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Foreword
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</NAME>
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<TEXT>
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in preparation
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</TEXT>
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<TEXT>
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I had the pleasure of meeting the amazing Alan Perlis and talking with
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him a few times, when I was still a student. Following in his
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footsteps is a daunting task, even though he blazed an excellent
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trail. Still, I would like to reexamine one comment he made in the
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original foreword to this book (and, please, you may wish to read his
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foreword before you finish this one). Is it really true that it is
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better to have 100 functions operate on one data structure than to
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have 10 functions operate on 10 data structures?
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</TEXT>
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<TEXT>
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To answer that question carefully, we first need to ask whether
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that one data structure is <QUOTE>universal</QUOTE>: can it conveniently
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fulfill the roles of those 10 more specialized data structures?
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</TEXT>
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<TEXT>
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For that matter, we can also ask: do we really need 100
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functions? Is there a single universal function that can fulfill
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the roles of all those other functions?
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</TEXT>
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<TEXT>
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The surprising answer to that last question is <QUOTE>yes</QUOTE>; it is
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only slightly tricky to construct a function that accepts (1) a
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data structure that serves as a description of some other
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function, and (2) a list of arguments, and behaves exactly as
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that other function would when applied to the given
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arguments. And it is only slightly tricky to design a data
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structure capable of describing any computation whatsoever. One
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such data structure (the tagged-list representation of
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expressions and statements, paired with environments that
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associate names with values) and one such universal function
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(<JAVASCRIPTINLINE>apply</JAVASCRIPTINLINE>) are described in
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Chapter 4 of this book. So maybe we need only one function and
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one data structure.
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</TEXT>
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<TEXT>
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That is true in theory. In practice, we find it convenient to
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draw distinctions that help us, as human beings constructing
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descriptions of computations, to organize the structure of our
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code so that we can better understand them. I believe that
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Perlis was making a remark not about computational capability,
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but about human abilities and human limitations.
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</TEXT>
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<TEXT>
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One thing the human mind seems to do well is to name things; we have
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powerful associative memories. Given a name, we can quickly recall
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some associated thing to mind. This is why we typically find it easier
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to work with the lambda calculus than the combinatory calculus; it is
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much easier for most people to interpret the Lisp expression
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<SCHEMEINLINE>(lambda (x) (lambda (y) (+ x y)))</SCHEMEINLINE>
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or the JavaScript expression
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<JAVASCRIPTINLINE>x => y => x + y</JAVASCRIPTINLINE>
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than the combinatory expression
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<BLOCKQUOTE>
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((S ((S (K S)) ((S ((S (K S)) ((S (K K)) (K +)))) ((S (K K)) I)))) (K I))
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</BLOCKQUOTE>
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even though there is a
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direct structural correspondence, easily expressed in five lines of
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Lisp code.
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</TEXT>
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<TEXT>
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So while in principle we could get by with just one universal
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function, we prefer to modularize our code, to give names to the
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various pieces, and to mention the names of function
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descriptions rather than constantly feeding the descriptions
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themselves to the universal function.
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</TEXT>
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<TEXT>
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In my 1998 talk <QUOTE>Growing a Language,</QUOTE> I commented
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that a good programmer <QUOTE>does not just write programs. A
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good programmer builds a working vocabulary.</QUOTE> As we
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design and define more and more parts of our programs, we give
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names to those parts, and the result is that we have a richer
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language in which to write the rest.
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</TEXT>
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<TEXT>
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But we also find it natural to draw distinctions among data
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structures, and to give them names.
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</TEXT>
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<TEXT>
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It may be that nested lists are a universal data structure (and
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it is worth noting that many modern and widely used data
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structures, such as HTML and XML and JSON, are also
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parenthetically nested representations, only slightly more
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elaborate than Lisp<APOS/>s bare parentheses). There are also many
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functions, such as finding the length of a list or applying a
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function to every element of a list and getting back a list of
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the results, that are useful in a wide variety of situations.
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And yet, when I am thinking about a specific computation, I
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often say to myself, <QUOTE>This list of two things I expect to be a
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personal name and a surname, but that list of two things I
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expect to be the real and imaginary parts of a complex number,
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and that other list of two things I will regard as the numerator
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and denominator of a fraction.</QUOTE> In other words, I draw
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distinctions<EMDASH/>and it may be useful to represent those
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distinctions explicitly in the data structure, in part to
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prevent mistakes such as accidentally treating a complex number
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as a fraction. (Again, this is a comment about human abilities
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and human limitations.)
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</TEXT>
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<TEXT>
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So maybe the truth is somewhere in between the extremes that
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Perlis so eloquently posited. Maybe the sweet spot is something
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more like 40 functions general enough to operate usefully on a
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universal data structure such as lists, but also 10 sets of 6
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functions each that are relevant when we take one of 10
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specialized views of that universal data structure. This is
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manageable if we give good names to these functions and
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specialized views.
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</TEXT>
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<TEXT>
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As you read this book, please pay attention not only to the
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programming language constructs and how they are used, but also
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to the <EM>names</EM> given to functions and variables and data
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structures. They have been chosen in a deliberate and systematic
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way to enhance your understanding of the overall program
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structure.
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</TEXT>
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<TEXT>
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Primitives, means of combination, abstraction, naming, and
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conventions for using a universal data structure in specialized
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ways by drawing distinctions: these are the fundamental building
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blocks of a good programming language. From there, imagination
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and good engineering judgment based on experience can do the
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rest.
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</TEXT>
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