# Equations, contractions, and unique solutions

2 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
Abstract : One of the most studied behavioural equivalences is bisimilarity, andthe main reason for its success is the associated bisimulation proofmethod, 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 solutions ofspecial forms of inequations called contractions, and inspired byMilner's theorem on unique-solution of equations. The method is atleast as powerful as the bisimulation proof method and its `up-tocontext' enhancements. The definition of contraction can betransferred onto other behavioural equivalences, possibly contextualand non-coinductive. This enables a coinductive reasoning style onsuch equivalences, either by applying the method based onunique-solution of contractions, or by injecting appropriatecontraction preoders into the bisimulation game.The techniques are illustrated on CCS-like languages; an example withhigher-order languages is also shown.
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Cited literature [34 references]

https://hal.archives-ouvertes.fr/hal-01089205
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Submitted on : Tuesday, December 9, 2014 - 3:10:20 PM
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Davide Sangiorgi. Equations, contractions, and unique solutions. POPL 2015 - Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Language, Jan 2015, Mumbai, India. ⟨10.1145/2676726.2676965⟩. ⟨hal-01089205⟩

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