8 Search Results for "Fiore, Marcelo"

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)

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@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.2025.23
∞-Categorical Models of Linear Logic

Authors: Eliès Harington and Samuel Mimram

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

Abstract
The notion of categorical model of linear logic is now well studied and established around the notion of linear-non-linear adjunction, which encompasses the earlier notions of Seely categories, Lafont categories and linear categories. These categorical structures have counterparts in the realm of ∞-categories, which can thus be thought of as weak forms of models of linear logic. The goal of this article is to formally introduce them and study their relationships. We show that ∞-linear-non-linear adjunctions still play the role of a unifying notion of model in this setting. Moreover, we provide a sufficient condition for a symmetric monoidal ∞-category to be Lafont. Finally, we illustrate our constructions by providing models: we construct linear-non-linear adjunctions that generalize well-known models in relations (and variants based on profunctors or spans), domains and vector spaces. In particular, we introduce a model based on spectra, a homotopical variant of abelian groups.
Cite as

Eliès Harington and Samuel Mimram. ∞-Categorical Models of Linear Logic. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{harington_et_al:LIPIcs.FSCD.2025.23,
  author =	{Harington, Eli\`{e}s and Mimram, Samuel},
  title =	{{∞-Categorical Models of Linear Logic}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{23:1--23:20},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-236381},
  doi =		{10.4230/LIPIcs.FSCD.2025.23},
  annote =	{Keywords: linear logic, linear-non-linear adjunction, ∞-category, spectrum}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2024.5
Implementing a Type Theory with Observational Equality, Using Normalisation by Evaluation

Authors: Matthew Sirman, Meven Lennon-Bertrand, and Neel Krishnaswami

Published in: LIPIcs, Volume 336, 30th International Conference on Types for Proofs and Programs (TYPES 2024)

Abstract
We report on an experimental implementation in Haskell of a dependent type theory featuring an observational equality type, based on Pujet et al.’s CCobs. We use normalisation by evaluation to produce an efficient normalisation function, which is used to implement a bidirectional type checker. To allow for greater expressivity, we extend the core CCobs calculus with quotient types and inductive types. To make the system usable, we explore various proof-assistant features, notably a rudimentary version of a "hole" system similar to Agda’s. While rather crude, this experience should inform other, more substantial implementation efforts of observational equality.
Cite as

Matthew Sirman, Meven Lennon-Bertrand, and Neel Krishnaswami. Implementing a Type Theory with Observational Equality, Using Normalisation by Evaluation. In 30th International Conference on Types for Proofs and Programs (TYPES 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 336, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sirman_et_al:LIPIcs.TYPES.2024.5,
  author =	{Sirman, Matthew and Lennon-Bertrand, Meven and Krishnaswami, Neel},
  title =	{{Implementing a Type Theory with Observational Equality, Using Normalisation by Evaluation}},
  booktitle =	{30th International Conference on Types for Proofs and Programs (TYPES 2024)},
  pages =	{5:1--5:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-376-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{336},
  editor =	{M{\o}gelberg, Rasmus Ejlers 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.2024.5},
  URN =		{urn:nbn:de:0030-drops-233673},
  doi =		{10.4230/LIPIcs.TYPES.2024.5},
  annote =	{Keywords: Dependent type theory, Bidirectional typing, Observational equality, Normalisation by evaluation}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.5
Sheaf Semantics of Termination-Insensitive Noninterference

Authors: Jonathan Sterling and Robert Harper

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

Abstract
We propose a new sheaf semantics for secure information flow over a space of abstract behaviors, based on synthetic domain theory: security classes are open/closed partitions, types are sheaves, and redaction of sensitive information corresponds to restricting a sheaf to a closed subspace. Our security-aware computational model satisfies termination-insensitive noninterference automatically, and therefore constitutes an intrinsic alternative to state of the art extrinsic/relational models of noninterference. Our semantics is the latest application of Sterling and Harper’s recent re-interpretation of phase distinctions and noninterference in programming languages in terms of Artin gluing and topos-theoretic open/closed modalities. Prior applications include parametricity for ML modules, the proof of normalization for cubical type theory by Sterling and Angiuli, and the cost-aware logical framework of Niu et al. In this paper we employ the phase distinction perspective twice: first to reconstruct the syntax and semantics of secure information flow as a lattice of phase distinctions between "higher" and "lower" security, and second to verify the computational adequacy of our sheaf semantics with respect to a version of Abadi et al.’s dependency core calculus to which we have added a construct for declassifying termination channels.
Cite as

Jonathan Sterling and Robert Harper. Sheaf Semantics of Termination-Insensitive Noninterference. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{sterling_et_al:LIPIcs.FSCD.2022.5,
  author =	{Sterling, Jonathan and Harper, Robert},
  title =	{{Sheaf Semantics of Termination-Insensitive Noninterference}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{5:1--5:19},
  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.2022.5},
  URN =		{urn:nbn:de:0030-drops-162869},
  doi =		{10.4230/LIPIcs.FSCD.2022.5},
  annote =	{Keywords: information flow, noninterference, denotational semantics, phase distinction, Artin gluing, modal type theory, topos theory, synthetic domain theory, synthetic Tait computability}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.31
A Combinatorial Approach to Higher-Order Structure for Polynomial Functors

Authors: Marcelo Fiore, Zeinab Galal, and Hugo Paquet

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

Abstract
Polynomial functors are categorical structures used in a variety of applications across theoretical computer science; for instance, in database theory, denotational semantics, functional programming, and type theory. A well-known problem is that the bicategory of finitary polynomial functors between categories of indexed sets is not cartesian closed, despite its success and influence on denotational models and linear logic. This paper introduces a formal bridge between the model of finitary polynomial functors and the combinatorial theory of generalised species of structures. Our approach consists in viewing finitary polynomial functors as free analytic functors, which correspond to free generalised species. In order to systematically consider finitary polynomial functors from this combinatorial perspective, we study a model of groupoids with additional logical structure; this is used to constrain the generalised species between them. The result is a new cartesian closed bicategory that embeds finitary polynomial functors.
Cite as

Marcelo Fiore, Zeinab Galal, and Hugo Paquet. A Combinatorial Approach to Higher-Order Structure for Polynomial Functors. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fiore_et_al:LIPIcs.FSCD.2022.31,
  author =	{Fiore, Marcelo and Galal, Zeinab and Paquet, Hugo},
  title =	{{A Combinatorial Approach to Higher-Order Structure for Polynomial Functors}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{31:1--31:19},
  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.2022.31},
  URN =		{urn:nbn:de:0030-drops-163129},
  doi =		{10.4230/LIPIcs.FSCD.2022.31},
  annote =	{Keywords: Bicategorical models, denotational semantics, stable domain theory, linear logic, polynomial functors, species of structures, groupoids}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2020.16
A Profunctorial Scott Semantics

Authors: Zeinab Galal

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

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

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

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@InProceedings{galal:LIPIcs.FSCD.2020.16,
  author =	{Galal, Zeinab},
  title =	{{A Profunctorial Scott Semantics}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.16},
  URN =		{urn:nbn:de:0030-drops-123387},
  doi =		{10.4230/LIPIcs.FSCD.2020.16},
  annote =	{Keywords: Linear Logic, Scott Semantics, Profunctors}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2019.31
Cubical Syntax for Reflection-Free Extensional Equality

Authors: Jonathan Sterling, Carlo Angiuli, and Daniel Gratzer

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

Abstract
We contribute XTT, a cubical reconstruction of Observational Type Theory [Altenkirch et al., 2007] which extends Martin-Löf’s intensional type theory with a dependent equality type that enjoys function extensionality and a judgmental version of the unicity of identity proofs principle (UIP): any two elements of the same equality type are judgmentally equal. Moreover, we conjecture that the typing relation can be decided in a practical way. In this paper, we establish an algebraic canonicity theorem using a novel extension of the logical families or categorical gluing argument inspired by Coquand and Shulman [Coquand, 2018; Shulman, 2015]: every closed element of boolean type is derivably equal to either true or false.
Cite as

Jonathan Sterling, Carlo Angiuli, and Daniel Gratzer. Cubical Syntax for Reflection-Free Extensional Equality. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 31:1-31:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{sterling_et_al:LIPIcs.FSCD.2019.31,
  author =	{Sterling, Jonathan and Angiuli, Carlo and Gratzer, Daniel},
  title =	{{Cubical Syntax for Reflection-Free Extensional Equality}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{31:1--31:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-107-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{131},
  editor =	{Geuvers, Herman},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.31},
  URN =		{urn:nbn:de:0030-drops-105387},
  doi =		{10.4230/LIPIcs.FSCD.2019.31},
  annote =	{Keywords: Dependent type theory, extensional equality, cubical type theory, categorical gluing, canonicity}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2017.16
List Objects with Algebraic Structure

Authors: Marcelo Fiore and Philip Saville

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

Abstract
We introduce and study the notion of list object with algebraic structure. The first key aspect of our development is that the notion of list object is considered in the context of monoidal structure; the second key aspect is that we further equip list objects with algebraic structure in this setting. Within our framework, we observe that list objects give rise to free monoids and moreover show that this remains so in the presence of algebraic structure. In addition, we provide a basic theory explicitly describing as an inductively defined object such free monoids with suitably compatible algebraic structure in common practical situations. This theory is accompanied by the study of two technical themes that, besides being of interest in their own right, are important for establishing applications. These themes are: parametrised initiality, central to the universal property defining list objects; and approaches to algebraic structure, in particular in the context of monoidal theories. The latter leads naturally to a notion of nsr (or near semiring) category of independent interest. With the theoretical development in place, we touch upon a variety of applications, considering Natural Numbers Objects in domain theory, giving a universal property for the monadic list transformer, providing free instances of algebraic extensions of the Haskell Monad type class, elucidating the algebraic character of the construction of opetopes in higher-dimensional algebra, and considering free models of second-order algebraic theories.
Cite as

Marcelo Fiore and Philip Saville. List Objects with Algebraic Structure. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{fiore_et_al:LIPIcs.FSCD.2017.16,
  author =	{Fiore, Marcelo and Saville, Philip},
  title =	{{List Objects with Algebraic Structure}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{16:1--16:18},
  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.2017.16},
  URN =		{urn:nbn:de:0030-drops-77262},
  doi =		{10.4230/LIPIcs.FSCD.2017.16},
  annote =	{Keywords: list object, free monoid, strong monad, (cartesian, linear, and second-order) algebraic theory, near semiring, Haskell Monad type class, opetope}
}
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