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Complete Lattices and Up-to Techniques

Abstract : 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.
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Contributor : Damien Pous <>
Submitted on : Tuesday, June 19, 2007 - 8:28:14 AM
Last modification on : Monday, October 22, 2018 - 12:56:02 PM
Long-term archiving on: : Friday, September 21, 2012 - 4:35:53 PM


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  • HAL Id : ensl-00155308, version 1



Damien Pous. Complete Lattices and Up-to Techniques. 2007. ⟨ensl-00155308v1⟩



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