On this page:
Systematic Program Design
Dr  Racket and the Teaching Languages
Skills that Transfer
This Book and its Parts
The Differences
Acknowledgments from the First Edition


Many professions require some form of programming. Accountants program spreadsheets; musicians program synthesizers; authors program word processors; and web designers program style sheets. When we wrote these words for the first edition of the book (1995–2000), people considered them futuristic; by now, programming has become a required skill and numerous outlets—books, on-line courses, K-12 curricula—cater to this need, always with the goal of enhancing people’s job prospects.

The typical course on programming teaches a “tinker until it works” approach. When it works, students exclaim “It works!” and move on. Sadly, this phrase is also the shortest lie in computing, and it has cost many people many hours of their lives. In contrast, this book focuses on habits of good programming, addressing both professional and vocational programmers.

With “good programming,” we mean an approach to the creation of software that relies on systematic thought, planning, and understanding from the very beginning, at every stage and for every step. To emphasize the point, we speak of systematic program design and systematically designed programs. Critically, the latter articulates the rationale of the desired functionality. Good programming also satisfies an aesthetic sense of accomplishment; the elegance of a good program is comparable to time-tested poems or the black-and-white photographs of a bygone era. In short, programming differs from good programming like crayon sketches in a diner from oil paintings in a museum.

No, this book won’t turn anyone into a master painter. But, we would not have spent fifteen years writing this edition if we didn’t believe that

everyone can design programs


everyone can experience the satisfaction that comes with creative design.

Indeed, we go even further and argue that

program design—but not programmingdeserves the same role in a liberal-arts education as mathematics and language skills.

A student of design who never touches a program again will still pick up universally useful problem-solving skills, experience a deeply creative activity, and learn to appreciate a new form of aesthetic. The rest of this preface explains in detail what we mean with “systematic design,” who benefits in what manner, and how we go about teaching it all.

Systematic Program Design

A program interacts with people, dubbed users, and each other, in which case we often speak of server and client components. Hence any reasonably complete program consists of many building blocks: some deal with input, some create output, some bridge the gap between those two. We choose to use functions as fundamental building blocks, because everyone encounters functions in pre-algebra and because the simplest programs are just such functions. The key is to discover which functions are needed, how to connect them, and how to build them from basic ingredients.

In this context, “systematic program design” refers to a mix of two concepts: design recipes and iterative refinement.We drew inspiration from Michael Jackson’s method for creating COBOL programs plus conversations with Daniel Friedman on recursion, Robert Harper on type theory, and Daniel Jackson on software design. The design recipes are a creation of the authors; and here, they enable the use of the latter.

  1. From Problem Analysis to Data Definitions

    Identify the information that must be represented and how it is represented in the chosen programming language. Formulate data definitions and illustrate them with examples.

  2. Signature, Purpose Statement, Header

    State which data the desired function consumes and produces. Articulate what the function computes as a concise one-line statement. Define a stub that lives up to the signature.

  3. Functional Examples

    Work through examples that illustrate the function’s purpose.

  4. Function Template

    Translate the data definitions into an outline of the function.

  5. Function Definition

    Fill in the gaps in the function template. Exploit the purpose statement and the examples.

  6. Testing

    Articulate the examples as tests and ensure that the function passes all. Doing so discovers mistakes and also helps others read and understand the definition when the need arises—and it will arise for any serious program.

Figure 1: The basic steps of a function design recipe

Design Recipes apply to both complete programs and individual functions. This book deals with just two recipes for complete programs: one for programs with graphical user interface (GUI) and one for batch programs. In contrast, design recipes for functions come in a wide variety of flavors: for atomic forms of data such as numbers; for enumerations of different kinds of data; for data that compounds other data in a fixed manner; for finite but arbitrarily large data; and so on.

The function-level design recipes share a common design process. Figure 1 displays its six essential steps. The title of each step specifies the expected outcome(s); the “commands” suggest the key activities. Examples play a central role at almost every stage.Instructors Have students copy figure 1 on one side of an index card. When students are stuck, ask them to produce their card and point them to the step where they are stuck. For the chosen data representation in step 1, writing down examples proves how real-world information is encoded as data and how data is interpreted as information. Step 3 says that a problem-solver must work through concrete scenarios to gain an understanding of what the desired function is expected to compute for specific examples. This understanding is exploited in step 5, when it is time to define the function. Finally, step 6 demands that examples are turned into automated test code, which ensures that the function works properly for some cases. Running the function on real-world data may reveal other discrepancies between expectations and results.

Each step of the design process comes with pointed questions. For certain steps—say, the creation of the functional examples or the template—the questions may appeal to the data definition. The answers almost automatically create an intermediate product.Instructors The most important questions are those for steps 4 and 5. Ask students to write down these questions in their own words on the back of their index card. This scaffolding pays off when it comes time to take the one creative step in the process: the completion of the function definition. And even then, help is available in almost all cases.

The novelty of this approach is the creation of intermediate products for beginner-level programs. When a novice is stuck, an expert or an instructor can inspect the existing intermediate products. The inspection is likely to use the generic questions from the design process and thus drive the novice to correct himself or herself. And this self-empowering process is the key difference between programming and program design.

Iterative Refinement addresses the issue that problems are complex and multi-faceted. Getting everything right at once is nearly impossible. Instead, computer scientists borrow iterative refinement from the physical sciences to tackle this design problem. In essence, iterative refinement recommends stripping away all inessential details at first and finding a solution for the remaining core problem. A refinement step adds in one of these omitted details and re-solves the expanded problem, using the existing solution as much as possible. A repetition, also called an iteration, of these refinement steps eventually leads to a complete solution.

In this sense a programmer is a mini-scientist. Scientists create approximate models for some idealized version of the world to make predictions about it. As long as the model’s predictions come true, everything is fine; when the predicted events differ from the actual ones, scientists revise their models to reduce the discrepancy. In a similar vein, when programmers are given a task, they create a first design, turn it into code, evaluate it with actual users, and iteratively refine the design until the program’s behavior closely matches the desired product.

This book introduces iterative refinement in two different ways. Since designing via refinement becomes useful as the design of programs becomes complex, the book introduces the technique explicitly in the fourth part, once the problems acquire a certain degree of difficulty. Furthermore, we use iterative refinement to state increasingly complex variants of the same problem over the course of the first three parts of the book. That is, we pick a core problem, deal with it in one chapter, and then pose a similar problem in a subsequent chapter—with details matching the newly introduced concepts.

DrRacket and the Teaching Languages

Learning to design programs calls for repeated hands-on practice. Just as nobody becomes a piano player without playing the piano, nobody becomes a program designer without creating actual programs and getting them to work properly. Hence, our book comes with a modicum of software support: a language in which to write down programs and a program development environment with which programs are edited like word documents and run on concrete inputs.

People often tell us they wish they knew how to program and then ask which programming language they should learn. Given the press that some programming languages get, this question is not surprising. But it is also wholly inappropriate.Instructors For courses not aimed at beginners, it may be possible to use an off-the-shelf language with the design recipes. Learning to program in a currently fashionable programming language often sets up students for failure. Fashion in this world is extremely short lived. A typical “quick programming in X” book or course fails to teach principles that transfer to the next fashion language. Worse, the language itself often distracts from the acquisition of transferable skills, both at the level of expressing solutions as well as dealing with programming mistakes.

In contrast, learning to design programs is primarily about the study of principles and the acquisition of transferable skills. The ideal programming language must support these two goals, but no off-the-shelf industrial language does so. The crucial problem is that beginners make mistakes before they know much of the language, yet programming languages always diagnose these errors as if the programmer already knew the whole language. As a result, diagnosis reports often stump beginners.

Our solution is to start with our own, tailor-made teaching language, dubbed “Beginning Student Language” or *SL. The language is essentially the “foreign” language that students acquire in pre-algebra courses. It includes notation for function definitions, function applications, and conditional expressions. Also, expressions can beInstructors You may wish to explain that BSL and friends are pre-algebra with additional forms of data and a host of pre-defined functions on those. nested. Put differently, this language is so small that a diagnosis report in terms of the whole language is still accessible to readers with nothing but pre-algebra under their belt.

When it comes to programming environments, we face an equally bad choice as the one for languages. A programming environment for professionals is analogous to the cockpit of a jumbo jet. It has numerous controls and displays, overwhelming anyone who first launches such a software application. Novice programmers need the equivalent of a two-seat, single-engine propeller aircraft with which they can practice basic skills. We have therefore created DrRacket, a programming environment for novices.

DrRacket supports highly playful, feedback-oriented learning with just two simple interactive panes: a definitions area, which contains function definitions, and an interactions area, which allows a programmer to ask for the evaluation of expressions that may refer to the definitions. In this context, it is as easy to explore “what if” scenarios as in a spreadsheet application. Experimentation can start on first contact, using conventional calculator-style examples and quickly proceeding to calculations with images, words, and other forms of data.

An interactive program development environment such as DrRacket simplifies the learning process in two ways. First, it enables novice programmers to manipulate data directly. Because no facilities for reading input information from files or devices are needed, novices don’t need to spend valuable time on figuring out how these work. Second, the arrangement strictly separates data and data manipulation from input and output of information from the “real world.”. Nowadays this separation is considered so fundamental to the systematic design of software that it has its own name: model-view-controller architecture. By working in DrRacket, new programmers are exposed to this fundamental software engineering idea in a natural way from the get-go.

Skills that Transfer

The skills acquired from learning to design programs systematically transfer in two directions. Naturally, they apply to programming in general and programming spreadsheets, synthesizers, style sheets, and even word processors. Our observations suggest that the design process from figure 1 carries over to almost any programming language, and it works for 10-line programs as well as for 10,000-line programs. It takes some reflection to adopt the design process across the spectrum of languages and scale of programming problems; but once the process becomes second nature, its use pays off in many ways.

Learning to design programs also means acquiring two kinds of universally useful skills. Program design certainly teaches the same analytical skills as mathematics, especially (pre)algebra and geometry. But, unlike mathematics, working with programs is an active approach to learning. Creating software provides immediate feedback and thus leads to exploration, experimentation, and self-evaluation. The results tend to be interactive products, which vastly increases the sense of accomplishment when compared to drill exercises in text books.

In addition to enhancing a student’s mathematical skills, program design teaches analytical reading and writing skills. Even the smallest design tasks are formulated as word problems. Without solid reading skills, it is impossible to design programs that solve a reasonably complex problem. Conversely, program design methods force a creator to articulate his or her thoughts in proper and precise language. Indeed, if students truly absorb the design recipe, they enhance articulation skills more than anything else.

To illustrate this point, first take a look back at figure 1. According to this process description, a designer must:
  1. analyze a problem statement, typically stated as a word problem;

  2. extract and express its essence, abstractly and with examples;

  3. make outlines and plans based on this analysis;

  4. evaluate results with respect to expected outcomes; and

  5. revise the product in light of failed checks and tests.

Each step requires analysis, precision, description, focus, and attention to details. Any experienced entrepreneur, engineer, journalist, lawyer, scientist, or any other professional can explain how many of these skills are necessary for his or her daily work. Practicing program design—on paper and in DrRacket—is a joyful way to acquire these skills.

Similarly, refining designs is not restricted to computer science and program creation. Architects, composers, writers, and other professionals do it, too. They start with ideas in their head and somehow articulate their essence. They refine these ideas on paper until their product reflects their mental image as much as possible. As they bring their ideas to paper, they employ skills analogous to fully absorbed design recipes: drawing, writing, or piano playing to express certain style elements of a building, describe a person’s character, or formulate portions of a melody. What makes them productive with an iterative development process is that they have absorbed their basic design recipes and learned how to choose which one to use for the current situation.

This Book and its Parts

The purpose of this book is to introduce readers without prior experience to the systematic design of programs. In tandem, it presents a symbolic view of computation, a method that explains how the application of a program to data works. Roughly speaking, this method generalizes what students learn in elementary school arithmetic and middle school algebra. But have no fear; DrRacket comes with a mechanism—the algebraic stepper—that can illustrate these step-by-step calculations.

The book consists of six parts separated by five intermezzos and bookended by a Prologue and an Epilogue. While the major parts focus on program design, the intermezzos introduce supplementary concepts concerning programming mechanics and computing.

Prologue: How to Program is a quick introduction to plain programming. It explains how to write a simple animation in *SL. Once finished, any beginner is bound to feel simultaneously empowered and overwhelmed. The final note therefore explains why plain programming is wrong and how a systematic, gradual approach to program design also eliminates this sense of dread that every beginning programmer usually experiences. Now the stage is set for the core of the book:
  • Fixed-Size Data explains the most fundamental concepts of systematic design using simple examples. The central idea is that designers typically have a rough idea of what data the program is supposed to consume and produce. A systematic approach to design must therefore extract as many hints as possible from the description of the data that flows into and out of a program. To keep things simple, this part starts with atomic data—numbers, images and so on—and then gradually introduces new ways of describing data: intervals, enumerations, itemizations, structures, and combinations of these.

  • Intermezzo: BSL describes the teaching language in complete detail: its vocabulary, its grammar, and its meaning. Computer scientists refer to these as syntax and semantics. Program designers use this model of computation to predict what their creations compute when run or to analyze error diagnostics.

  • Arbitrarily Large Data extends Fixed-Size Data with the means to describe the most interesting and useful forms of data: arbitrarily large compound data. While a programmer may nest the kinds of data from Fixed-Size Data to represent information, the nesting is always of a fixed depth and breadth. This part shows how a subtle generalization gets us from there to data of arbitrary size. The focus then switches to the systematic design of programs that process this kind of data.

  • Intermezzo: Quote, Unquote introduces a concise and powerful notation for writing down large pieces of data: quotation and anti-quotation.

  • Abstraction acknowledges that many of the functions from Arbitrarily Large Data look alike. No programming language should force programmers to create pieces of code that are so similar to each other. Conversely, every good programming language comes with ways to eliminate such similarities. Computer scientists call both the step of eliminating similarities and its result abstraction, and they know that abstractions greatly increase a programmer’s productivity. Hence, this part introduces design recipes for creating and using abstractions.

  • Intermezzo: Scope and Abstraction plays two roles. On one hand, it injects the concept of lexical scope, the idea that a programming language ties every occurrence of a name to a definition that a programmer can find with an inspection of the code. Second, it explains a library with additional mechanisms for abstraction, including so-called for loops.

  • Intertwined Data generalizes Arbitrarily Large Data and explicitly introduces the idea of iterative refinement into the catalog of design concepts.

  • Intermezzo: The Nature of Numbers explains why decimal numbers work in such strange ways in all programming languages. Every budding programmer ought to know these basic facts; and in the context of this book, the ideas are easy to discuss and illustrate.

  • Generative Recursion injects a completely new design concept. While structural design and abstraction suffice for most problems that programmers encounter, they occasionally lead to insufficiently “performant” programs. In other words, structurally designed programs might need too much time or memory or energy to compute the desired answers. Computer scientists therefore replace structurally designed programs with programs that benefit from ad hoc insights into the problem domain. This part of the book shows how to design a large class of just such programs.

  • Intermezzo: The Cost of Computation uses examples from Generative Recursion to illustrate how computer scientists think about performance.

  • Accumulators adds one final trick to the tool box of designers: accumulators. Roughly speaking, an accumulator adds “memory” to a function. The addition of memory greatly improves the performance of structurally designed functions from the first four parts of the book. For the ad hoc programs from Generative Recursion, accumulators can make the difference between finding an answer at all and never finding one.

Epilogue: Moving On is both an assessment and a look ahead to what’s next.


Figure 2: The dependencies among parts and intermezzos (draft)

Independent readers ought to work through the entire book, from the first page to the last. We say “work” because we really mean that a reader ought to solve all exercises or at least know how to solve them.

Similarly, instructors ought to cover as many elements as possible, starting from the Prologue all the way through the Epilogue. Our teaching experience suggests that this is doable. Typically, we organize our courses so that our readers create a sizable and entertaining program over the course of the semester. We understand, however, that some circumstances call for significant cuts and that some instructors’ tastes call for slightly different ways to use the book.

Figure 2 is a navigation chart for those who wish to pick and choose from the elements of the book. The figure is a dependency graph. A solid arrow from one element to another suggests a mandatory ordering; for example, Part II requires an understanding of Part I. In contrast, a dotted arrow is mostly a suggestion; for example, understanding the Prologue is unnecessary to get through the rest of the book.

Based on this chart, here are three feasible paths through the book:

Iteration of Sample Topics The book revisits certain exercise and sample topics time and again. For example, virtual pets are found all over Fixed-Size Data and even show up in Arbitrarily Large Data. Similarly, both Fixed-Size Data and Arbitrarily Large Data cover alternative approaches to implementing an interactive text editor. Graphs appear in Generative Recursion and immediately again in Accumulators. The purpose of these iterations is to motivate iterative refinement and to introduce it through the backdoor. We urge instructors to assign these themed sequences of exercises or to create their own such sequences.

The Differences

This second edition of “How to Design Programs” differs from the first one in several major aspects:
  1. The second edition explicitly acknowledges the difference between designing a whole program and the functions that make up a program. Specifically, this edition focuses on two kinds of programs: event-driven (mostly GUI, but also networking) programs and batch programs.

  2. The design of a program proceeds in a top-down planning phase followed by a bottom-up construction phase. We explicitly show how the interface to libraries dictates the shape of certain program elements. In particular, the very first phase of a program design yields a wish list of functions. While the concept of a wish list exists in the first edition, the second edition treats it as an explicit design element.

  3. Fulfilling an entry from the wish list relies on the function design recipe, which is the subject of the six major parts.

  4. A key element of structural design is the definition of functions that compose others. This design-by-composition is especially useful for the world of batch programs. Like generative recursion,We thank Kathi Fisler for calling our attention to this point. it requires a eureka!, specifically a recognition that the creation of intermediate data by one function and processing this intermediate result by a second function simplifies the overall design. This approach also needs a wish list, but formulating these wishes calls for an insightful development of an intermediate data definition. This edition of the book weaves in a number of explicit exercises on design-by-composition.

  5. While testing has always been a part of our design philosophy, the teaching languages and DrRacket started supporting it properly only in 2002, just after we had released the first edition. This new edition heavily relies on this testing support.

  6. This edition of the book drops the design of imperative programs. The old chapters remain available on-line. An adaptation of this material will appear in the second volume of this series, “How to Design Components.”

  7. The book’s examples and exercises employ new teachpacks. The preferred style is to link in these libraries via require, but it is still possible to add teachpacks via a menu in DrRacket.

  8. Finally, this second edition differs from the first in bits of terminology and notation:

    Second Edition


    First Edition
















    The last three differences greatly improve quotation for lists.

Acknowledgments from the First Edition

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 DrRacket’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 courses and/or gave detailed comments on early drafts. We are grateful to them for their help and patience: Ian Barland, John Clements, Bruce Duba, Mike Ernst, Kathi Fisler, Daniel P. Friedman, John Greiner, John Stone, Géraldine 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.


As in 2001, we are grateful to John Clements for designing, validating, implementing, and maintaining DrRacket’s algebraic stepper. He has done so for nearly 20 years now, and the stepper has become an indispensable tool of explanation and instruction.

Over the past few years, several colleagues have made significant comments on the various drafts and what kind of improvements they would like to see in a second one. We gratefully acknowledge the thoughtful conversations and exchanges with these individuals:

Kathi Fisler, Gregor Kiczales, Prabhakar Ragde, and Norman Ramsey.

Thousands of teachers and instructors attended our various workshops over the years, and many provided valuable feedback. But Dan Anderson, Stephen Bloch, Jack Clay, Nadeem Abdul Hamid, and Viera Proulx stand out, and we wish to call out their role in the crafting of this edition.

Celeste Hollenbeck is the most amazing reader ever. She never tired of pushing back until she understood the prose. She never stopped until a section supported its thesis, its organization matched, and its sentences connected. Thank you very much for your incredible efforts.

We also thank the following: Ennas Abdussalam, Anisa Anuar, Saad Bashir, Suzanne Becker, Steven Belknap, Stephen Bloch, Elijah Botkin, Joseph Bogart, William Brown, Tomas Cabrera, Xuyuqun C, Colin Caine, Anthony Carrico, Rodolfo Carvalho, Estevo Castro, Maria Chacon, Stephen Chang, Tung Cheng, Nelson Chiu, Jack Clay, Richard Cleis, John Clements, Scott Crymble, Pierce Darragh, Jonas Decraecker, Qu Dongfang, Mark Engelberg, Andrew Fallows, Christopher Felleisen, Sebastian Felleisen, Vladimir Gajić, Adrian German, Jack Gitelson, Kyle Gillette, Scott Greene, Ben Greenman, Ryan Golbeck, Josh Grams, Jane Griscti, Tyler Hammond, Nan Halberg, Li Junsong, Nadeem Abdul Hamid, Jeremy Hanlon, Craig Holbrook, Connor Hetzler, Wayne Iba, John Jackaman, Jordan Johnson, Blake Johnson, Erwin Junge, Marc Kaufmann, Gregor Kiczales, Eugene Kohlbecker, Caitlin Kramer, Jackson Lawler, Devon LePage, Ben Lerner, Shicheng Li, Chen Lj, Ed Maphis, YuSheng Mei, Andres Meza, Saad Mhmood, Jay Martin, Jay McCarthy, James McDonell, Mike McHugh, Wade McReynolds, Elena Machkasova, David Moses, Ann E. Moskol, Scott Newson, Paul Ojanen, Prof. Robert Ordóñez, Laurent Orseau, Klaus Ostermann, S. Pehlivanoglu, Eric Parker, Nick Pleatsikas, Prathyush Pramod, Norman Ramsey, Krishnan Ravikumar, Jacob Rubin, Luis Sanjuán, Brian Schack, Ryan “Havvy” Scheel, Lisa Scheuing, Willi Schiegel, Vinit Shah, Nick Shelley, Tubo Shi, Matthew Singer, Stephen Siegel, Milton Silva, Kartik Singhal, Joe Snikeris, Marc Smith, Dave Smylie, Vincent St-Amour, Reed Stevens, Kevin Sullivan, Asumu Takikawa, Éric Tanter, Sam Tobin-Hochstadt, Thanos Tsouanas, Aaron Tsay, Mariska Twaalfhoven, Bor Gonzalez Usach, Manuel del Valle, David Van Horn, Andre Venter, Jan Vitek, Marco Villotta, Mitch Wand, Michael Wijaya, G. Clifford Williams, Ewan Whittaker-Walker, Julia Wlochowski, Roelof Wobben, Mardin Yadegar, Huang Yichao, Yuwang Yin, Andrew Zipperer for comments on drafts of this second edition.

The HTML layout is due to Matthew Butterick who created these styles for the Racket documentation.

Finally, we are grateful to Ada Brunstein and Marie Lufkin Lee, our editors at MIT Press, who gave us permission to develop this second edition of "How to Design Programs" on the web.