158 lines
10 KiB
HTML
158 lines
10 KiB
HTML
|
<!DOCTYPE HTML PUBLIC "-//W3O//DTD W3 HTML 2.0//EN">
|
||
|
|
<!Converted with LaTeX2HTML 0.6.5 (Tue Nov 15 1994) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds >
|
||
|
|
<HEAD>
|
||
|
|
<TITLE>A.2.3. Truncation and Other Simple Transducers</TITLE>
|
||
|
|
</HEAD>
|
||
|
|
<BODY>
|
||
|
|
<meta name="description" value=" Truncation and Other Simple Transducers">
|
||
|
|
<meta name="keywords" value="clm">
|
||
|
|
<meta name="resource-type" value="document">
|
||
|
|
<meta name="distribution" value="global">
|
||
|
|
<P>
|
||
|
|
<b>Common Lisp the Language, 2nd Edition</b>
|
||
|
|
<BR> <HR><A NAME=tex2html6104 HREF="node353.html"><IMG ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME=tex2html6102 HREF="node349.html"><IMG ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME=tex2html6096 HREF="node351.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <A NAME=tex2html6106 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="contents" SRC="icons/contents_motif.gif"></A> <A NAME=tex2html6107 HREF="index.html"><IMG ALIGN=BOTTOM ALT="index" SRC="icons/index_motif.gif"></A> <BR>
|
||
|
|
<B> Next:</B> <A NAME=tex2html6105 HREF="node353.html"> Conditional and Other </A>
|
||
|
|
<B>Up:</B> <A NAME=tex2html6103 HREF="node349.html"> Series Functions</A>
|
||
|
|
<B> Previous:</B> <A NAME=tex2html6097 HREF="node351.html"> Mapping</A>
|
||
|
|
<HR> <P>
|
||
|
|
<H2><A NAME=SECTION003423000000000000000>A.2.3. Truncation and Other Simple Transducers</A></H2>
|
||
|
|
<P>
|
||
|
|
<img align=bottom alt="change_begin" src="gif/change_begin.gif"><br>
|
||
|
|
Transducers compute series from series and form the heart of most series
|
||
|
|
expressions. Mapping is by far the most common transducer. This section
|
||
|
|
presents a number of additional simple transducers.
|
||
|
|
<P>
|
||
|
|
<BR><b>[Function]</b><BR>
|
||
|
|
<tt>cotruncate &rest <i>series-inputs</i> <BR></tt><tt>until <i>bools</i> &rest <i>series-inputs</i> <BR></tt><tt>until-if <i>pred</i> &rest <i>series-inputs</i></tt><P>Each of these functions accepts one or more series inputs <i>S1</i>, <b>...</b>, <i>Sn</i> as its <tt>&rest</tt> argument and returns <b><i>n</i></b> series
|
||
|
|
outputs <i>T1</i>, <b>...</b>, <i>Tn</i> that contain the same elements in the same
|
||
|
|
order-that is, <i>Ti<IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44030.gif">=Si<IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44030.gif"></i>.
|
||
|
|
Let <b><i>k</i></b> be the length of the
|
||
|
|
shortest input <i>Si</i>. <tt>cotruncate</tt> truncates the series so that
|
||
|
|
each output has length <b><i>k</i></b>. Let <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44119.gif"> be the position of the first element
|
||
|
|
in the boolean series <i>bools</i> that is not <tt>nil</tt> or, if every
|
||
|
|
element is <tt>nil</tt>, the length of <i>bools</i>. <tt>until</tt> truncates the
|
||
|
|
series so that each output has length <tt>(min <i>k</i> <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44081.gif">)</tt>.
|
||
|
|
Let <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44121.gif"> be the position of the first element in <i>S1</i> such that
|
||
|
|
<tt>(<i>pred</i> <i>S1<IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44082.gif"></i>)</tt>
|
||
|
|
is not <tt>nil</tt> or, if there is no such
|
||
|
|
element, the length of <i>S1</i>. <tt>until-if</tt> truncates the series so
|
||
|
|
that each output has length <tt>(min <i>k</i> <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44083.gif">)</tt>.
|
||
|
|
<P><pre>
|
||
|
|
(cotruncate #Z(1 2 -3 4) #Z(a b c))
|
||
|
|
=> #Z(1 2 -3) and #Z(a b c)
|
||
|
|
(until #Z(nil nil t nil) #Z(1 2 -3 4) #Z(a b c))
|
||
|
|
=> #Z(1 2) and #Z(a b)
|
||
|
|
(until-if #'minusp #Z(1 2 -3 4) #Z(a b c))
|
||
|
|
=> #Z(1 2) and #Z(a b)
|
||
|
|
</pre><P>
|
||
|
|
<P>
|
||
|
|
<BR><b>[Function]</b><BR>
|
||
|
|
<tt>previous <i>items</i> &optional (<i>default</i> nil) (<i>amount</i> 1)</tt><P>The series returned by <tt>previous</tt> is the same as the input series
|
||
|
|
<i>items</i> except that it is shifted to the right by the positive
|
||
|
|
integer <i>amount</i>. The shifting is done by inserting <i>amount</i>
|
||
|
|
copies of <i>default</i> before <i>items</i> and discarding <i>amount</i>
|
||
|
|
elements from the end of <i>items</i>.
|
||
|
|
<P><pre>
|
||
|
|
(previous #Z(10 11 12) 0) => #Z(0 10 11)
|
||
|
|
</pre><P>
|
||
|
|
<P>
|
||
|
|
<BR><b>[Function]</b><BR>
|
||
|
|
<tt>latch <i>items</i> &key :after :before :pre :post</tt><P>The series returned by <tt>latch</tt> is the same as the input series
|
||
|
|
<i>items</i> except that some of the elements are replaced by other
|
||
|
|
values. <tt>latch</tt> acts like a <i>latch</i> electronic circuit
|
||
|
|
component. Each input element causes the creation of a corresponding
|
||
|
|
output element. After a specified number of non-null input elements
|
||
|
|
have been encountered, the latch is triggered and the output mode is
|
||
|
|
permanently changed.
|
||
|
|
<P>
|
||
|
|
The <tt>:after</tt> and <tt>:before</tt> arguments specify the latch point.
|
||
|
|
The latch point is just after the <tt>:after</tt>-th non-null element in
|
||
|
|
<i>items</i> or just before the <tt>:before</tt>-th non-null element. If
|
||
|
|
neither <tt>:after</tt> nor <tt>:before</tt> is specified, an <tt>:after</tt>
|
||
|
|
of <tt>1</tt> is assumed. If both are specified, it is an error.
|
||
|
|
<P>
|
||
|
|
If a <tt>:pre</tt> is specified, every element prior to the latch point
|
||
|
|
is replaced by this value. If a <tt>:post</tt> is specified, every element
|
||
|
|
after the latch point is replaced by this value. If neither is
|
||
|
|
specified, a <tt>:post</tt> of <tt>nil</tt> is assumed.
|
||
|
|
<P><pre>
|
||
|
|
(latch #Z(nil c nil d e)) => #Z(nil c nil nil nil)
|
||
|
|
(latch #Z(nil c nil d e) :before 2 :post t) => #Z(nil c nil t t)
|
||
|
|
</pre><P>
|
||
|
|
<P>
|
||
|
|
<BR><b>[Function]</b><BR>
|
||
|
|
<tt>collecting-fn type init function &rest series-inputs</tt><P>The higher-order function <tt>collecting-fn</tt> supports the general concept of
|
||
|
|
a simple transducer with internal state. The <i>type</i> argument is a type
|
||
|
|
specifier indicating the type of values returned by <i>function</i>.
|
||
|
|
The <tt>values</tt> construct can be used to indicate multiple types; however,
|
||
|
|
<i>type</i> cannot indicate zero values. If <i>type</i> indicates <b><i>m</i></b> types
|
||
|
|
<IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44125.gif">,
|
||
|
|
then <tt>collecting-fn</tt> returns <b><i>m</i></b> series <i>T1</i>, <b>...</b>, <i>Tm</i>, where <i>Ti</i> has the
|
||
|
|
type <tt>(series <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap43969.gif">)</tt>. The
|
||
|
|
arguments <i>init</i> and <i>function</i> are functions. The remaining
|
||
|
|
arguments (if any) are all series. Let these series be <i>S1</i>, <b>...</b>, <i>Sn</i> and suppose that <i>Si</i> has the type
|
||
|
|
<tt>(series <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44051.gif">)</tt>.
|
||
|
|
<P>
|
||
|
|
The <i>init</i> must be of type
|
||
|
|
<tt>(function () (values <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap43961.gif"> ... <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44143.gif">))</tt>.
|
||
|
|
<P>
|
||
|
|
The <i>function</i> must be of type
|
||
|
|
<P><pre>
|
||
|
|
(function (<IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap43961.gif"> ... <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44143.gif"> <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44145.gif"> ... <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44055.gif">) (values <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap43961.gif"> ... <IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44143.gif">))
|
||
|
|
</pre><P>
|
||
|
|
<P>
|
||
|
|
The length of each output is the same as the length of the shortest input.
|
||
|
|
If there are no bounded series inputs, the outputs are unbounded.
|
||
|
|
The elements of the <i>Ti</i> are computed as follows:
|
||
|
|
<P><pre>
|
||
|
|
(values <i>T1</i><IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44031.gif"> ... <i>Tm</i><IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44031.gif">) ==
|
||
|
|
(multiple-value-call <i>function</i> (funcall <i>init</i>) <i>S1</i><IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44031.gif"> ... <i>Sn</i><IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44031.gif">)
|
||
|
|
|
||
|
|
(values <i>T1</i><IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44030.gif"> ... <i>Tm</i><IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44030.gif">) ==
|
||
|
|
(funcall <i>function</i> <i>T1</i><IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap43947.gif"> ... <i>Tm</i><IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap43947.gif"> <i>S1</i><IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44030.gif"> ... <i>Sn</i><IMG ALIGN=BOTTOM ALT="" SRC="_24769_tex2html_wrap44030.gif">)
|
||
|
|
</pre><P>
|
||
|
|
<P>
|
||
|
|
If <i>init</i> or <i>function</i> has side effects, it can count on
|
||
|
|
being called in the order indicated by the equations above. However,
|
||
|
|
given the lazy evaluation nature of series, these functions will not be called
|
||
|
|
until their outputs are actually used (if ever). In addition, no
|
||
|
|
assumptions can be made about the relative order of evaluation of these
|
||
|
|
calls with regard to execution in other parts of a given series expression.
|
||
|
|
The second example below computes a series of partial sums of the numbers in
|
||
|
|
an input series. The third example computes two output series: the
|
||
|
|
partial sums of its first input and the partial products of its second
|
||
|
|
input.
|
||
|
|
<P><pre>
|
||
|
|
(defun running-averages (float-list)
|
||
|
|
(multiple-value-call #'map-fn
|
||
|
|
'float #'/
|
||
|
|
(collecting-fn '(values float integer)
|
||
|
|
#'(lambda () (values 0.0 0)
|
||
|
|
#'(lambda (s n x) (values (+ s x) (+ n 1))))
|
||
|
|
float-list)))
|
||
|
|
</pre><P>
|
||
|
|
<P><pre>
|
||
|
|
(collecting-fn 'integer #'(lambda () 0) #'+ #Z(1 2 3))
|
||
|
|
=> #Z(1 3 6)
|
||
|
|
|
||
|
|
(collecting-fn '(values integer integer)
|
||
|
|
#'(lambda () (values 0 1))
|
||
|
|
#'(lambda (sum prod x y)
|
||
|
|
(values (+ sum x) (* prod y)))
|
||
|
|
#Z(4 6 8)
|
||
|
|
#Z(1 2 3))
|
||
|
|
=> #Z(4 10 18) and #Z(1 2 6)
|
||
|
|
</pre><P>
|
||
|
|
<br><img align=bottom alt="change_end" src="gif/change_end.gif">
|
||
|
|
<P>
|
||
|
|
<BR> <HR><A NAME=tex2html6104 HREF="node353.html"><IMG ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME=tex2html6102 HREF="node349.html"><IMG ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME=tex2html6096 HREF="node351.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <A NAME=tex2html6106 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="contents" SRC="icons/contents_motif.gif"></A> <A NAME=tex2html6107 HREF="index.html"><IMG ALIGN=BOTTOM ALT="index" SRC="icons/index_motif.gif"></A> <BR>
|
||
|
|
<B> Next:</B> <A NAME=tex2html6105 HREF="node353.html"> Conditional and Other </A>
|
||
|
|
<B>Up:</B> <A NAME=tex2html6103 HREF="node349.html"> Series Functions</A>
|
||
|
|
<B> Previous:</B> <A NAME=tex2html6097 HREF="node351.html"> Mapping</A>
|
||
|
|
<HR> <P>
|
||
|
|
<HR>
|
||
|
|
<P><ADDRESS>
|
||
|
|
AI.Repository@cs.cmu.edu
|
||
|
|
</ADDRESS>
|
||
|
|
</BODY>
|