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.
@InProceedings{bucciarelli_et_al:LIPIcs.CSL.2011.97, author = {Bucciarelli, Antonio and Carraro, Alberto and Ehrhard, Thomas and Manzonetto, Giulio}, title = {{Full Abstraction for Resource Calculus with Tests}}, booktitle = {Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL}, pages = {97--111}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-32-3}, ISSN = {1868-8969}, year = {2011}, volume = {12}, editor = {Bezem, Marc}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.97}, URN = {urn:nbn:de:0030-drops-32250}, doi = {10.4230/LIPIcs.CSL.2011.97}, annote = {Keywords: resource lambda calculus, relational semantics, full abstraction, differential linear logic} }
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