[eeps] Proposal for /\ and \/ operators

[Richard O'Keefe]

On 27 Feb 2009, at 3:52 am, David-Sarah Hopwood wrote:

> Richard O'Keefe wrote:
>> Maximum and minimum DO have very well established mathematical
>> symbols.  In ASCII, those symbols look like /\ and \/.
>
> No, they normally look like '⊓' and '⊔'.

No, they _sometimes_ look like that.
Take for example the first book I picked up,
	A Course in Universal Algebra,
	Burris & Sankappanavar
	Springer Graduate Texts in Mathematics 1981.
>
>
> '∧' is more commonly used for logical-and, and '∨' for logical-or.

Page 4 introduces the meet and join operators, and it uses
'∧' and '∨' for them.

The second book I picked up was a book about discrete mathematics
for computer scientists.  It had a section on Boolean Algebras
(not just 'true' and 'false', but the generalised ones) and it
uses '∧' and '∨', BUT it also uses '<' on (generalised) Boolean
values.

One rule that does apply is that the "square" meet and join symbols
are used only when you are using the "square" less than, less than
or equal to, greater than, and greater than or equal to symbols.
If you're using "pointy" less than, you use "pointy" meet.

Since Erlang doesn't use "square" comparison operators,
it would be quite inconsistent for it to use "square" meet and join.

> (Yes, the logical operators can be viewed as maximum and minimum in
> a Boolean lattice, but that is not what the proposed /\ and \/  
> operators
> do; they are a maximum and minimum on arbitrary values as defined by  
> '<'.)

There is no convention that restricts the pointy meet and join to
only those lattices that have a complement operator.  They are even
used with semilattices.

"Square" and "pointy" are stylistic variations that let you keep
track of more than one kind of poset/semilattice/lattice/whatever
at the same time without getting lost in subscripts, that's all.