106 lines
5.9 KiB
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106 lines
5.9 KiB
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<!DOCTYPE HTML PUBLIC "-//W3O//DTD W3 HTML 2.0//EN">
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<!Converted with LaTeX2HTML 0.6.5 (Tue Nov 15 1994) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds >
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<HEAD>
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<TITLE>A.1. Introduction</TITLE>
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</HEAD>
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<BODY>
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<meta name="description" value=" Introduction">
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<meta name="keywords" value="clm">
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<meta name="resource-type" value="document">
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<meta name="distribution" value="global">
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<P>
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<b>Common Lisp the Language, 2nd Edition</b>
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<BR> <HR><A NAME=tex2html6050 HREF="node349.html"><IMG ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME=tex2html6048 HREF="node347.html"><IMG ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME=tex2html6042 HREF="node347.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <A NAME=tex2html6052 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="contents" SRC="icons/contents_motif.gif"></A> <A NAME=tex2html6053 HREF="index.html"><IMG ALIGN=BOTTOM ALT="index" SRC="icons/index_motif.gif"></A> <BR>
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<B> Next:</B> <A NAME=tex2html6051 HREF="node349.html"> Series Functions</A>
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<B>Up:</B> <A NAME=tex2html6049 HREF="node347.html"> Series</A>
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<B> Previous:</B> <A NAME=tex2html6043 HREF="node347.html"> Series</A>
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<HR> <P>
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<H1><A NAME=SECTION003410000000000000000>A.1. Introduction</A></H1>
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<P>
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<img align=bottom alt="change_begin" src="gif/change_begin.gif"><br>
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Series combine aspects of sequences, streams, and loops. Like sequences,
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series represent totally ordered multi-sets. In addition, the series
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functions have the same flavor as the sequence functions-namely, they
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operate on whole series, rather than extracting elements to be
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processed by other functions. For instance, the series expression below
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computes the sum of the positive elements in a list.
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<P><pre>
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(collect-sum (choose-if #'plusp (scan '(1 -2 3 -4)))) => 4
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</pre><P>
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<P>
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Like streams, series can represent unbounded sets of elements and are
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supported by lazy evaluation: each element of a series is not
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computed until it is needed. For instance, the series expression below
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returns a list of the first five even natural numbers and their sum. The
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call on <tt>scan-range</tt> returns a series of all the even natural numbers.
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However, since no elements beyond the first five are ever used, no elements
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beyond the first five are ever computed.
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<P><pre>
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(let ((x (subseries (scan-range :from 0 :by 2) 0 5)))
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(values (collect x) (collect-sum x)))
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=> (0 2 4 6 8) and 20
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</pre><P>
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<P>
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Like sequences and unlike streams, a series is not altered
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when its elements are accessed. For instance, both users of <tt>x</tt>
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above receive the same elements.
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<P>
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A totally ordered multi-set of elements can be represented in a loop by the
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successive values of a variable. This is extremely efficient, because it
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avoids the need to store the elements as a group in any kind of data
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structure. In most situations, series expressions achieve this same high
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level of efficiency, because they are automatically transformed into loops
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before being evaluated or compiled. For instance, the first expression
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above is transformed into a loop like the following.
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<P><pre>
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(let ((sum 0))
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(dolist (i '(1 -2 3 -4) sum)
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(when (plusp i) (setq sum (+ sum i))))) => 4
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</pre><P>
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<P>
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A wide variety of algorithms can be expressed clearly and succinctly with
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series expressions. In particular, at least 90 percent of the loops
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programmers typically write can be replaced by series expressions that are
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much easier to understand and modify, and just as efficient. From this
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perspective, the key feature of series is that they are supported by a rich
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set of functions. These functions more or less correspond to the union of
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the operations provided by the sequence functions, the <tt>loop</tt> clauses,
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and the vector operations of APL.
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<P>
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Some series expressions cannot be transformed into loops.
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This is unfortunate, because while transformable series expressions are much more
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efficient than equivalent expressions involving sequences or streams,
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non-transformable series expressions are much less efficient. Whenever a
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problem comes up that blocks the transformation of a series expression, a
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warning message is issued. On the basis of information in the message, it is
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usually easy to provide an efficient fix for the problem (see
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section <A HREF="node356.html#SERIESESECTION">A.3</A>).
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<P>
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Fortunately, most series expressions can be transformed into loops. In
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particular, pure expressions (ones that do not store series in variables)
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can always be transformed. As a result, the best approach for programmers
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to take is simply to write series expressions without worrying about
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transformability. When problems come up, they can be ignored (since they
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cannot lead to the computation of incorrect results) or dealt with on an
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individual basis.
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<P>
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<hr>
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<b>Implementation note:</b> The series functions and the theory
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underlying them are described in greater detail
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in [<A HREF="node368.html#WATERSSERIESDESIGN">52</A>,<A HREF="node368.html#WATERSSERIESIMPLEMENTATION">53</A>].
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These reports also discuss the algorithms required to transform series
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expressions into loops and explain how to obtain a portable implementation.
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<hr>
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<br><img align=bottom alt="change_end" src="gif/change_end.gif">
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<P>
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<BR> <HR><A NAME=tex2html6050 HREF="node349.html"><IMG ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME=tex2html6048 HREF="node347.html"><IMG ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME=tex2html6042 HREF="node347.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <A NAME=tex2html6052 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="contents" SRC="icons/contents_motif.gif"></A> <A NAME=tex2html6053 HREF="index.html"><IMG ALIGN=BOTTOM ALT="index" SRC="icons/index_motif.gif"></A> <BR>
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<B> Next:</B> <A NAME=tex2html6051 HREF="node349.html"> Series Functions</A>
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<B>Up:</B> <A NAME=tex2html6049 HREF="node347.html"> Series</A>
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<B> Previous:</B> <A NAME=tex2html6043 HREF="node347.html"> Series</A>
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<HR> <P>
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<HR>
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<P><ADDRESS>
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AI.Repository@cs.cmu.edu
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</ADDRESS>
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</BODY>
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