Question

1. Given the grammar:

\(\rightarrow+\langle\) expr \(\rangle\)

\(|*

\(\mid(\) \(>)\)

| \(\rangle\)

\(\langle\mathrm{id}>\rightarrow \mathrm{A}|\mathrm{B}| \mathrm{C}\)

(a) Show the parse tree of expression: \(A+C^{*} B\)

(b) Show the parse tree of expression: \(A^{*}(B+(C))\)

Answer 1

Derivation for A+C*B :

-> +

-> + *

-> + *

-> A + C * B

Derivation for A * (B+(C)) :

-> *

-> * ()

-> * ( + )

-> * ( + ())

-> * ( + ())

-> A * (B + (C))
Parse tree for A+C* B expr> id> expr> id> id>

Parse tree forA* (B+(C)) expr> id> expr> id> expr expr> id>