Changes

====Example====

====Example====

The following example shows how context-free grammars can cope with arithmetic expressions involving possibly nested brackets. Also an expression such as "2 + 3 * 4" could be interpreted as either "(2 + 3) * 4" or as "2 + (3 * 4)". The latter interpretation is that which is normally used - multiplication "*" is said to have a higher priority than addition "+" - so the example also needs to incorporate this priority concept into the grammar. Furthermore, consecutive operators of the same priority are applied from left to right, so that "8 - 2 + 3" is normally interpreted as "(8 - 2) + 3" = 9, rather than as "8 - (2 + 3)" = 3.  This ordering must also be built in to the grammar.

The following example shows how context-free grammars can cope with arithmetic expressions involving possibly nested brackets. Also an expression such as "2 + 3 * 4" could be interpreted as either "(2 + 3) * 4" = 20 or as "2 + (3 * 4)" = 14. The latter interpretation is that which is normally used - multiplication "*" is said to have a higher priority than addition "+" - so the grammar must incorporate this priority concept. Furthermore, consecutive operators of the same priority are normally applied from left to right, so that "8 - 2 + 3" is interpreted as "(8 - 2) + 3" = 9, rather than as "8 - (2 + 3)" = 3.  This ordering must also be built in to the grammar.

To avoid distracting side-issues, this example only deals with numbers which consist solely of a single digit. The example is a simplified version of the definition of an arithmetic expression given in the Revised Algol 60 Report (Section 3.3.1).

To avoid distracting side-issues, this example only deals with numbers which consist solely of a single digit. The example is a simplified version of the definition of an arithmetic expression given in the Revised Algol 60 Report (Section 3.3.1).