Dear all, http://isabelle.in.tum.de/reports/Isabelle/rev/838025c6e278 introduces type classes »(sem)idom_divide« with an explicit partial divide operations in integral (semi)domains, which specialises smoothly to field division or euclidean division later on. In _ you see how this allows to formulate certain results uniformly for both kind of divisions.
So far, this generic division does not carry any infix syntax. Maybe it should, but I am uncertain which path to follow: a) The radical solution: there is only »_ / _« for both field division and euclidean division. How natural is notation like »a / b * b + a mod b = a« then? b) The conservative solution: partial division has »_ div _«, an (the more special) field division »_ / _«. This seems more sensible than the other way round since »_ div _« suggests some kind of »incompleteness«. Any opinions? Cheers, Florian -- PGP available: http://home.informatik.tu-muenchen.de/haftmann/pgp/florian_haftmann_at_informatik_tu_muenchen_de
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