Full Abstraction for Resource Calculus with Tests

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\u27s resource calculus and is derived from Ehrhard and Regnier\u27s 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\u27\u27 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