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Equations, Contractions, and Unique Solutions

Published:14 January 2015Publication History
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Abstract

One of the most studied behavioural equivalences is bisimilarity. Its success is much due to the associated bisimulation proof method, which can be further enhanced by means of "up-to bisimulation" techniques such as "up-to context".

A different proof method is discussed, based on unique solution of special forms of inequations called contractions, and inspired by Milner's theorem on unique solution of equations. The method is as powerful as the bisimulation proof method and its "up-to context" enhancements. The definition of contraction can be transferred onto other behavioural equivalences, possibly contextual and noncoinductive.

This enables a coinductive reasoning style on such equivalences, either by applying the method based on unique solution of contractions, or by injecting appropriate contraction preorders into the bisimulation game. The techniques are illustrated on CCS-like languages; an example dealing with higher-order languages is also shown.

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            • Published in

              cover image ACM SIGPLAN Notices
              ACM SIGPLAN Notices  Volume 50, Issue 1
              POPL '15
              January 2015
              682 pages
              ISSN:0362-1340
              EISSN:1558-1160
              DOI:10.1145/2775051
              • Editor:
              • Andy Gill
              Issue’s Table of Contents
              • cover image ACM Conferences
                POPL '15: Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
                January 2015
                716 pages
                ISBN:9781450333009
                DOI:10.1145/2676726

              Copyright © 2015 ACM

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              • Published: 14 January 2015

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