13 Search Results for "Mazza, Damiano"

Document
DOI: 10.4230/LIPIcs.ITP.2025.11
Animating MRBNFs: Truly Modular Binding-Aware Datatypes in Isabelle/HOL

Authors: Jan van Brügge, Andrei Popescu, and Dmitriy Traytel

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Nominal Isabelle provides powerful tools for meta-theoretic reasoning about syntax of logics or programming languages, in which variables are bound. It has been instrumental to major verification successes, such as Gödel’s incompleteness theorems. However, the existing tooling is not compositional. In particular, it does not support nested recursion, linear binding patterns, or infinitely branching syntax. These limitations are fundamental in the way nominal datatypes and functions on them are constructed within Nominal Isabelle. Taking advantage of recent theoretical advancements that overcome these limitations through a modular approach using the concept of map-restricted bounded natural functor (MRBNF), we develop and implement a new definitional package for binding-aware datatypes in Isabelle/HOL, called MrBNF. We describe the journey from the user specification to the end-product types, constants and theorems the tool generates. We validate MrBNF in two formalization case studies that so far were out of reach of nominal approaches: (1) Mazza’s isomorphism between the finitary and the infinitary affine λ-calculus, and (2) the POPLmark 2B challenge, which involves non-free binders for linear pattern matching.
Cite as

Jan van Brügge, Andrei Popescu, and Dmitriy Traytel. Animating MRBNFs: Truly Modular Binding-Aware Datatypes in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{vanbrugge_et_al:LIPIcs.ITP.2025.11,
  author =	{van Br\"{u}gge, Jan and Popescu, Andrei and Traytel, Dmitriy},
  title =	{{Animating MRBNFs: Truly Modular Binding-Aware Datatypes in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.11},
  URN =		{urn:nbn:de:0030-drops-246091},
  doi =		{10.4230/LIPIcs.ITP.2025.11},
  annote =	{Keywords: syntax with bindings, datatypes, inductive predicates, Isabelle/HOL}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.12
Ohana Trees and Taylor Expansion for the λI-Calculus: No variable gets left behind or forgotten!

Authors: Rémy Cerda, Giulio Manzonetto, and Alexis Saurin

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

Abstract
Although the λI-calculus is a natural fragment of the λ-calculus, obtained by forbidding the erasure, its equational theories did not receive much attention. The reason is that all proper denotational models studied in the literature equate all non-normalizable λI-terms, whence the associated theory is not very informative. The goal of this paper is to introduce a previously unknown theory of the λI-calculus, induced by a notion of evaluation trees that we call "Ohana trees". The Ohana tree of a λI-term is an annotated version of its Böhm tree, remembering all free variables that are hidden within its meaningless subtrees, or pushed into infinity along its infinite branches. We develop the associated theories of program approximation: the first approach - more classic - is based on finite trees and continuity, the second adapts Ehrhard and Regnier’s Taylor expansion. We then prove a Commutation Theorem stating that the normal form of the Taylor expansion of a λI-term coincides with the Taylor expansion of its Ohana tree. As a corollary, we obtain that the equality induced by Ohana trees is compatible with abstraction and application. We conclude by discussing the cases of Lévy-Longo and Berarducci trees, and generalizations to the full λ-calculus.
Cite as

Rémy Cerda, Giulio Manzonetto, and Alexis Saurin. Ohana Trees and Taylor Expansion for the λI-Calculus: No variable gets left behind or forgotten!. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{cerda_et_al:LIPIcs.FSCD.2025.12,
  author =	{Cerda, R\'{e}my and Manzonetto, Giulio and Saurin, Alexis},
  title =	{{Ohana Trees and Taylor Expansion for the \lambdaI-Calculus: No variable gets left behind or forgotten!}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{12:1--12:20},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-236277},
  doi =		{10.4230/LIPIcs.FSCD.2025.12},
  annote =	{Keywords: \lambda-calculus, program approximation, Taylor expansion, \lambdaI-calculus, persistent free variables, B\"{o}hm trees, Ohana trees}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.5
The Cost of Skeletal Call-By-Need, Smoothly

Authors: Beniamino Accattoli, Francesco Magliocca, Loïc Peyrot, and Claudio Sacerdoti Coen

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

Abstract
Skeletal call-by-need is an optimization of call-by-need evaluation also known as "fully lazy sharing": when the duplication of a value has to take place, it is first split into "skeleton", which is then duplicated, and "flesh" which is instead kept shared. Here, we provide two cost analyses of skeletal call-by-need. Firstly, we provide a family of terms showing that skeletal call-by-need can be asymptotically exponentially faster than call-by-need in both time and space; it is the first such evidence, to our knowledge. Secondly, we prove that skeletal call-by-need can be implemented efficiently, that is, with bi-linear overhead. This result is obtained by providing a new smooth presentation of ideas by Shivers and Wand for the reconstruction of skeletons, which is then smoothly plugged into the study of an abstract machine following the distillation technique by Accattoli et al.
Cite as

Beniamino Accattoli, Francesco Magliocca, Loïc Peyrot, and Claudio Sacerdoti Coen. The Cost of Skeletal Call-By-Need, Smoothly. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{accattoli_et_al:LIPIcs.FSCD.2025.5,
  author =	{Accattoli, Beniamino and Magliocca, Francesco and Peyrot, Lo\"{i}c and Sacerdoti Coen, Claudio},
  title =	{{The Cost of Skeletal Call-By-Need, Smoothly}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{5:1--5:22},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-236206},
  doi =		{10.4230/LIPIcs.FSCD.2025.5},
  annote =	{Keywords: \lambda-calculus, abstract machines, call-by-need, cost models}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.13
Unifying Boolean and Algebraic Descriptive Complexity

Authors: Baptiste Chanus, Damiano Mazza, and Morgan Rogers

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

Abstract
We introduce ultrarings, which simultaneously generalize commutative rings and Boolean lextensive categories. As such, they allow to blend together standard algebraic notions (from commutative algebra) and logical notions (from categorical logic), providing a unifying descriptive framework in which complexity classes over arbitrary rings (as in the Blum, Schub, Smale model) and usual, Boolean complexity classes may be captured in a uniform way.
Cite as

Baptiste Chanus, Damiano Mazza, and Morgan Rogers. Unifying Boolean and Algebraic Descriptive Complexity. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chanus_et_al:LIPIcs.FSCD.2025.13,
  author =	{Chanus, Baptiste and Mazza, Damiano and Rogers, Morgan},
  title =	{{Unifying Boolean and Algebraic Descriptive Complexity}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{13:1--13:22},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-236286},
  doi =		{10.4230/LIPIcs.FSCD.2025.13},
  annote =	{Keywords: Descriptive complexity theory, Categorical logic, Blum-Shub-Smale complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.68
Slightly Non-Linear Higher-Order Tree Transducers

Authors: Lê Thành Dũng (Tito) Nguyễn and Gabriele Vanoni

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We investigate the tree-to-tree functions computed by "affine λ-transducers": tree automata whose memory consists of an affine λ-term instead of a finite state. They can be seen as variations on Gallot, Lemay and Salvati’s Linear High-Order Deterministic Tree Transducers. When the memory is almost purely affine (à la Kanazawa), we show that these machines can be translated to tree-walking transducers (and with a purely affine memory, we get a reversible tree-walking transducer). This leads to a proof of an inexpressivity conjecture of Nguyễn and Pradic on "implicit automata" in an affine λ-calculus. We also prove that a more powerful variant, extended with preprocessing by an MSO relabeling and allowing a limited amount of non-linearity, is equivalent in expressive power to Engelfriet, Hoogeboom and Samwel’s invisible pebble tree transducers. The key technical tool in our proofs is the Interaction Abstract Machine (IAM), an operational avatar of Girard’s geometry of interaction, a semantics of linear logic. We work with ad-hoc specializations to λ-terms of low exponential depth of a tree-generating version of the IAM.
Cite as

Lê Thành Dũng (Tito) Nguyễn and Gabriele Vanoni. Slightly Non-Linear Higher-Order Tree Transducers. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 68:1-68:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{nguyen_et_al:LIPIcs.STACS.2025.68,
  author =	{Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng (Tito) and Vanoni, Gabriele},
  title =	{{Slightly Non-Linear Higher-Order Tree Transducers}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{68:1--68:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.68},
  URN =		{urn:nbn:de:0030-drops-228934},
  doi =		{10.4230/LIPIcs.STACS.2025.68},
  annote =	{Keywords: Almost affine lambda-calculus, geometry of interaction, reversibility, tree transducers, tree-walking automata}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.23
How to Play the Accordion: Uniformity and the (Non-)Conservativity of the Linear Approximation of the λ-Calculus

Authors: Rémy Cerda and Lionel Vaux Auclair

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Twenty years after its introduction by Ehrhard and Regnier, differentiation in λ-calculus and in linear logic is now a celebrated tool. In particular, it allows to write the Taylor formula in various λ-calculi, hence providing a theory of linear approximations for these calculi. In the standard λ-calculus, this linear approximation is expressed by results stating that the (possibly) infinitary β-reduction of λ-terms is simulated by the reduction of their Taylor expansion: in terms of rewriting systems, the resource reduction (operating on Taylor approximants) is an extension of the β-reduction. In this paper, we address the converse property, conservativity: are there reductions of the Taylor approximants that do not arise from an actual β-reduction of the approximated term? We show that if we restrict the setting to finite terms and β-reduction sequences, then the linear approximation is conservative. However, as soon as one allows infinitary reduction sequences this property is broken. We design a counter-example, the Accordion. Then we show how restricting the reduction of the Taylor approximants allows to build a conservative extension of the β-reduction preserving good simulation properties. This restriction relies on uniformity, a property that was already at the core of Ehrhard and Regnier’s pioneering work.
Cite as

Rémy Cerda and Lionel Vaux Auclair. How to Play the Accordion: Uniformity and the (Non-)Conservativity of the Linear Approximation of the λ-Calculus. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{cerda_et_al:LIPIcs.STACS.2025.23,
  author =	{Cerda, R\'{e}my and Vaux Auclair, Lionel},
  title =	{{How to Play the Accordion: Uniformity and the (Non-)Conservativity of the Linear Approximation of the \lambda-Calculus}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{23:1--23:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.23},
  URN =		{urn:nbn:de:0030-drops-228480},
  doi =		{10.4230/LIPIcs.STACS.2025.23},
  annote =	{Keywords: program approximation, quantitative semantics, lambda-calculus, linear approximation, Taylor expansion, conservativity}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.32
A Mixed Linear and Graded Logic: Proofs, Terms, and Models

Authors: Victoria Vollmer, Danielle Marshall, Harley Eades III, and Dominic Orchard

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

Abstract
Graded modal logics generalise standard modal logics via families of modalities indexed by an algebraic structure whose operations mediate between the different modalities. The graded "of-course" modality !_r captures how many times a proposition is used and has an analogous interpretation to the of-course modality from linear logic; the of-course modality from linear logic can be modelled by a linear exponential comonad and graded of-course can be modelled by a graded linear exponential comonad. Benton showed in his seminal paper on Linear/Non-Linear logic that the of-course modality can be split into two modalities connecting intuitionistic logic with linear logic, forming a symmetric monoidal adjunction. Later, Fujii et al. demonstrated that every graded comonad can be decomposed into an adjunction and a "strict action". We give a similar result to Benton, leveraging Fujii et al.’s decomposition, showing that graded modalities can be split into two modalities connecting a graded logic with a graded linear logic. We propose a sequent calculus, its proof theory and categorical model, and a natural deduction system which we show is isomorphic to the sequent calculus system. Interestingly, our system can also be understood as Linear/Non-Linear logic composed with an action that adds the grading, further illuminating the shared principles between linear logic and a class of graded modal logics.
Cite as

Victoria Vollmer, Danielle Marshall, Harley Eades III, and Dominic Orchard. A Mixed Linear and Graded Logic: Proofs, Terms, and Models. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 32:1-32:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{vollmer_et_al:LIPIcs.CSL.2025.32,
  author =	{Vollmer, Victoria and Marshall, Danielle and Eades III, Harley and Orchard, Dominic},
  title =	{{A Mixed Linear and Graded Logic: Proofs, Terms, and Models}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{32:1--32:21},
  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.2025.32},
  URN =		{urn:nbn:de:0030-drops-227892},
  doi =		{10.4230/LIPIcs.CSL.2025.32},
  annote =	{Keywords: linear logic, graded modal logic, adjoint decomposition}
}
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.
Cite as

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)

Copy BibTex To Clipboard

@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.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.
Cite as

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)

Copy BibTex To Clipboard

@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.CSL.2024.8
Infinitary Cut-Elimination via Finite Approximations

Authors: Matteo Acclavio, Gianluca Curzi, and Giulio Guerrieri

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

Abstract
We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a global level by adapting a standard progressing criterion. We present an infinitary version of cut-elimination based on finite approximations, and we prove that, in presence of the progressing criterion, it returns well-defined non-wellfounded proofs at its limit. Furthermore, we show that cut-elimination preserves the progressing criterion and various regularity conditions internalizing degrees of proof-theoretical uniformity. Finally, we provide a denotational semantics for our systems based on the relational model.
Cite as

Matteo Acclavio, Gianluca Curzi, and Giulio Guerrieri. Infinitary Cut-Elimination via Finite Approximations. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{acclavio_et_al:LIPIcs.CSL.2024.8,
  author =	{Acclavio, Matteo and Curzi, Gianluca and Guerrieri, Giulio},
  title =	{{Infinitary Cut-Elimination via Finite Approximations}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{8:1--8:19},
  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.2024.8},
  URN =		{urn:nbn:de:0030-drops-196510},
  doi =		{10.4230/LIPIcs.CSL.2024.8},
  annote =	{Keywords: cut-elimination, non-wellfounded proofs, parsimonious logic, linear logic, proof theory, approximation, sequent calculus, non-uniform proofs}
}
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
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2019.123
From Normal Functors to Logarithmic Space Queries (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors: Lê Thành Dũng Nguyễn and Cécilia Pradic

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We introduce a new approach to implicit complexity in linear logic, inspired by functional database query languages and using recent developments in effective denotational semantics of polymorphism. We give the first sub-polynomial upper bound in a type system with impredicative polymorphism; adding restrictions on quantifiers yields a characterization of logarithmic space, for which extensional completeness is established via descriptive complexity.
Cite as

Lê Thành Dũng Nguyễn and Cécilia Pradic. From Normal Functors to Logarithmic Space Queries (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 123:1-123:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{nguyen_et_al:LIPIcs.ICALP.2019.123,
  author =	{Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng and Pradic, C\'{e}cilia},
  title =	{{From Normal Functors to Logarithmic Space Queries}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{123:1--123:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.123},
  URN =		{urn:nbn:de:0030-drops-106994},
  doi =		{10.4230/LIPIcs.ICALP.2019.123},
  annote =	{Keywords: coherence spaces, elementary linear logic, semantic evaluation}
}
Document
DOI: 10.4230/LIPIcs.CSL.2015.24
Simple Parsimonious Types and Logarithmic Space

Authors: Damiano Mazza

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract
We present a functional characterization of deterministic logspace-computable predicates based on a variant (although not a subsystem) of propositional linear logic, which we call parsimonious logic. The resulting calculus is simply-typed and contains no primitive besides those provided by the underlying logical system, which makes it one of the simplest higher-order languages capturing logspace currently known. Completeness of the calculus uses the descriptive complexity characterization of logspace (we encode first-order logic with deterministic closure), whereas soundness is established by executing terms on a token machine (using the geometry of interaction).
Cite as

Damiano Mazza. Simple Parsimonious Types and Logarithmic Space. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 24-40, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{mazza:LIPIcs.CSL.2015.24,
  author =	{Mazza, Damiano},
  title =	{{Simple Parsimonious Types and Logarithmic Space}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{24--40},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.24},
  URN =		{urn:nbn:de:0030-drops-54053},
  doi =		{10.4230/LIPIcs.CSL.2015.24},
  annote =	{Keywords: implicit computational complexity, linear logic, geometry of interaction}
}
  • Refine by Type
  • 13 Document/PDF
  • 7 Document/HTML

  • Refine by Publication Year
  • 8 2025
  • 2 2024
  • 1 2020
  • 1 2019
  • 1 2015

  • Refine by Author
  • 3 Mazza, Damiano
  • 2 Cerda, Rémy
  • 2 Nguyễn, Lê Thành Dũng
  • 2 Pradic, Cécilia
  • 1 Accattoli, Beniamino
  • Show More...

  • Refine by Series/Journal
  • 13 LIPIcs

  • Refine by Classification
  • 6 Theory of computation → Linear logic
  • 5 Theory of computation → Lambda calculus
  • 2 Theory of computation → Complexity theory and logic
  • 2 Theory of computation → Denotational semantics
  • 2 Theory of computation → Finite Model Theory
  • Show More...

  • Refine by Keyword
  • 3 Böhm trees
  • 3 Taylor expansion
  • 3 linear logic
  • 2 geometry of interaction
  • 2 program approximation
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact