Full Abstraction for Resource Calculus with Tests

Bucciarelli, Antonio; Carraro, Alberto; Ehrhard, Thomas; Manzonetto, Giulio

doi:10.4230/LIPIcs.CSL.2011.97

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Full Abstraction for Resource Calculus with Tests

Authors Antonio Bucciarelli, Alberto Carraro, Thomas Ehrhard, Giulio Manzonetto

Part of: Volume: Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (CSL 2011)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Computer Science Logic (CSL)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2011-08-31

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LIPIcs.CSL.2011.97.pdf

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Document Identifiers

DOI: 10.4230/LIPIcs.CSL.2011.97
URN: urn:nbn:de:0030-drops-32250

Subject Classification

Keywords

resource lambda calculus
relational semantics
full abstraction
differential linear logic

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Abstract

We study the semantics of a resource sensitive extension of the lambda-calculus in a canonical reflexive object of a category of sets and relations, a relational version of the original Scott D infinity model of the pure lambda-calculus. This calculus is related to Boudol's resource calculus and is derived from Ehrhard and Regnier's differential extension of Linear Logic and of the lambda-calculus.  We extend it with new constructions, to be understood as implementing a very simple exception mechanism, and with a ``must'' parallel composition. These new operations allow to associate a context of this calculus with any point of the model and to prove full abstraction for the finite sub-calculus where ordinary lambda-calculus application is not allowed. The result is then extended to the full calculus by means of a Taylor Expansion formula.

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Antonio Bucciarelli, Alberto Carraro, Thomas Ehrhard, and Giulio Manzonetto. Full Abstraction for Resource Calculus with Tests. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 97-111, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011) https://doi.org/10.4230/LIPIcs.CSL.2011.97

Author Details

Antonio Bucciarelli

Alberto Carraro

Thomas Ehrhard

Giulio Manzonetto

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