+1 On Tue, May 10, 2011 at 12:49 AM, Daniel Fischer < daniel.is.fischer@googlemail.com> wrote:
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:
In a commutative ring, a greatest common divisor of two elements a, b is a common divisor g of a and b such that every common divisor d of a and b also divides g (if R is a commutative ring, a \in R, d \in R is a divisor of a iff there exists c \in R with a = d*c [leaving out noncommutative rings for simplicity]). Since every ring element divides 0, the above definition entails gcd 0 0 = 0.
Further, in a principal ideal ring, the greatest common divisors of two elements a and b are the generators of the ideal (a,b), again that characterisation of greatest common divisors says gcd 0 0 = 0: (0,0) = {0} = (0).
Pros: see above.
Cons: ? I'm not aware of any, the change shouldn't break existing code, since that would have to check for the special case anyway.
Daniel
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