On 6 Aug 2005, at 03:05, Aaron Hurst wrote:
I'm trying to parse a simple algebraic (Boolean) expression using
the grammar described below. However, I would like to be able to
parse implicit multiplication (i.e. if two expression appear next
to each other without an operator, they should be mulitplied).
I once wrote such a grammar, but I concluded that in a computer
program, the effort of refining the grammr does not seem worth the
effort.
For example,
a b + (c + d)g
should parse the same as
a * b + (c + d) * g
As written below, there are several shift/reduce conflicts caused
by the last rule (the implicit multiplication). I have no idea how
to rewrite this unambiguously.
%left '|' '+'
%left '^'
%left '&' '*'
%nonassoc '\''
%nonassoc '!'
expression:
IDENTIFIER
| '(' expression ')'
| expression '*' expression
| expression '&' expression
| expression '+' expression
| expression '|' expression
| expression '^' expression
| '!' expression
| expression '\''
| expression expression %prec '*' /* this rule causes problems */
;
By your last rule, for example a + b c + d becomes ambiguous, as it
admits the interpretations (a + b) (c + d) and a + (b c) + d.
Grammatically, implicit multiplication only applies to certain
situations, where one of the operands is an identifier, a constant,
or enclosed in parenthesizes. The precedences, %prec '*', only apply
to tokens, and you have none in that rule.
Hans Aberg
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