Statement Constructor

The string constructor for building a statement (which holds logical statements as a tree) is recursive, and requires that the given input is passed in a very specfic format.

A statement takes in a string S, and S can be constructed using the following CFG to build any desired statement.

S -> (S) | (S) or (S) & (S)

• etc. For other arguments S -> A or B or C or Hello
• etc. For other variables

As an example, consider A and B or C.

1. S * Transform this S into (S) | (S)
2. (S) | (S) * Transform the first S into (S) & (S)
3. ((S) & (S)) | (S) * Transform the S's into their respective variables
4. ((A) & (B)) | (C)`

Given the above string, the statement constructor will parse this into a tree with the root containing '|', its left holding a node with '&', etc.