Question

1. Given the Grammar

<expr> --> <expr> + <term> | <term>

<term> --> <term> * <factor> | <factor>

<factor> --> ( <expr> ) | number

For the given string 3 * ( 2 + 5 * 6), perform the following:

1. Left-most derivation

2. Draw a parse tree

3. Draw an abstract syntax tree

Note: number as a terminal has multiple values

Answer 1

1. Left-most derivation

<expr>
-> <term>
-> <term> * <factor>
-> <factor> * <factor>
-> number * <factor>
-> 3 * <factor>
-> 3 * ( <expr> )
-> 3 * (<expr> + <term>)
-> 3 * (<term> + <term>)
-> 3 * (<factor> + <term>)
-> 3 * (number + <term>)
-> 3 * (2 + <term>)
-> 3 * (2 + <term> * <factor>)
-> 3 * (2 + <factor> * <factor>)
-> 3 * (2 + number * <factor>)
-> 3 * (2 + 5 * <factor>)
-> 3 * (2 + 5 * number)
-> 3 * (2 + 5 * 6)

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