Proposal: Make gcd total

[wren ng thornton]

On 5/28/11 6:59 AM, Daniel Fischer wrote:
> The Proposal:
>
> I would like to propose the elimination of the special error case
>
> gcd 0 0 = error "Prelude.gcd: gcd 0 0 is undefined"
>
> to replace it with
>
> gcd 0 0 = 0
>
> (which would be an automatic consequence of removing the above line).
>
> Rationale:
>
> 1. It makes gcd a total function.
> 2. It makes gcd associative.
> 3. It makes folding gcd over a list safe.
> 4. It conforms to common mathematical practice:

Just in case I'm not already on the record for this one, +1.

The only con I can envision is that, in the general case, the uniqueness 
of gcd is guaranteed by various properties; whereas every number is a 
divisor of 0. So, given the uniqueness criterion one could make an 
argument. However, the common mathematical practice takes gcd 0 0 == 0, 
and I'm unaware of a compelling reason not to do so.

-- 
Live well,
~wren