DROPS

Document

Invited Paper

DOI: 10.4230/LIPIcs.CSL.2026.3

Rational Lawvere Logic (Invited Paper)

Authors: Giorgio Bacci, Radu Mardare, Prakash Panangaden, and Gordon Plotkin

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

Abstract

We study Rational Lawvere logic (RL). This logic is defined over the extended positive reals with an algebraic structure combining the Lawvere quantale (with the reversed order on the extended reals and a sum as tensor) and a multiplicative quantale (with the usual order on the extended reals and a multiplication as tensor); together they provide a semiring structure. The logic is designed for complex quantitative reasoning, including sequents expressing inequalities between rational functions over the extended positive reals. We give a deduction system and demonstrate its expressiveness by deriving a classical result from probability theory relating the Kantorovich and total variation distances. Our deductive system is complete for finitely axiomatizable theories. The proof of completeness relies on the Krivine-Stengle Positivstellensatz. We additionally provide complexity results for both RL and its affine fragment AL. We consider two decision problems: the satisfiability of a set of sequents and whether a sequent follows from a finite set of sequent. We show that both problems lie in PSPACE for RL, and we give sharper complexity bounds for AL: the first problem is NP-complete, while the second is co-NP-complete.

Cite as

Giorgio Bacci, Radu Mardare, Prakash Panangaden, and Gordon Plotkin. Rational Lawvere Logic (Invited Paper). In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{bacci_et_al:LIPIcs.CSL.2026.3,
  author =	{Bacci, Giorgio and Mardare, Radu and Panangaden, Prakash and Plotkin, Gordon},
  title =	{{Rational Lawvere Logic}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{3:1--3:21},
  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.2026.3},
  URN =		{urn:nbn:de:0030-drops-254277},
  doi =		{10.4230/LIPIcs.CSL.2026.3},
  annote =	{Keywords: Quantitative reasoning, complete deductive system, Lawvere’s quantale}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2025.11

A Sound and Complete Characterization of Fair Asynchronous Session Subtyping

Authors: Mario Bravetti, Luca Padovani, and Gianluigi Zavattaro

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract

Session types are abstractions of communication protocols enabling the static analysis of message-passing processes. Refinement notions for session types are key to support safe forms of process substitution while preserving their compatibility with the rest of the system. Recently, a fair refinement relation for asynchronous session types has been defined allowing the anticipation of message outputs with respect to an unbounded number of message inputs. This refinement is useful to capture common patterns in communication protocols that take advantage of asynchrony. However, while the semantic (à la testing) definition of such refinement is straightforward, its characterization has proved to be quite challenging. In fact, only a sound but not complete characterization is known so far. In this paper we close this open problem by presenting a sound and complete characterization of asynchronous fair refinement for session types. We relate this characterization to those given in the literature for synchronous session types by leveraging a novel labelled transition system of session types that embeds their asynchronous semantics.

Cite as

Mario Bravetti, Luca Padovani, and Gianluigi Zavattaro. A Sound and Complete Characterization of Fair Asynchronous Session Subtyping. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bravetti_et_al:LIPIcs.CONCUR.2025.11,
  author =	{Bravetti, Mario and Padovani, Luca and Zavattaro, Gianluigi},
  title =	{{A Sound and Complete Characterization of Fair Asynchronous Session Subtyping}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.11},
  URN =		{urn:nbn:de:0030-drops-239615},
  doi =		{10.4230/LIPIcs.CONCUR.2025.11},
  annote =	{Keywords: Binary sessions, session types, fair asynchronous subtyping}
}

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.

Cite as

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)

Copy BibTex To Clipboard

@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.ECOOP.2025.24

Fair Termination of Asynchronous Binary Sessions

Authors: Luca Padovani and Gianluigi Zavattaro

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract

We study a theory of asynchronous session types ensuring that well-typed processes terminate under a suitable fairness assumption. Fair termination entails starvation freedom and orphan message freedom namely that all messages, including those that are produced early taking advantage of asynchrony, are eventually consumed. The theory is based on a novel fair asynchronous subtyping relation for session types that is coarser than the existing ones. The type system is also the first of its kind that is firmly rooted in linear logic: fair asynchronous subtyping is incorporated as a natural generalization of the cut and axiom rules of linear logic and asynchronous communication is modeled through a suitable set of commuting conversions and of deep cut reductions in linear logic proofs.

Cite as

Luca Padovani and Gianluigi Zavattaro. Fair Termination of Asynchronous Binary Sessions. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 24:1-24:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{padovani_et_al:LIPIcs.ECOOP.2025.24,
  author =	{Padovani, Luca and Zavattaro, Gianluigi},
  title =	{{Fair Termination of Asynchronous Binary Sessions}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{24:1--24:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan 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.ECOOP.2025.24},
  URN =		{urn:nbn:de:0030-drops-233169},
  doi =		{10.4230/LIPIcs.ECOOP.2025.24},
  annote =	{Keywords: Binary sessions, fair asynchronous subtyping, fair termination, linear logic}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2025.7

Monadic Type-And-Effect Soundness

Authors: Francesco Dagnino, Paola Giannini, and Elena Zucca

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract

We introduce the abstract notions of monadic operational semantics, a small-step semantics where computational effects are modularly modeled by a monad, and type-and-effect system, including effect types whose interpretation lifts well-typedness to its monadic version. In this meta-theory, as usual in the non-monadic case, we can express progress and subject reduction, and provide a proof, given once and for all, that they imply soundness. The approach is illustrated on a lambda calculus with generic effects, equipped with an expressive type-and-effect system We provide proofs of progress and subject reduction, parametric on the interpretation of effect types. In this way, we obtain as instances many significant examples, such as checking exceptions, preventing/limiting non-determinism, constraining order/fairness of outputs. We also provide an extension with constructs to raise and handle computational effects, which can be instantiated to model different policies.

Cite as

Francesco Dagnino, Paola Giannini, and Elena Zucca. Monadic Type-And-Effect Soundness. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 7:1-7:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{dagnino_et_al:LIPIcs.ECOOP.2025.7,
  author =	{Dagnino, Francesco and Giannini, Paola and Zucca, Elena},
  title =	{{Monadic Type-And-Effect Soundness}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{7:1--7:31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan 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.ECOOP.2025.7},
  URN =		{urn:nbn:de:0030-drops-233009},
  doi =		{10.4230/LIPIcs.ECOOP.2025.7},
  annote =	{Keywords: Effects, monads, type soundness}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2025.8

An Effectful Object Calculus

Authors: Francesco Dagnino, Paola Giannini, and Elena Zucca

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract

We show how to smoothly incorporate in the object-oriented paradigm constructs to raise, compose, and handle effects in an arbitrary monad. The underlying pure calculus is meant to be a representative of the last generation of OO languages, and the effectful extension is manageable enough for ordinary programmers; notably, constructs to raise effects are just special methods. We equip the calculus with an expressive type-and-effect system, which, again by relying on standard features such as inheritance and generic types, allows a simple form of effect polymorphism. The soundness of the type-and-effect system is expressed and proved by a recently introduced technique, where the semantics is formalized by a one-step reduction relation from language expressions into monadic ones, so that it is enough to prove progress and subject reduction properties on this relation.

Cite as

Francesco Dagnino, Paola Giannini, and Elena Zucca. An Effectful Object Calculus. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 8:1-8:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{dagnino_et_al:LIPIcs.ECOOP.2025.8,
  author =	{Dagnino, Francesco and Giannini, Paola and Zucca, Elena},
  title =	{{An Effectful Object Calculus}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{8:1--8:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan 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.ECOOP.2025.8},
  URN =		{urn:nbn:de:0030-drops-233017},
  doi =		{10.4230/LIPIcs.ECOOP.2025.8},
  annote =	{Keywords: Object calculi, handlers, type-and-effect systems}
}

Document

DOI: 10.4230/LIPIcs.TYPES.2023.3

Categorical Models of Subtyping

Authors: Greta Coraglia and Jacopo Emmenegger

Published in: LIPIcs, Volume 303, 29th International Conference on Types for Proofs and Programs (TYPES 2023)

Abstract

Most categorical models for dependent types have traditionally been heavily set based: contexts form a category, and for each we have a set of types in said context - and for each type a set of terms of said type. This is the case for categories with families, categories with attributes, and natural models; in particular, all of them can be traced back to certain discrete Grothendieck fibrations. We extend this intuition to the case of general, not necessarily discrete, fibrations, so that over a given context one has not only a set but a category of types. We argue that the added structure can be attributed to a notion of subtyping that shares many features with that of coercive subtyping, in the sense that it is the product of thinking about subtyping as an abbreviation mechanism: we say that a given type A' is a subtype of A if there is a unique coercion from A' to A. Whenever we need a term of type A, then, it suffices to have a term of type A', which we can "plug-in" into A. For this version of subtyping we provide rules, coherences, and explicit models, and we compare and contrast it to coercive subtyping as introduced by Z. Luo and others. We conclude by suggesting how the tools we present can be employed in finding appropriate rules relating subtyping and certain type constructors.

Cite as

Greta Coraglia and Jacopo Emmenegger. Categorical Models of Subtyping. In 29th International Conference on Types for Proofs and Programs (TYPES 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 303, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{coraglia_et_al:LIPIcs.TYPES.2023.3,
  author =	{Coraglia, Greta and Emmenegger, Jacopo},
  title =	{{Categorical Models of Subtyping}},
  booktitle =	{29th International Conference on Types for Proofs and Programs (TYPES 2023)},
  pages =	{3:1--3:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-332-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{303},
  editor =	{Kesner, Delia and Reyes, Eduardo Hermo and van den Berg, Benno},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2023.3},
  URN =		{urn:nbn:de:0030-drops-204811},
  doi =		{10.4230/LIPIcs.TYPES.2023.3},
  annote =	{Keywords: dependent types, subtyping, coercive subtyping, categorical semantics, categories with families, monad}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2023.3

Multi-Graded Featherweight Java

Authors: Riccardo Bianchini, Francesco Dagnino, Paola Giannini, and Elena Zucca

Published in: LIPIcs, Volume 263, 37th European Conference on Object-Oriented Programming (ECOOP 2023)

Abstract

Resource-aware type systems statically approximate not only the expected result type of a program, but also the way external resources are used, e.g., how many times the value of a variable is needed. We extend the type system of Featherweight Java to be resource-aware, parametrically on an arbitrary grade algebra modeling a specific usage of resources. We prove that this type system is sound with respect to a resource-aware version of reduction, that is, a well-typed program has a reduction sequence which does not get stuck due to resource consumption. Moreover, we show that the available grades can be heterogeneous, that is, obtained by combining grades of different kinds, via a minimal collection of homomorphisms from one kind to another. Finally, we show how grade algebras and homomorphisms can be specified as Java classes, so that grade annotations in types can be written in the language itself.

Cite as

Riccardo Bianchini, Francesco Dagnino, Paola Giannini, and Elena Zucca. Multi-Graded Featherweight Java. In 37th European Conference on Object-Oriented Programming (ECOOP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 263, pp. 3:1-3:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{bianchini_et_al:LIPIcs.ECOOP.2023.3,
  author =	{Bianchini, Riccardo and Dagnino, Francesco and Giannini, Paola and Zucca, Elena},
  title =	{{Multi-Graded Featherweight Java}},
  booktitle =	{37th European Conference on Object-Oriented Programming (ECOOP 2023)},
  pages =	{3:1--3:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-281-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{263},
  editor =	{Ali, Karim and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2023.3},
  URN =		{urn:nbn:de:0030-drops-181960},
  doi =		{10.4230/LIPIcs.ECOOP.2023.3},
  annote =	{Keywords: Graded modal types, Java}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2023.25

Quotients and Extensionality in Relational Doctrines

Authors: Francesco Dagnino and Fabio Pasquali

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

Abstract

Taking a quotient roughly means changing the notion of equality on a given object, set or type. In a quantitative setting, equality naturally generalises to a distance, measuring how much elements are similar instead of just stating their equivalence. Hence, quotients can be understood quantitatively as a change of distance. Quotients are crucial in many constructions both in mathematics and computer science and have been widely studied using categorical tools. Among them, Lawvere’s doctrines stand out, providing a fairly simple functorial framework capable to unify many notions of quotient and related constructions. However, abstracting usual predicate logics, they cannot easily deal with quantitative settings. In this paper, we show how, combining doctrines and the calculus of relations, one can unify quantitative and usual quotients in a common picture. More in detail, we introduce relational doctrines as a functorial description of (the core of) the calculus of relations. Then, we define quotients and a universal construction adding them to any relational doctrine, generalising the quotient completion of existential elementary doctrine and also recovering many quantitative examples. This construction deals with an intensional notion of quotient and breaks extensional equality of morphisms. Then, we describe another construction forcing extensionality, showing how it abstracts several notions of separation in metric and topological structures.

Cite as

Francesco Dagnino and Fabio Pasquali. Quotients and Extensionality in Relational Doctrines. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 25:1-25:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{dagnino_et_al:LIPIcs.FSCD.2023.25,
  author =	{Dagnino, Francesco and Pasquali, Fabio},
  title =	{{Quotients and Extensionality in Relational Doctrines}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{25:1--25:23},
  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.2023.25},
  URN =		{urn:nbn:de:0030-drops-180090},
  doi =		{10.4230/LIPIcs.FSCD.2023.25},
  annote =	{Keywords: Quantitative Reasoning, Calculus of Relations, Hyperdoctrines, Metric Spaces}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2022.36

An Infinitary Proof Theory of Linear Logic Ensuring Fair Termination in the Linear π-Calculus

Authors: Luca Ciccone and Luca Padovani

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract

Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative extension of μMALL^∞, the infinitary proof system of the multiplicative additive fragment of linear logic with least and greatest fixed points, such that cut elimination corresponds to fair termination. Proof terms are processes of πLIN, a variant of the linear π-calculus with (co)recursive types into which binary and (some) multiparty sessions can be encoded. As a result we obtain a behavioral type system for πLIN (and indirectly for session calculi through their encoding into πLIN) that ensures fair termination: although well-typed processes may engage in arbitrarily long interactions, they are fairly guaranteed to eventually perform all pending actions.

Cite as

Luca Ciccone and Luca Padovani. An Infinitary Proof Theory of Linear Logic Ensuring Fair Termination in the Linear π-Calculus. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{ciccone_et_al:LIPIcs.CONCUR.2022.36,
  author =	{Ciccone, Luca and Padovani, Luca},
  title =	{{An Infinitary Proof Theory of Linear Logic Ensuring Fair Termination in the Linear \pi-Calculus}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{36:1--36:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir 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.CONCUR.2022.36},
  URN =		{urn:nbn:de:0030-drops-170990},
  doi =		{10.4230/LIPIcs.CONCUR.2022.36},
  annote =	{Keywords: Linear \pi-calculus, Linear Logic, Fixed Points, Fair Termination}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2022.3

A Fibrational Tale of Operational Logical Relations

Authors: Francesco Dagnino and Francesco Gavazzo

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

Abstract

Logical relations built on top of an operational semantics are one of the most successful proof methods in programming language semantics. In recent years, more and more expressive notions of operationally-based logical relations have been designed and applied to specific families of languages. However, a unifying abstract framework for operationally-based logical relations is still missing. We show how fibrations can provide a uniform treatment of operational logical relations, using as reference example a λ-calculus with generic effects endowed with a novel, abstract operational semantics defined on a large class of categories. Moreover, this abstract perspective allows us to give a solid mathematical ground also to differential logical relations - a recently introduced notion of higher-order distance between programs - both pure and effectful, bringing them back to a common picture with traditional ones.

Cite as

Francesco Dagnino and Francesco Gavazzo. A Fibrational Tale of Operational Logical Relations. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{dagnino_et_al:LIPIcs.FSCD.2022.3,
  author =	{Dagnino, Francesco and Gavazzo, Francesco},
  title =	{{A Fibrational Tale of Operational Logical Relations}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{3:1--3:21},
  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.2022.3},
  URN =		{urn:nbn:de:0030-drops-162840},
  doi =		{10.4230/LIPIcs.FSCD.2022.3},
  annote =	{Keywords: logical relations, operational semantics, fibrations, generic effects, program distance}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2022.26

Fair Termination of Multiparty Sessions

Authors: Luca Ciccone, Francesco Dagnino, and Luca Padovani

Published in: LIPIcs, Volume 222, 36th European Conference on Object-Oriented Programming (ECOOP 2022)

Abstract

There exists a broad family of multiparty sessions in which the progress of one session participant is not unconditional, but depends on the choices performed by other participants. These sessions fall outside the scope of currently available session type systems that guarantee progress. In this work we propose the first type system ensuring that well-typed multiparty sessions, including those exhibiting the aforementioned dependencies, fairly terminate. Fair termination is termination under a fairness assumption that disregards those interactions deemed unfair and therefore unrealistic. Fair termination, combined with the usual safety properties ensured within sessions, not only is desirable per se, but it entails progress and enables a compositional form of static analysis such that the well-typed composition of fairly terminating sessions results in a fairly terminating program.

Cite as

Luca Ciccone, Francesco Dagnino, and Luca Padovani. Fair Termination of Multiparty Sessions. In 36th European Conference on Object-Oriented Programming (ECOOP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 222, pp. 26:1-26:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{ciccone_et_al:LIPIcs.ECOOP.2022.26,
  author =	{Ciccone, Luca and Dagnino, Francesco and Padovani, Luca},
  title =	{{Fair Termination of Multiparty Sessions}},
  booktitle =	{36th European Conference on Object-Oriented Programming (ECOOP 2022)},
  pages =	{26:1--26:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-225-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{222},
  editor =	{Ali, Karim and Vitek, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2022.26},
  URN =		{urn:nbn:de:0030-drops-162544},
  doi =		{10.4230/LIPIcs.ECOOP.2022.26},
  annote =	{Keywords: Multiparty sessions, fair termination, fair subtyping, deadlock freedom}
}

Document

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

DOI: 10.4230/LIPIcs.ICALP.2021.125

Inference Systems with Corules for Fair Subtyping and Liveness Properties of Binary Session Types

Authors: Luca Ciccone and Luca Padovani

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

Abstract

Many properties of communication protocols stem from the combination of safety and liveness properties. Characterizing such combined properties by means of a single inference system is difficult because of the fundamentally different techniques (coinduction and induction, respectively) usually involved in defining and proving them. In this paper we show that Generalized Inference Systems allow for simple and insightful characterizations of (at least some of) these combined inductive/coinductive properties for dependent session types. In particular, we illustrate the role of corules in characterizing weak termination (the property of protocols that can always eventually terminate), fair compliance (the property of interactions that can always be extended to reach client satisfaction) and also fair subtyping, a liveness-preserving refinement relation for session types.

Cite as

Luca Ciccone and Luca Padovani. Inference Systems with Corules for Fair Subtyping and Liveness Properties of Binary Session Types. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 125:1-125:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{ciccone_et_al:LIPIcs.ICALP.2021.125,
  author =	{Ciccone, Luca and Padovani, Luca},
  title =	{{Inference Systems with Corules for Fair Subtyping and Liveness Properties of Binary Session Types}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{125:1--125:16},
  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.2021.125},
  URN =		{urn:nbn:de:0030-drops-141941},
  doi =		{10.4230/LIPIcs.ICALP.2021.125},
  annote =	{Keywords: Inference systems, session types, safety, liveness, induction, coinduction}
}

Document

DOI: 10.4230/LIPIcs.ITP.2021.13

Flexible Coinduction in Agda

Authors: Luca Ciccone, Francesco Dagnino, and Elena Zucca

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract

We provide an Agda library for inference systems, also supporting their recent generalization allowing flexible coinduction, that is, interpretations which are neither inductive, nor purely coinductive. A specific inference system can be obtained as an instance by writing a set of meta-rules, in an Agda format which closely resembles the usual one. In this way, the user gets for free the related properties, notably the inductive and coinductive intepretation and the corresponding proof principles. Moreover, a significant modularity is achieved. Indeed, rather than being defined from scratch and with a built-in interpretation, an inference system can also be obtained by composition operators, such as union and restriction to a smaller universe, and its semantics can be modularly chosen as well. In particular, flexible coinduction is obtained by composing in a certain way the interpretations of two inference systems. We illustrate the use of the library by several examples. The most significant one is a big-step semantics for the λ-calculus, where flexible coinduction allows to obtain a special result (∞) for all and only the diverging computations, and the proof of equivalence with small-step semantics is carried out by relying on the proof principles offered by the library.

Cite as

Luca Ciccone, Francesco Dagnino, and Elena Zucca. Flexible Coinduction in Agda. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{ciccone_et_al:LIPIcs.ITP.2021.13,
  author =	{Ciccone, Luca and Dagnino, Francesco and Zucca, Elena},
  title =	{{Flexible Coinduction in Agda}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.13},
  URN =		{urn:nbn:de:0030-drops-139083},
  doi =		{10.4230/LIPIcs.ITP.2021.13},
  annote =	{Keywords: inference systems, induction, coinduction}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2020.1

Sound Regular Corecursion in coFJ

Authors: Davide Ancona, Pietro Barbieri, Francesco Dagnino, and Elena Zucca

Published in: LIPIcs, Volume 166, 34th European Conference on Object-Oriented Programming (ECOOP 2020)

Abstract

The aim of the paper is to provide solid foundations for a programming paradigm natively supporting the creation and manipulation of cyclic data structures. To this end, we describe coFJ, a Java-like calculus where objects can be infinite and methods are equipped with a codefinition (an alternative body). We provide an abstract semantics of the calculus based on the framework of inference systems with corules. In coFJ with this semantics, FJ recursive methods on finite objects can be extended to infinite objects as well, and behave as desired by the programmer, by specifying a codefinition. We also describe an operational semantics which can be directly implemented in a programming language, and prove the soundness of such semantics with respect to the abstract one.

Cite as

Davide Ancona, Pietro Barbieri, Francesco Dagnino, and Elena Zucca. Sound Regular Corecursion in coFJ. In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 1:1-1:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{ancona_et_al:LIPIcs.ECOOP.2020.1,
  author =	{Ancona, Davide and Barbieri, Pietro and Dagnino, Francesco and Zucca, Elena},
  title =	{{Sound Regular Corecursion in coFJ}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{1:1--1:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.1},
  URN =		{urn:nbn:de:0030-drops-131582},
  doi =		{10.4230/LIPIcs.ECOOP.2020.1},
  annote =	{Keywords: Operational semantics, coinduction, programming paradigms, regular terms}
}

17 Search Results for "Dagnino, Francesco"

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Thanks for your feedback!

Could not send message