Translator – Parentheses (More on Dummy Tokens)

Not all cases of adding dummy parentheses tokens occur when an operand is about to be added to the output list.  Next consider the expression:

A Op1 (B Op2 C)

This expression will be translated to A B C Op2 Op1. When this is recreated, the parentheses will only be added if the precedence of Op2 is lower than or the same as Op1 (in other words, when the parentheses are required). The dummy token is only required after Op2 when the precedence of Op2 is higher than Op1.

This decision, whether to add the dummy token, needs to be made before the Op1 operator is added to the list. At this point, Op1 is on the top of the hold stack and the EOL is being processed (the stack is about to be emptied). Therefore, in the code at the point that an operator is about to be added to the output list from the top of the hold stack, there needs to be the check if a closing parentheses was just processed and the precedence of the last operator added (Op2) during the processing of closing parentheses (handling the case that the parentheses is just around an operand) is higher than the operator on top of the hold stack (Op1) then add the closing parentheses token to the list.  Now consider the extension on the above expression:

A Op1 (B Op2 C) Op3 D

At the point of the decision, Op3 is being processed and Op1 is on top of the hold stack. Either Op1 will be popped off the stack and added to the list (Op1 is higher precedence than Op3), or Op3 will be pushed on the stack (Op3 is higher precedence than Op1). For the former case, the precedence check for the dummy token is made between Op2 (the last operator added during the parentheses processing) and Op1. For the later case, the precedence check is made between Op2 and Op3, which is on top of the stack at the EOL processing (Op1 would be popped and added last).

Remember that EOL is processed as a low precedence operator. Ditto for a closing parentheses, which is also processed as a low precedence operator. Therefore the dummy token check is made whenever an operator is going to be added to the output list.  Almost done, but a few more expressions need to be considered...