From: Doug Gregor (gregod_at_[hidden])
Date: 2001-01-13 20:45:46
On Friday 12 January 2001 07:00, you wrote:
> Paris (U.E;), le 13/01/2001
>
> I would absolutely welcome algebraic classes!
These are algebraic concept classes, not general algebraic classes. The idea
behind them is that they can be used to determine algebraic properties of a
given type. For instance, given the following integer exponentiation
algorithm (borrowed from some class notes at
http://www.cs.rpi.edu/~schupp/entries/COURSES/pl/notes/gp.html):
template<class SemigroupElement, class Integer>
SemigroupElement
exponentiate2(SemigroupElement x, Integer n) {
while (even(n)) {
x = x * x;
n = n/2;
}
SemigroupElement P=x;
n = integral_part(n/2);
while (n>0) {
x=x*x;
if (odd(n))
P = P*x;
n = integral_part(n/2);
}
return P;
}
We should be checking that the type bound to SemigroupElement does indeed
form a semigroup with the operation *. The algebraic concept classes allow us
to do this check statically, so compilation will fail if the user does not
assert the associativity of * for the type bound to SemigroupElement.
Doug Gregor
gregod_at_[hidden]