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## Solution for Programmming Exercise 10.6

This page contains a sample solution to one of the exercises from Introduction to Programming Using Java.

### Exercise 10.6:

The sample program SimpleInterpreter.java from Subsection 10.4.1 can carry out commands of the form "let variable = expression" or "print expression". That program can handle expressions that contain variables, numbers, operators, and parentheses. Extend the program so that it can also handle the standard mathematical functions sin, cos, tan, abs, sqrt, and log. For example, the program should be able to evaluate an expression such as sin(3*x-7)+log(sqrt(y)), assuming that the variables x and y have been given values. Note that the name of a function must be followed by an expression that is enclosed in parentheses.

In the original program, a symbol table holds a value for each variable that has been defined. In your program, you should add another type of symbol to the table to represent standard functions. You can use the following nested enumerated type and class for this purpose:

    private enum Functions { SIN, COS, TAN, ABS, SQRT, LOG }

    /**
     * An object of this class represents one of the standard functions.
     */
    private static class StandardFunction {

       /**
        * Tells which function this is.
        */
       Functions functionCode;

       /**
        * Constructor creates an object to represent one of
        * the standard functions
        * @param code which function is represented.
        */
       StandardFunction(Functions code) {
          functionCode = code;
       }

       /**
        * Finds the value of this function for the specified
        * parameter value, x.
        */
       double evaluate(double x) {
          switch(functionCode) {
          case SIN:
             return Math.sin(x);
          case COS:
             return Math.cos(x);
          case TAN:
             return Math.tan(x);
          case ABS:
             return Math.abs(x);
          case SQRT:
             return Math.sqrt(x);
          default:
             return Math.log(x);
          }
       }

    } // end class StandardFunction

Add a symbol to the symbol table to represent each function. The key is the name of the function and the value is an object of type StandardFunction that represents the function. For example:

    symbolTable.put("sin", new StandardFunction(StandardFunction.SIN));

In SimpleInterpreter.java, the symbol table is a map of type HashMap<String,Double>. It's not legal to use a StandardFunction as the value in such a map, so you will have to change the type of the map. The map has to hold two different types of objects. The easy way to make this possible is to create a map of type HashMap<String,Object>. (A better way is to create a general type to represent objects that can be values in the symbol table, and to define two subclasses of that class, one to represent variables and one to represent standard functions, but for this exercise, you should do it the easy way.)

In your parser, when you encounter a word, you have to be able to tell whether it's a variable or a standard function. Look up the word in the symbol table. If the associated object is non-null and is of type Double, then the word is a variable. If it is of type StandardFunction, then the word is a function. Remember that you can test the type of an object using the instanceof operator. For example: if (obj instanceof Double)

Discussion

The changes that must be made to SimpleInterpreter.java are remarkably small, aside from defining the StandardFunction class. In my solution, I included this class as a static nested class in my main program class. It would also make sense to define it as a separate class.

I changed the type of the map to HashMap<String,Object>, as suggested in the exercise. I added a few lines of code at the beginning of the main() routine to add the six standard functions to the symbol table. I could have done this with six lines of the same form as the one given in the exercise:

    symbolTable.put("sin", new StandardFunction(StandardFunction.SIN));
    symbolTable.put("cos", new StandardFunction(StandardFunction.COS));
    symbolTable.put("tan", new StandardFunction(StandardFunction.TAN));
    symbolTable.put("abs", new StandardFunction(StandardFunction.ABS));
    symbolTable.put("sqrt", new StandardFunction(StandardFunction.SQRT));
    symbolTable.put("log", new StandardFunction(StandardFunction.LOG));

However, it's easier to do it with a for-each loop that iterates through all the possible values of the enum Functions (see Subsection 3.4.4):

    for ( Functions func : Functions.values() )
        symbolTable.put( func.toString().toLowerCase(), new StandardFunction(func) );

The only other change is in the parsing routines. The change is in the primaryValue() method. When a word is encountered, the computer must check whether the word is a variable or a standard function. This is done, as suggested in the exercise, by looking up the word in the symbol table and checking the type of the associated value. If the word is a standard function, then we have to read and evaluate the argument of the function and then find the value of the function at that argument value:

    else if ( Character.isLetter(ch) ) {
          // The factor is a variable or a standard function.  Read its name and
          // look up its value in the symbol table.  If the name is not in the symbol table,
          // an error occurs.  (Note that the values in the symbol table are objects of type
          // Double or StandardFunction.)
       String name = readWord();
       Object obj = symbolTable.get(name);
       if (obj == null)
          throw new ParseError("Unknown word \"" + name + "\"");
       assert (obj instanceof Double || obj instanceof StandardFunction);
       if (obj instanceof Double) {
             // The name is a variable; return value of that variable.
          Double val = (Double)obj;
          return val.doubleValue();
       }
       else {
             // The name is a standard function.  Read the argument
             // of the function and return the value of the function
             // at that argument.  The argument must be an expression
             // in parentheses.
          StandardFunction func = (StandardFunction)obj;
          TextIO.skipBlanks();
          if ( TextIO.peek() != '(' )
             throw new ParseError("Parenthesis missing after standard function");
          TextIO.getChar(); // discard the '('
          double argument = expressionValue();  // read and evaluate expression
          TextIO.skipBlanks();
          if ( TextIO.peek() != ')' )
             throw new ParseError("Missing right parenthesis.");
          TextIO.getChar(); // discard the ')'
          return func.evaluate(argument);
       }
    }

There is one additional change that I might have made. As the program stands, it allows the user to use a "let" command to assign a value to one of the standard function names. For example: "let sin = 42". This effectively changes the name so that it is a variable, and the standard function is no longer available for use in expressions. It would probably be better to give an error message when the user tries to assign a value to a standard function name. This could be done in the doLetCommand() method. After reading the variable name in the "let" command, we have to check test whether the name is already in the symbol table as the name of a standard function:

    private static void doLetCommand() throws ParseError {
       TextIO.skipBlanks();
       if ( ! Character.isLetter(TextIO.peek()) )
          throw new ParseError("Expected variable name after 'let'.");
       String varName = readWord();  // The name of the variable.
       Object symbol = symbolTable.get(name);
       if (symbol != null && symbol instanceof StandardFunction)
           throw new ParseError("Can't assign a value to a standard function name.");
       TextIO.skipBlanks();
       if ( TextIO.peek() != '=' )
          throw new ParseError("Expected '=' operator for 'let' command.");
       TextIO.getChar();
       double val = expressionValue();  // The value of the variable.
       TextIO.skipBlanks();
       if ( TextIO.peek() != '\n' )
          throw new ParseError("Extra data after end of expression.");
       symbolTable.put( varName, val );  // Add to symbol table.
       TextIO.putln("ok");
    }

In this program, I use an enum and a class to represent standard functions. Every object that belongs to the class will correspond to one of the values of the enum. I could make the program prettier by using the fact that enums are classes. The fact is that an enum can contain more than a list of enum constants. It can also contain methods and variables and most other things that any other class can contain. Instead of using a separate enum to list the possible standard functions, we could make StandardFunction itself into an enum:

    private enum StandardFunction {

       SIN, COS, TAN, ABS, SQRT, LOG;

       /**
        * Finds the value of this function for the specified
        * parameter value, x.
        */
       double evaluate(double x) {
          switch(this) {
          case SIN:
             return Math.sin(x);
          case COS:
             return Math.cos(x);
          case TAN:
             return Math.tan(x);
          case ABS:
             return Math.abs(x);
          case SQRT:
             return Math.sqrt(x);
          default:
             return Math.log(x);
          }
       }

    } // end enum StandardFunction

With this definition, the possible values of type StandardFucntion are the enum constants SIN, COS, etc. These values are objects and each object contains an evaluate(x) method that can be used to find the value of the standard function for a given argument x. With this definition, the code for adding the standard functions to the symbol table becomes

    for ( StandardFunction func : StandardFunction.values() )
        symbolTable.put( func.toString().toLowerCase(), func);

or:

    symbolTable.put("sin", StandardFunction.SIN);
    symbolTable.put("cos", StandardFunction.COS);
    symbolTable.put("tan", StandardFunction.TAN);
    symbolTable.put("abs", StandardFunction.ABS);
    symbolTable.put("sqrt", StandardFunction.SQRT);
    symbolTable.put("log", StandardFunction.LOG);

No other changes are necessary in the program.

The Solution

Changes from the program SimpleInterpreter.java are shown in red.

    /*
        This program can evaluate expressions that can include
        numbers, variables, parentheses, and the operators +,
        -, *, /, and ^ (where ^ indicates raising to a power),
        and standard functions sin, cos, tan, abs, sqrt, and log.
        A variable name must consist of letters and digits,
        beginning with a letter.  Names are case-sensitive.
        This program accepts commands of two types from the user.
        For a command of the form  print <expression> , the expression
        is evaluated and the value is output.  For a command of
        the form  let <variable> = <expression> , the expression is
        evaluated and the value is assigned to the variable.
        If a variable is used in an expression before it has been
        assigned a value, an error occurs.  A number must begin with
        a digit (i.e., not a decimal point).

        Commands are formally defined by the BNF rules:

                <command>  ::=  "print" <expression>
                                   |  "let" <variable> "=" <expression>

                <expression>  ::=  [ "-" ] <term> [ [ "+" | "-" ] <term> ]...

                <term>  ::=  <factor> [ [ "*" | "/" ] <factor> ]...

                <factor>  ::=  <primary> [ "^" <primary> ]...

                <primary>  ::=  <number> | <variable> | "(" <expression> ")"
                                     | <standard-function-name> "(" <expression> ")"

        A line of input must contain exactly one such command.  If extra
        data is found on a line after an expression has been read, it is
        considered an error.  The variables "pi" and "e" are defined
        when the program starts to represent the usual mathematical
        constants.

        This program demonstrates the use of a HashMap as a symbol
        table.

        SimpleInterpreter2.java is based on the program SimpleInterpreter.java,
        which did not handle standard functions in expressions.

        This program depends on the non-standard class, TextIO.
     */

    import java.util.HashMap;

    public class SimpleInterpreter2 {

       /**
        * Represents a syntax error found in the user's input.
        */
       private static class ParseError extends Exception {
          ParseError(String message) {
             super(message);
          }
       } // end nested class ParseError

       /**
        * An enumerated type whose values represent the possible
        * standard functions.
        */
       private enum Functions { SIN, COS, TAN, ABS, SQRT, LOG }

       /**
        * An object of this class represents one of the standard functions.
        * Objects of this type are stored in the symbol table, associated
        * with the name of the standard functions.  Note that an object
        * of this type also knows how to evaluate the corresponding function.
        */
       private static class StandardFunction {

          /**
           * Tells which function this is.
           */
          Functions functionCode;

          /**
           * Constructor creates an object to represent one of
           * the standard functions
           * @param code which function is represented.
           */
          StandardFunction(Functions code) {
             functionCode = code;
          }

          /**
           * Finds the value of this function for the specified
           * parameter value, x.
           */
          double evaluate(double x) {
             switch(functionCode) {
             case SIN:
                return Math.sin(x);
             case COS:
                return Math.cos(x);
             case TAN:
                return Math.tan(x);
             case ABS:
                return Math.abs(x);
             case SQRT:
                return Math.sqrt(x);
             default:
                return Math.log(x);
             }
          }

       } // end class StandardFunction

       /**
        * The symbolTable contains information about the values of variables.  When a variable
        * is assigned a value, it is recorded in the symbol table. The key is the name of the
        * variable, and the  value is an object of type Double that contains the value of the
        * variable.
        *    The symbol table can also contain standard functions.  The key is the name of
        * of the function, and the value is the corresponding StandardFunction object.
        */
       private static HashMap<String,Object> symbolTable;

       public static void main(String[] args) {

          // Create the map that represents symbol table.

          symbolTable = new HashMap<String,Object>();

          // To start, add variables named "pi" and "e" to the symbol
          // table.  Their values are the usual mathematical constants.

          symbolTable.put("pi", Math.PI);
          symbolTable.put("e", Math.E);

          // Add the standard functions to the hash table.

          for ( Functions func : Functions.values() )
             symbolTable.put( func.toString().toLowerCase(), new StandardFunction(func) );

          TextIO.putln("\n\nEnter commands; press return to end.");
          TextIO.putln("Commands must have the form:\n");
          TextIO.putln("      print <expression>");
          TextIO.putln("  or");
          TextIO.putln("      let <variable> = <expression>");

          while (true) {
             TextIO.put("\n?  ");
             TextIO.skipBlanks();
             if ( TextIO.peek() == '\n' ) {
                break;  // A blank input line ends the while loop and the program.
             }
             try {
                String command = TextIO.getWord();
                if (command.equalsIgnoreCase("print"))
                   doPrintCommand();
                else if (command.equalsIgnoreCase("let"))
                   doLetCommand();
                else
                   throw new ParseError("Command must begin with 'print' or 'let'.");
                TextIO.getln();
             }
             catch (ParseError e) {
                TextIO.putln("\n*** Error in input:    " + e.getMessage());
                TextIO.putln("*** Discarding input:  " + TextIO.getln());
             }
          }

          TextIO.putln("\n\nDone.");

       } // end main()

       /**
        * Process a command of the form  let <variable> = <expression>.
        * When this method is called, the word "let" has already
        * been read.  Read the variable name and the expression, and
        * store the value of the variable in the symbol table.
        */
       private static void doLetCommand() throws ParseError {
          TextIO.skipBlanks();
          if ( ! Character.isLetter(TextIO.peek()) )
             throw new ParseError("Expected variable name after 'let'.");
          String varName = readWord();  // The name of the variable.
          TextIO.skipBlanks();
          if ( TextIO.peek() != '=' )
             throw new ParseError("Expected '=' operator for 'let' command.");
          TextIO.getChar();
          double val = expressionValue();  // The value of the variable.
          TextIO.skipBlanks();
          if ( TextIO.peek() != '\n' )
             throw new ParseError("Extra data after end of expression.");
          symbolTable.put( varName, val );  // Add to symbol table.
          TextIO.putln("ok");
       }

       /**
        * Process a command of the form  print <expression>.
        * When this method is called, the word "print" has already
        * been read.  Evaluate the expression and print the value.
        */
       private static void doPrintCommand() throws ParseError {
          double val = expressionValue();
          TextIO.skipBlanks();
          if ( TextIO.peek() != '\n' )
             throw new ParseError("Extra data after end of expression.");
          TextIO.putln("Value is " + val);
       }

       /**
        * Read an expression from the current line of input and return its value.
        */
       private static double expressionValue() throws ParseError {
          TextIO.skipBlanks();
          boolean negative;  // True if there is a leading minus sign.
          negative = false;
          if (TextIO.peek() == '-') {
             TextIO.getAnyChar();
             negative = true;
          }
          double val;  // Value of the expression.
          val = termValue();  // An expression must start with a term.
          if (negative)
             val = -val; // Apply the leading minus sign
          TextIO.skipBlanks();
          while ( TextIO.peek() == '+' || TextIO.peek() == '-' ) {
                // Read the next term and add it to or subtract it from
                // the value of previous terms in the expression.
             char op = TextIO.getAnyChar();
             double nextVal = termValue();
             if (op == '+')
                val += nextVal;
             else
                val -= nextVal;
             TextIO.skipBlanks();
          }
          return val;
       } // end expressionValue()

       /**
        * Read a term from the current line of input and return its value.
        */
       private static double termValue() throws ParseError {
          TextIO.skipBlanks();
          double val;  // The value of the term.
          val = factorValue();  // A term must start with a factor.
          TextIO.skipBlanks();
          while ( TextIO.peek() == '*' || TextIO.peek() == '/' ) {
                // Read the next factor, and multiply or divide
                // the value-so-far by the value of this factor.
             char op = TextIO.getAnyChar();
             double nextVal = factorValue();
             if (op == '*')
                val *= nextVal;
             else
                val /= nextVal;
             TextIO.skipBlanks();
          }
          return val;
       } // end termValue()

       /**
        * Read a factor from the current line of input and return its value.
        */
       private static double factorValue() throws ParseError {
          TextIO.skipBlanks();
          double val;  // Value of the factor.
          val = primaryValue();  // A factor must start with a primary.
          TextIO.skipBlanks();
          while ( TextIO.peek() == '^' ) {
                // Read the next primary, and exponentiate
                // the value-so-far by the value of this primary.
             TextIO.getChar();
             double nextVal = primaryValue();
             val = Math.pow(val,nextVal);
             if (Double.isNaN(val))
                throw new ParseError("Illegal values for ^ operator.");
             TextIO.skipBlanks();
          }
          return val;
       } // end termValue()

       /**
        *  Read a primary from the current line of input and
        *  return its value.  A primary must be a number,
        *  a variable, or an expression enclosed in parentheses.
        */
       private static double primaryValue() throws ParseError {
          TextIO.skipBlanks();
          char ch = TextIO.peek();
          if ( Character.isDigit(ch) ) {
                // The factor is a number.  Read it and
                // return its value.
             return TextIO.getDouble();
          }
          else if ( Character.isLetter(ch) ) {
                // The factor is a variable or a standard function.  Read its name and
                // look up its value in the symbol table.  If the name is not in the symbol table,
                // an error occurs.  (Note that the values in the symbol table are objects of type
                // Double or StandardFunction.)
             String name = readWord();
             Object obj = symbolTable.get(name);
             if (obj == null)
                throw new ParseError("Unknown word \"" + name + "\"");
             assert (obj instanceof Double || obj instanceof StandardFunction);
             if (obj instanceof Double) {
                   // The name is a variable; return value of that variable.
                Double val = (Double)obj;
                return val.doubleValue();
             }
             else {
                   // The name is a standard function.  Read the argument
                   // of the function and return the value of the function
                   // at that argument.  The argument must be an expression
                   // in parentheses.
                StandardFunction func = (StandardFunction)obj;
                TextIO.skipBlanks();
                if ( TextIO.peek() != '(' )
                   throw new ParseError("Parenthesis missing after standard function");
                TextIO.getChar(); // discard the '('
                double argument = expressionValue();  // read and evaluate expression
                TextIO.skipBlanks();
                if ( TextIO.peek() != ')' )
                   throw new ParseError("Missing right parenthesis.");
                TextIO.getChar(); // discard the ')'
                return func.evaluate(argument);
             }
          }
          else if ( ch == '(' ) {
                // The factor is an expression in parentheses.
                // Return the value of the expression.
             TextIO.getAnyChar();  // Read the "("
             double val = expressionValue();
             TextIO.skipBlanks();
             if ( TextIO.peek() != ')' )
                throw new ParseError("Missing right parenthesis.");
             TextIO.getAnyChar();  // Read the ")"
             return val;
          }
          else if ( ch == '\n' )
             throw new ParseError("End-of-line encountered in the middle of an expression.");
          else if ( ch == ')' )
             throw new ParseError("Extra right parenthesis.");
          else if ( ch == '+' || ch == '-' || ch == '*' || ch == '/')
             throw new ParseError("Misplaced operator.");
          else
             throw new ParseError("Unexpected character \"" + ch + "\" encountered.");
       }

       /**
        *  Reads a word from input.  A word is any sequence of
        *  letters and digits, starting with a letter.  When
        *  this subroutine is called, it should already be
        *  known that the next character in the input is
        *  a letter.
        */
       private static String readWord() {
          String word = "";  // The word.
          char ch = TextIO.peek();
          while (Character.isLetter(ch) || Character.isDigit(ch)) {
             word += TextIO.getChar(); // Add the character to the word.
             ch = TextIO.peek();
          }
          return word;
       }

    } // end class SimpleInterpreter

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