The number 0 is the additive identity for numbers. But informally, the additive identity for other things can be called "zero" without problem. Heck, even the wikipedia page on Additive Identity uses this example for groups:
> Let (G, +) be a group and let 0 and 0' in G both denote additive identities, > so for any g in G, > > 0 + g = g = g + 0 and 0' + g = g = g + 0' > It follows from the above that > > (0') = (0') + 0 = 0' + (0) = (0) Look at that, an additive identity for something other than a number, and zero (0) is used to denote this additive identity. The only issue comes in when you define addition in multiple different ways for a single type. Of course, right now I believe compiler bugs prevent you from actually using multiple implementations of Add<> with different type parameters for a given type, so this isn't actually a problem right now. And when that bug is fixed, it's still reasonable to consider Zero to be the additive identity for any addition where the receiver type is the right-hand side of the addition. In other words, if you define Add<uint, Matrix> for Matrix, then the additive identity here is Zero::<for uint>, not Zero::<for Matrix>. Regarding "You can't assign a zero to a 2x2 matrix", additive identity does not require the ability to assign. And this is only a problem when considering addition between disparate types. If you consider matrix addition (e.g. 2x2 matrix + 2x2 matrix) then you certainly can assign the additive identity back to one of the matrix values. let m: Matrix = Zero::zero(); looks fine to me. It produces a matrix m that, when added to any other Matrix m', produces the same matrix m'. This is presumably a Matrix where every element is 0. But again, this only makes sense if you've actually defined Add<Matrix,Matrix> for Matrix. Regardless, we've already made the decision not to go down numeric type hierarchy hell. We're trying to keep a reasonable simple numeric hierarchy. And part of that means using straightforward "lay-person" terms instead of perhaps more precise mathematical names. As such, we have std::num::Zero as the additive identity and std::num::One as the multiplicative identity. If you really want to complain about something, complain about std::num::One being used for things other than multiplicative identity, e.g. std::iter::range() uses Add and One to produce the next value in the range. -Kevin On Apr 9, 2014, at 1:25 PM, Tommi Tissari <rusty.ga...@icloud.com> wrote: >> On 09 Apr 2014, at 20:46, Kevin Ballard <ke...@sb.org> wrote: >> >> Why? Zero is the additive identity. > > Zero is _an_ additive identity for numbers, but not for vectors or matrices. > > use std::slice::Items; > use std::iter::RandomAccessIterator; > use std::num::Zero; > > Items is a RandomAccessIterator, but a RandomAccessIterator is not an Items. > 0 is an additive identity, but an additive identity is not 0. You can't > assign a zero to a 2x2 matrix, and therefore this trait is incorrectly named. > The following just looks wrong: > > let m: Matrix = Zero::zero(); > >> AdditiveIdentity is the only reasonable alternative, but that's a mouthful >> of a name and I think changing the name to this would be more confusing. > > Naming a trait something that it's not is even more confusing. I don't think > we should give an incorrect name to this trait on the grounds of the correct > name being longer. Just look at RandomAccessIterator. > _______________________________________________ Rust-dev mailing list Rust-dev@mozilla.org https://mail.mozilla.org/listinfo/rust-dev
