On this page:
17.1 Motivation
17.2 First failed attempt
17.3 Second failed attempt
17.4 Third flawed-but-successful attempt
17.5 Interlude:   local variables
17.6 Interlude:   Statements versus expressions
17.7 Warning:   Side effects may vary
17.7.1 Non-termination
17.7.2 Non-determinism
17.7.3 Non-testable code
17.8 Discussion

Lecture 17: Mutation🔗

Creating cyclic data, hazards of working with mutation

17.1 Motivation🔗

When you go to a bookstore and ask a sales clerk to look up a book whose author you remember but whose title you have forgotten, the clerk goes to a computer, types in the name of the author, and retrieves the list of books that the author has written. If you remember the title of the book but not the author, the clerk enters the title of the book and retrieves the author’s name. Even though it is feasible for the program to maintain two copies of all the information about books, it is much more natural to think of a data representation in which books and authors directly refer to each other in a circular manner.

17.2 First failed attempt🔗

We’ll define our classes to represent Books and Authors as follows:
       |               +------------+           |
       V               |            V           |
+--------------+       |     +---------------+  |
| Author       |       |     | Book          |  |
+--------------+       |     +---------------+  |
| String first |       |     | String title  |  |
| String last  |       |     | int price     |  |
| int yob      |       |     | int quantity  |  |
| Book book    |-------+     | Author author |--+
+--------------+             +---------------+
The corresponding code is straightforward:
// Represents authors of books class Author {
String first;
String last;
int yob;
Book book;
Author(String fst, String lst, int yob, Book bk) {
this.first = fst;
this.last = lst;
this.yob = yob;
this.book = bk;
// Represent books class Book {
String title;
int price;
int quantity;
Author author;
Book(String title, int price, int quantity, Author ath) {
this.title = title;
this.price = price;
this.quantity = quantity;
this.author = ath;

The next step of our design recipe is to construct examples of these data types.

Do Now!

Try creating an example of the following classic text in computer science, using the data representation above:

Donald E. Knuth.  The Art of Computer Programming (volume 1).

Addison Wesley, Reading, Massachusetts.  1968.

(Knuth was born in 1938.) Can you do it?

If we were to use the data representation above, and start with the author, we can easily get this far:
// In ExamplesBooks class Author knuth = new Author("Donald", "Knuth", 1938,
new Book("The Art of Computer Programming (volume 1)", 100, 2, ???));
The ??? need to be replaced by some Author, but we don’t have any yet. Well, this Book was written by Donald Knuth, so we could continue...
Author knuth = new Author("Donald", "Knuth", 1938,
new Book("The Art of Computer Programming (volume 1)", 100, 2,
new Author("Donald", "Knuth", 1938, ???)));
But now we’d need a Book for Knuth to have written... There’s no end to this process if we keep going down this path. We could try starting with the Book,
Book taocp = new Book("The Art of Computer Programming (volume 1)", 100, 2,
new Author("Donald", "Knuth", 1938, ???));
But that just leads to the same problem: in this case the ??? should be replaced with a Book, and we don’t have one of those yet. And if we keep trying to make one, we’d be stuck in an infinite process.

17.3 Second failed attempt🔗

We might be tempted to think, “Since we’re defining knuth as an Author, we ought to be able to use knuth exactly where the ??? appear!” But doing that doesn’t quite work: suppose we write
Author knuth = new Author("Donald", "Knuth", 1938,
new Book("The Art of Computer Programming (volume 1)", 100, 2, this.knuth));
Java will (surprisingly) allow this definition, but it isn’t actually doing what we’d like it to do. Our goal is for knuth’s book to be The Art of Computer Progamming, and for that book’s author to be knuth. We can write a test to check for that:
boolean testBookAuthorCycle(Tester t) {
return t.checkExpect(knuth.book.author, knuth);
This test will fail! The test expression, knuth.book.author, will evaluate to null instead of to knuth. Why? Java executes programs in a particular order, and the execution order for initialization statements like this one is to evaluate the right-hand side, completely, and then initialize the variable to the computed value. But notice that the right-hand side refers to the variable that is being defined, and it hasn’t been initialized yet! So the usage of knuth on the right hand side will evaluate to null, and the Book will then be constructed with null as its author, and the Author with be constructed with this resulting Book as its book, and the whole thing is then the value for knuth...so the reference knuth.book.author will still be null.

17.4 Third flawed-but-successful attempt🔗

If we want to construct an Author that refers to a Book that refers back to the Author, and we can’t refer to the Author before we’ve finished creating it, somehow we’ll have to create one of these objects in an “incomplete” state, and then change it to fix up the missing references. We can choose to create either the Book or the Author first. Since in real life, authors can’t write books before they are born, this suggests we might want to create the Author first, then the Book, and then change the Author to refer to the Book. We’ve never written any code that actually changes existing objects before; this is a new language feature. Let’s see how it might work:
// In ExamplesClass boolean testBookAuthorCycle(Tester t) {
// Creates an Author whose book is **null**... Author knuth = new Author("Donald", "Knuth", 1938, null);
// Creates a Book whose author is ok, but the author's book is still null... Book taocp =
new Book("The Art of Computer Programming (volume 1)", 100, 2, knuth);
// Now *change* the author's book field to be our newly created book... knuth.book = taocp;
// This now passes! return t.checkExpect(knuth.book.author, knuth);

There are two new features in this code. In the first line, we initialize the Author’s book field to null, a new value that we have never (deliberately) seen before. Null values have fairly strange behavior: any variable of any class or interface type can be initialized to null, but we cannot invoke any methods on null values. We’ll explain more about null shortly; for now, think of it as a “wildcard” value.

The key line here is the third line, which actually modifes the book field of knuth. We call this an assignment statement, and its meaning is to change the value of the field or variable on the left side of the equals sign to the result of evaluating the expression on the right hand side. Just like initialization statements, the right hand side is evaluated completely, before the left hand side gets modified and set to the result.

Incidentally, assignment statements are why we call variables variables. Without assignment statements, variables never actually vary; they just remain fixed at whatever value they were initialized to be. (This is why, up until now, we have been very careful to refer to “identifiers” and not to “variables”.)

Syntactically, this is very similar to how we initialize fields in the constructors of objects. But don’t be fooled: assignment statements are very different! Initializing fields lets us “define the field” to be equal to the given value, and in that sense initializations are at least somewhat like mathematical equations that assert two things to be equal. But assignment statements do not assert such an equality — in the assignment statement above, we know that knuth.book is equal to null! Assignments change the meaning of the variable on the left hand side, for the rest of the program...or at least until the next assignment to that same variable changes its meaning again.

17.5 Interlude: local variables🔗

There is a third salient point in the code above: we defined knuth and taocp as new variables inside a method, instead of as fields of a class or as parameters to a method. These local variables exist only within the body of the method, and disappear again when we return from the method. They are analogous to (local (...) ...) definitions in Racket.

17.6 Interlude: Statements versus expressions🔗

In the section above, we talk about statements and expressions, but what exactly is the difference between them? We know from Fundies 1 that an expression is a piece of a program that can evaluate to a value. Expressions can be composed to form bigger expressions, and these too evaluate to values.

Statements, however, do not evaluate to values. They simply execute, performing whatever specialized behavior is indicated by the statement. We have seen just three statements so far:
  • Return statements, return someExpression;, that exit a method and cause the method overall to evaluate to someExpression’s value.

  • If statements, if (cond) { ... } else { ... }, which mean “If cond is true then execute the first block of statments, otherwise execute the second block.”

Notice that neither of these statements, on their own, evaluates to a value. To these two, we can now add a third statement, the assignment statement. Its job is to change a variable to have a new value. But the assignment statement overall does not evaluate to anything. It stands by itself on a line, like a return statement, ending with a semicolon. You can only tell that the statement has run because of its effect on the rest of the program.

17.7 Warning: Side effects may vary🔗

The net effect of an assignment statement, namely a change to a variable, is known as mutation. Since statements on their own do not evaluate to values, the only way we can observe what they’ve done is by their side effects. This has some fairly drastic consequences for our programs.

17.7.1 Non-termination🔗

We’ve successfully created knuth and taocp above, and both objects refer to each other. Suppose we successfully create a second Author (call it knuth2) with the same name and age, and a second Book (call it taocp2) with the same title, and suppose they too refer to each other. What happens if we ask, “is taocp the sameBook as taocp2?”

Do Now!

What do you think will happen? Why?

  • We defined sameBook to check whether the fields of this Book are the same as the corresponding fields of the given Book. We’ve constructed taocp2 to have the same title as taocp, so we need to check the authors, knuth and knuth2, for sameness.

  • We defined sameAuthor to check whether the fields of this Author are the same as the corresponding fields of the given Author. We’ve constructed knuth2 to have the same name and age as knuth, so we need to check the books, taocp and taocp2, for sameness.

  • We defined sameBook to check whether the fields of this Book are the same as the corresponding fields of the given Book...

We’ve effectively gotten stuck in an infinite recursion! Even though we are recurring on fields of our object, just as our templates allow, when we recur two steps we wind up back where we started, and our program hangs.


The last line of the code above invokes checkExpect, and passes it two Authors...and yet the test terminates and passes! How do you think the tester library manages this, when our definitions of sameness (so far) would result in our program running forever?

Solving this problem in general, as the tester library does, is quite hard; we won’t see a solution to it for a while. For now, we have to compromise and redefine how we check sameness for either Authors or Books in order to break the cycle. We’ll arbitrarily decide to define sameAuthor to check only names and years of birth and ignore books, and thereby break the cycle.
// In Author // Computes whether the given author has the same name and year of birth // as this author (i.e., we're ignoring their books) boolean sameAuthor(Author that) {
return this.first.equals(that.first)
&& this.last.equals(that.first)
&& this.yob == that.yob;

17.7.2 Non-determinism🔗

So far, every function we have seen in Fundies 1, and every method we have seen in this course, has been deterministic: if we call a function or method twice with the same arguments, we get the same result. In other words, these tests should succeed:
;; In Racket
(check-expect (some-function arg-1 arg-2 arg-3) (some-function arg-1 arg-2 arg-3))
// In Java t.checkExpect(anObj.aMethod(arg1, arg2, arg3), anObj.aMethod(arg1, arg2, arg3));
Except for one function.

Do Now!

Which one?

The (random ...) function (or in Java, Math.random()) does not obey this rule. In fact, its whole purpose is to break this rule: every time we call Math.random() we would like a different random number!

But how does random-number generation actually work? We don’t invoke random with any arguments, and yet it produces different outputs. That means it must have some extra information hidden away inside its implementation, which it uses to “keep track” of the previous random values. And in particular, it updates that information every time it’s called, which is how it can produce different values despite not having any obvious inputs.

This is a subtle and powerful point: the ability to modify local state (e.g. by assigning to local variables or fields) means that methods may no longer be deterministic, and may not produce equal answers for equal inputs. In other words, they’re no longer functions! This means that our program behavior is no longer obviously predictable.

17.7.3 Non-testable code🔗

Maybe the previous point isn’t so catastrophic: perhaps if we just stayed away from using random numbers, everything would be good? No! Here’s a small class that demonstrates that even without randomness, our code is no longer functional:
class Counter {
int val;
Counter() {
Counter(int initialVal) {
this.val = initialVal;
int get() {
int ans = this.val;
this.val = this.val + 1;
return ans;
class ExamplesCounter {
boolean testCounter(Tester t) {
Counter c1 = new Counter();
Counter c2 = new Counter(2);
// What should these tests be? return t.checkExpect(c1.get(), ???) // Test 1 && t.checkExpect(c2.get(), ???) // Test 2 && t.checkExpect(c1.get() == c1.get(), ???) // Test 3 && t.checkExpect(c2.get() == c1.get(), ???) // Test 4 && t.checkExpect(c2.get() == c1.get(), ???) // Test 5 && t.checkExpect(c1.get() == c1.get(), ???) // Test 6 && t.checkExpect(c2.get() == c1.get(), ???); // Test 7 }

Do Now!

Fill in the ??? in the tests above.

  • We initialize c1 to a new counter, with a default initial value of 0.

  • We initialize c2 to a new counter with an initial value of 2.

  • In test 1, we get c1’s value, which is currently 0 and c1 updates its internal value to 1.

  • In test 2, we get c2’s value, which is currently 2 and c2 updates its internal value to 3.

  • In test 3, we get c1’s value, which is now 1, and then we immediately get it again — and it’s now 2! So this equality test evaluates to false also — this function’s return value is not even equal to itself.

  • In test 4, we get c2’s value, which is now 3, and then we get c1’s value, which is also now 3, so this equality test happens to be true.

  • Just to be sure, we try it again in test 5. This time, c2 and c1 both evaluate to 4, so the test still is true.

  • Something seems fishy, so we try tests 3 and 4 again. In test 6, we get c1’s value (which is 5), then get it again (now it’s 6), so this test evaluates to false.

  • Finally, in test 7, we try getting c2’s value (which is 5), and c1’s value (which is now 7), so this test, which was true twice, is now false.

So much for predictable output! The result of invoking get() depends on which object we use to invoke the method, and on how many times we’ve invoked the method already. There’s no randomness involved here, but already figuring out this behavior is very confusing.

17.8 Discussion🔗

With all these potential hazards, what are mutation and side effects actually good for? Let’s not forget that it is essential for creating these cyclic data structures, and we’ll see that cyclic data comes up naturally over and over again.

Additionally, side effects are very useful when interacting with the rest of the world (i.e., the part outside the computer). Once words appear on the screen and the user has read them, they can’t be un-read; once a user has sent an email, it can’t be un-sent. Side effects let us describe these changes to the state of the world. We’ll see more examples of dealing with these kinds of side effects later.

Do Now!

If side effects are so convenient for interacting with the outside world, how does (big-bang ...) work? We certainly had no mutation in Racket, yet big-bang could draw to the screen and get input from the user.

The big-bang library (and the funworld library in Java) both are abstractions that hide the side effects from the programmer: they provide a simpler, cleaner interface for programming that lets us concentrate on the functionality of our programs, on testing that functionality, and not have to care at all about the low-level mechanics of actual input and output. If you are interested in the concepts behind how big-bang is implemented, there are plenty of more advanced courses which will teach you how to produce input and output yourself, or write games from scratch, or any of the other world programs we have written.

A final word of caution: in the third example above, we finally managed to construct a cycle between our two objects. But we only accomplished it by mutating a field of one of those objects, from within the examples class. This is bad programming practice: surely we ought to be able to work with our data in the rest of our program, too, and not just in the somewhat constrained setting of our examples and tests? In the next lecture, we will see a much better approach for hiding the particular details of what assignment statements we need to execute, and we’ll see in more detail how to test code that deals with mutation.