Re: cross operator and empty list

HaloO, Larry Wall wrote: (@a X @b X @c).elems == @a.elems * @b.elems * @c.elems Sorry, I was aiming at defining a neutral element of the X operator. In cartesian products of sets this is achieved by having a set that contains as sole member the empty tuple. So how would that be written? ((

Re: cross operator and empty list

On Mon, Apr 7, 2008 at 4:50 AM, TSa <[EMAIL PROTECTED]> wrote: > HaloO, > > > Larry Wall wrote: > > >(@a X @b X @c).elems == @a.elems * @b.elems * @c.elems > > > > Sorry, I was aiming at defining a neutral element of the X > operator. A neutral element for the cross operator seems weird if

Re: cross operator and empty list

Adriano, I think perhaps what Tsa is trying to get at is the identity value for the X operator, and I believe I know what it is. In the relational model of data, both the version of the model where tuples have unordered named attributes/elements (which I prefer), and the version where tuples h

Re: cross operator and empty list

Technically the Cartesian cross operator doesn't have an identity value. There is no set X such that A x X = A. Now any singleton set gives a result that is naturally isomorphic to the original set, I.e, there is a obvious bijection between the two sets, but they are not equal sets. -- Mark

Re: cross operator and empty list

[EMAIL PROTECTED] wrote: Technically the Cartesian cross operator doesn't have an identity value. There is no set X such that A x X = A. Now any singleton set gives a result that is naturally isomorphic to the original set, I.e, there is a obvious bijection between the two sets, but they are no

Protected data member access considered harmful

Larry Wall wrote: How private is private? I wonder if what you've called private things are really more like "protected" in C++ (accessible by the derived class) and that 'my' attributes are really private, as are submethods. It's all confused. Who is allowed to access what? >>

What I'm Working On

I'm taking a stab at turning the S\d\d documents into a formal standard. Going through S02, each factoid gets filed away in a developing outline. I'm using a single ODT file to make it easy to manipulate the outline (currently mostly stubs). Here is an early effort to flesh out imprecise spec

Re: Protected data member access considered harmful

Thom Boyer thom-at-boyers.org |Perl 6| wrote: I believe Mr. Stroustrup's deprecation of 'protected' access applies only to data data members, not function members: Fortunately, you don't have to use protected data in C++; 'private' is the default in classes and is usually the better choice.