Complete Lattices and Up-To Techniques

  • Damien Pous
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4807)


We propose a theory of up-to techniques for proofs by coinduction, in the setting of complete lattices. This theory improves over existing results by providing a way to compose arbitrarily complex techniques with standard techniques, expressed using a very simple and modular semi-commutation property.

Complete lattices are enriched with monoid operations, so that we can recover standard results about labelled transitions systems and their associated behavioural equivalences at an abstract, “point-free” level.

Our theory gives for free a powerful method for validating up-to techniques. We use it to revisit up to contexts techniques, which are known to be difficult in the weak case: we show that it is sufficient to check basic conditions about each operator of the language, and then rely on an iteration technique to deduce general results for all contexts.


Complete Lattice Parallel Composition Label Transition System Behavioural Equivalence Weak Case 
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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Damien Pous
    • 1
  1. 1.LIP: UMR CNRS - ENS Lyon - UCB Lyon - INRIA 5668France

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