An Expression Interpreter

Case Study

The case study for this module incorporates two of the language features that we discussed—expressions and assignments. The program interprets fully parenthesized arithmetic expressions that contain either literal values or variables. The variables must then subsequently be assigned values.

The grammar for the language that this interpreter accepts is defined by the following grammar: See image.

The regular expressions defining the three tokens are the following: See image.

So, if you were to enter the following expression:

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

the interpreter would respond:

Value = 20

The interpreter itself is written in C++. The complete program consists of 10 classes. We will present 7 of them. Your instructor may ask you to complete this program, perhaps enhance it, and add some error checking as one of the programming projects.

We begin with the main function and one subordinate function, which are contained in module3.cpp. The main function reads in the program, calls upon the static function parse of the SubExpression class to parse it, and builds an arithmetic expression tree. It then calls the subordinate function parseAssignments to parse the assignments and enter them into the symbol table, and then evaluates the expression and displays the result. That code is shown below: See image.

The arithmetic expression tree is built using an inheritance hierarchy. At the root of the hierarchy is the abstract class Expression. The class definition for Expression is contained in the file expression.h, shown below: See image.

This abstract class has two subclasses. The first of these is SubExpression, which defines the node of the binary arithmetic expression tree. The class definition for SubExpression is contained in the file subexpression.h, shown below: See image.

As is customary in C++, the bodies of the member functions of that class are contained in the file subexpression.cpp, shown below: See image.

The SubExpression class has four subclasses. We show one of them—Plus. The class definition for Plus is contained in the file plus.h, shown below: See image.

Because the bodies of both member functions are inline, no corresponding .cpp file is required. The other subclass of Expression is Operand, which defines the leaf nodes of the arithmetic expression tree. The class definition for Operand is contained in the file operand.h, shown below: See image.

The body of its only member function is contained in operand.cpp, shown below: See image.

The Operand class has two subclasses. The first is Variable, which defines leaf nodes of the tree that contain variables. The class definition for Variable is contained in the file variable.h, shown below: See image.

The body of its member function evaluate is contained in variable.cpp, shown below: See image.

The other subclass of Operand is Literal, which defines leaf nodes of the tree that contain literal values. The class definition for Literal is contained in the file literal.h, shown below: See image.

This interpreter uses a symbol table that is implemented with an unsorted list defined by the class SymbolTable. Its class definition is contained in the file symboltable.h, shown below: See image.

The bodies of its member functions are in the file symboltable.cpp, shown below: See image.

Finally, one utility function, parseName, is needed by this program. Its function prototype is the file parse.h, shown below:

string parseName();

Its body is in parse.cpp, shown below: See image.

The second project involves completing and modifying the C++ program that evaluates statements of an expression language contained in the case study.

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 in the case study.

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 two 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.