10.6.  Parse Trees

A parse tree for a grammar G is a tree where

• the root is the start symbol for G

• the interior nodes are the nonterminals of G

• the leaves are the terminal symbols of G.

• the children of a node T (from left to right) correspond to the symbols on the right hand side of some production for T in G.

Every terminal string generated by a grammar has a corresponding parse tree; every valid parse tree represents a string generated by the grammar.

Example: Given the following grammar, find a parse tree for the string 1 + 2 + 3:

1.   <E>:   <N>
2.   <E>:   ( <E> )
3.   <E>:   <E> + <E>
4.   <E>:   <E> - <E>
5.   <E>:   <E> * <E>
6.   <E>:   <E> / <E>
7.   <N>:   0 | 1 | 2 | ... 9

Parse the tree in In-order and substitute the values in the nodes ASAP. The result is 6.

A possible parse tree is also:

Parse the tree in In-order and substitute the values in the nodes ASAP. The result is 6.

Last modified: 27/July/98 (12:14)