## Regular expressions, Theory of Computation

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The project 2 involves completing and modifying the C++ program that evaluates statements of an expression language contained in the Expression Interpreter that interprets fully parenthesized arithmetic expressions that contain either literal values or variables. For example, the grammar for the language that this interpreter accepts is defined by the following grammar:

, ;

→ ( )

| |

, |

=

The regular expressions defining the three tokens are the following:

[+-*/]

[a-zA-Z][a-zA-Z0-9]*

[0-9]+

So, if you were to enter the following expression:

(x + (y * 3)), x = 2, y = 6;

the interpreter would respond:

Value = 20

The statements of that expression language consist of an arithmetic expression followed by a list of assignments. Assignments are separated from the expression and each other by commas. A semicolon terminates the expression. The arithmetic expressions are fully parenthesized infix expressions containing integer literals and variables. The valid operators are +, -, *, /. Tokens can be separated by any number of spaces. Variable names begin with an alphabetic character, followed by any number of alphanumeric characters. Variable names are case sensitive. This syntax is described by BNF and regular expressions.

The program reads in the arithmetic expression and encodes the expression as a binary tree. After the expression has been read in, the variable assignments are read in and the variables and their values of the variables are placed into the symbol table. Finally the expression is evaluated recursively.

Your first task is to complete the program provided by providing the three missing classes, Minus, Times and Divide.

Next, you should modify the program to detect and report the following error conditions:

• Division by zero should be reported as a division error and the program should proceed to the next expression.

• Input containing uninitialized variables should be reported as an initialization error and the program should proceed to the next expression.

• Variables initialized but never used should be reported as a warning.

• Syntax errors including mismatched parentheses, invalid operator, missing comma, semicolon or assignment operator should be reported as a syntax error and the program should proceed to the next expression.

Your final task is to make the following three modifications to the program:

• The program should accept input from a file, allowing for multiple expressions arranged one per line.

• The SymbolTable class should be modified so that if a variable is assigned multiple values, the last assignment applies.

• The Literal class should be modified so that expressions containing floating point literals are properly evaluated.

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