On 2017-07-21 1:33 PM, Elizabeth Mattijsen wrote:

On 21 Jul 2017, at 21:30, Darren Duncan <dar...@darrenduncan.net> wrote: Firstly, I believe ∆ (U+2206) is the standard symbol for symmetric difference, and not circled minus as the above url currently gives.## Advertising

https://en.wikipedia.org/wiki/Symmetric_difference seems to agree, showing it as the first choice. However, ⊖ appears to be the second choice. FWIW, I think ∆ better matches the Texas variant (^) .

`The circled plus is also overloaded for XOR (which itself has at least 2`

`more-preferred alternatives) and other things, while ∆ (U+2206) isn't AFAIK`

`overloaded for anything and in any event ∆ (U+2206) is much more consistent with`

`all the other standard set/bag operators in format and it is what the literature`

`prefers to use.`

`What you say about (^) Texas version isn't a similarity I thought about, but`

`then that gives my proposal extra support if anything.`

The circled plus should be dropped from use for this meaning.

Secondly, I see there's an operator for multiplying 2 bags (which I hadn't heard of before, but okay), but there should also be an operator for multiplying 1 bag by a natural number, that is a scalar multiply of a bag. Unless it is assumed the standard hyper-operator syntax is best for this.If I get this right, you’d want: <a b b>.Bag * 3 give (:3a,:6b).Bag ? I guess that with * being commutative, 3 * <a b b>.Bag would be the same result.

You are correct in all points above.

But then, what would <a b b>.Bag * <a a b>.Bag be?

`I would suggest that this option is either undefined or it has the same meaning`

`as the bag multiplication operator, eg, (:2a,:2b).Bag.`

`Another way of looking at this is, say if we're starting with the existing bag`

`circled-times bag operator, replacing one bag operand with a number N is like`

`replacing it with what is conceptually an infinite-cardinality bag having :Ne`

`for "e" in turn being every possible value in the type system; the infinite bag`

`reduces to one having only matching unique members and replicates those matches`

`by a cardinality of N.`

-- Darren Duncan