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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>15.6. Association Lists</TITLE>
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<BODY>
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<meta name="description" value=" Association Lists">
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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=tex2html3435 HREF="node154.html"><IMG ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME=tex2html3433 HREF="node147.html"><IMG ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME=tex2html3429 HREF="node152.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <A NAME=tex2html3437 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="contents" SRC="icons/contents_motif.gif"></A> <A NAME=tex2html3438 HREF="index.html"><IMG ALIGN=BOTTOM ALT="index" SRC="icons/index_motif.gif"></A> <BR>
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<B> Next:</B> <A NAME=tex2html3436 HREF="node154.html"> Hash Tables</A>
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<B>Up:</B> <A NAME=tex2html3434 HREF="node147.html"> Lists</A>
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<B> Previous:</B> <A NAME=tex2html3430 HREF="node152.html"> Using Lists as </A>
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<HR> <P>
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<H1><A NAME=SECTION001960000000000000000>15.6. Association Lists</A></H1>
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<P>
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An <i>association list</i>, or <i>a-list</i>, is a data structure
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used very frequently in Lisp. An a-list is a list of pairs (conses);
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each pair is an association. The <i>car</i> of a pair is called the <i>key</i>,
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and the <i>cdr</i> is called the <i>datum</i>.
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<P>
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An advantage of the a-list representation is that an a-list can be
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incrementally augmented simply by adding new entries to the front.
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Moreover, because the searching function <tt>assoc</tt> searches the
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a-list in order, new entries can ``shadow'' old entries. If an a-list is
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viewed as a mapping from keys to data, then the mapping can be not only
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augmented but also altered in a non-destructive manner by adding new
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entries to the front of the a-list.
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<P>
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Sometimes an a-list represents a bijective mapping, and it is desirable
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to retrieve a key given a datum. For this purpose, the ``reverse'' searching
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function <tt>rassoc</tt> is provided. Other variants of a-list searches
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can be constructed using the function <tt>find</tt> or <tt>member</tt>.
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<P>
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It is permissible to let <tt>nil</tt> be an element of an a-list in place of
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a pair. Such an element is not considered to be a pair but is simply
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passed over when the a-list is searched by <tt>assoc</tt>.
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<P>
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<BR><b>[Function]</b><BR>
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<tt>acons <i>key</i> <i>datum</i> <i>a-list</i></tt><P><tt>acons</tt> constructs a new association list by adding the pair
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<tt>(<i>key</i> . <i>datum</i>)</tt> to the old <i>a-list</i>.
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<P><pre>
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(acons x y a) == (cons (cons x y) a)
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</pre><P>
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<img align=bottom alt="change_begin" src="gif/change_begin.gif"><br>
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This is a trivial convenience function, but I find I use it a lot.
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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><b>[Function]</b><BR>
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<tt>pairlis <i>keys</i> <i>data</i> &optional <i>a-list</i></tt><P><tt>pairlis</tt> takes two lists and makes an association list that associates
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elements of the first list to corresponding elements of the second
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list. It is an error if the two lists <i>keys</i> and <i>data</i> are not of
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the same length. If the optional argument <i>a-list</i> is provided, then the
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new pairs are added to the front of it.
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<P>
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The new pairs may appear in the resulting a-list in any order;
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in particular, either forward or backward order is permitted.
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Therefore the result of the call
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<P><pre>
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(pairlis '(one two) '(1 2) '((three . 3) (four . 19)))
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</pre><P>
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might be
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<P><pre>
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((one . 1) (two . 2) (three . 3) (four . 19))
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</pre><P>
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but could equally well be
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<P><pre>
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((two . 2) (one . 1) (three . 3) (four . 19))
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</pre><P>
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<P>
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<BR><b>[Function]</b><BR>
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<tt>assoc <i>item</i> <i>a-list</i> &key :test :test-not :key <BR></tt><tt>assoc-if <i>predicate</i> <i>a-list</i> <BR></tt><tt>assoc-if-not <i>predicate</i> <i>a-list</i></tt><P>
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<img align=bottom alt="change_begin" src="gif/change_begin.gif"><br>
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X3J13 voted in March 1988
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(ASSOC-RASSOC-IF-KEY) <A NAME=17126> </A>
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to allow <tt>assoc-if</tt> and <tt>assoc-if-not</tt>
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also to take a keyword argument named <tt>:key</tt>, to be used
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to determine whether a pair ``satisfies the test'' in the same manner as
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for sequence functions. The new function descriptions are therefore as follows:
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<P>
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<BR><b>[Function]</b><BR>
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<tt>assoc-if <i>predicate</i> <i>a-list</i> &key :key <BR></tt><tt>assoc-if-not <i>predicate</i> <i>a-list</i> &key :key</tt><P>
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The omission of <tt>:key</tt> arguments for these
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functions in the first edition was probably an oversight.
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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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Each of these searches the association list
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<i>a-list</i>. The value is the first pair in the a-list such that
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the <i>car</i> of the pair satisfies the test, or <tt>nil</tt> if there is
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no such pair in the a-list.
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For example:
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<P><pre>
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(assoc 'r '((a . b) (c . d) (r . x) (s . y) (r . z)))
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=> (r . x)
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(assoc 'goo '((foo . bar) (zoo . goo))) => <tt>nil</tt>
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(assoc '2 '((1 a b c) (2 b c d) (-7 x y z))) => (2 b c d)
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</pre><P>
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It is possible to <tt>rplacd</tt> the result of <tt>assoc</tt> <i>provided</i>
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that it is not <tt>nil</tt>,
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in order to ``update'' the ``table'' that was <tt>assoc</tt>'s second argument.
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(However, it is often better to update an a-list by adding new pairs
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to the front, rather than altering old pairs.)
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For example:
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<P><pre>
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(setq values '((x . 100) (y . 200) (z . 50)))
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(assoc 'y values) => (y . 200)
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(rplacd (assoc 'y values) 201)
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(assoc 'y values) => (y . 201) now
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</pre><P>
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A typical trick is to say
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<tt>(cdr (assoc x y))</tt>.
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Because the <i>cdr</i> of <tt>nil</tt> is guaranteed to be <tt>nil</tt>,
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this yields <tt>nil</tt> if no pair is found <i>or</i> if a pair is
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found whose <i>cdr</i> is <tt>nil</tt>. This is useful if <tt>nil</tt> serves
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its usual role as a ``default value.''
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<P>
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The two expressions
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<P><pre>
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(assoc <i>item</i> <i>list</i> :test <i>fn</i>)
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</pre><P>
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and
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<P><pre>
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(find <i>item</i> <i>list</i> :test <i>fn</i> :key #'car)
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</pre><P>
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are equivalent in meaning with one important exception:
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if <tt>nil</tt> appears in the a-list in place of a pair,
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and the <i>item</i> being searched for is <tt>nil</tt>,
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<tt>find</tt> will blithely compute the <i>car</i> of the <tt>nil</tt> in the a-list,
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find that it is equal to the <i>item</i>, and return <tt>nil</tt>,
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whereas <tt>assoc</tt> will ignore the <tt>nil</tt> in the a-list and continue
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to search for an actual pair (cons) whose <i>car</i> is <tt>nil</tt>.
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See <tt>find</tt> and <tt>position</tt>.
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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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X3J13 voted in January 1989
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(MAPPING-DESTRUCTIVE-INTERACTION) <A NAME=17182> </A>
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to restrict user side effects; see section <A HREF="node92.html#STRUCTURETRAVERSALSECTION">7.9</A>.
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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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<hr>
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<b>Compatibility note:</b> In MacLisp, the <tt>assoc</tt> function uses
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an <tt>equal</tt> comparison rather than <tt>eql</tt>, which is the default
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test for <tt>assoc</tt> in Common Lisp. Where in MacLisp one would write
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<tt>(assoc x y)</tt>, in Common Lisp one must write <tt>(assoc x y :test #'equal)</tt>
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to get the completely identical effect. Similarly, one can get the
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precise effect, and no more, of the MacLisp <tt>(assq x y)</tt>
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by writing in Common Lisp <tt>(assoc x y :test #'eq)</tt>.
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<hr>
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<P>
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In Interlisp, <tt>assoc</tt> uses an <tt>eq</tt> test, and <tt>sassoc</tt>
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uses an Interlisp <tt>equal</tt> test.
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<P>
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<BR><b>[Function]</b><BR>
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<tt>rassoc <i>item</i> <i>a-list</i> &key :test :test-not :key <BR></tt><tt>rassoc-if <i>predicate</i> <i>a-list</i> <BR></tt><tt>rassoc-if-not <i>predicate</i> <i>a-list</i></tt><P>
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<img align=bottom alt="change_begin" src="gif/change_begin.gif"><br>
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X3J13 voted in March 1988
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(ASSOC-RASSOC-IF-KEY) <A NAME=17202> </A>
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to allow <tt>rassoc-if</tt> and <tt>rassoc-if-not</tt>
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also to take a keyword argument named <tt>:key</tt>, to be used
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to determine whether a pair ``satisfies the test'' in the same manner as
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for sequence functions. The new function descriptions are therefore as follows:
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<P>
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<BR><b>[Function]</b><BR>
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<tt>rassoc-if <i>predicate</i> <i>a-list</i> &key :key <BR></tt><tt>rassoc-if-not <i>predicate</i> <i>a-list</i> &key :key</tt><P>
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The omission of <tt>:key</tt> arguments for these
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functions in the first edition was probably an oversight.
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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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<tt>rassoc</tt> is the reverse form of <tt>assoc</tt>; it searches for
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a pair whose <i>cdr</i> satisfies the test, rather than the <i>car</i>.
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If the <i>a-list</i> is considered to be a mapping, then <tt>rassoc</tt>
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treats the <i>a-list</i> as representing the inverse mapping.
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For example:
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<P><pre>
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(rassoc 'a '((a . b) (b . c) (c . a) (z . a))) => (c . a)
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</pre><P>
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<P>
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The expressions
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<P><pre>
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(rassoc <i>item</i> <i>list</i> :test <i>fn</i>)
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</pre><P>
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and
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<P><pre>
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(find <i>item</i> <i>list</i> :test <i>fn</i> :key #'cdr)
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</pre><P>
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are equivalent in meaning, except when the <i>item</i> is <tt>nil</tt>
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and <tt>nil</tt> appears in place of a pair in the a-list. See the discussion
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of the function <tt>assoc</tt>.
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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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X3J13 voted in January 1989
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(MAPPING-DESTRUCTIVE-INTERACTION) <A NAME=17234> </A>
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to restrict user side effects; see section <A HREF="node92.html#STRUCTURETRAVERSALSECTION">7.9</A>.
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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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<P>
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<BR> <HR><A NAME=tex2html3435 HREF="node154.html"><IMG ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME=tex2html3433 HREF="node147.html"><IMG ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME=tex2html3429 HREF="node152.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <A NAME=tex2html3437 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="contents" SRC="icons/contents_motif.gif"></A> <A NAME=tex2html3438 HREF="index.html"><IMG ALIGN=BOTTOM ALT="index" SRC="icons/index_motif.gif"></A> <BR>
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<B> Next:</B> <A NAME=tex2html3436 HREF="node154.html"> Hash Tables</A>
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<B>Up:</B> <A NAME=tex2html3434 HREF="node147.html"> Lists</A>
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<B> Previous:</B> <A NAME=tex2html3430 HREF="node152.html"> Using Lists as </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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