Simple precedence grammar

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

Formal definition

G = (N, Σ, P, S) is a Simple precedence grammar such that all the productions rules in P complies with the following constraints:

• There is no Erasing Rules (ε-productions)
• There is 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 number 1

$S\to aSSb|c$

precedence table:

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

As there is no conflict present in the table, and there is no Useless Rules nor Erasing Rules, and the grammar is Uniquely Inversible, this grammar is a Simple precedence grammar