YAP (was Re: Proposal: Remove Show and Eq superclasses of Num)

[Tyson Whitehead]

On November 2, 2011 18:00:05 Paterson, Ross wrote:
> The two concepts are similar for Int and Integer, except that signum 0 = 0
> while unit 0 = 1, but the meanings of abs and signum on other types
> generalize in a different way.
> 
> These functions are pretty common in computer algebra systems.

<snip>

> The Euclidean function is the measure function into a well-ordered set
> (the naturals) used in the proof that gcd terminates.  You don't actually
> use it in the code.  On the other hand you do need to be able to get a
> canonical associate.

Am I correct in understanding then that there could actually be euclidean 
domains that don't have good definitions unit and associate?

Thanks!  -Tyson