Questions

$($Adapted from $AU$ ex$.5\mathrm{.}2\mathrm{.}7)$ Give expression trees for the following expressions. Use the Order

of Operations for precedence and associativity of operators. Each expression has $!1$ expression

tree. E$.$g$.,$ even though addition is associative, the Order of Operations indicates that we

evaluate left$-$to$-$right.

Please remember, multiplication and division have the same precedence, as do addition and

subtraction $($which is lower than multiplication$).$

Also, please remember, Exponentiation associates right$-$to$-$left.

a$)(x+1)(x-y+4)$

b$)1+2+3+4+5+6$

c$)98+76+5$

d$)2^{3^2}5-8$

$($Adapted from AU ex$.5\mathrm{.}4\mathrm{.}6)$ For each of the expressions in question $1,$ above, provide the

equivalent preorder expression.

$($Adapted from AU ex$.5\mathrm{.}4\mathrm{.}6)$ For each of the expressions in question $1,$ above, provide the

equivalent postorder expression.

$($AU ex$.11\mathrm{.}2\mathrm{.}1)$ Give a grammar to define the syntactic category $$ Identifier $>,$ for all those

strings that are $C$ identifiers. You may find it useful to define some auxiliary syntactic categories

like Digit :$).($Note$,$ valid $C$ identifiers are exactly the same symbols in Python, Bash, Java,

$C$#$,$ and many others.$)$

$($AU ex$.11\mathrm{.}2\mathrm{.}2)$ Arithmetic expressions in $C$ can take identifiers, as well as numbers, as

operands. Modify the grammar of Fig. $11\mathrm{.}2$ so that operands can also be identifiers. Use

the syntactic category $$ Identifier $>$ from question $4,$ above. No need to define it again.