Question

1. Consider the following BNF definition of arithmetic expressions: <expression> <expression>+ <term> | <expression>-<term> <term> <term> ::= <term>*<factor> <term>/<factor> | <factor> <factor> :: <digit>«<exponent> | <didgit>^«<exponent> <digit>(<expression> <digit>:= 01|2|3|4151617181910. <exponent> :: <sign> <val> <sign>=+1 - <val 1121314 Draw the expression trees of the following expressions, parsed according to the BNF above. a) 46 - 6/4-243. b) 4*6 -(6/4 - 243) c) 31-2-3*2 + 3/2 d) 3^2*5. e) ((3^2)).

Answer 1

This Grammar is left recursive(the leftmost veriable in RHS is same as its LHS veriable)

Eg: <expression> = <expression> + <term>

So the expression tree also left assosiative.

Read the leaf nodes in the tree from left to right.

a) 4*6 - 6/4 - 2^3

<expression> <expression> <term> <expression> <term> sfactor> <term> A <term> 1 <factor> <digit> <exponent> <term> * sfactor> <factor> <digit> 2 <sign> <val> <factor> <digit> <digit> 4 + 3 6 co <digit> 4

b) 4*6 - (6/4 - 2^3)

c) 3^-2 - 3*2 + 3/2

<expression> <expression> <term> <term> <factor> <expression> * <term> <factor> ( sfactor> <term> <digit> <expression> 6 <factor> <digit> <term> 4 <term> <factor> <digit> ^ <exponent> <factor> <digit> <sign> <val> N <digit> 4 + 3 6

<expression> <expression> + <term> <expression> <term> <term> <factor <term> <term> * <factor> sfactor> <digit> <factor> <factor> <digit> <digit> 2 A <digit> <exponent> <digit> 2 3 کا <sign> <val> 3 N

d) 3^2*5

<expression> <term> * <term> <factor> <factor> <digit> A <digit> <exponent> 5 3 <sign> <val> + N

e) ((3^2))

<expression> <term> <factor> ( <expression> <term> sfactor> <expression> <term> <factor> <digit> ^<exponent> 3 <sign> <val> + N