Re: Comments on parsing steps:

>> Mathematica's parsing, which works in a manner similar to what Bruce
>> describes, has no problem handling complex embellishments.
>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.
>If these embellishment prefix and postfix operators have a high
>precedence and hence bind tightly to the adjacent operator then
>I don't see any problems. Am I missing something?

I think that there is a problem with prefix embellishments.
The arguments are technical, so people who don't care can stop reading.

When the parser encounters something like a +_2 b,
it knows by the time of reading the '+' that it must have a right operand.
The most reasonable "error correction" would be to have the '_' embellishe '+'.
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}}
To get what you probably wanted, you would need to write
    {&bold +} 2
For a large number of cases, such as '&bold x + 2', the right thing would
happen.  It is just when you try to embellish an operator.
A high-precedence postfix &bold would not have this problem.
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.