Re: Noob parser question
- From: Gene <gene.ressler@xxxxxxxxx>
- Date: Thu, 28 Feb 2008 17:54:43 -0800 (PST)
On Feb 28, 12:05 am, imissfloppydi...@xxxxxxxxx wrote:
This is a CFG listed in the Aho (dragon) compiler text:
expr -> expr + term | expr - term | term
term -> term * factor | term / factor | factor
factor -> digit | (expr)
digit -> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
It is intended to parse simple arithmetic expressions taking into
account the precedence of operators. What I don't understand is why
you parse the operators with lower precedence first. I have worked
through several examples by hand and it works but I don't understand
why it works. Perhaps I should be content with that but I am a
perfectionist.
Here's rough intuition.
Think about the parse tree you want to finish with when parsing, say a
* b + c * d. The expr should have a + node at the top of the tree,
with equal or higher precedence operations (in this case *) or else
terminals as the operands. To get the + at the top, it must be in the
production for expr itself. The higher precedence operators are
"lower" in the grammar.
.
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