154 lines
5.1 KiB
HTML
154 lines
5.1 KiB
HTML
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<!DOCTYPE HTML PUBLIC "-//W3O//DTD W3 HTML 2.0//EN">
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<!Originally converted to HTML using LaTeX2HTML 95 (Thu Jan 19 1995) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds >
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<HEAD>
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<TITLE> Ensuring Proper Termination</TITLE>
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</HEAD>
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<BODY>
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<meta name="description" value=" Ensuring Proper Termination">
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<meta name="keywords" value="lp">
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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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<BR> <HR>
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<A HREF="node47.html"><IMG ALIGN=BOTTOM ALT="next" SRC="next_motif.gif"></A>
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<A HREF="node41.html"><IMG ALIGN=BOTTOM ALT="up" SRC="up_motif.gif"></A>
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<A HREF="node45.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="previous_motif.gif"></A> <BR>
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<A HREF="lp.html"><B>Contents</B></A>
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<B> Next:</B>
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<A HREF="node47.html"> Abstraction</A>
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<B>Up:</B>
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<A HREF="node41.html"> Programming Techniques</A>
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<B> Previous:</B>
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<A HREF="node45.html"> Recursion on Numbers</A>
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<BR> <HR> <P>
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<H1> Ensuring Proper Termination</H1>
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<P>
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Often it happens that the Lisp programmer unknowingly
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implements an infinite loop. This could happen in two different ways:
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an infinite ``do'' loop, or an improper recursion. In the first case,
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it may be that the programmer is using the general ``do'' construct and
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has specified a test for termination that will never occur. This
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problem can be avoided by using the more specific constructs ``dotimes'' or
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``dolist'' (chapter 3). These constructs have a built-in test for
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termination; ``dotimes'' iterates a specified number of times, and
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``dolist'' iterates once for each element in a given list. Improper
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recursion, however, is often more difficult to discover.
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<BLOCKQUOTE>
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<PRE><TT> <H4><b>Example 8:
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<P>
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The following definition wrongly implements the function to determine
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<P>
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the length of a list:
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<P>
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<tt> (defun length (lst)</tt>
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<P>
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<tt> (cond ((null lst) 0)</tt>
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<P>
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<tt> (t (+ 1 (length lst)))))</tt>
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<P>
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</b></h4></TT></PRE>
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</BLOCKQUOTE>
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The following notation illustrates why the above function does
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not terminate:
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<BLOCKQUOTE>
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<PRE>(length '(a b c))
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= (+ 1 (length '(a b c)))
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= (+ 1 (+ 1 (length '(a b c))))
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= (+ 1 (+ 1 (+ 1 (length '(a b c)))))
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= (+ 1 (+ 1 (+ 1 (+ 1 (length '(a b c))))))
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= (+ 1 (+ 1 (+ 1 (+ 1 (+ 1 (length '(a b c)))))))
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= ...
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= ...
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</PRE>
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</BLOCKQUOTE>
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The list is passed-in unmodified in the recursive call. Such simple
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mistakes are very common, and their frequency increases with longer and
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more complicated programs. Compare this definition of ``length'' with
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the one given in section 4.2.
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<BLOCKQUOTE>
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<PRE><TT> <H4><b>RULE OF THUMB 7:
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<P>
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To ensure proper termination do two things:
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<P>
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(1) make sure that you are changing at least one argument
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<P>
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in your recursive call;
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<P>
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(2) make sure that your test for termination looks at the
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<P>
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arguments that change in the recursive call.
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<P>
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</b></h4></TT></PRE>
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</BLOCKQUOTE>
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<BLOCKQUOTE>
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<PRE><TT> <H4><b>Example 9:
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<P>
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A function, ``exp,'' takes two positive, non-zero integers, x and y, and
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<P>
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raises x to the y power. Will the following recursive definition for
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<P>
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``exp'' terminate properly?
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<P>
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<tt> (defun exp (x y)</tt>
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<P>
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<tt> (cond ((= y 0) 1)</tt>
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<P>
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<tt> (t (* x (exp x (- y 1))))))</tt>
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<P>
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</b></h4></TT></PRE>
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</BLOCKQUOTE>
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Yes, the above definition is correct and will terminate properly
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according to Rule of Thumb 7. We fulfill both requirements of the
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rule:
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<DL COMPACT><DT>(1)
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<DD> We are changing at least one argument in the
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recursive call, namely y, which is decremented
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by one.
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<DT>(2)
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<DD> In our test for termination, <code>(= y 0)</code>, we are
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using an argument that we change in the
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recursive call, namely y.
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<P>
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</DL>
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<div style="border: 1px solid red; background: #ffffdd; margin: 10px; text-align: center"><b>NOTE:</b> The example above again illustrates that you are allowed to redefine functions that are built into Lisp. Programmer beware!!</div>
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<BLOCKQUOTE>
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<PRE><TT> <H4><b>RULE OF THUMB 8:
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<P>
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<b>Two simple cases may occur when changing an argument in a
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<P>
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<b>recursive call:
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<P>
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<b>(1) if you are using ``rest'' to change an argument which is
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<P>
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<b>a list, use ``null'' in the test for termination;
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<P>
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<b>(2) if you are decreasing an argument which is a number,
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<P>
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<b>compare it with 0 in the test for termination.
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<P>
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</TT></PRE>
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</BLOCKQUOTE></H4></b></H4></b></b></b></b></b></b></H4></b></H4></b></b></b></b></b></b></b><BR> <HR>
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<A HREF="node47.html"><IMG ALIGN=BOTTOM ALT="next" SRC="next_motif.gif"></A>
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<A HREF="node41.html"><IMG ALIGN=BOTTOM ALT="up" SRC="up_motif.gif"></A>
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<A HREF="node45.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="previous_motif.gif"></A> <BR>
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<A HREF="lp.html"><B>Contents</B></A>
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<B> Next:</B>
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<A HREF="node47.html"> Abstraction</A>
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<B>Up:</B>
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<A HREF="node41.html"> Programming Techniques</A>
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<B> Previous:</B>
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<A HREF="node45.html"> Recursion on Numbers</A>
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<BR> <HR> <P>
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<BR> <HR>
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<P>
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<ADDRESS>
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<I>© Colin Allen & Maneesh Dhagat <BR>
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March 2007 </I>
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</ADDRESS>
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</BODY>
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