7 Search Results for "Honsell, Furio"


Document
Principal Types as Lambda Nets

Authors: Pietro Di Gianantonio and Marina Lenisa

Published in: LIPIcs, Volume 239, 27th International Conference on Types for Proofs and Programs (TYPES 2021)


Abstract
We show that there are connections between principal type schemata, cut-free λ-nets, and normal forms of the λ-calculus, and hence there are correspondences between the normalisation algorithms of the above structures, i.e. unification of principal types, cut-elimination of λ-nets, and normalisation of λ-terms. Once the above correspondences have been established, properties of the typing system, such as typability, subject reduction, and inhabitation, can be derived from properties of λ-nets, and vice-versa. We illustrate the above pattern on a specific type assignment system, we study principal types for this system, and we show that they correspond to λ-nets with a non-standard notion of cut-elimination. Properties of the type system are then derived from results on λ-nets.

Cite as

Pietro Di Gianantonio and Marina Lenisa. Principal Types as Lambda Nets. In 27th International Conference on Types for Proofs and Programs (TYPES 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 239, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{digianantonio_et_al:LIPIcs.TYPES.2021.5,
  author =	{Di Gianantonio, Pietro and Lenisa, Marina},
  title =	{{Principal Types as Lambda Nets}},
  booktitle =	{27th International Conference on Types for Proofs and Programs (TYPES 2021)},
  pages =	{5:1--5:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-254-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{239},
  editor =	{Basold, Henning and Cockx, Jesper and Ghilezan, Silvia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2021.5},
  URN =		{urn:nbn:de:0030-drops-167744},
  doi =		{10.4230/LIPIcs.TYPES.2021.5},
  annote =	{Keywords: Lambda calculus, Principal types, Linear logic, Lambda nets, Normalization, Cut elimination}
}
Document
On Quantitative Algebraic Higher-Order Theories

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

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


Abstract
We explore the possibility of extending Mardare et al.’s quantitative algebras to the structures which naturally emerge from Combinatory Logic and the λ-calculus. First of all, we show that the framework is indeed applicable to those structures, and give soundness and completeness results. Then, we prove some negative results clearly delineating to which extent categories of metric spaces can be models of such theories. We conclude by giving several examples of non-trivial higher-order quantitative algebras.

Cite as

Ugo Dal Lago, Furio Honsell, Marina Lenisa, and Paolo Pistone. On Quantitative Algebraic Higher-Order Theories. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{dallago_et_al:LIPIcs.FSCD.2022.4,
  author =	{Dal Lago, Ugo and Honsell, Furio and Lenisa, Marina and Pistone, Paolo},
  title =	{{On Quantitative Algebraic Higher-Order Theories}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.4},
  URN =		{urn:nbn:de:0030-drops-162851},
  doi =		{10.4230/LIPIcs.FSCD.2022.4},
  annote =	{Keywords: Quantitative Algebras, Lambda Calculus, Combinatory Logic, Metric Spaces}
}
Document
Λ-Symsym: An Interactive Tool for Playing with Involutions and Types

Authors: Furio Honsell, Marina Lenisa, and Ivan Scagnetto

Published in: LIPIcs, Volume 188, 26th International Conference on Types for Proofs and Programs (TYPES 2020)


Abstract
We present the web portal Λ-symsym, available at http://158.110.146.197:31780/automata/, for experimenting with game semantics of λ^!-calculus, and its normalizing elementary sub-calculus, the λ^{EAL}-calculus. The λ^!-calculus is a generalization of the λ-calculus obtained by introducing a modal operator !, giving rise to a pattern β-reduction. Its sub-calculus corresponds to an applicatively closed class of terms normalizing in an elementary number of steps, in which all elementary functions can be encoded. The game model which we consider is the Geometry of Interaction model I introduced by Abramsky to study reversible computations, consisting of partial involutions over a very simple language of moves. Given a λ^!- or a λ^{EAL}-term, M, Λ-symsym provides: - an abstraction algorithm A^!, for compiling M into a term, A^!(M), of the linear combinatory logic CL^{!}, or the normalizing combinatory logic CL^{EAL}; - an interpretation algorithm [[ ]]^I yielding a specification of the partial involution [[A^!(M)]]^I in the model I; - an algorithm, I2T, for synthesizing from [[A^!(M)]]^I a type, I2T([[A^!(M)]]^I), in a multimodal, intersection type assignment discipline, ⊢_!. - an algorithm, T2I, for synthesizing a specification of a partial involution from a type in ⊢_!, which is an inverse to the former. We conjecture that ⊢_! M : I2T([[A^!(M)]]^I). Λ-symsym permits to investigate experimentally the fine structure of I, and hence the game semantics of the λ^!- and λ^{EAL}-calculi. For instance, we can easily verify that the model I is a λ^!-algebra in the case of strictly linear λ-terms, by checking all the necessary equations, and find counterexamples in the general case. We make this tool available for readers interested to play with games (-semantics). The paper builds on earlier work by the authors, the type system being an improvement.

Cite as

Furio Honsell, Marina Lenisa, and Ivan Scagnetto. Λ-Symsym: An Interactive Tool for Playing with Involutions and Types. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{honsell_et_al:LIPIcs.TYPES.2020.7,
  author =	{Honsell, Furio and Lenisa, Marina and Scagnetto, Ivan},
  title =	{{\Lambda-Symsym: An Interactive Tool for Playing with Involutions and Types}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-182-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{188},
  editor =	{de'Liguoro, Ugo and Berardi, Stefano and Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2020.7},
  URN =		{urn:nbn:de:0030-drops-138867},
  doi =		{10.4230/LIPIcs.TYPES.2020.7},
  annote =	{Keywords: game semantics, lambda calculus, involutions, linear logic, implicit computational complexity}
}
Document
System Description
A Type Checker for a Logical Framework with Union and Intersection Types (System Description)

Authors: Claude Stolze and Luigi Liquori

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


Abstract
We present the syntax, semantics, typing, subtyping, unification, refinement, and REPL of BULL, a prototype theorem prover based on the Δ-Framework, i.e. a fully-typed Logical Framework à la Edinburgh LF decorated with union and intersection types, as described in previous papers by the authors. BULL also implements a subtyping algorithm for the Type Theory Ξ of Barbanera-Dezani-de'Liguoro. BULL has a command-line interface where the user can declare axioms, terms, and perform computations and some basic terminal-style features like error pretty-printing, subexpressions highlighting, and file loading. Moreover, it can typecheck a proof or normalize it. These terms can be incomplete, therefore the typechecking algorithm uses unification to try to construct the missing subterms. BULL uses the syntax of Berardi’s Pure Type Systems to improve the compactness and the modularity of the kernel. Abstract and concrete syntax are mostly aligned and similar to the concrete syntax of Coq. BULL uses a higher-order unification algorithm for terms, while typechecking and partial type inference are done by a bidirectional refinement algorithm, similar to the one found in Matita and Beluga. The refinement can be split into two parts: the essence refinement and the typing refinement. Binders are implemented using commonly-used de Bruijn indices. We have defined a concrete language syntax that will allow user to write Δ-terms. We have defined the reduction rules and an evaluator. We have implemented from scratch a refiner which does partial typechecking and type reconstruction. We have experimented BULL with classical examples of the intersection and union literature, such as the ones formalized by Pfenning with his Refinement Types in LF and by Pierce. We hope that this research vein could be useful to experiment, in a proof theoretical setting, forms of polymorphism alternatives to Girard’s parametric one.

Cite as

Claude Stolze and Luigi Liquori. A Type Checker for a Logical Framework with Union and Intersection Types (System Description). In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 37:1-37:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{stolze_et_al:LIPIcs.FSCD.2020.37,
  author =	{Stolze, Claude and Liquori, Luigi},
  title =	{{A Type Checker for a Logical Framework with Union and Intersection Types}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{37:1--37:24},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.37},
  URN =		{urn:nbn:de:0030-drops-123597},
  doi =		{10.4230/LIPIcs.FSCD.2020.37},
  annote =	{Keywords: Intersection types, Union types, Dependent types, Subtyping, Type checker, Refiner, \Delta-Framework}
}
Document
lambda!-calculus, Intersection Types, and Involutions

Authors: Alberto Ciaffaglione, Pietro Di Gianantonio, Furio Honsell, Marina Lenisa, and Ivan Scagnetto

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


Abstract
Abramsky’s affine combinatory algebras are models of affine combinatory logic, which refines standard combinatory logic in the direction of Linear Logic. Abramsky introduced various universal models of computation based on affine combinatory algebras, consisting of partial involutions over a suitable formal language {of moves}, in order to discuss reversible computation in a Geometry of Interaction setting. We investigate partial involutions from the point of view of the model theory of lambda!-calculus. The latter is a refinement of the standard lambda-calculus, corresponding to affine combinatory logic. We introduce intersection type systems for the lambda!-calculus, by extending standard intersection types with a !_u-operator. These induce affine combinatory algebras, and, via suitable quotients, models of the lambda!-calculus. In particular, we introduce an intersection type system for assigning principal types to lambda!-terms, and we state a correspondence between the partial involution interpreting a combinator and the principal type of the corresponding lambda!-term. This analogy allows for explaining as unification between principal types the somewhat awkward linear application of involutions arising from Geometry of Interaction.

Cite as

Alberto Ciaffaglione, Pietro Di Gianantonio, Furio Honsell, Marina Lenisa, and Ivan Scagnetto. lambda!-calculus, Intersection Types, and Involutions. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{ciaffaglione_et_al:LIPIcs.FSCD.2019.15,
  author =	{Ciaffaglione, Alberto and Di Gianantonio, Pietro and Honsell, Furio and Lenisa, Marina and Scagnetto, Ivan},
  title =	{{lambda!-calculus, Intersection Types, and Involutions}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{15:1--15:16},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.15},
  URN =		{urn:nbn:de:0030-drops-105228},
  doi =		{10.4230/LIPIcs.FSCD.2019.15},
  annote =	{Keywords: Affine Combinatory Algebra, Affine Lambda-calculus, Intersection Types, Geometry of Interaction}
}
Document
The Delta-calculus: Syntax and Types

Authors: Luigi Liquori and Claude Stolze

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


Abstract
We present the Delta-calculus, an explicitly typed lambda-calculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T, e.g. the Coppo-Dezani, the Coppo-Dezani-Sallé, the Coppo-Dezani-Venneri and the Barendregt-Coppo-Dezani ones, producing a family of Delta-calculi with related intersection typed systems. We prove the main properties like Church-Rosser, unicity of type, subject reduction, strong normalization, decidability of type checking and type reconstruction. We state the relationship between the intersection type assignment systems à la Curry and the corresponding intersection typed systems à la Church by means of an essence function translating an explicitly typed Delta-term into a pure lambda-term one. We finally translate a Delta-term with type coercions into an equivalent one without them; the translation is proved to be coherent because its essence is the identity. The generic Delta-calculus can be parametrized to take into account other intersection type theories as the ones in the Barendregt et al. book.

Cite as

Luigi Liquori and Claude Stolze. The Delta-calculus: Syntax and Types. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{liquori_et_al:LIPIcs.FSCD.2019.28,
  author =	{Liquori, Luigi and Stolze, Claude},
  title =	{{The Delta-calculus: Syntax and Types}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{28:1--28:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.28},
  URN =		{urn:nbn:de:0030-drops-105354},
  doi =		{10.4230/LIPIcs.FSCD.2019.28},
  annote =	{Keywords: intersection types, lambda calculus \`{a} la Church and \`{a} la Curry, proof-functional logics}
}
Document
The Delta-Framework

Authors: Furio Honsell, Luigi Liquori, Claude Stolze, and Ivan Scagnetto

Published in: LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)


Abstract
We introduce the Delta-framework, LF_Delta, a dependent type theory based on the Edinburgh Logical Framework LF, extended with the strong proof-functional connectives, i.e. strong intersection, minimal relevant implication and strong union. Strong proof-functional connectives take into account the shape of logical proofs, thus reflecting polymorphic features of proofs in formulae. This is in contrast to classical or intuitionistic connectives where the meaning of a compound formula depends only on the truth value or the provability of its subformulae. Our framework encompasses a wide range of type disciplines. Moreover, since relevant implication permits to express subtyping, LF_Delta subsumes also Pfenning's refinement types. We discuss the design decisions which have led us to the formulation of LF_Delta, study its metatheory, and provide various examples of applications. Our strong proof-functional type theory can be plugged in existing common proof assistants.

Cite as

Furio Honsell, Luigi Liquori, Claude Stolze, and Ivan Scagnetto. The Delta-Framework. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 37:1-37:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{honsell_et_al:LIPIcs.FSTTCS.2018.37,
  author =	{Honsell, Furio and Liquori, Luigi and Stolze, Claude and Scagnetto, Ivan},
  title =	{{The Delta-Framework}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{37:1--37:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Ganguly, Sumit and Pandya, Paritosh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.37},
  URN =		{urn:nbn:de:0030-drops-99367},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.37},
  annote =	{Keywords: Logic of programs, type theory, lambda-calculus}
}
  • Refine by Author
  • 4 Honsell, Furio
  • 4 Lenisa, Marina
  • 3 Liquori, Luigi
  • 3 Scagnetto, Ivan
  • 3 Stolze, Claude
  • Show More...

  • Refine by Classification
  • 3 Theory of computation → Lambda calculus
  • 3 Theory of computation → Linear logic
  • 2 Theory of computation → Program semantics
  • 2 Theory of computation → Type theory
  • 1 Theory of computation → Logic and verification
  • Show More...

  • Refine by Keyword
  • 1 Affine Combinatory Algebra
  • 1 Affine Lambda-calculus
  • 1 Combinatory Logic
  • 1 Cut elimination
  • 1 Dependent types
  • Show More...

  • Refine by Type
  • 7 document

  • Refine by Publication Year
  • 2 2019
  • 2 2022
  • 1 2018
  • 1 2020
  • 1 2021

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail