Simple precedence grammar

A simple precedence grammar is a context-free formal grammar that can be parsed with a simple precedence parser.

Formal definition

G = (N, Σ, P, S) is a simple precedence grammar if all the production rules in P comply with the following constraints:

• There are no erasing rules (ε-productions)
• There are no useless rules (unreacheable symbols or unproductives rules)
• For each pair of symbols X, Y (X, Y $\in$ (N ∪ Σ)) there is only one Wirth-Weber precedence relation.
• G is uniquely inversible

Examples

Example 1

$S\to aSSb|c$

precedence table:

	S	a	b	c
S	${\dot {=}}$	${\dot {<}}$	${\dot {=}}$	${\dot {<}}$
a	${\dot {=}}$	${\dot {<}}$		${\dot {<}}$
b		${\dot {>}}$	${\dot {>}}$	${\dot {>}}$
c		${\dot {>}}$	${\dot {>}}$	${\dot {>}}$