It goes against the grain of modern education to teach children to program. What fun is there in making plans, acquiring discipline in organizing thoughts, devoting attention to detail and learning to be self-critical?
      -- Alan Perlis, Epigrams in Programming

Many professions require some form of computer programming. Accountants program spreadsheets and word processors; photographers program photo editors; musicians program synthesizers; and professional programmers instruct plain computers. Programming has become a required skill.

Yet programming is more than just a vocational skill. Indeed, good programming is a fun activity, a creative outlet, and a way to express abstract ideas in a tangible form. And designing programs teaches a variety of skills that are important in all kinds of professions: critical reading, analytical thinking, creative synthesis, and attention to detail.

We therefore believe that the study of program design deserves the same central role in general education as mathematics and English. Or, put more succinctly,

everyone should learn how to design programs.
On one hand, program design teaches the same analytical skills as mathematics. But, unlike mathematics, working with programs is an active approach to learning. Interacting with software provides immediate feedback and thus leads to exploration, experimentation, and self-evaluation. Furthermore, designing programs produces useful and fun things, which vastly increases the sense of accomplishment when compared to drill exercises in mathematics. On the other hand, program design teaches the same analytical reading and writing skills as English. Even the smallest programming tasks are formulated as word problems. Without critical reading skills, a student cannot design programs that match the specification. Conversely, good program design methods force a student to articulate thoughts about programs in proper English.

The Design Recipe for Functions
Problem Analysis & Data Definition
Contract, Purpose & Effect Statements, Header
Function Template
Function Definition

Figure 1:  The basic steps of a program design recipe

This book is the first book on programming as the core subject of a liberal arts education. Its main focus is the design process that leads from problem statements to well-organized solutions; it deemphasizes the study of programming language details, algorithmic minutiae, and specific application domains. Our desire to focus on the design process requires two radical innovations for introductory courses. The first innovation is a set of explicit design guidelines. Existing curricula tend to provide vague and ill-defined suggestions, such as ``design from top to bottom'' or ``make the program structural.'' We have instead developed design guidelines that lead students from a problem statement to a computational solution in step-by-step fashion with well-defined intermediate products. In the process they learn to read, to analyze, to organize, to experiment, to think in a systematic manner. The second innovation is a radically new programming environment. In the past, texts on programming ignored the role of the programming environment in the learning process; they simply assumed that students had access to a professional environment. This book provides a programming environment for beginners. It also grows with the students as they master more and more of the material until it supports a full-fledged language for the whole spectrum of programming tasks: large-scale programming as well as scripting.

Our guidelines are formulated as a number of program design recipes.1 A design recipe guides a beginning programmer through the entire problem-solving process. With design recipes, a beginner almost never again stares at a blank piece of paper or a blank computer screen. Instead, the student will check the design recipe and use the question-and-answer guidelines to make some progress.

We created the design recipes by identifying categories of problems. The identification of a problem category is based on the classes of data that are used to represent the relevant information. Starting from the structure of this class description students derive the programs with a checklist. Figure 1 shows the basic six steps of a design recipe checklist. Each step produces a well-defined intermediate product:

  1. the description of the class of problem data;

  2. the informal specification of a program's behavior;

  3. the illustration of the behavior with examples;

  4. the development of a program template or layout;

  5. the transformation of the template into a complete definition; and

  6. the discovery of errors through testing.

The major difference concerns the relationship of steps 1 and 4.

Design recipes help beginners and teachers alike. Teachers can use the recipes to inspect a beginner's problem-solving skills, to diagnose weaknesses, and to suggest specific remedial steps. After all, each stage of the design recipe yields a well-defined, checkable product. If a beginner is stuck, a teacher can inspect the intermediate products and determine what the problem is. Based on this analysis, the teacher can then provide guidance for a specific step in the recipe, raise appropriate questions, and recommend additional practice exercises.

Why Everyone Should Learn to Program

And as imagination bodies forth
The forms of things to unknown, and the poet's pen
Turns them to shapes, and gives to airy nothing
A local habitation and a name.
      -- Shakespeare, A Midsummer Night's Dream V(i)

Our claim that everyone programs or should learn to program might appear strange considering that, at first glance, fewer and fewer people seem to program these days. Instead, the majority of people use application packages, which don't seem to require any programming. Even programmers use ``program generators,'' packages that create programs from, say, business rules. So why should anyone learn to program?

The answer consists of two parts. First, it is indeed true that traditional forms of programming are useful for just a few people. But, programming as we the authors understand it is useful for everyone: the administrative secretary who uses spreadsheets as well as the high-tech programmer. In other words, we have a broader notion of programming in mind than the traditional one. We explain our notion in a moment. Second, we teach our idea of programming with a technology that is based on the principle of minimal intrusion. Hence our notion of programming teaches problem-analysis and problem-solving skills without imposing the overhead of traditional programming notations and tools.

To get a better understanding of modern programming, take a closer look at spreadsheets, one of today's popular application packages. A user enters formulas into a spreadsheet. The formulas describe how a cell A depends on another cell B. Then, as the user enters a number into B, the spreadsheet automatically calculates the contents of cell A. For complicated spreadsheets, a cell may depend on many other cells, not just one.

Other application packages require similar activities. Consider word processors and style sheets. A style sheet specifies how to create a (part of a) document from yet-to-be-determined words or sentences. When someone provides specific words and a style sheet, the word processor creates the document by replacing names in the style sheet with specific words. Similarly, someone who conducts a Web search may wish to specify what words to look for, what words should be next to each other, and what words should not occur in the page. In this case, the output depends on the search engine's cache of Web pages and the user's search expression.

Finally, using a program generator in many ways relies on the same skills as those necessary for application packages. A program generator creates a program in a traditional programming language, such as C++ or Java, from high-level descriptions, such as business rules or scientific laws. Such rules typically relate quantities, sales, and inventory records and thus specify computations. The other parts of the program, especially how it interacts with a user and how it stores data in the computer's disk, are generated with little or no human intervention.

All of these activities instruct some computer software to do something for us. Some use scientific notation, some may use stylized English, some use a concrete programming notation. All of them are some form of programming. The essence of these activities boils down to two concepts:

  1. relating one quantity to another quantity, and

  2. evaluating a relationship by substituting values for names.

Indeed, the two concepts characterize programming at the lowest level, the computer's native language, and in a modern fashionable language such as Java. A program relates its inputs to outputs; and, when a program is used for specific inputs, the evaluation substitutes concrete values for names.

No one can predict what kind of application packages will exist five or ten years from now. But application packages will continue to require some form of programming. To prepare students for these kinds of programming activities, schools can either force them to study algebra, which is the mathematical foundation of programming, or expose them to some form of programming. Using modern programming languages and environments, schools can do the latter, they can do it effectively, and they can make algebra fun.

Design Recipes

Cooking is at once child's play and adult joy. And cooking done with care is an act of love.
      -- Craig Claiborne (1920-2000), Food Editor, New York Times

Learning to design programs is like learning to play soccer. A player must learn to trap a ball, to dribble with a ball, to pass, and to shoot a ball. Once the player knows those basic skills, the next goals are to learn to play a position, to play certain strategies, to choose among feasible strategies, and, on occasion, to create variations of a strategy because none of the existing strategies fits.

A programmer is also very much like an architect, a composer, or a writer. They are creative people who start with ideas in their heads and blank pieces of paper. They conceive of an idea, form a mental outline, and refine it on paper until their writings reflect their mental image as much as possible. As they bring their ideas to paper, they employ basic drawing, writing, and instrumental skills to express certain style elements of a building, to describe a person's character, or to formulate portions of a melody. They can practice their trade because they have honed their basic skills for a long time and can use them on an instinctive level.

Programmers also form outlines, translate them into first designs, and iteratively refine them until they truly match the initial idea. Indeed, the best programmers edit and rewrite their programs many times until they meet certain aesthetic standards. And just like soccer players, architects, composers, or writers, programmers must practice the basic skills of their trade for a long time before they can be truly creative.

Design recipes are the equivalent of soccer ball handling techniques, writing techniques, techniques of arrangements, and drawing skills. A single design recipe represents a point of the program design space. We have studied this space and have identified many important categories. This book selects the most fundamental and the most practical recipes and presents them in increasing order of difficulty.2

About half the design recipes focus on the connection between input data and programs. More specifically, they show how the template of a program is derived from the description of the input data. We call this data-driven program design, and it is the most frequently used form of design. Data-driven designs are easy to create, easy to understand, and easy to extend and modify. Other design recipes introduce the notion of generative recursion, accumulation, and history sensitivity. The first one produces recursive programs that generate new instances of problems as they recur; accumulator-style programs collect data as they process inputs; and history-sensitive programs remember information between successive applications. Last, but not least, we also introduce a design recipe for abstracting over programs. Abstracting is the act of generalizing two (or more) similar designs into one and of deriving the original instances from it.

On many occasions, a problem naturally suggests one design recipe. On others, a programmer must choose from among several possibilities; each choice may produce programs with vastly different organizations. Making choices is natural for a creative programmer. But, unless a programmer is thoroughly familiar with the bag of design recipes to choose from and completely understands the consequences of choosing one over the other, the process is necessarily ad hoc and leads to whimsical, bad designs. We hope that by mapping out a collection of design recipes, we can help programmers understand what to choose from and how to choose.

Now that we have explained what we mean by ``programming'' and ``program design,'' the reader can see why and how teaching program design instills thinking skills that are important in a variety of professions. To design a program properly, a student must:

  1. analyze a problem statement, typically stated as a word problem;

  2. express its essence, abstractly and with examples;

  3. formulate statements and comments in a precise language;

  4. evaluate and revise these activities in light of checks and tests; and

  5. pay attention to details.

All of these are activities that are useful for a businessman, a lawyer, a journalist, a scientist, an engineer, and many others.

While traditional programming requires these skills, too, beginners often don't understand this connection. The problem is that traditional programming languages and traditional forms of programming force students to perform a large amount of book-keeping work and to memorize a large number of language-specific facts. In short, menial work drowns the teaching of essential skills. To avoid this problem, teachers must use a programming environment that imposes as little overhead as possible and that accommodates beginners. Because such tools didn't exist when we started, we developed them.

The Choice of Scheme and DrScheme

We ascribe beauty to that which is simple,
which has no superfluous parts;
which exactly answers its end,
which stands related to all things,
which is the mean of many extremes.
      -- Ralph Waldo Emerson, The Conduct of Life

We have chosen Scheme as the programming language for this book, and we have designed and implemented DrScheme, a programming environment for the language with special assistance for beginning students. The programming environment is freely available at the book's official Web site.3

Still, the book it is not about programming in Scheme. We only use a small number of Scheme constructs in this book. Specifically, we use six constructs (function definition and application, conditional expressions, structure definition, local definitions, and assignments) plus a dozen or so basic functions. This tiny subset of the language is all that is needed to teach the principles of computing and programming. Someone who wishes to use Scheme as a tool will need to read additional material.

The choice of Scheme for beginners is natural. First, the core of Scheme permits programmers to focus on just those two elements of programming that we pointed out at the beginning of the preface: programs as relations between quantities and evaluating programs for specific inputs. Using just this core language, students can develop complete programs during the first session with a teacher.

Second, Scheme can easily be arranged as a tower of language levels. This property is crucial for beginners who make simple notational mistakes that generate obscure error messages about advanced features of a language. The result is often a wasteful search and a feeling of frustration on the student's part. To avoid this problem, our programming environment, DrScheme, implements several carefully chosen sublanguages of Scheme. Based on this arrangement, the environment can signal error messages that are appropriate to a student's level of knowledge. Better still, the layering of languages prevents many basic mistakes. We developed the layers and the protection modes by observing beginners for weeks in Rice's computer lab. As students learn more about programming and the language, the teacher can expose students to richer layers of the language, which allows students to write more interesting and more concise programs.

Third, the DrScheme programming environment offers a truly interactive evaluator. It consists of two windows: a Definitions window, where students define programs, and an Interactions window, which acts like a pocket calculator. Students can enter expressions into the latter, and DrScheme determines their values. In other words, computation starts with pocket-calculator arithmetic, which they know quite well, and quickly proceeds from there to calculations with structures, lists, and trees -- the kinds of data that computer programs really manipulate. Furthermore, an interactive mode of evaluation encourages students to experiment in all kinds of ways and thus stimulates their curiosity.

Finally, the use of an interactive evaluator with a rich data language permits students to focus on problem solving and program design activities. The key improvement is that interactive evaluation renders a discussion of input and output operations (almost) superfluous. This has several consequences. First, input and output operations require memorization. Learning these things is tedious and boring. Conversely, students are better off learning problem-solving skills and using canned input and output support. Second, good text-oriented input requires deep programming skills, which are best acquired in a course on computational problem-solving. Teaching bad text-oriented input is a waste of the teachers' and the students' time. Third, modern software employs graphical user interfaces (GUI), which programmers design with editors and ``wizards'' but not by hand. Again, students are best off learning to design the functions that are connected to rulers, buttons, text fields and so on, rather than memorizing the specific protocols that currently fashionable GUI libraries impose. In short, discussing input and output is a waste of valuable learning time during a first introduction to programming. If students decide to pursue programming in more depth, acquiring the necessary (Scheme) knowledge about input and output procedures is straightforward.

In summary, students can learn the core of Scheme in a couple of hours, yet the language is as powerful as a conventional programming language. As a result, students can focus immediately on the essence of programming, which greatly enhances their general problem-solving skills.

The Parts of the Book

The book consists of eight parts and seven intermezzos. The parts focus on program design; the intermezzos introduce other topics concerning programming and computing. Figure 2 shows the dependence graph for the pieces of the book. The graph demonstrates that there are several paths through the book and that a partial coverage of the material is feasible.

Parts I through III cover the foundations of data-driven program design. Part IV introduces abstraction in designs. Parts V and VI are about generative recursion and accumulation. For these first six parts, the book uses a completely functional -- or algebraic -- form of programming. One and the same expression always evaluates to the same result, no matter how often we evaluate it. This property makes it easy to design, and to reason about, programs. To cope with interfaces between programs and the rest of the world, however, we enrich the language with assignment statements and abandon some of our algebraic reasoning. The last two parts show what this means for the design of programs. More precisely, they show how the design recipes of the first six parts apply and why we must be much more careful once assignments are added.

Intermezzos introduce topics that are important for computing and programming in general but not for program design per se. Some introduce the syntax and semantics of our chosen subsets of Scheme on a rigorous basis, a few introduce additional programming constructs. Intermezzo 5 is a discussion of the abstract cost of computing (time, space, energy) and introduces vectors. Intermezzo 6 contrasts two ways of representing numbers and processing them.

The coverage of some intermezzos can be delayed until a specific need arises. This is especially true of the intermezzos on Scheme's syntax and semantics. But, considering the central role of intermezzo 3 in figure 2, it should be covered in a timely fashion.


Figure 2:  The dependencies among parts and intermezzos

ITERATIVE REFINEMENT AND ITERATION OF TOPICS: Systematic program design is particularly interesting and important for large projects. The step from small single-function problems to small multifunction projects requires an additional design idea: iterative refinement. The goal is to design the core of a program and to add functionality to this core until the entire set of requirements is met.

Students in a first course can, and must, get their first taste of iterative refinement. Hence, in order to acquaint students with the technique, we have included extended exercises. Typically, a brief overview sets the stage for a collection of exercises. The exercises gently guide students through some design iterations. In section 16, the idea is spelled out explicitly.

Furthermore, the book revisits certain exercise and example topics time and again. For example, sections 6.6, 7.4, 10.3, 21.4, 41.4, and a few exercises in between the last two sections cover the idea of moving pictures across a canvas. The students thus see the same problem several times, each time with more and more knowledge about how to organize programs.

Adding pieces of functionality to a program demonstrates why programmers must follow a design discipline. Solving the problem again shows students how to choose from alternative design recipes. Finally, on occasion, new knowledge just helps students improve the program organization; in other words, students learn that programs aren't finished after they work for the first time but that, like papers and books, they need editing.

TEACHPACKS: A second aspect of working on projects is that programmers have to work in teams. In an instructional context, this means that one student's program has to fit precisely to someone else's. To simulate what ``fitting one's function to someone else's'' means, we provide DrScheme teachpacks. Roughly speaking, a teachpack simulates a team partner yet avoids the frustration of working with mistakes in a partner's program component. More technically, the projects almost always consist of a view and a model program component (in the sense of the model-view software architecture). In a typical setting, students design the model component. The teachpacks provide the view components, often in the form of (graphical) user interfaces. Thus they eliminate the tedious, mindless portions of coding. Furthermore, this particular separation of concerns mimics that of real-world projects.

Fitting model components to view components requires students to pay attention to precise specifications of functions. It demonstrates the paramount importance of following a design discipline. It is also a critical skill for programmers and is often underemphasized in beginning courses. In part IV we show how to construct some simple GUIs and how GUI events trigger the application of model functions. The goal is to explain that constructing GUIs is no mystery, but not to spend a lot of time on a topic that requires mostly rote learning and little computational thinking.

SCHEDULE: Each university, college, and school has its own needs and must find an appropriate schedule. At Rice University, we conventionally cover the entire book plus some additional material in a single semester. An instructor at a research university should probably keep up a similar pace. A high school teacher will necessarily pursue a slower pace. Many of the high schools that tested the book covered the first three parts in a semester; some used only the first part to teach algebraic problem solving from a computational perspective; and yet others worked through the entire book in a year. For more information on schedules, visit the book's Web site.

THE BOOK ON THE WEB: The book comes in two versions: a paper copy and a freely accessible on-line version at

The Web site also provides additional material, especially extended exercises of the style mentioned above. At this time, the Web page offers exercises on the visual simulation of ball games and the management of Web site. More exercises will be added.

The two versions of the book come with different kinds of hints. Each is marked with one of the following three icons:

This marker refers to DrScheme hints; they are available in both versions of the book. The programming environment has been designed with students in mind. The hints suggest how to use DrScheme at the various stages of the learning process.
This marker refers to teacher hints, which suggest strategies on how to present a section, on how to approach an exercise, or on how to supplement some material.
This marker links to on-line solutions. Some solutions are freely available; others are accessible to registered teachers only. To find out more about registration, see the book's Web site.

TYPOGRAPHY AND DEFINITIONS: For readability, Scheme programs are typeset using a small number of fonts. Italic words refer to program names and variables. Sans Serif items are constants and built-in operations. Boldface words are Scheme keywords.

Definitions come in three varieties. There are those terms that concern the principles of programming and computing. The book lists the first occurrence of such terms with SMALL CAPITAL LETTERS. Other definitions are of a more fleeting nature; they introduce terms that are important for a section, an example, an exercise, or some other small part of the book. The book uses slanted words to emphasize such definitions. Finally, the book also defines classes of data. Most data definitions are boxed, and the first occurrence of the defined name is also typeset using slanted words.


Four people deserve special thanks: Robert ``Corky'' Cartwright, who co-developed a predecessor of Rice's introductory course with the first author; Daniel P. Friedman, for asking the first author to rewrite The Little LISPer (also MIT Press) in 1984, because it started this project; John Clements, who designed, implemented, and maintains DrScheme's stepper; and Paul Steckler, who faithfully supported the team with contributions to our suite of programming tools.

The development of the book benefited from many other friends and colleagues who used it in their courses and/or gave detailed comments on early drafts. We are grateful to them for their help and their patience: Ian Barland, John Clements, Bruce Duba, Mike Ernst, Kathi Fisler, Daniel P. Friedman, John Greiner, John Stone, Geraldine Morin, and Valdemar Tamez.

A dozen generations of Comp 210 students at Rice University used early drafts of the text and contributed improvements in various ways. In addition, numerous attendees of our TeachScheme! workshops used early drafts in their classrooms. Many sent in comments and suggestions. As representative of these we mention the following active contributors: Ms. Barbara Adler, Dr. Stephen Bloch, Mr. Jack Clay, Dr. Richard Clemens, Mr. Kyle Gillette, Ms. Karen Buras, Mr. Marvin Hernandez, Mr. Michael Hunt, Ms. Karen North, Mr. Jamie Raymond, and Mr. Robert Reid. Christopher Felleisen patiently worked through the first few parts of the book with his father and provided direct insight into the views of a young student. Hrvoje Blazevic (sailing, at the time, as Master of the LPG/C Harriette), Joe Zachary (University of Utah) and Daniel P. Friedman (Indiana University) discovered numerous typos in the first printing, which we have now fixed. Thank you to everyone.

Finally, Matthias expresses his gratitude to Helga for her many years of patience and for creating a home for an absent-minded husband and father. Robby is grateful to Hsing-Huei Huang for her support and encouragement; without her, he would not have gotten anything done. Matthew thanks Wen Yuan for her constant support and enduring music. Shriram is indebted to Kathi Fisler for support, patience and puns, and for her participation in this project.



1 Readers whose experience is exclusively based on programming languages such as C/C++, Basic, and Pascal should read ``procedure'' or ``method'' where the preface mentions ``program.''

2 Our design recipes were inspired by work with Daniel P. Friedman on structural recursion, with Robert Harper on type theory, and by Michael A. Jackson's design method.

3 Scheme has an official definition -- the Revised Report on Scheme, edited by Richard Kelsey, William Clinger, and Jonathan Rees -- and many implementations. For a copy of the report and for a list of alternative Scheme implementations, visit on the Web. Note, however, that the language of this book extends that of the report and is tailored to beginners.