[isabelle-dev] Evaluation of floor and ceiling

Florian Haftmann florian.haftmann at informatik.tu-muenchen.de
Sun Jul 10 08:44:00 CEST 2011

>> I wrote to Florian about this exact issue back in February 2010.
>> Florian's recommended solution at the time was to add a new subclass
>> of archimedean_field that fixes the floor function and assumes a
>> correctness property about it. This solution is really easy to
>> implement (see attached diff). If people think this is a reasonable
>> design, then I'll let someone else go ahead and test and commit the
>> patch.

> I want to add important context for that recommendation: a few years
> ago, around 2006, when I entered this type class adventure in more deep,
> I came to the conclusion that it is usually better to have
> »constructive« type classes, e.g. if we specify a semilattice as type
> class, we don't assume »there exists a inf such that …« but we add an
> explicit parameter »inf« which a corresponding set of properties.

Another addition: it would also be possible to turn floor and ceiling to
parameters of archimedean_field, similar to complete_lattice which also
includes bot and top, although both could be defined as derived operations.




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