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APLAS
2007
ACM

Complete Lattices and Up-To Techniques

9 years 5 months ago
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 ed 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.
Damien Pous
Added 12 Aug 2010
Updated 12 Aug 2010
Type Conference
Year 2007
Where APLAS
Authors Damien Pous
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