docno|NN =|SYM "|'' lists-|NN 046|CD -|: 12162937|CD "|'' name|NN =|SYM "|'' Dave|NNP Raggett|NNP "|'' email|NN =|SYM "|'' dsr@w3.org|NN "|'' sent|VBD =|SYM "|'' Thu|NNP ,|, 06|CD Jun|NNP 1996|CD 11:10:10|NN -|: 0400|CD "|'' id|NN =|SYM "|'' 199606061510.AA181383810@w3.org|NN "|'' subject|JJ =|SYM "|'' Re|NNP :|: Comments|NNS on|IN parsing|VBG steps|NNS :|: "|'' To|TO :|: w3c-math-erb@w3.org|NN <|NN 199606060206.AA06946@drizzle.wri.com|NN >|NN Neil|NNP ,|, 

>|NN >|NN I|PRP can|MD see|VB value|NN in|IN allowing|VBG prefix|NN and|CC postfix|NN operators|NNS to|TO act|VB as|IN >|NN >|NN operator|NN embellishments|NNS ,|, for|IN instance|NN to|TO add|VB accents|NNS to|TO operators|NNS or|CC >|NN >|NN to|TO change|VB their|PRP$ relative|JJ size|NN ,|, or|CC position|NN .|. 

...|... >|NN Since|IN the|DT details|NNS of|IN why|WRB a|DT prefix|NN embellishing|VBG operator|NN sometimes|RB "|'' works|VBZ "|'' >|NN right|NN and|CC sometimes|RB does|VBZ n't|RB are|VBP probably|RB beyond|IN most|JJS authors|NNS ,|, I|PRP think|VBP we|PRP >|NN should|MD avoid|VB them|PRP .|. 
Or|CC if|IN we|PRP must|MD have|VB them|PRP ,|, tell|VB people|NNS to|TO always|RB uses|VBZ >|NN braces|NNS to|TO properly|RB group|VB it|PRP .|. 

I|PRP am|VBP unconvinced|JJ by|IN your|PRP$ examples|NNS .|. 

>|NN When|WRB the|DT parser|NN encounters|VBZ something|NN like|IN a|DT +|NN _|NN 2|CD b|SYM ,|, >|NN it|PRP knows|VBZ by|IN the|DT time|NN of|IN reading|VBG the|NNP '|POS +|NN '|'' that|IN it|PRP must|MD have|VB a|DT right|JJ operand|NN .|. 

Fine|NNP ,|, but|CC that|WDT also|RB applies|VBZ to|TO :|: a|DT &|CC big|JJ +|NN b|SYM with|IN the|DT information|NN that|IN &|CC big|JJ can|MD act|VB as|IN a|DT prefix|NN embellishment|NN operator|NN this|DT yields|NNS :|: {|( a|DT {|( &|CC big|JJ +|NN }|) b|SYM }|) 
Otherwise|RB this|DT would|MD parse|NN as|IN :|: {|( a|DT .|. {|( &|CC big|JJ {|( +|NN b|SYM }|) }|) }|) where|WRB `|`` .|. '|'' is|VBZ an|DT inferred|JJ infix|NN operator|NN ,|, presumably|RB denoting|VBG multiplication|NN .|. 

>|NN However|RB ,|, consider|VBP the|DT following|VBG :|: >|NN &|CC bold|JJ +|NN 2|CD >|NN with|IN '|POS &|CC bold|JJ '|POS being|VBG a|DT high-precedence|JJ prefix|NN operator|NN .|. 
When|WRB the|DT parser|NN sees|VBZ >|NN the|NNP '|POS +|NN '|'' ,|, it|PRP sees|VBZ that|IN it|PRP must|MD be|VB a|DT prefix|NN operator|NN ,|, and|CC so|RB will|MD shift|VB the|DT >|NN `|`` 2|CD '|'' on|IN .|. 
So|RB ,|, this|DT expression|NN would|MD result|VB in|IN :|: >|NN {|( &|CC bold|JJ {|( +|NN 2|CD }|) }|) 

If|IN each|DT operator|NN has|VBZ a|DT property|NN indicating|VBG that|IN it|PRP can|MD act|VB as|IN an|DT embellishment|NN on|IN other|JJ operators|NNS ,|, then|RB we|PRP can|MD use|VB this|DT fact|NN to|TO make|VB the|DT above|JJ parse|NN as|IN {|( &|CC bold|JJ +|NN }|) 2|CD in|IN preference|NN to|TO the|DT interpretation|NN of|IN &|CC bold|JJ as|IN a|DT normal|JJ prefix|NN operator|NN .|. 
In|IN essence|NN we|PRP sort|NN the|DT operator|NN precedence|NN reduction|NN rules|NNS into|IN a|DT sequence|NN that|WDT resolves|NNS potential|JJ ambiguities|NNS between|IN different|JJ operator|NN roles|NNS defined|VBN by|IN the|DT dictionary|JJ for|IN each|DT symbol|NN .|. 

You|PRP have|VBP already|RB asserted|VBN that|IN people|NNS are|VBP comfortable|JJ with|IN dictionary|JJ definitions|NNS for|IN the|DT roles|NNS of|IN symbols|NNS as|IN prefix|NN ,|, infix|NN or|CC postfix|NN operators|NNS (|( including|VBG their|PRP$ precedences|NNS )|) .|. 
Extending|NNP the|DT dictionary|JJ to|TO define|VB whether|IN each|DT symbol|NN can|MD act|VB as|IN prefix|NN ,|, infix|NN or|CC postfix|NN embellishment|NN operators|NNS seems|VBZ a|DT straightforward|JJ addition|NN .|. 

Can|MD you|PRP give|VB me|PRP examples|NNS that|WDT would|MD be|VB hard|JJ to|TO explain|VB to|TO a|DT user|NN ?|. 

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