Part I:

Unary minuses can be added in several ways to the arithmetic expression grammar of Figure $6\mathrm{.}17$ or Figure $6\mathrm{.}18.$ Revise the BNF and EBNF for each of the cases that follow so that it satisfies the stated rule:

At most, one unary minus is allowed in each expression, and it must come at the beginning of an expression, so $-2+3$ is legal $($and equals $1)$ and $-2+(-3)$ is legal, but $-2+-3$ is not.

At most, one unary minus is allowed before a number or left parenthesis, so $-2+-3$ and $-2*-3$ are legal, but $--2$ and $-2+--3$ are not.

Arbitrarily many unary minuses are allowed before numbers and left parentheses, so everything above is legal.

Part II:

Using the grammar of Figure $6\mathrm{.}17,$ draw parse trees and abstract syntax trees for the arithmetic expression:

$((2))$

$3+4*5+6*7$

$3*4+5*6+7$

$3*(4+5)*(6+7)$

$(2+(3+(4+5)))$