A Theory of Explicit Substitutions with Safe and Full Composition

Delia Kesner

doi:10.2168/LMCS-5(3:1)2009

Delia Kesner - A Theory of Explicit Substitutions with Safe and Full Composition

lmcs:816 - Logical Methods in Computer Science, July 15, 2009, Volume 5, Issue 3 - https://doi.org/10.2168/LMCS-5(3:1)2009

A Theory of Explicit Substitutions with Safe and Full CompositionArticle

Authors: Delia Kesner

Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the first part of this paper. Then, very simple technology in named variable-style notation is used to establish a theory of explicit substitutions for the lambda-calculus which enjoys a whole set of useful properties such as full composition, simulation of one-step beta-reduction, preservation of beta-strong normalisation, strong normalisation of typed terms and confluence on metaterms. Normalisation of related calculi is also discussed.

https://doi.org/10.2168/LMCS-5(3:1)2009

Source: arXiv.org:0905.2539

Volume: Volume 5, Issue 3

Published on: July 15, 2009

Imported on: December 8, 2008

Keywords: Computer Science - Programming Languages,Computer Science - Logic in Computer Science,F.3.2,D.1.1,F.4.1

Licence: arXiv.org - Non-exclusive license to distribute

Classifications

Mathematics Subject Classification 2020¹

Sources:

[1] zbMATH Open.

Bibliographic References

14 Documents citing this article

Delia Kesner;Loïc Peyrot;Daniel Ventura, Lecture notes in computer science, The Spirit of Node Replication, pp. 344-364, 2021, 10.1007/978-3-030-71995-1_18, https://doi.org/10.1007/978-3-030-71995-1_18.

Thibaut Balabonski;Antoine Lanco;Guillaume Melquiond, A strong call-by-need calculus, 2021, 10.4230/lipics.fscd.2021.9, https://hal.inria.fr/hal-03149692.

Xiaohong Chen;Grigore Roşu, 2020, A general approach to define binders using matching logic, Proceedings of the ACM on Programming Languages, 4, ICFP, pp. 1-32, 10.1145/3408970, https://doi.org/10.1145/3408970.

Benedikt Ahrens;André Hirschowitz;Ambroise Lafont;Marco Maggesi, 2019, Reduction monads and their signatures, Proceedings of the ACM on Programming Languages, 4, POPL, pp. 1-29, 10.1145/3371099, https://doi.org/10.1145/3371099.

ÁLVARO GARCÍA-PÉREZ;PABLO NOGUEIRA, 2019, The full-reducing Krivine abstract machine KN simulates pure normal-order reduction in lockstep: A proof via corresponding calculus, Journal of Functional Programming, 29, 10.1017/s0956796819000017.

Thibaut Balabonski;Pablo Barenbaum;Eduardo Bonelli;Delia Kesner, 2017, Foundations of strong call by need, Proceedings of the ACM on Programming Languages, 1, ICFP, pp. 1-29, 10.1145/3110264, https://doi.org/10.1145/3110264.

Beniamino Accattoli;Pablo Barenbaum;Damiano Mazza, Proceedings of the 19th ACM SIGPLAN international conference on Functional programming, Distilling abstract machines, 2014, Gothenburg Sweden, 10.1145/2628136.2628154.

Beniamino Accattoli;Pablo Barenbaum;Damiano Mazza, 2014, Distilling abstract machines, ACM SIGPLAN Notices, 49, 9, pp. 363-376, 10.1145/2692915.2628154.

Delia Kesner;Daniel Ventura, Lecture notes in computer science, Quantitative Types for the Linear Substitution Calculus, pp. 296-310, 2014, 10.1007/978-3-662-44602-7_23, https://doi.org/10.1007/978-3-662-44602-7_23.

Beniamino Accattoli;Delia Kesner, 2012, Preservation of Strong Normalisation modulo permutations for the structural lambda-calculus, Logical Methods in Computer Science, Volume 8, Issue 1, 10.2168/lmcs-8(1:28)2012, https://doi.org/10.2168/lmcs-8(1:28)2012.

Ariel Mendelzon;Alejandro Ríos;Beta Ziliani, 2011, Swapping: a natural bridge between named and indexed explicit substitution calculi, arXiv (Cornell University), 49, pp. 1-15, 10.4204/eptcs.49.1, https://arxiv.org/abs/1102.3730.

F.L.C. de Moura;A.V. Barbosa;M. Ayala-Rincón;F. Kamareddine, 2011, A Flexible Framework for Visualisation of Computational Properties of General Explicit Substitutions Calculi, Electronic Notes in Theoretical Computer Science, 269, pp. 41-54, 10.1016/j.entcs.2011.03.004.

José Espírito Santo;Luís Pinto, 2011, A calculus of multiary sequent terms, ACM Transactions on Computational Logic, 12, 3, pp. 1-41, 10.1145/1929954.1929959, https://doi.org/10.1145/1929954.1929959.

Stefan Hetzl, A Sequent Calculus with Implicit Term Representation, pp. 351-365, 2010, 10.1007/978-3-642-15205-4_28, https://hal.science/hal-00498707.

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