Homework 1 - Calculator grammar
For the first homework you should implement a simple calculator. The calculator should accept expressions with addition, subtraction, multiplication, and division operators, as well as parentheses. The grammar (for single-digit numbers) is summarized in:

exp  ->   num | exp op exp | (exp)
op    ->   + | - | * | /
num ->   0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

You need to change this grammar to support priority between addition and multiplication, to remove the left recursion for LL parsing, etc. The homework deliverables are divided into 3 parts.

1. You have to write (and provide in a .txt of .pdf file) the FIRST & FOLLOW sets for the LL(1) version of the above grammar. In the end you will summarize them in a single lookahead table (include a row for every derivation in your final grammar).

2. Based on your LL(1) grammar, you have to write a recursive descent parser in Java that reads expressions from standard input and prints them in prefix notation, where every sub-expression is surrounded with parentheses*, or prints "parse error" if there is a syntax error. You don't need to identify blank space or multi-digit numbers. You can read the symbols one by one (as in the C getchar function). The expression must end with a newline or EOF.
*That is, the expression "3 * 5 + 5 - 4 - 3" must be transformed to " (+ (* 3 5) (- (- 5 4) 3))"

3. You will write a full LR grammar for a calculator using sableCC. The calculator must support the 4 operations, but here you have to do normal parsing, i.e., to ignore blank space and receive non-negative integers of any length. This program will only recognize whether the expression is correct, and will not process it further.