4 Search Results for "Bucciarelli, Antonio"

Document
DOI: 10.4230/LIPIcs.FSCD.2023.29
A Quantitative Version of Simple Types

Authors: Daniele Pautasso and Simona Ronchi Della Rocca

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

Abstract
This work introduces a quantitative version of the simple type assignment system, starting from a suitable restriction of non-idempotent intersection types. The resulting system is decidable and has the same typability power as the simple type system; thus, assigning types to terms supplies the very same qualitative information given by simple types, but at the same time can provide some interesting quantitative information. It is well known that typability for simple types is equivalent to unification; we prove a similar result for the newly introduced system. More precisely, we show that typability is equivalent to a unification problem which is a non-trivial extension of the classical one: in addition to unification rules, our typing algorithm makes use of an expansion operation that increases the cardinality of multisets whenever needed.
Cite as

Daniele Pautasso and Simona Ronchi Della Rocca. A Quantitative Version of Simple Types. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 29:1-29:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{pautasso_et_al:LIPIcs.FSCD.2023.29,
  author =	{Pautasso, Daniele and Ronchi Della Rocca, Simona},
  title =	{{A Quantitative Version of Simple Types}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{29:1--29:21},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.29},
  URN =		{urn:nbn:de:0030-drops-180137},
  doi =		{10.4230/LIPIcs.FSCD.2023.29},
  annote =	{Keywords: \lambda-calculus, intersection types, unification}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2019.3
A Quantitative Understanding of Pattern Matching

Authors: Sandra Alves, Delia Kesner, and Daniel Ventura

Published in: LIPIcs, Volume 175, 25th International Conference on Types for Proofs and Programs (TYPES 2019)

Abstract
This paper shows that the recent approach to quantitative typing systems for programming languages can be extended to pattern matching features. Indeed, we define two resource-aware type systems, named U and E, for a λ-calculus equipped with pairs for both patterns and terms. Our typing systems borrow some basic ideas from [Antonio Bucciarelli et al., 2015], which characterises (head) normalisation in a qualitative way, in the sense that typability and normalisation coincide. But, in contrast to [Antonio Bucciarelli et al., 2015], our systems also provide quantitative information about the dynamics of the calculus. Indeed, system U provides upper bounds for the length of (head) normalisation sequences plus the size of their corresponding normal forms, while system E, which can be seen as a refinement of system U, produces exact bounds for each of them. This is achieved by means of a non-idempotent intersection type system equipped with different technical tools. First of all, we use product types to type pairs instead of the disjoint unions in [Antonio Bucciarelli et al., 2015], which turn out to be an essential quantitative tool because they remove the confusion between "being a pair" and "being duplicable". Secondly, typing sequents in system E are decorated with tuples of integers, which provide quantitative information about normalisation sequences, notably time (cf. length) and space (cf. size). Moreover, the time resource information is remarkably refined, because it discriminates between different kinds of reduction steps performed during evaluation, so that beta, substitution and matching steps are counted separately. Another key tool of system E is that the type system distinguishes between consuming (contributing to time) and persistent (contributing to space) constructors.
Cite as

Sandra Alves, Delia Kesner, and Daniel Ventura. A Quantitative Understanding of Pattern Matching. In 25th International Conference on Types for Proofs and Programs (TYPES 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 175, pp. 3:1-3:36, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{alves_et_al:LIPIcs.TYPES.2019.3,
  author =	{Alves, Sandra and Kesner, Delia and Ventura, Daniel},
  title =	{{A Quantitative Understanding of Pattern Matching}},
  booktitle =	{25th International Conference on Types for Proofs and Programs (TYPES 2019)},
  pages =	{3:1--3:36},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-158-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{175},
  editor =	{Bezem, Marc and Mahboubi, Assia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2019.3},
  URN =		{urn:nbn:de:0030-drops-130672},
  doi =		{10.4230/LIPIcs.TYPES.2019.3},
  annote =	{Keywords: Intersection Types, Pattern Matching, Exact Bounds}
}
Document
DOI: 10.4230/LIPIcs.TLCA.2015.123
Observability for Pair Pattern Calculi

Authors: Antonio Bucciarelli, Delia Kesner, and Simona Ronchi Della Rocca

Published in: LIPIcs, Volume 38, 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)

Abstract
Inspired by the notion of solvability in the λ-calculus, we define a notion of observability for a calculus with pattern matching. We give an intersection type system for such a calculus which is based on non-idempotent types. The typing system is shown to characterize the set of terms having canonical form, which properly contains the set of observable terms, so that typability alone is not sufficient to characterize observability. However, the inhabitation problem associated with our typing system turns out to be decidable, a result which — together with typability — allows to obtain a full characterization of observability.
Cite as

Antonio Bucciarelli, Delia Kesner, and Simona Ronchi Della Rocca. Observability for Pair Pattern Calculi. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 123-137, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{bucciarelli_et_al:LIPIcs.TLCA.2015.123,
  author =	{Bucciarelli, Antonio and Kesner, Delia and Ronchi Della Rocca, Simona},
  title =	{{Observability for Pair Pattern Calculi}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{123--137},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TLCA.2015.123},
  URN =		{urn:nbn:de:0030-drops-51596},
  doi =		{10.4230/LIPIcs.TLCA.2015.123},
  annote =	{Keywords: solvability, pattern calculi, intersection types, inhabitation}
}
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.
Cite as

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-dev.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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