Variable Binding, Symmetric Monoidal Closed Theories, and Bigraphs

Richard Garner; Tom Hirschowitz; Aurélien Pardon

doi:10.1007/978-3-642-04081-8_22

Variable Binding, Symmetric Monoidal Closed Theories, and Bigraphs

Richard Garner^*, Tom Hirschowitz, Aurélien Pardon

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

2 Citations (Scopus)

Abstract

This paper investigates the use of symmetric monoidal closed (smc) structure for representing syntax with variable binding, in particular for languages with linear aspects. In this setting, one first specifies an smc theory, which may express binding operations, in a way reminiscent from higher-order abstract syntax (hoas). This theory generates an smc category whose morphisms are, in a sense, terms in the desired syntax. We apply our approach to Jensen and Milner's (abstract binding) bigraphs, in which processes behave linearly, but names do not. This leads to an alternative category of bigraphs, which we compare to the original.

Original language	English
Title of host publication	CONCUR 2009 - Concurrency Theory 20th International Conference, CONCUR 2009, Bologna, Italy, September 1-4, 2009. Proceedings
Editors	Mario Bravetti, Gianluigi Zavattaro
Place of Publication	Berlin; Heidelberg
Publisher	Springer, Springer Nature
Pages	321-337
Number of pages	17
Volume	5710 LNCS
ISBN (Electronic)	9783642040818
ISBN (Print)	3642040802, 9783642040801
DOIs	https://doi.org/10.1007/978-3-642-04081-8_22
Publication status	Published - Sept 2009
Externally published	Yes
Event	20th International Conference on Concurrency Theory, CONCUR - 2009 - Bologna, Italy Duration: 1 Sept 2009 → 4 Sept 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5710 LNCS
ISSN (Print)	03029743
ISSN (Electronic)	16113349

Other

Other	20th International Conference on Concurrency Theory, CONCUR - 2009
Country/Territory	Italy
City	Bologna
Period	1/09/09 → 4/09/09

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10.1007/978-3-642-04081-8_22

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Garner, R., Hirschowitz, T., & Pardon, A. (2009). Variable Binding, Symmetric Monoidal Closed Theories, and Bigraphs. In M. Bravetti, & G. Zavattaro (Eds.), CONCUR 2009 - Concurrency Theory 20th International Conference, CONCUR 2009, Bologna, Italy, September 1-4, 2009. Proceedings (Vol. 5710 LNCS, pp. 321-337). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5710 LNCS). Springer, Springer Nature. https://doi.org/10.1007/978-3-642-04081-8_22

Garner, Richard ; Hirschowitz, Tom ; Pardon, Aurélien. / Variable Binding, Symmetric Monoidal Closed Theories, and Bigraphs. CONCUR 2009 - Concurrency Theory 20th International Conference, CONCUR 2009, Bologna, Italy, September 1-4, 2009. Proceedings. editor / Mario Bravetti ; Gianluigi Zavattaro. Vol. 5710 LNCS Berlin; Heidelberg : Springer, Springer Nature, 2009. pp. 321-337 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "This paper investigates the use of symmetric monoidal closed (smc) structure for representing syntax with variable binding, in particular for languages with linear aspects. In this setting, one first specifies an smc theory, which may express binding operations, in a way reminiscent from higher-order abstract syntax (hoas). This theory generates an smc category whose morphisms are, in a sense, terms in the desired syntax. We apply our approach to Jensen and Milner's (abstract binding) bigraphs, in which processes behave linearly, but names do not. This leads to an alternative category of bigraphs, which we compare to the original.",

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Garner, R, Hirschowitz, T & Pardon, A 2009, Variable Binding, Symmetric Monoidal Closed Theories, and Bigraphs. in M Bravetti & G Zavattaro (eds), CONCUR 2009 - Concurrency Theory 20th International Conference, CONCUR 2009, Bologna, Italy, September 1-4, 2009. Proceedings. vol. 5710 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5710 LNCS, Springer, Springer Nature, Berlin; Heidelberg, pp. 321-337, 20th International Conference on Concurrency Theory, CONCUR - 2009, Bologna, Italy, 1/09/09. https://doi.org/10.1007/978-3-642-04081-8_22

Variable Binding, Symmetric Monoidal Closed Theories, and Bigraphs. / Garner, Richard; Hirschowitz, Tom; Pardon, Aurélien.
CONCUR 2009 - Concurrency Theory 20th International Conference, CONCUR 2009, Bologna, Italy, September 1-4, 2009. Proceedings. ed. / Mario Bravetti; Gianluigi Zavattaro. Vol. 5710 LNCS Berlin; Heidelberg: Springer, Springer Nature, 2009. p. 321-337 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5710 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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AB - This paper investigates the use of symmetric monoidal closed (smc) structure for representing syntax with variable binding, in particular for languages with linear aspects. In this setting, one first specifies an smc theory, which may express binding operations, in a way reminiscent from higher-order abstract syntax (hoas). This theory generates an smc category whose morphisms are, in a sense, terms in the desired syntax. We apply our approach to Jensen and Milner's (abstract binding) bigraphs, in which processes behave linearly, but names do not. This leads to an alternative category of bigraphs, which we compare to the original.

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Garner R, Hirschowitz T, Pardon A. Variable Binding, Symmetric Monoidal Closed Theories, and Bigraphs. In Bravetti M, Zavattaro G, editors, CONCUR 2009 - Concurrency Theory 20th International Conference, CONCUR 2009, Bologna, Italy, September 1-4, 2009. Proceedings. Vol. 5710 LNCS. Berlin; Heidelberg: Springer, Springer Nature. 2009. p. 321-337. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-04081-8_22

Variable Binding, Symmetric Monoidal Closed Theories, and Bigraphs

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