Translator – Parentheses

Parentheses are used to override the precedence of operators in expressions. For the Translator, parentheses will be handled as operators themselves.

The opening parentheses will be considered a unary operator as it's placement in expressions is the same as for other unary operators – expected when an operand or optional unary operator is expected. The precedence of the opening parentheses will very low, above the Null operator, but below the EOL operator. Above the Null operator because the Null operator should never be removed from the hold stack until the very end. However, below the EOL operator because the opening parentheses token should not be removed from the hold stack at the end of the line – this would be a “missing closing parentheses” error.

The closing parentheses will be considered an ordinary binary operator as it's placement in expressions is the same as for other binary operators, in other words, after operands where a binary operator is expected. The precedence of the closing parentheses will be the same as the EOL operator. This will cause the hold stack to be emptied down to either the Null token at the bottom of the stack or an opening parentheses token.

A closing parentheses operator will require a little extra processing than other operators, similar to the EOL operator. Also, the closing parentheses token will not actually be pushed onto the hold stack. After the hold stack is emptied, if the Null token is on top of hold stack, then a “missing opening parentheses” error would occur. Otherwise, there must be an opening parentheses token on the top of the hold stack which would be popped off of the stack. Nothing needs to be put into the output RPN list...