[isabelle-dev] Infix syntax for division?

Florian Haftmann florian.haftmann at informatik.tu-muenchen.de
Tue Jun 2 20:17:39 CEST 2015

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?



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