This exercise focusses on two topics:

• inheritance, and
• representing logical expressions as Java data types.

You should have encountered propositional logic in the Logic and Computation course last semester. In this exercise, you will take initial steps in represent formulas of propositional logic in Java. We will restrict our attention to expressions such as $P\mathrm{\&}Q$ and $P\to Q$. Both of these are examples of Well-Formed Formulas (Wffs). They can each be broken down into smaller parts: a left conjunct $P$, an operator (either $\mathrm{\&}$ or $\to$) and a right conjunct $Q$. The left and right conjuncts are examples of Propositional Variables. We will treat these as data types where the lexical form of the variable is passed as a String argument to the constructor. That is, we’ll be able to say things like:

PropVar p = new PropVar("P");

Here is an implementation of the class PropVar:

public class PropVar {

     private String propVar;

     public PropVar(String str) {
             this.propVar = str;
     }

     public String toString() {
             return propVar;
     }

 }

The method toString() simply returns the string we used in initialization.

Let’s return to the Wffs $P\mathrm{\&}Q$ and $P\to Q$. From a semantic point of view, what matters most in distinguishing the two types of Wff is the the operator, that is, $\mathrm{\&}$ versus $\to$. We will define two types of ‘Binary Wff’, which we will call AndWff and IfWff. As we’ve already observed, these both have data in common: a leftmost PropVar, a rightmost PropVar and a binary operator. Rather than duplicating this information, we should try to place it in a superclass, which we will call BinaryWff. Then we can say that AndWff and IfWff are subclasses of BinaryWff.

We will want to control the syntactic aspects of BinaryWffs, by listing the allowed operators. To do this, we will use Java’s enum type. This is is a type whose instance variable consist of a fixed set of constants. We will take these to be AND, OR and IF. Each of the variables can be defined to have its own toString() method.

public enum Operator {

     AND {
             public String toString() {
                     return "&";
             }
     },

     OR {
             public String toString() {
                     return "|";
             }
     },

     IF {
             public String toString() {
                     return "->";
             }
     }

 }

You can look at the Oracle Java Tutorial to find out more about enum types. Note that client code will be able to use the values in the enum type as Operator.AND and so on.

Here is an example of client code to construct instances of AndWff:

PropVar p = new PropVar("P");
PropVar q = new PropVar("Q");
AndWff andWff = new AndWff(p, q);
System.out.println(andWff); // (P & Q)

Create an class BinaryWff which meets the following API:

public BinaryWff(PropVar left, PropVar right)

public void setOp(Operator op)

public Operator getOp()

public PropVar getLeft()

public PropVar getRight()

public String toString()

Return a string of the form (<left> <op> <right>).

Next, create a class AndWff which is a subclass of BinaryWff. The only thing that you need to specify is the constructor:

public AndWff(PropVar left, PropVar right)

Class constructor. This should call the constructor of its superclass, and also specify that its operator is Operator.AND.

The definition for IfWff would be exactly the same, except that the operator would be specified as Operator.IF. However, you can skip this.