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The Reasoned Schemer.pdf

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    (Preface ix)
    ((l. Playthings) 2)
    ((2. Teaching Old Toys New Tricks) 16)
    ((3. Seeing Old Friends in New Ways) 26)
    ((4. Members Only) 46)
    ((5. Double Your Fun) ((5. 60)
    ((6. The Fun Never Ends ...) 76)
    ((7. A Bit Too Much) 86)
    ((8. Just a Bit More) 108)
    ((9. Under the Hood) 130)
    ((10. Thin Ice) 144)
    (Connecting the Wires 158)
    (Welcome to the Club 162)
    (Index 164))
    Our main assumption is that you understand the first eight chapters of The Little Schemer'.
    Streams contain either zero, one, or more substitutions.'
    Given a stream s°° and a goal g, we can feed each value in s° to the goal g to get a new stream, the
    Daniel P. Friedman William E. Byrd Oleg Kiselyov Drawings by Duane Bibby To Mary, Sarah, Rachel, Shannon and Rob, and to the memory of Brian.
    To Mom, Dad, Brian, Mary, and Renzhong.
    (Preface ix) ((l. Playthings) 2) ((2. Teaching Old Toys New Tricks) 16) ((3. Seeing Old Friends in New Ways) 26) ((4. Members Only) 46) ((5. Double Your Fun) ((5. 60) ((6. The Fun Never Ends ...) 76) ((7. A Bit Too Much) 86) ((8. Just a Bit More) 108) ((9. Under the Hood) 130) ((10. Thin Ice) 144) (Connecting the Wires 158) (Welcome to the Club 162) (Index 164))
    The goal of this book is to show the beauty of relational programming. We believe that it is natural to extend functional programming to relational programming. We demonstrate this by extending Scheme with a few new constructs, thereby combining the benefits of both styles. This extension also captures the essence of Prolog, the most well-known logic programming language. Our main assumption is that you understand the first eight chapters of The Little Schemer'. The only true requirement, however, is that you understand functions as values. That is, a function can be both an argument to and the value of a function call. Furthermore, you should know that functions remember the context in which they were created. And that's it we assume no further knowledge of mathematics or logic. Readers of the appendix Connecting the Wires, however, must also have a rudimentary knowledge of Scheme macros at the level of let, and, and cond. In order to do relational programming, we need only two constants: #s and #u, and only three operators: , fresh, and conde. These are introduced in the first chapter and are the only operators used until chapter 6. The additional operators we introduce are variants of these three. In order to keep this extension simple, we mimicked existing Scheme syntax. Thus, #s and #u are reminiscent of the Boolean constants: #t and #f; fresh expressions resemble lambda expressions; and conde expressions are syntactically like cond expressions. We use a few notational conventions throughout the text primarily changes in font for different classes of symbols. Lexical variables are in italics, forms are in boldface, data are in sans serif, and lists are wrapped by boldfaced parentheses `O'. A relation, a function that returns a goal as its value, ends its name with a superscript `o' (e.g., car° and nullo). We also use a superscript with our interface to Scheme, run, which is fully explained in the first chapter. We have taken certain liberties with punctuation to increase clarity, such as frequently omitting a question mark when a question ends with a special symbol. We do this to avoid confusion with function names that might end with a question mark. In chapters 7 and 8 we define arithmetic operators as relations. The +° relation can not only add but also subtract; *° can not only multiply but also factor numbers; and logo can not only find the logarithm given a number and a base but also find the base given a logarithm and a number. Just as we can define the subtraction relation from the addition relation, we can define the exponentiation relation from the logarithm relation. In general, given (*° x y z) we can specify what we know about these numbers (their values, whether they are odd or even, etc.) and ask *° to find the unspecified values. We don't specify how to accomplish the task: rather, we describe what we want in the result.
    This book would not have been possible without earlier work on implementing and using logic systems with Matthias Felleisen, Anurag Mendhekar, Jon Rossie, Michael Levin, Steve Ganz, and Venkatesh Choppella. Steve showed how to partition Prolog's named relations into unnamed functions, while Venkatesh helped characterize the types in this early logic system. We thank them for their effort during this developmental stage. There are many others we wish to thank. Mitch Wand struggled through an early draft and spent several days in Bloomington clarifying the semantics of the language, which led to the elimination of superfluous language forms. We also appreciate Kent Dybvig's and Yevgeniy Makarov's comments on the first few chapters of an early draft and Amr Sabry's Haskell implementation of the language. We gratefully acknowledge Abdulaziz Ghuloum's insistence that we remove some abstract material from the introductory chapter. In addition, Aziz's suggestions significantly clarified the run interface. Also incredibly helpful were the detailed criticisms of Chung-chieh Shan, Erik Hilsdale, John Small, Ronald Garcia, Phill Wolf, and Jos Koot. We are especially grateful to Chung-chieh for Connecting the Wires so masterfully in the final implementation. We thank David Mack and Kyle Blocher for teaching this material to students in our undergraduate programming languages course and for making observations that led to many improvements to this book. We also thank those students who not only learned from the material but helped us to clarify its presentation. There are several people we wish to thank for contributions not directly related to the ideas in the book. We would be remiss if we did not acknowledge Dorai Sitaram's incredibly clever Scheme typesetting program, SLAT. We are grateful for Matthias Felleisen's typesetting macros (created for The Little Schemer), and for Oscar Waddell's implementation of a tool that selectively expands Scheme macros. Also, we thank Shriram Krishnamurthi for reminding us of a promise we made that the food would be vegetarian in the next little book. Finally, we thank Bob Prior, our editor, for his encouragement and enthusiasm for this effort. Food appears in examples throughout the book for two reasons. First, food is easier to visualize than abstract symbols: we hope the food imagery helps you to better understand the examples and concepts. Second, we want to provide a little distraction. We know how frustrating the subject matter can be, thus these culinary diversions are for whetting your appetite. As such, we hope that thinking about food will cause you to stop reading and have a bite. You are now ready to start. Good luck! We hope you enjoy the book. Bon appetit! Daniel P. Friedman William E. Byrd Bloomington, Indiana
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