Our proposed alternative is the programming language Scheme.

Scheme was originally designed at MIT. Subsequent work has been done at MIT, Yale, Indiana, Rice, and other institutions; there is an active community that is dedicated to developing and maintaining Scheme. It is one of the most widely used teaching languages. Its two developers have both won major awards: Guy Lewis Steele, Jr won the ACM's Grace Murray Hopper Award in 1988, awarded to a young computer scientist who has made an outstanding technical contribution to the field; and Gerald Jay Sussman won the ACM's Karl Karlstrom Outstanding Educator Award in 1990. Both awards were Scheme-related.

Scheme uses a prefix syntax for algebra. Here are some examples of algebraic expressions and their Scheme equivalents. The key mantra to remember about Scheme's syntax is the following: ``left-paren, operator, arguments, right-paren''.

Algebra	Scheme
1 + 2	(+ 1 2)
1 + 2 x 3.5	(+ 1 (* 2 3.5))
f(x) = x^2 - 3	(define (f x) (- (* x x) 3))
f(4)	(f 4)
f(2+3)	(f (+ 2 3))

These examples involve one keyword: define. define defines functions. In this case, f is declared to be a function of one argument, x; the body of the function is the next expression, (- (* x x) 3).

The syntax of Scheme is a little unusual, but it has numerous benefits:

• The syntax is completely regular. There is no distinction between built-in and user-defined operations; in contrast, languages like Pascal and C++ use infix for built-in operators and prefix for user-defined ones. More regularity means there are fewer rules to learn, and less chance of confusion.
• The syntax is unambiguous. For example, in the second example above, we used our knowledge of algebra to determine that multiplication is performed before addition. But programming languages introduce many, many more operators with no ``natural'' ordering for these operations. This can lead to difficult-to-find errors. In contrast, in the Scheme version, there is no ambiguity.

At Rice, we have developed an implementation of Scheme called DrScheme. Here's a screen shot of what the Windows version of DrScheme looks like. DrScheme's window has two parts. The upper region is a text editor, as found in most programming environments. The lower part is called the Interactions window. Here's how it works.

The Interactions window gives the user a prompt (>). The user can then type in an expression and hit Enter. In response, DrScheme computes the value of the expression, prints it out, and prints the next prompt. In this way, users can experiment with as many expressions as they wish. Here's an example of a sequence of interactions with DrScheme:

> (+ 1 2)
3
> (+ 1 (* 2 3.5))
8
> (define (f x) (- (* x x) 3))
> (f 4)
13
> (f (+ 2 3))
22
>

In this respect, DrScheme is much like a calculator. However, its calculator doesn't only do arithmetic: it is an algebraic calculator. Indeed, Scheme is a complete programming language, and DrScheme can calculate with numbers, strings, lists, vectors, and a host of other types of data.

Last modified at 22:38:38 CST on Sunday, February 08, 1998