# Correctness and full abstraction of metric semantics for concurrency

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## Abstract

Four different semantic models are given for a simple uniform programming language, containing constructs for parallel composition, global nondeterminism and communication: linear semantics, failure semantics, readiness semantics, and branching semantics. The mathematical framework used consists of complete metric spaces. All models and operators are given as fixed points of suitably defined contractions. This allows for a uniform presentation and an easy comparison of these models. It is shown that the latter three semantics all are correct and that the failure semantics is fully abstract with respect to the linear semantics. Although these results are not new, we believe the uniformity of the way they are presented here to be of some interest.

## Key words and phrases

concurrency complete metric spaces contractions operational semantics denotational semantics compositionality correctness full abstraction## Preview

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