relational semantics, Differential lambda-calculus, Tropical semiring, Program metrics, Lawvere quantale}
}
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.
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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.FSCD.2022.4
On Quantitative Algebraic Higher-Order Theories

Authors: Ugo Dal Lago, Furio Honsell, Marina Lenisa, and Paolo Pistone

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

Abstract
We explore the possibility of extending Mardare et al.’s quantitative algebras to the structures which naturally emerge from Combinatory Logic and the λ-calculus. First of all, we show that the framework is indeed applicable to those structures, and give soundness and completeness results. Then, we prove some negative results clearly delineating to which extent categories of metric spaces can be models of such theories. We conclude by giving several examples of non-trivial higher-order quantitative algebras.
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Ugo Dal Lago, Furio Honsell, Marina Lenisa, and Paolo Pistone. On Quantitative Algebraic Higher-Order Theories. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dallago_et_al:LIPIcs.FSCD.2022.4,
  author =	{Dal Lago, Ugo and Honsell, Furio and Lenisa, Marina and Pistone, Paolo},
  title =	{{On Quantitative Algebraic Higher-Order Theories}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{4:1--4:18},
  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.2022.4},
  URN =		{urn:nbn:de:0030-drops-162851},
  doi =		{10.4230/LIPIcs.FSCD.2022.4},
  annote =	{Keywords: Quantitative Algebras, Lambda Calculus, Combinatory Logic, Metric Spaces}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2021.27
What’s Decidable About (Atomic) Polymorphism?

Authors: Paolo Pistone and Luca Tranchini

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Abstract
Due to the undecidability of most type-related properties of System F like type inhabitation or type checking, restricted polymorphic systems have been widely investigated (the most well-known being ML-polymorphism). In this paper we investigate System Fat, or atomic System F, a very weak predicative fragment of System F whose typable terms coincide with the simply typable ones. We show that the type-checking problem for Fat is decidable and we propose an algorithm which sheds some new light on the source of undecidability in full System F. Moreover, we investigate free theorems and contextual equivalence in this fragment, and we show that the latter, unlike in the simply typed lambda-calculus, is undecidable.
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Paolo Pistone and Luca Tranchini. What’s Decidable About (Atomic) Polymorphism?. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 27:1-27:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{pistone_et_al:LIPIcs.FSCD.2021.27,
  author =	{Pistone, Paolo and Tranchini, Luca},
  title =	{{What’s Decidable About (Atomic) Polymorphism?}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{27:1--27:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.27},
  URN =		{urn:nbn:de:0030-drops-142652},
  doi =		{10.4230/LIPIcs.FSCD.2021.27},
  annote =	{Keywords: Atomic System F, Predicative Polymorphism, ML-Polymorphism, Type-Checking, Contextual Equivalence, Free Theorems}
}
Document
DOI: 10.4230/LIPIcs.CSL.2021.23
A Partial Metric Semantics of Higher-Order Types and Approximate Program Transformations

Authors: Guillaume Geoffroy and Paolo Pistone

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

Abstract
Program semantics is traditionally concerned with program equivalence. However, in fields like approximate, incremental and probabilistic computation, it is often useful to describe to which extent two programs behave in a similar, although non equivalent way. This has motivated the study of program (pseudo)metrics, which have found widespread applications, e.g. in differential privacy. In this paper we show that the standard metric on real numbers can be lifted to higher-order types in a novel way, yielding a metric semantics of the simply typed lambda-calculus in which types are interpreted as quantale-valued partial metric spaces. Using such metrics we define a class of higher-order denotational models, called diameter space models, that provide a quantitative semantics of approximate program transformations. Noticeably, the distances between objects of higher-types are elements of functional, thus non-numerical, quantales. This allows us to model contextual reasoning about arbitrary functions, thus deviating from classic metric semantics.
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Guillaume Geoffroy and Paolo Pistone. A Partial Metric Semantics of Higher-Order Types and Approximate Program Transformations. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{geoffroy_et_al:LIPIcs.CSL.2021.23,
  author =	{Geoffroy, Guillaume and Pistone, Paolo},
  title =	{{A Partial Metric Semantics of Higher-Order Types and Approximate Program Transformations}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{23:1--23:18},
  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.2021.23},
  URN =		{urn:nbn:de:0030-drops-134578},
  doi =		{10.4230/LIPIcs.CSL.2021.23},
  annote =	{Keywords: Simply typed \lambda-calculus, program metrics, approximate program transformations, partial metric spaces}
}
Document
DOI: 10.4230/LIPIcs.CSL.2021.35
The Yoneda Reduction of Polymorphic Types

Authors: Paolo Pistone and Luca Tranchini

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

Abstract
In this paper we explore a family of type isomorphisms in System F whose validity corresponds, semantically, to some form of the Yoneda isomorphism from category theory. These isomorphisms hold under theories of equivalence stronger than βη-equivalence, like those induced by parametricity and dinaturality. We show that the Yoneda type isomorphisms yield a rewriting over types, that we call Yoneda reduction, which can be used to eliminate quantifiers from a polymorphic type, replacing them with a combination of monomorphic type constructors. We establish some sufficient conditions under which quantifiers can be fully eliminated from a polymorphic type, and we show some application of these conditions to count the inhabitants of a type and to compute program equivalence in some fragments of System F.
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Paolo Pistone and Luca Tranchini. The Yoneda Reduction of Polymorphic Types. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 35:1-35:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{pistone_et_al:LIPIcs.CSL.2021.35,
  author =	{Pistone, Paolo and Tranchini, Luca},
  title =	{{The Yoneda Reduction of Polymorphic Types}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{35:1--35:22},
  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.2021.35},
  URN =		{urn:nbn:de:0030-drops-134696},
  doi =		{10.4230/LIPIcs.CSL.2021.35},
  annote =	{Keywords: System F, Type isomorphisms, Yoneda isomorphism, Program equivalence}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.135
Implicit Automata in Typed λ-Calculi I: Aperiodicity in a Non-Commutative Logic

Authors: Lê Thành Dũng Nguyễn and Cécilia Pradic

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We give a characterization of star-free languages in a λ-calculus with support for non-commutative affine types (in the sense of linear logic), via the algebraic characterization of the former using aperiodic monoids. When the type system is made commutative, we show that we get regular languages instead. A key ingredient in our approach – that it shares with higher-order model checking – is the use of Church encodings for inputs and outputs. Our result is, to our knowledge, the first use of non-commutativity in implicit computational complexity.
Cite as

Lê Thành Dũng Nguyễn and Cécilia Pradic. Implicit Automata in Typed λ-Calculi I: Aperiodicity in a Non-Commutative Logic. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 135:1-135:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{nguyen_et_al:LIPIcs.ICALP.2020.135,
  author =	{Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng and Pradic, C\'{e}cilia},
  title =	{{Implicit Automata in Typed \lambda-Calculi I: Aperiodicity in a Non-Commutative Logic}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{135:1--135:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.135},
  URN =		{urn:nbn:de:0030-drops-125426},
  doi =		{10.4230/LIPIcs.ICALP.2020.135},
  annote =	{Keywords: Church encodings, ordered linear types, star-free languages}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2017.29
On Dinaturality, Typability and beta-eta-Stable Models

Authors: Paolo Pistone

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

Abstract
We present two results which relate dinaturality with a syntactic property (typability) and a semantic one (interpretability by beta-eta-stable sets). First, we prove that closed dinatural lambda-terms are simply typable, that is, the converse of the well-known fact that simply typable closed terms are dinatural. The argument exposes a syntactical aspect of dinaturality, as lambda-terms are type-checked by computing their associated dinaturality equation. Second, we prove that a closed lambda-term belonging to all beta-eta-stable interpretations of a simple type must be dinatural, that is, we prove dinaturality by semantical means. To do this, we show that such terms satisfy a suitable version of binary parametricity and we derive dinaturality from it. By combining the two results we obtain a new proof of the completeness of beta-eta-stable semantics with respect to simple types. While the completeness of this semantics is well-known in the literature, the technique here developed suggests that dinaturality might be exploited to prove completeness also for other, less manageable, semantics (like saturated families or reducibility candidates) for which a direct argument is not yet known.
Cite as

Paolo Pistone. On Dinaturality, Typability and beta-eta-Stable Models. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{pistone:LIPIcs.FSCD.2017.29,
  author =	{Pistone, Paolo},
  title =	{{On Dinaturality, Typability and beta-eta-Stable Models}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{29:1--29:17},
  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.2017.29},
  URN =		{urn:nbn:de:0030-drops-77291},
  doi =		{10.4230/LIPIcs.FSCD.2017.29},
  annote =	{Keywords: Dinaturality, simply-typed lambda-calculus, beta-eta-stable semantics, completeness}
}
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