[isabelle-dev] Permutations

[Johannes Hölzl]

Am Dienstag, den 05.07.2016, 20:02 +0200 schrieb Florian Haftmann:
> 
> > 
> > 
> > What about adding it to the ab_group_add typeclass? I know this is
> > not
> > the usual mathematical syntax for permutations, but at least we can
> > reuse a lot of theorems from this type class.
> There *is* reuse since there is a separate interpretation of the
> abstract ab_group locale.
I meant of course group_add, not ab_group_add. I still think that the
type class interpretation gives us more theorems. Not everything is
expressible in the class-locale.

> 
> I once met an algebraist who preferred + for abelian groups and *
> otherwise, and this makes sense.
And I agree that * is much nicer, but not as practicable in our
concrete Isabelle setting.

> 
> Cheers,
> 	Florian
> 
> 
> > 
> > 
> > 
> >  - Johannes
> > 
> > Am Dienstag, den 05.07.2016, 19:40 +0200 schrieb Florian Haftmann:
> > > 
> > > 
> > > > 
> > > > 
> > > > 
> > > > One question: why did you only set it up for monoid_mult and
> > > > inverse,
> > > > and not as a ab_group_mult?
> > > The answer is simple: there is no type class
> > > ab_group_mult.  Why?  Since
> > > our multiplicative structures are tailored towards rings where 0
> > > is
> > > no
> > > part of the multiplicative group.
> > > 
> > > Cheers,
> > > 	Florian