You are given a grammar, called SimpleExpr (see below). 1. [30 points] List the strings/sentences that are in the language specified by the grammar above (SimpleExpr). 2. How many token types are needed in a lexer to parse strings in the language? Please list all the token types needed in a lexer to parser strings in the language specified by the grammar above. 3. [40 points] Using Pattern 2, LL(1) Recursive-Descent Lexer, specify the functions necessary to build a lexer for the language specified by the grammar above. Here, you are expected to just list the name of the functions, no need to provide the code.

You are given a grammar, called SimpleExpr (see below). grammar SimpleExpr; expr : expr '+' expr | expr **? expr | ID | Number; // allow add or mult ID :('a' ... 'z' 'A'... 'Z'); // ID is Seq of > 1 letter Number : (0'... '9'); // Number is seq of> 1 digit