Compound Procedures

Defining Procedures

You already know how to define simple procedures such as square. The standard way to define a procedure is (define (name formal-parameters) body).


  • Compound Procedure: a compound procedure is a procedure that is defined in terms of Racket primitive procedures.
  • Name: the name of the procedure is a symbol used to refer to the procedure.
  • Formal Parameters: the formal parameters of a procedure are the names used within the body of the procedure to refer to the arguments.
  • Body: the body of the procedure is the "meat" of the procedure. It is formally defined as "an expression that will yield the value of the procedure application when the formal parameters are replaced by the actual arguments to which the procedure is applied", but you can think of it as instructions for the computer to follow.

In the procedure definition (define (square x) (* x x)), the name is square, the formal parameter is x, and the body is (* x x).

Suppose I define a procedure as such: (define (foo x y) (+ (* 3 x) (* 4 y))). Please answer the following questions.

What is the name of the above procedure?
What are the two formal parameters?
What is the body of the procedure?

Procedures with Multiple Formal Parameters

Procedures don't have to have just one formal parameter, such as in square. They can also have multiple formal parameters. The way to create procedures with multiple arguments is fairly straightforward. It looks something like this: (define (foo x y z) (* x y z)).

We can also create procedures with no arguments at all! The code for that looks something like this: (define (foo) 3)). Now, whenever you call (foo), it will return 3.


One of the most useful (and coolest!) parts about programming is that, once you've defined a procedure, not only can you can use it over and over again, you can also use it to define other procedures.

Since you're probably sick of square right now, let's use another function as an example. Let's define a predicate vowel?, and use it to define another procedure:

(define (vowel? letter) (member? letter '(a e i o u))

Now that we have vowel?, we can use it in different procedures. For example, one of the problems in 0.3 deals with Pig Latin. If a word starts with a vowel, translating that word into Pig Latin is as simple as adding "ay" to the end of the word. We're not going to worry about translating words into Pig Latin right now; we're just going to define yet another predicate to check if a word starts with a vowel.

(define (pig-complete? wd) (vowel? (first wd)))

As you can see, we used one user-defined procedure (vowel?), to define another one.