8.5

#### Lecture 12: Defining sameness for complex data, part 2

Using double-dispatch to test for sameness

##### Motivation

In Lecture 11: Defining sameness for complex data, part 1 we took up the question, “How can we test when two values are ‘the same’?” We introduced two new language mechanisms: casting to try to convince Java to treat an identifier as if it were declared at a more specific type, and instanceof to check whether a given value actually is of a particular type. But our implementations were brittle and suffered from clumsy helper methods that were not useful outside this limited context, and still potentially could throw exceptions and crash. Plus, our design sense should be warning us: any time we feel tempted to try to do a type-test in Java, we ought to find a better way...preferably using dynamic dispatch.

Recall our desired properties for a sameness test:
• Reflexivity: every object should be the same as itself.

• Symmetry: if object x is the same as object y, then y is the same as x.

• Transitivity: if two objects are both the same as a third object, then they are the same as each other.

• Totality: we can compare any two objects of the same type, and obtain a correct answer.

Let’s also bring back our tests from last time:
 // In test method in an Examples class Circle c1 = new Circle(3, 4, 5); Circle c2 = new Circle(4, 5, 6); Circle c3 = new Circle(3, 4, 5); Rect r1 = new Rect(3, 4, 5, 5); Rect r2 = new Rect(4, 5, 6, 7); Rect r3 = new Rect(3, 4, 5, 5); Square s1 = new Square(3, 4, 5); Square s2 = new Square(4, 5, 6); Square s3 = new Square(3, 4, 5); t.checkExpect(c1.sameCircle(c2), false) t.checkExpect(c2.sameCircle(c1), false) t.checkExpect(c1.sameCircle(c3), true) t.checkExpect(c3.sameCircle(c1), true) t.checkExpect(r1.sameRect(r2), false) t.checkExpect(r2.sameRect(r1), false) t.checkExpect(r1.sameRect(r3), true) t.checkExpect(r3.sameRect(r1), true) t.checkExpect(s1.sameShape(s2), false) t.checkExpect(s2.sameShape(s1), false) t.checkExpect(s1.sameShape(s3), true) t.checkExpect(s3.sameShape(s1), true) // Comparing a Square with a Rect of a different size t.checkExpect(s1.sameShape(r2), false) t.checkExpect(r2.sameShape(s1), false) // Comparing a Square with a Rect of the same size t.checkExpect(s1.sameShape(r1), false) t.checkExpect(r1.sameShape(s1), false)

To design a better mechanism for checking sameness...we have actually already written nearly all the helpers we need. We just need to use them more cleverly!

##### 12.1Sameness for unions: Successful attempt using double-dispatch

Let’s retrace our steps to see what went wrong when trying to define sameShape for the Circle class:
 // In Circle: public boolean sameShape(IShape that) { /* * Fields: * this.x, this.y, this.radius * * Methods: * this.sameShape(IShape) -> boolean * this.sameCircle(Circle) -> boolean * * Methods on fields: * * Fields of parameters: * * Methods on parameters: * that.sameShape(IShape) -> boolean */ ??? }
We had nothing in our template that we could use: we didn’t have enough information about that to determine what sort of shape it was.

Suppose we had the following idea: the sameCircle, sameRect and sameSquare methods were at least somewhat useful, so let’s add those methods to the IShape interface.
 interface IShape { boolean sameShape(IShape that); boolean sameCircle(Circle that); boolean sameRect(Rect that); boolean sameSquare(Square that); }

Do Now!

Now the Circle class needs implementations for sameRect and sameSquare, the Rect class is missing sameCircle and sameSquare, and Square is missing sameCircle and sameRect. Implement them — they should be very short!

Now let’s look at how our template has changed:
 // In Circle: public boolean sameShape(IShape that) { /* * Fields: * this.x, this.y, this.radius * * Methods: * this.sameShape(IShape) -> boolean * this.sameCircle(Circle) -> boolean * this.sameRect(Rect) -> boolean * this.sameSquare(Square) -> boolean * * Methods on fields: * * Fields of parameters: * * Methods on parameters: * that.sameShape(IShape) -> boolean * that.sameCircle(Circle) -> boolean * that.sameRect(Rect) -> boolean * that.sameSquare(Square) -> boolean */ ??? }
We have several more methods to choose from; perhaps we can use one of them to finish our method.

Do Now!

Looking at the types for this and that, which method in the template is most likely to be useful?

We’d be going around in circles...

We could try invoking that.sameShape(this), but that doesn’t really make any progress. (In fact, if that is also a Circle, we’d end up stuck in an infinite recursion, with no base case.) We know that that is some IShape. And we know—because we’re in the Circle class—that this is a Circle, and not just another IShape. Which means we can invoke that.sameCircle(...) using this as the argument:
 // In Circle: public boolean sameShape(IShape that) { return that.sameCircle(this); }
And we’re done! Let’s trace through a few examples: if we test c1.sameShape(c3):
• c1 is a Circle, so we invoke the sameShape method defined in Circle, inside of which this is c1 and that is c3.

• This method immediately invokes sameCircle on that, and passes it this. Because that is c3, and c3 is a Circle, we invoke the sameCircle method defined in the Circle class, inside of which this will be c3 and that will be c1 they’ve swapped roles.

• Inside sameCircle, this is now c3 and that is now c1, and we can easily compare their fields. The fields are all equal, so we return true.

If we try a similar test with c1.sameShape(c2):
• c1 is a Circle, so we invoke the sameShape method defined in Circle, inside of which this is c1 and that is c2.

• This method immediately invokes sameCircle on that, and passes it this. Because that is c2, and c2 is a Circle, we invoke the sameCircle method defined in the Circle class, inside of which this will be c2 and that will be c1 they’ve swapped roles.

• Inside sameCircle, this is now c2 and that is now c1, and we can easily compare their fields. The fields are not equal, so we return false.

Perfect — we can compare Circles correctly.

Let’s try something trickier: let’s test c1.sameShape(r1):
• c1 is a Circle, so we invoke the sameShape method defined in Circle, inside of which this is c1 and that is r1.

• This method immediately invokes sameCircle on that, and passes it this. Because that is r1, and r1 is a Rect, we invoke the sameCircle method defined in the Rect class, inside of which this will be r1 and that will be c1 they’ve swapped roles.

• ...

Oops — we haven’t implemented sameCircle for the Rect class yet. But it’s easy: read through the purpose statement in your head, “when is this Rect the same Circle as that Circle?” Answer: never!
 // In Rect public boolean sameCircle(Circle that) { return false; }
In fact, we can implement all the “mismatched” methods this way:
 // In Circle public boolean sameRect(Rect that) { return false; } public boolean sameSquare(Square that) { return false; }
 // In Rect public boolean sameCircle(Circle that) { return false; } public boolean sameSquare(Square that) { return false; }
 // In Square public boolean sameCircle(Circle that) { return false; } public boolean sameRect(Rect that) { return false; }
With these methods defined, we can finish the trace above:
• The sameCircle method in the Rect class always returns false: Circles and Rects are never the same.

Now let’s try the two trickiest examples: comparing a Square with a Rect and symmetrically a Rect with a Square:

Do Now!

Do this yourself, following the pattern of the step-by-step walkthroughs above.

To compare s1.sameShape(r1):
• s1 is a Square, so we invoke the sameShape method defined in Square, inside of which this is s1 and that is r1.

• This method immediately invokes sameSquare on that, and passes it this. Because that is r1, and r1 is a Rect, we invoke the sameSquare method defined in the Rect class, inside of which this will be r1 and that will be s1 they’ve swapped roles.

• The sameSquare method in the Rect class always returns false: Squares and Rects are never the same.

Conversely, to compare r1.sameShape(s1):
• r1 is a Rect, so we invoke the sameShape method defined in Rect, inside of which this is r1 and that is s1.

• This method immediately invokes sameRect on that, and passes it this. Because that is s1, and s1 is a Square, we invoke the sameRect method defined in the Square class, inside of which this will be s1 and that will be r1 they’ve swapped roles.

• The sameRect method in the Square class always returns false: Rects and Squares are never the same.

Perfect!

##### 12.2Summarizing the double-dispatch pattern for sameness testing

Suppose we have an interface IFoo, and classes X, Y and Z that implement this interface. In the interface, we define a method sameFoo that takes an IFoo, and we define one method for each class that implements the interface:
 interface IFoo { boolean sameFoo(IFoo that); boolean sameX(X that); boolean sameY(Y that); boolean sameZ(Z that); }
In each class, the interesting behavior is in the sameFoo method and the method with the same name as the class:
 // In X: public boolean sameFoo(IFoo that) { return that.sameX(this); } public boolean sameX(X that) { ... compares two X values ... }
All the other methods just return false:
 // In X: public boolean sameY(Y that) { return false; } public boolean sameZ(Z that) { return false; }

How does this all work? The key observation is that when we want to compare two IFoo values f1 and f2 for sameness, we need to determine which kind of IFoo f1 is, and also which kind of IFoo f2 is. We get the answer to the first part automatically: by invoking a method on f1, dynamic dispatch will automatically route us to the appropriate method for the actual type of f1. Then, instead of trying to cobble together some form of type testing to figure out the answer for f2, we just invoke a method on it, using dispatch again to figure out the answer there. The trick lies in using our helper methods cleverly: by having sameFoo invoke sameX (in the example above), we are essentially answering the question “is f1 the same IFoo as f2?” by rebounding the question: “well we’ve figured out that f1 is an X, so is f2 the same X as f1?”

This pattern, of using two method invocations to get the benefits of dynamic dispatch twice, is called double dispatch, and it is a very common and very elegant pattern.

Exercise

Look back at Lecture 7: Accumulator methods, continued. Where did we use the double-dispatch pattern to answer a similar kind of question, that had to distinguish between different variants of a union data type?

Do Now!

Confirm that all of the properties we want out of a sameness operation are satisfied by our implementation. Notice in particular that totality is easy to confirm: there are no exceptions possible in this code!

Exercise

Implement a sameness operator for two IAT ancestry trees.

##### 12.3Cleaning up the code

You may have noticed that there are a lot of methods in the pattern above that always return false. (For n variants, there are n * n helper methods, of which n * (n - 1) of them should always return false.) In fact, all of the sameClass methods always return false, except in one case in each class. This sort of pattern, where the behavior is always the same except for a few cases where it differs, calls for the abstraction recipe for methods: we create an abstract class, put the default versions of these methods in there once and for all, then override them as needed in each subclass:
 abstract class AFoo implements IFoo { public boolean sameX(X that) { return false; } public boolean sameY(Y that) { return false; } public boolean sameZ(Z that) { return false; } } class X extends AFoo { public boolean sameFoo(IFoo that) { return that.sameX(this); } public boolean sameX(X that) { ... compares two X values ... } } class Y extends AFoo { public boolean sameFoo(IFoo that) { return that.sameY(this); } public boolean sameY(Y that) { ... compares two Y values ... } } class Z extends AFoo { public boolean sameFoo(IFoo that) { return that.sameZ(this); } public boolean sameZ(Z that) { ... compares two Z values ... } }

Exercise

Implement an AShape class, and abstract all the default cases you can. Be careful with the Square class!