Data Definitions

Consider the following expression:

(make-posn 'Albert 'Meyer)

  (distance-to-0 (make-posn 'Albert 'Meyer))

= (sqrt 
    (+ (square (posn-x (make-posn 'Albert 'Meyer))) 
       (square (posn-y (make-posn 'Albert 'Meyer)))))

= (sqrt 
    (+ (square 'Albert) 
       (square (posn-y (make-posn 'Albert 'Meyer)))))

= (sqrt 
    (+ (* 'Albert 'Albert) 
       (square (posn-y (make-posn 'Albert 'Meyer))))) 

(make-star 'Albert 'Meyer 10000 'electric-organ)

To avoid such problems and to assist with the development of functions, we must add a data definition to each structure definition. A DATA DEFINITION states, in a mixture of English and Scheme, how we intend to use a class of structures and how we construct elements of this class of data. For example, here is a data definition for posn structures:

A posn is a structure: (make-posn x y) where x and y are numbers.

It says that a valid posn structure always contains two numbers, and nothing else. Hence, when we use make-posn to create a posn structure, we must apply it to two numbers; when a function contains selector expressions for posn structures, we may now assume that their result is a number.

The data definition for star structures is only slightly more complicated:

A star is a structure: (make-star last first instrument sales) where last, first, and instrument are symbols and sales is a number.

This data definition says that valid star structures contain symbols in the fields for last name, first name, and instrument, and a number in the sales field.

Figure: The meaning of data definitions

In general, a data definition identifies a subclass of Scheme's universe of values: see figure . As we have seen so far, Scheme's universe contains numbers, symbols, images, strings, chars, booleans, and many different classes of structures. Our functions, however, are intended to work only for a subclass of values. For example, area-of-disk consumes only numbers; reply from section  consumes only symbols. A few subclasses, such as number, already have names, because they are useful for all kinds of programming tasks. Others are only interesting in the context of a specific problem. For those cases, a programmer should introduce a data definition.

The most important role of a data definition is that of a covenant between programmers and users. We expect both groups to respect such data definitions, and we expect the programmer to exploit it for the function construction. For example, when the programmer of distance-to-0 specifies that all posns contain two numbers, a user must always apply distance-to-0 to a posn structure with two numbers. Furthermore, as we will discuss over the next few sections, we expect a programmer to exploit data definitions for function developments. Naturally, a data definition in English and Scheme does not prevent us from abusing make-posn. It is, however, a written statement of intent, and a person who willingly violates or ignores this covenant must face the consequences of ill-behaving computations.

Exercise 6.4.1

Provide data definitions for the following structure definitions:

1. (define-struct movie (title producer))
2. (define-struct boyfriend (name hair eyes phone))
3. (define-struct cheerleader (name number))
4. (define-struct CD (artist title price))
5. (define-struct sweater (material size producer))

Exercise 6.4.2

Provide a structure definition and a data definition for representing points in time since midnight. A point in time consists of three numbers: hours, minutes, and seconds. Solution

Exercise 6.4.3

Provide a structure definition and a data definition for representing three-letter words. A word consists of letters, which we represent with the symbols 'a through 'z. Solution