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A Resource Aware Computational Interpretation for Herbelin's Syntax
[chapter]
2015
Lecture Notes in Computer Science
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We investigate a new computational interpretation for an intuitionistic focused sequent calculus which is compatible with a resource aware semantics. ...
For that, we associate to Herbelin's syntax a type system based on non-idempotent intersection types, together with a set of reduction rules -inspired from the substitution at a distance paradigm-that ...
Conclusion This paper proposes a resource aware computational semantics for Herbelin's syntax. ...
doi:10.1007/978-3-319-25150-9_23
fatcat:a4pnehwarnechmoedtf3bqrhma
Resource control and strong normalisation
[article]
2013
arXiv
pre-print
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We propose a general intersection type system for the resource control cube calculi. Our main contribution is a characterisation of strong normalisation of reductions in this cube. ...
We introduce the resource control cube, a system consisting of eight intuitionistic lambda calculi with either implicit or explicit control of resources and with either natural deduction or sequent calculus ...
Another direction will involve the investigation of the use of intersection types, being a powerful means for building models of lambda calculus [7, 17] , in constructing models for sequent lambda calculi ...
arXiv:1112.3455v3
fatcat:o2vopn7svvdw3b3qfguqs2iyuq
A journey through resource control lambda calculi and explicit substitution using intersection types (an account)
[article]
2013
arXiv
pre-print
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Along this journey, we propose intersection type assignment systems for all three resource control calculi. ...
In this paper we invite the reader to a journey through three lambda calculi with resource control: the lambda calculus, the sequent lambda calculus, and the lambda calculus with explicit substitution. ...
We would also like to thank DragišaŽunić for participating in the earlier stages of the work. ...
arXiv:1306.2283v1
fatcat:5d5jdpwuynfavaquqqbpnwzx4q
Quantitative Types for the Linear Substitution Calculus
[chapter]
2014
Lecture Notes in Computer Science
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Laboratory in Computer Science INFINIS. ...
Acknowledgment This work was partially funded by the international project DeCOPA STIC-AmSud 146/2012 (second author partially supported by a PDJ grant from the Brazilian agency CAPES) and the French-Argentinian ...
Non-Idempotent Intersection Types: The use of non-idempotent types [11] gives rise to resource aware semantics, which is suitable for computational complexity since it allows to extract quantitative ...
doi:10.1007/978-3-662-44602-7_23
fatcat:hug2ox65pbbojbphfzmkuccflq
A Quantitative Understanding of Pattern Matching
2020
Types for Proofs and Programs
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Indeed, we define two resource-aware type systems, named U and E, for a λ-calculus equipped with pairs for both patterns and terms. ...
Indeed, system U provides upper bounds for the length of (head) normalisation sequences plus the size of their corresponding normal forms, while system E, which can be seen as a refinement of system U, ...
Acknowledgements We are grateful to Antonio Bucciarelli and Simona Ronchi Della Rocca for fruitful discussions. ...
doi:10.4230/lipics.types.2019.3
dblp:conf/types/AlvesKV19
fatcat:q7yo2rgejbe7nmcvtetbbk65gm
Non-idempotent types for classical calculi in natural deduction style
2018
Logical Methods in Computer Science
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In the first part of this paper, we define two resource aware typing systems for the {\lambda}{\mu}-calculus based on non-idempotent intersection and union types. ...
The {\lambda}{\mu}s-calculus turns out to be compatible with a natural extensionof the non-idempotent interpretations of {\lambda}{\mu}, i.e., {\lambda}{\mu}s-reduction preserves and decreases typing derivations ...
Acknowledgment: We would like to thank Vincent Guisse, who started a reflexion on quantitative types for the λµ-calculus during his M1 internship in Univ. Paris-Diderot. ...
doi:10.23638/lmcs-16(1:3)2020
fatcat:ghfab5vbhrastlgb37kimi2wfe
Non-idempotent types for classical calculi in natural deduction style
[article]
2020
arXiv
pre-print
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In the first part of this paper, we define two resource aware typing systems for the λμ-calculus based on non-idempotent intersection and union types. ...
The λμs-calculus turns out to be compatible with a natural extensionof the non-idempotent interpretations of λμ, i.e., λμs-reduction preserves and decreases typing derivations in an extended appropriate ...
Acknowledgment: We would like to thank Vincent Guisse, who started a reflexion on quantitative types for the λµ-calculus during his M1 internship in Univ. Paris-Diderot. ...
arXiv:1802.05494v6
fatcat:krkutzpm7rc7fbj2nbuvshyozy
A Quantitative Understanding of Pattern Matching
[article]
2019
arXiv
pre-print
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Indeed, we define two resource aware type systems, named U and E, for a lambda-calculus equipped with pairs for both patterns and terms. ...
exact bounds for each of them. ...
Quantitative types for the linear substitution calculus. In IFIP TCS, LNCS 8705, 2014. 33 D. Kesner and D. Ventura. A resource aware computational interpretation for Herbelin's syntax. ...
arXiv:1912.01914v1
fatcat:ga3evrsoofccvepaqmoxr365ve
Ludics with Repetitions (Exponentials, Interactive Types and Completeness)
2009
2009 24th Annual IEEE Symposium on Logic In Computer Science
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The semantical types which are interpretation of logical formulas enjoy a fundamental property, called internal completeness, which characterizes ludics and sets it apart also from realizability. ...
the same way to a set of tests. ...
{A 1 , A 2 } , B for (ξ, {1, 2}) − .E and D for the interpretation of π respectively. ...
doi:10.1109/lics.2009.46
dblp:conf/lics/BasaldellaF09
fatcat:xscyzyd46veototi43cuwzl3du
Organization Programme Committee Organizing Committee
2015
21st International Conference on Types for Proofs and Programs TYPES 2015
unpublished
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The TYPES meetings are a forum to present new and ongoing work in all aspects of type theory and its applications, especially in formalized and computer assisted reasoning and computer programming. ...
A formal post-proceedings volume is prepared after the conference; papers submitted to that must represent unpublished work and are subjected to a full review process. ...
A ∼ U i B ≡ Σ(∼: A → B → U). Π(x : A).isContr(Σ(y : B).x ∼ y) × Π(y : B).isContr(Σ(x : A).x ∼ y) , we are forced to add Kan fillers for every type, as in [4]. This is ongoing work [1]. ...
fatcat:ej5sa3lm7bc6tdhhjd3w3hwos4
LIPIcs, Volume 175, TYPES 2019, Complete Volume
[article]
2020
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Acknowledgements We would like to thank Chris League for his comments on earlier drafts of the paper, as well as the reviewers for their careful reading and very helpful feedback.
Acknowledgements ...
In a similar vein we want to preserve the structure of more high-level declarations -e.g. HOL-type definitions, inductive types. ...
A resource aware computational interpretation for Herbelin's syntax. In ICTAC, volume 9399 of LNCS, pages 388-403. Springer, 2015. 40 Delia Kesner and Pierre Vial. ...
doi:10.4230/lipics.types.2019
fatcat:v6eui47enralxpnan467cnt2r4
9th International Conference on Types for Proofs and Programs LIPIcs-Leibniz International Proceedings in Informatics
2013
unpublished
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The 19th International Conference on Types for Proofs and Programs (TYPES 2013) was held in Toulouse, France from April 22 to 26, 2013, consisting of the main conference and several satellite events. ...
We are grateful for the generous support by the IAS and the Fund for Math. ...
Danel Ahman thanks Ohad Kammar for discussions. ...
fatcat:4uii2lg7hrdvbosn2ar2ljgnhm