[Om3] binary vs n-ary relations

[Jan Willem Knopper]

Paul Libbrecht wrote:
> 
> Le 25-sept.-08 à 11:14, Jan Willem Knopper a écrit :
...
> > There are no obvious semantics differences here, and I am not sure
> > enough that I actually need anything like the semantics of a formula
> > manipulation.
> 
> I think the ball is on your side Jan Willem... many users and user- 
> guides (e.g. teachers) will want something to look like a<b<c and  
> other such...

The main problem is indeed with parsing and notation.

What I want is an easy way to parse this. 

With the OpenMath currently suggested for a=b=c (namely a=b/\b=c) I will
have to check whether the OpenMath subexpression is "the same" for the
b's (that is strip whitespace around XML elements, possibly strip spaces
inside OMIs, and string-compare the result). 

Another option would be to compare available output of the partial
expressions (which could be an internal semantic tree, or mathml-p, or
...), but this might not always give the desired result.

> - how are you going to offer this to users ? (e.g. wiris input editor
> does it by reparsing the mathml-p)

Probably the user wants a choice on what OpenMath they get from a=b=c.
In my editor I have binary and n-ary infix symbol and they are parsed
such that a+b+c is (a+b)+c, a=b is binary and a=b=c is n-ary. The user
can enter them typing or inserting the symbol several times.

The nicest would probably be to have an option in the editor to get the
output I like, (for our software) or the official ouput, (for other
users of the editor). When using an attribution this might be easier.

To input a=b=c from OpenMath in the editor, or to show a=b=c in a
webpage I would probably require users to use "my" format, otherwise
it would be shown unchanged as a=b/\b=c.

> - how are you going to express the underlying OpenMath (as above I  
> suppose)
One solution is to use some private OpenMath symbol(s) which probably
won't make it to OpenMath 3/MathML 3. 

Another option could be to add some attribute to the application of the
and, indicating that it should be possible to display the expression
differently. 
The advantage of this would be that the OpenMath is the same and should
be handled the same by other programs. The disadvantage is that we
currently do not always have support for OMATTR attributes (is
annotations1 defined somewhere ? It is mentioned in the standard as an
example for OMATTR, but I couldn't find a CD online). 
Another disadvantage is that a OMATTR symbol that shouldn't be there
would might the meaning (am I really going to do all the checks required
for the meaning to stay the same?).

> 
> I think the first question is crucial and needs an elaborate answer  
> much further than "just apply this symbol here" as is done with most  
> "simple application symbols".
> It probably is a general issue of binary operators.


Jan Willem
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