The questions in this section are based on the grammar given as the following:

prog -> assign | expr assign -> id = expr expr -> expr + term | expr - term | term term -> factor | factor * term factor -> ( expr ) | id | num id -> A | B | C num -> 0 | 1 | 2 | 3

(2a) What is the associativity of the * operator? (5 points)

(2b) What is the associativity of the + operator? (5 points)

(2c) For the * and + operators, do they have the same precedence, does the * operator have greater precedence than +, or does + have greater precedence than * ? (5 points)

(2d) Using this grammar show a leftmost derivation and a parse tree for the strings in d.1 (10 points)

Show the parse tree as a graphical tree.

(2d) C = (1 + A) * B

(2e) Modify the grammar to add a new operator as it follows. (10 points)

A unary minus operator (-) that has precedence higher than any of *, +, or binary minus.