LIPIcs.CSL.2011.97.pdf
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Full Abstraction for Resource Calculus with Tests
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Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (CSL 2011)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Computer Science Logic (CSL) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2011-08-31
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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
https://doi.org/10.4230/LIPIcs.CSL.2011.97
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.
Keywords
- resource lambda calculus
- relational semantics
- full abstraction
- differential linear logic
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