||| The greatest common divisor of two natural numbers.
|||
||| If we take the word "greatest" to refer to the usual less-than
||| relation on natural numbers, then gcd(0,0) would be undefined:
||| every natural number evenly divides 0, and there is no greatest
||| natural number.  However, we should instead think of the
||| divisibility relation: gcd is really the meet (greatest lower
||| bound) in the divisibility lattice on the natural numbers.  That
||| is, gcd(a,b) = d if for every d' such that d' evenly divides both
||| a and b, we have that d' also evenly divides (NOT "is less than"!)
||| d.  Under this definition, gcd(0,0) is perfectly well defined and
||| equal to 0.  0 is in fact the "greatest" natural number under the
||| divisibility relation, because it is divisible by every natural
||| number.

!!! gcd(7,6)   == 1
!!! gcd(12,18) == 6
!!! gcd(0,0)   == 0

gcd : N * N -> N
gcd(a,0) = a
gcd(a,b) = gcd(b, a mod b)