

docno="lists-046-12162937"
name="Dave Raggett"
email="dsr@w3.org"
sent="Thu, 06 Jun 1996 11:10:10 -0400"
id="199606061510.AA181383810@w3.org"
subject="Re: Comments on parsing steps:"
To: w3c-math-erb@w3.org<199606060206.AA06946@drizzle.wri.com>



     
   

Neil,

>>I can see value in allowing prefix and postfix operators to act as
>>operator embellishments, for instance to add accents to operators or
>>to change their relative size, or position.
...
> Since the details of why a prefix embellishing operator sometimes "works"
> right and sometimes doesn't are probably beyond most authors, I think we
> should avoid them.  Or if we must have them, tell people to always uses
> braces to properly group it.

I am unconvinced by your examples.

> When the parser encounters something like a + _2 b,
> it knows by the time of reading the '+' that it must have a right operand.

Fine, but that also applies to:

        a &big + b

with the information that &big can act as a prefix embellishment operator
this yields:

        {a {&big +} b}

Otherwise this would parse as:

        {a . {&big {+ b}}}

where `.' is an inferred infix operator, presumably denoting multiplication.

> However, consider the following:

>       &bold + 2

> with '&bold' being a high-precedence prefix operator. When the parser sees
> the '+', it sees that it must be a prefix operator, and so will shift the
> `2' on.  So, this expression would result in:

>       {&bold {+ 2}}

If each operator has a property indicating that it can act as an
embellishment on other operators, then we can use this fact to make
the above parse as

        {&bold +} 2

in preference to the interpretation of &bold as a normal prefix operator.
In essence we sort the operator precedence reduction rules into a sequence
that resolves potential ambiguities between different operator roles defined
by the dictionary for each symbol.

You have already asserted that people are comfortable with dictionary
definitions for the roles of symbols as prefix, infix or postfix operators
(including their precedences). Extending the dictionary to define whether
each symbol can act as prefix, infix or postfix embellishment operators
seems a straightforward addition.

Can you give me examples that would be hard to explain to a user?

-- Dave Raggett <dsr@w3.org> tel: +1 (617) 258 5741 fax: +1 (617) 258 5999
   World Wide Web Consortium, 545 Technology Square, Cambridge, MA 02139
   url = http://www.w3.org/People/Raggett


