3065 lines
128 KiB
HTML
3065 lines
128 KiB
HTML
<!doctype html public '-//W3C//DTD HTML 4.0//EN'
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'http://www.w3.org/TR/REC-html40/strict.dtd'>
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<!-- Is there a portable way to write an em-dash?
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Can I have bangs, plusses, or slashes in #tags? Spaces?
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Yes: plus, bang, star No: space Yes: slash, question, ampersand
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You can't put sharp in a path, so anything goes, really.
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Nonetheless, some of these confuse Netscape, so I'll avoid them.
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-->
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<!--========================================================================-->
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<html lang=en-US>
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<head>
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<meta name="keywords" content="Scheme, programming language, list processing, SRFI, underage lesbian sluts">
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<link rev=made href="mailto:shivers@ai.mit.edu">
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<title>SRFI 1: List Library</title>
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<!-- Should have a media=all to get, for example, printing to work.
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== But my Netscape will completely ignore the tag if I do that.
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-->
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<style type="text/css">
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/* A little general layout hackery for headers & the title. */
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body { margin-left: +7%;
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font-family: "Helvetica", sans-serif;
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}
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/* Netscape workaround: */
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td, th { font-family: "Helvetica", sans-serif; }
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code, pre { font-family: "courier new", "courier"; }
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h1 { margin-left: -5%; }
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h1, h2 { clear: both; }
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h1, h2, h3, h4, h5, h6 { color: blue }
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div.title-text { font-size: large; font-weight: bold; }
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div.indent { margin-left: 2em; } /* General indentation */
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pre.code-example { margin-left: 2em; } /* Indent code examples. */
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/* This stuff is for definition lists of defined procedures.
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** A proc-def2 is used when you want a stack of procs to go
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** with one <dd> ... </dd> body. In this case, make the first
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** proc a proc-def1, following ones proc-defi's, and the last one
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** a proc-defn.
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**
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** Unfortunately, Netscape has huge bugs with respect to style
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** sheets and dl list rendering. We have to set truly random
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** values here to get the rendering to come out. The proper values
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** are in the following style sheet, for Internet Explorer.
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** In the following settings, the *comments* say what the
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** setting *really* causes Netscape to do.
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**
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** Ugh. Professional coders sacrifice their self-respect,
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** that others may live.
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*/
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/* m-t ignored; m-b sets top margin space. */
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dt.proc-def1 { margin-top: 0ex; margin-bottom: 3ex; }
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dt.proc-defi { margin-top: 0ex; margin-bottom: 0ex; }
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dt.proc-defn { margin-top: 0ex; margin-bottom: 0ex; }
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/* m-t works weird depending on whether or not the last line
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** of the previous entry was a pre. Set to zero.
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*/
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dt.proc-def { margin-top: 0ex; margin-bottom: 3ex; }
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/* m-b sets space between dd & dt; m-t ignored. */
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dd.proc-def { margin-bottom: 0.5ex; margin-top: 0ex; }
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/* Boldface the name of a procedure when it's being defined. */
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code.proc-def { font-weight: bold; font-size: 110%}
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/* For the index of procedures.
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** Same hackery as for dt.proc-def, above.
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*/
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/* m-b sets space between dd & dt; m-t ignored. */
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dd.proc-index { margin-bottom: 0ex; margin-top: 0ex; }
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/* What the fuck? */
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pre.proc-index { margin-top: -2ex; }
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/* Pull the table of contents back flush with the margin.
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** Both NS & IE screw this up in different ways.
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*/
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#toc-table { margin-top: -2ex; margin-left: -5%; }
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/* R5RS proc names are in italic; extended R5RS names
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** in italic boldface.
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*/
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span.r5rs-proc { font-weight: bold; }
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span.r5rs-procx { font-style: italic; font-weight: bold; }
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/* Spread out bibliographic lists. */
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/* More Netscape-specific lossage; see the following stylesheet
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** for the proper values (used by IE).
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*/
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dt.biblio { margin-bottom: 1ex; }
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/* Links to draft copies (e.g., not at the official SRFI site)
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** are colored in red, so people will use them during the
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** development process and kill them when the document's done.
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*/
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a.draft { color: red; }
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</style>
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<style type="text/css"; media=all>
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/* Nastiness: Here, I'm using a bug to work around a bug.
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** Netscape rendering bugs mean you need bogus <dt> and <dd>
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** margin settings -- settings which screw up IE's proper rendering.
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** Fortunately, Netscape has *another* bug: it will ignore this
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** media=all style sheet. So I am placing the (proper) IE values
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** here. Perhaps, one day, when these rendering bugs are fixed,
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** this gross hackery can be removed.
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*/
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dt.proc-def1 { margin-top: 3ex; margin-bottom: 0ex; }
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dt.proc-defi { margin-top: 0ex; margin-bottom: 0ex; }
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dt.proc-defn { margin-top: 0ex; margin-bottom: 0.5ex; }
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dt.proc-def { margin-top: 3ex; margin-bottom: 0.5ex; }
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pre { margin-top: 1ex; }
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dd.proc-def { margin-bottom: 2ex; margin-top: 0.5ex; }
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/* For the index of procedures.
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** Same hackery as for dt.proc-def, above.
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*/
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dd.proc-index { margin-top: 0ex; }
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pre.proc-index { margin-top: 0ex; }
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/* Spread out bibliographic lists. */
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dt.biblio { margin-top: 3ex; margin-bottom: 0ex; }
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dd.biblio { margin-bottom: 1ex; }
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</style>
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</head>
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<body>
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<!--========================================================================-->
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<h1>Title</h1>
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<div class=title-text>
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List Library
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</div>
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<!--========================================================================-->
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<h1>Author</H1>
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<address>
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<a href="http://www.ai.mit.edu/~shivers/">Olin Shivers</A> /
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<a href="mailto:shivers@ai.mit.edu">shivers@ai.mit.edu</A>
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</address>
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<!--========================================================================-->
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<h1>Table of contents</H1>
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<!-- A bug in netscape (?) keeps the first link in this UL from being active.
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==== So the Abstract link be dead. 99/8/22 -Olin
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-->
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<ul id=toc-table>
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<li><a href="#Abstract">Abstract</a>
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<li><a href="#Introduction">Introduction</a>
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<li><a href="#ProcedureIndex">Procedure index</a>
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<li><a href="#GeneralDiscussion">General discussion</a>
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<ul>
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<li><a href="#LinearUpdateProcedures">"Linear update" procedures</a>
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<li><a href="#ImproperLists">Improper lists</a>
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<li><a href="#Errors">Errors</a>
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<li><a href="#NotIncludedInThisLibrary">Not included in this library</a>
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</ul>
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<li><a href="#TheProcedures">The procedures</a>
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<ul>
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<li><a href="#Constructors">Constructors</a>
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<li><a href="#Predicates">Predicates</a>
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<li><a href="#Selectors">Selectors</a>
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<li><a href="#Miscellaneous">Miscellaneous: length, append, reverse, zip & count</a>
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<li><a href="#FoldUnfoldMap">Fold, unfold, and map</a>
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<li><a href="#FilteringPartitioning">Filtering & partitioning</a>
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<li><a href="#Searching">Searching</a>
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<li><a href="#Deletion">Deletion</a>
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<li><a href="#AssociationLists">Association lists</a>
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<li><a href="#SetOperationsOnLists">Set operations on lists</a>
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<li><a href="#PrimitiveSideEffects">Primitive side-effects</a>
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</ul>
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<li><a href="#Acknowledgements">Acknowledgements</a>
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<li><a href="#ReferencesLinks">References & links</a>
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<li><a href="#Copyright">Copyright</a>
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</ul>
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<!--========================================================================-->
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<h1><a name="Abstract">Abstract</a></H1>
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<p>
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<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr> Scheme has an impoverished set of list-processing utilities, which is a
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problem for authors of portable code. This <abbr title="Scheme Request for Implementation">SRFI</abbr> proposes a coherent and
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comprehensive set of list-processing procedures; it is accompanied by a
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reference implementation of the spec. The reference implementation is
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<ul>
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<li>portable
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<li>efficient
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<li>completely open, public-domain source
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</ul>
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<strong><em>Note: This is a working draft, and tends to lag the plain-text version in terms of actual content.
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See <a href="ftp://ftp.ai.mit.edu/people/shivers/srfi/srfi-1/srfi-1.txt">
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ftp://ftp.ai.mit.edu/people/shivers/srfi/srfi-1/srfi-1.txt</a>
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for the latest copy of the plain-text draft.
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</em></strong>
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<!--========================================================================-->
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<h1><a name="Introduction">Introduction</a></h1>
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<p>
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The set of basic list and pair operations provided by R4RS/<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr> Scheme is far
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from satisfactory. Because this set is so small and basic, most
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implementations provide additional utilities, such as a list-filtering
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function, or a "left fold" operator, and so forth. But, of course, this
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introduces incompatibilities -- different Scheme implementations provide
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different sets of procedures.
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<p>
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I have designed a full-featured library of procedures for list processing.
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While putting this library together, I checked as many Schemes as I could get
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my hands on. (I have a fair amount of experience with several of these
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already.) I missed Chez -- no on-line manual that I can find -- but I hit most
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of the other big, full-featured Schemes. The complete list of list-processing
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systems I checked is:
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<div class=indent>
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<abbr title="Revised^4 Report on Scheme">R4RS</abbr>/<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr> Scheme, MIT Scheme, Gambit, RScheme, MzScheme, slib,
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<a href="#CommonLisp">Common Lisp</a>, Bigloo, guile, T, APL and the SML standard basis
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</div>
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<p>
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As a result, the library I am proposing is fairly rich.
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<p>
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Following this initial design phase, this library went through several
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months of discussion on the SRFI mailing lists, and was altered in light
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of the ideas and suggestions put forth during this discussion.
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<p>
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In parallel with designing this API, I have also written a reference
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implementation. I have placed this source on the Net with an unencumbered,
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"open" copyright. A few notes about the reference implementation:
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<ul>
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<li>Although I got procedure names and specs from many Schemes, I wrote this
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code myself. Thus, there are <em>no</em> entanglements.
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Any Scheme implementor
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can pick this library up with no worries about copyright problems -- both
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commercial and non-commercial systems.
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<li>The code is written for portability and should be trivial to port to
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any Scheme. It has only four deviations from <abbr title="Revised^4 Report on Scheme">R4RS</abbr>, clearly discussed
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in the comments: <ul>
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<li>Use of an <code>error</code> procedure;
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<li>Use of the <abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr> <code>values</code> and a simple <code>receive</code> macro for producing
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and consuming multiple return values;
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<li>Use of simple <code>:optional</code> and <code>let-optionals</code> macros for optional
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argument parsing and defaulting;
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<li>Use of a simple <code>check-arg</code> procedure for argument checking.
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</ul>
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<li>It is written for clarity and well-commented. The current source is
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706 lines of source code and 818 lines of comments and white space.
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<li>It is written for efficiency. Fast paths are provided for common
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cases. Side-effecting procedures such as <code>filter!</code> avoid unnecessary,
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redundant <code>set-cdr!</code>s which would thrash a generational GC's write barrier
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and the store buffers of fast processors. Functions reuse longest common
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tails from input parameters to construct their results where
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possible. Constant-space iterations are used in preference to recursions;
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local recursions are used in preference to consing temporary intermediate
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data structures.
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<p>
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This is not to say that the implementation can't be tuned up for
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a specific Scheme implementation. There are notes in comments addressing
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ways implementors can tune the reference implementation for performance.
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</ul>
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<p>
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In short, I've written the reference implementation to make it as painless
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as possible for an implementor -- or a regular programmer -- to adopt this
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library and get good results with it.
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<!--========================================================================-->
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<h1><a name="ProcedureIndex">Procedure Index</a></h1>
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<p>
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Here is a short list of the procedures provided by the list-lib package.
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<a href="#R5RS">R5RS</a></abbr> procedures are shown in
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<span class=r5rs-proc>bold</span class=r5rs-proc>;
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extended <a href="#R5RS">R5RS</a></abbr>
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procedures, in <span class=r5rs-procx>bold italic</span>.
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<div class=indent>
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<dl>
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<dt class=proc-index> Constructors
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<dd class=proc-index>
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<pre class=proc-index>
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<span class=r5rs-proc><a href="#cons">cons</a> <a href="#list">list</a></span>
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<a href="#xcons">xcons</a> <a href="#cons*">cons*</a> <a href="#make-list">make-list</a> <a href="#list-tabulate">list-tabulate</a>
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<a href="#list-copy">list-copy</a> <a href="#circular-list">circular-list</a> <a href="#iota">iota</a>
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</pre>
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<dt class=proc-index> Predicates
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<dd class=proc-index>
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<pre class=proc-index>
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<span class=r5rs-proc><a href="#pair-p">pair?</a> <a href="#null-p">null?</a></span>
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<a href="#proper-list-p">proper-list?</a> <a href="#circular-list-p">circular-list?</a> <a href="#dotted-list-p">dotted-list?</a>
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<a href="#not-pair-p">not-pair?</a> <a href="#null-list-p">null-list?</a>
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<a href="#list=">list=</a>
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</pre>
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<dt class=proc-index> Selectors
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<dd class=proc-index>
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<pre class=proc-index>
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<span class=r5rs-proc><a href="#car">car</a> <a href="#cdr">cdr</a> ... <a href="#cddadr">cddadr</a> <a href="#cddddr">cddddr</a> <a href="#list-ref">list-ref</a></span>
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<a href="#first">first</a> <a href="#second">second</a> <a href="#third">third</a> <a href="#fourth">fourth</a> <a href="#fifth">fifth</a> <a href="#sixth">sixth</a> <a href="#seventh">seventh</a> <a href="#eighth">eighth</a> <a href="#ninth">ninth</a> <a href="#tenth">tenth</a>
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<a href="#car+cdr">car+cdr</a>
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<a href="#take">take</a> <a href="#drop">drop</a>
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<a href="#take-right">take-right</a> <a href="#drop-right">drop-right</a>
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<a href="#take!">take!</a> <a href="#drop-right!">drop-right!</a>
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<a href="#last">last</a> <a href="#last-pair">last-pair</a>
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</pre>
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<dt class=proc-index> Miscellaneous: length, append, reverse, zip & count
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<dd class=proc-index>
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<pre class=proc-index>
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<span class=r5rs-proc><a href="#length">length</a></span> <a href="#length+">length+</a>
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<span class=r5rs-proc><a href="#append">append</a> <a href="#reverse">reverse</a></span>
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<a href="#append!">append!</a> <a href="#reverse!">reverse!</a>
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<a href="#append-reverse">append-reverse</a> <a href="#append-reverse!">append-reverse!</a>
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<a href="#zip">zip</a> <a href="#unzip1">unzip1</a> <a href="#unzip2">unzip2</a> <a href="#unzip3">unzip3</a> <a href="#unzip4">unzip4</a> <a href="#unzip5">unzip5</a>
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<a href="#count">count</a>
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</pre>
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<dt class=proc-index> Fold, unfold & map
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<dd class=proc-index>
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<pre class=proc-index>
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<span class=r5rs-procx><a href="#map">map</a> <a href="#for-each">for-each</a></span>
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<a href="#fold">fold</a> <a href="#unfold">unfold</a> <a href="#pair-fold">pair-fold</a> <a href="#reduce">reduce</a>
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<a href="#fold-right">fold-right</a> <a href="#unfold-right">unfold-right</a> <a href="#pair-fold-right">pair-fold-right</a> <a href="#reduce-right">reduce-right</a>
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<a href="#append-map">append-map</a> <a href="#append-map!">append-map!</a>
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<a href="#map!">map!</a> <a href="#pair-for-each">pair-for-each</a> <a href="#filter-map">filter-map</a> <a href="#map-in-order">map-in-order</a>
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</pre>
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<dt class=proc-index> Filtering & partitioning
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<dd class=proc-index>
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<pre class=proc-index>
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<a href="#filter">filter</a> <a href="#partition">partition</a> <a href="#remove">remove</a>
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<a href="#filter!">filter!</a> <a href="#partition!">partition!</a> <a href="#remove!">remove!</a>
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</pre>
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<dt class=proc-index> Searching
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<dd class=proc-index>
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<pre class=proc-index>
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<span class=r5rs-procx><a href="#member">member</a></span> <span class=r5rs-proc><a href="#memq">memq</a> <a href="#memv">memv</a></span>
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<a href="#find">find</a> <a href="#find-tail">find-tail</a>
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<a href="#any">any</a> <a href="#every">every</a>
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<a href="#list-index">list-index</a>
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</pre>
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<dt class=proc-index> Deleting
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<dd class=proc-index>
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<pre class=proc-index>
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<a href="#delete">delete</a> <a href="#delete-duplicates">delete-duplicates</a>
|
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<a href="#delete!">delete!</a> <a href="#delete-duplicates!">delete-duplicates!</a>
|
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</pre>
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<dt class=proc-index> Association lists
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<dd class=proc-index>
|
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<pre class=proc-index>
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<span class=r5rs-procx><a href="#assoc">assoc</a></span> <span class=r5rs-proc><a href="#assq">assq</a> <a href="#assv">assv</a></span>
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<a href="#alist-cons">alist-cons</a> <a href="#alist-copy">alist-copy</a>
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<a href="#alist-delete">alist-delete</a> <a href="#alist-delete!">alist-delete!</a>
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</pre>
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<dt class=proc-index> Set operations on lists
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<dd class=proc-index>
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<pre class=proc-index>
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<a href="#lset<=">lset<=</a> <a href="#lset=">lset=</a> <a href="#lset-adjoin">lset-adjoin</a>
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<a href="#lset-union">lset-union</a> <a href="#lset-union!">lset-union!</a>
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<a href="#lset-intersection">lset-intersection</a> <a href="#lset-intersection!">lset-intersection!</a>
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<a href="#lset-difference">lset-difference</a> <a href="#lset-difference!">lset-difference!</a>
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<a href="#lset-xor">lset-xor</a> <a href="#lset-xor!">lset-xor!</a>
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<a href="#lset-diff+intersection">lset-diff+intersection</a> <a href="#lset-diff+intersection!">lset-diff+intersection!</a>
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</pre>
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<dt class=proc-index> Primitive side-effects
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<dd class=proc-index>
|
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<pre class=proc-index>
|
|
<span class=r5rs-proc><a href="#set-car!">set-car!</a> <a href="#set-cdr!">set-cdr!</a></span>
|
|
</pre>
|
|
</dl>
|
|
</div>
|
|
|
|
<p>
|
|
Four <abbr title="Revised^4 Report on Scheme">R4RS</abbr>/<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr> list-processing procedures are extended by this library in
|
|
backwards-compatible ways:
|
|
<div class=indent>
|
|
<table cellspacing=0>
|
|
<tr valign=baseline><td><code>map for-each</code>
|
|
<td>(Extended to take lists of unequal length)
|
|
<tr valign=baseline><td><code>member assoc</code>
|
|
<td>(Extended to take an optional comparison procedure.)
|
|
</table>
|
|
</div>
|
|
|
|
<p>
|
|
The following <abbr title="Revised^4 Report on Scheme">R4RS</abbr>/<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr> list- and pair-processing procedures are also part of
|
|
list-lib's exports, as defined by the <abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>:
|
|
<div class=indent>
|
|
<pre>
|
|
cons pair? null?
|
|
car cdr ... cdddar cddddr
|
|
set-car! set-cdr!
|
|
list append reverse
|
|
length list-ref
|
|
memq memv assq assv
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The remaining two <abbr title="Revised^4 Report on Scheme">R4RS</abbr>/<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr> list-processing
|
|
procedures are <em>not</em> part of
|
|
this library:
|
|
<div class=indent>
|
|
<table cellspacing=0>
|
|
<tr><td><code>list-tail</code>
|
|
<td>(renamed <code>drop</code>)
|
|
<tr valign=baseline><td><code>list?</code>
|
|
<td>(see <code>proper-list?</code>,
|
|
<code>circular-list?</code> and
|
|
<code>dotted-list?</code>)
|
|
</table>
|
|
</div>
|
|
|
|
<!--========================================================================-->
|
|
<h1><a name="GeneralDiscussion">General discussion</a></h1>
|
|
<p>
|
|
|
|
A set of general criteria guided the design of this library.
|
|
|
|
<p>
|
|
|
|
I don't require "destructive" (what I call "linear update") procedures to
|
|
alter and recycle cons cells from the argument lists. They are allowed to, but
|
|
not required to. (And the reference implementations I have written <em>do</em>
|
|
recycle the argument lists.)
|
|
|
|
<p>
|
|
List-filtering procedures such as <code>filter</code> or <code>delete</code> do not disorder
|
|
lists. Elements appear in the answer list in the same order as they appear in
|
|
the argument list. This constrains implementation, but seems like a desirable
|
|
feature, since in many uses of lists, order matters. (In particular,
|
|
disordering an alist is definitely a bad idea.)
|
|
<p>
|
|
Contrariwise, although the reference implementations of the list-filtering
|
|
procedures share longest common tails between argument and answer lists,
|
|
it not is part of the spec.
|
|
<p>
|
|
Because lists are an inherently sequential data structure (unlike, say,
|
|
vectors), list-inspection functions such as <code>find</code>, <code>find-tail</code>, <code>for-each</code>, <code>any</code>
|
|
and <code>every</code> commit to a left-to-right traversal order of their argument list.
|
|
<p>
|
|
However, constructor functions, such as <code><code>list-tabulate</code></code> and the mapping
|
|
procedures (<code>append-map</code>, <code>append-map!</code>, <code>map!</code>, <code>pair-for-each</code>, <code>filter-map</code>,
|
|
<code>map-in-order</code>), do <em>not</em> specify the dynamic order in which their procedural
|
|
argument is applied to its various values.
|
|
<p>
|
|
Predicates return useful true values wherever possible. Thus <code>any</code> must return
|
|
the true value produced by its predicate, and <code>every</code> returns the final true
|
|
value produced by applying its predicate argument to the last element of its
|
|
argument list.
|
|
<p>
|
|
Functionality is provided both in pure and linear-update (potentially
|
|
destructive) forms wherever this makes sense.
|
|
<p>
|
|
No special status accorded Scheme's built-in equality functions.
|
|
Any functionality provided in terms of <code>eq?</code>, <code>eqv?</code>, <code>equal?</code> is also
|
|
available using a client-provided equality function.
|
|
<p>
|
|
Proper design counts for more than backwards compatibility, but I have tried,
|
|
<em>ceteris paribus</em>,
|
|
to be as backwards-compatible as possible with existing
|
|
list-processing libraries, in order to facilitate porting old code to run as a
|
|
client of the procedures in this library. Name choices and semantics are, for
|
|
the most part, in agreement with existing practice in many current Scheme
|
|
systems. I have indicated some incompatibilities in the following text.
|
|
<p>
|
|
These procedures are <em>not</em> "sequence generic" -- <em>i.e.</em>, procedures that
|
|
operate on either vectors and lists. They are list-specific. I prefer to
|
|
keep the library simple and focussed.
|
|
<p>
|
|
I have named these procedures without a qualifying initial "list-" lexeme,
|
|
which is in keeping with the existing set of list-processing utilities in
|
|
Scheme.
|
|
I follow the general Scheme convention (vector-length, string-ref) of
|
|
placing the type-name before the action when naming procedures -- so
|
|
we have <code>list-copy</code> and <code>pair-for-each</code> rather than the perhaps
|
|
more fluid, but less consistent, <code>copy-list</code> or <code>for-each-pair</code>.
|
|
<p>
|
|
I have generally followed a regular and consistent naming scheme, composing
|
|
procedure names from a set of basic lexemes.
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="LinearUpdateProcedures">"Linear update" procedures</a></h2>
|
|
<p>
|
|
|
|
Many procedures in this library have "pure" and "linear update" variants. A
|
|
"pure" procedure has no side-effects, and in particular does not alter its
|
|
arguments in any way. A "linear update" procedure is allowed -- but <em>not</em>
|
|
required -- to side-effect its arguments in order to construct its
|
|
result. "Linear update" procedures are typically given names ending with an
|
|
exclamation point. So, for example, <code>(append! list1 list2)</code> is allowed to
|
|
construct its result by simply using <code>set-cdr!</code> to set the cdr of the last pair
|
|
of <var>list<sub>1</sub></var> to point to <var>list<sub>2</sub></var>, and then returning <var>list<sub>1</sub></var> (unless <var>list<sub>1</sub></var> is the
|
|
empty list, in which case it would simply return <var>list<sub>2</sub></var>). However, <code>append!</code> may
|
|
also elect to perform a pure append operation -- this is a legal definition
|
|
of <code>append!</code>:
|
|
<pre class=code-example>
|
|
(define append! append)
|
|
</pre>
|
|
<p>
|
|
This is why we do not call these procedures "destructive" -- because they
|
|
aren't <em>required</em> to be destructive. They are <em>potentially</em> destructive.
|
|
<p>
|
|
What this means is that you may only apply linear-update procedures to
|
|
values that you know are "dead" -- values that will never be used again
|
|
in your program. This must be so, since you can't rely on the value passed
|
|
to a linear-update procedure after that procedure has been called. It
|
|
might be unchanged; it might be altered.
|
|
<p>
|
|
The "linear" in "linear update" doesn't mean "linear time" or "linear space"
|
|
or any sort of multiple-of-n kind of meaning. It's a fancy term that
|
|
type theorists and pure functional programmers use to describe
|
|
systems where you are only allowed to have exactly one reference to each
|
|
variable. This provides a guarantee that the value bound to a variable is
|
|
bound to no other variable. So when you <em>use</em> a variable in a variable
|
|
reference, you "use it up." Knowing that no one else has a pointer to that
|
|
value means the a system primitive is free to side-effect its arguments to
|
|
produce what is, observationally, a pure-functional result.
|
|
<p>
|
|
In the context of this library, "linear update" means you, the programmer,
|
|
know there are <em>no other</em> live references to the value passed to the
|
|
procedure -- after passing the value to one of these procedures, the
|
|
value of the old pointer is indeterminate. Basically, you are licensing
|
|
the Scheme implementation to alter the data structure if it feels like
|
|
it -- you have declared you don't care either way.
|
|
<p>
|
|
You get no help from Scheme in checking that the values you claim are "linear"
|
|
really are. So you better get it right. Or play it safe and use the non-!
|
|
procedures -- it doesn't do any good to compute quickly if you get the wrong
|
|
answer.
|
|
<p>
|
|
Why go to all this trouble to define the notion of "linear update" and use it
|
|
in a procedure spec, instead of the more common notion of a "destructive"
|
|
operation? First, note that destructive list-processing procedures are almost
|
|
always used in a linear-update fashion. This is in part required by the
|
|
special case of operating upon the empty list, which can't be side-effected.
|
|
This means that destructive operators are not pure side-effects -- they have
|
|
to return a result. Second, note that code written using linear-update
|
|
operators can be trivially ported to a pure, functional subset of Scheme by
|
|
simply providing pure implementations of the linear-update operators. Finally,
|
|
requiring destructive side-effects ruins opportunities to parallelise these
|
|
operations -- and the places where one has taken the trouble to spell out
|
|
destructive operations are usually exactly the code one would want a
|
|
parallelising compiler to parallelise: the efficiency-critical kernels of the
|
|
algorithm. Linear-update operations are easily parallelised. Going with a
|
|
linear-update spec doesn't close off these valuable alternative implementation
|
|
techniques. This list library is intended as a set of low-level, basic
|
|
operators, so we don't want to exclude these possible implementations.
|
|
<p>
|
|
The linear-update procedures in this library are
|
|
<div class=indent><code>
|
|
take! drop-right!
|
|
append! reverse! append-reverse!
|
|
append-map! map!
|
|
filter! partition! remove!
|
|
delete! alist-delete! delete-duplicates!
|
|
lset-adjoin! lset-union! lset-intersection!
|
|
lset-difference! lset-xor! lset-diff+intersection!
|
|
</code></div>
|
|
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="ImproperLists">Improper Lists</a></h2>
|
|
<p>
|
|
|
|
Scheme does not properly have a list type, just as C does not have a string
|
|
type. Rather, Scheme has a binary-tuple type, from which one can build binary
|
|
trees. There is an <em>interpretation</em> of Scheme values that allows one to
|
|
treat these trees as lists. Further complications ensue from the fact that
|
|
Scheme allows side-effects to these tuples, raising the possibility of lists
|
|
of unbounded length, and trees of unbounded depth (that is, circular data
|
|
structures).
|
|
|
|
<p>
|
|
However, there is a simple view of the world of Scheme values that considers
|
|
every value to be a list of some sort. that is, every value is either
|
|
<ul>
|
|
<li>a "proper list" -- a finite, nil-terminated list, such as:<br>
|
|
<code>(a b c)</code><br>
|
|
<code>()</code><br>
|
|
<code>(32)</code><br>
|
|
<li>a "dotted list" -- a finite, non-nil terminated list, such as:<br>
|
|
<code>(a b c . d)</code><br>
|
|
<code>(x . y)</code><br>
|
|
<code>42</code><br>
|
|
<code>george</code><br>
|
|
<li>or a "circular list" -- an infinite, unterminated list.
|
|
</ul>
|
|
<p>
|
|
Note that the zero-length dotted lists are simply all the non-null, non-pair
|
|
values.
|
|
|
|
<p>
|
|
This view is captured by the predicates <code>proper-list?</code>, <code>dotted-list?</code>, and
|
|
<code>circular-list?</code>. List-lib users should note that dotted lists are not commonly
|
|
used, and are considered by many Scheme programmers to be an ugly artifact of
|
|
Scheme's lack of a true list type. However, dotted lists do play a noticeable
|
|
role in the <em>syntax</em> of Scheme, in the "rest" parameters used by n-ary
|
|
lambdas: <code>(lambda (x y . rest) ...)</code>.
|
|
|
|
<p>
|
|
Dotted lists are <em>not</em> fully supported by list-lib. Most procedures are
|
|
defined only on proper lists -- that is, finite, nil-terminated lists. The
|
|
procedures that will also handle circular or dotted lists are specifically
|
|
marked. While this design decision restricts the domain of possible arguments
|
|
one can pass to these procedures, it has the benefit of allowing the
|
|
procedures to catch the error cases where programmers inadvertently pass
|
|
scalar values to a list procedure by accident,
|
|
<em>e.g.</em>, by switching the arguments to a procedure call.
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="Errors">Errors</a></h2>
|
|
<p>
|
|
|
|
Note that statements of the form "it is an error" merely mean "don't
|
|
do that." They are not a guarantee that a conforming implementation will
|
|
"catch" such improper use by, for example, raising some kind of exception.
|
|
Regrettably, <abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr> Scheme requires no firmer guarantee even for basic operators such
|
|
as <code>car</code> and <code>cdr</code>, so there's little point in requiring these procedures to do
|
|
more. Here is the relevant section of the <abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>:
|
|
<blockquote>
|
|
<p>
|
|
When speaking of an error situation, this report uses the phrase "an
|
|
error is signalled" to indicate that implementations must detect and
|
|
report the error. If such wording does not appear in the discussion
|
|
of an error, then implementations are not required to detect or
|
|
report the error, though they are encouraged to do so. An error
|
|
situation that implementations are not required to detect is usually
|
|
referred to simply as "an error."
|
|
<p>
|
|
For example, it is an error for a procedure to be passed an argument
|
|
that the procedure is not explicitly specified to handle, even though
|
|
such domain errors are seldom mentioned in this report.
|
|
Implementations may extend a procedure's domain of definition to
|
|
include such arguments.
|
|
</blockquote>
|
|
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="NotIncludedInThisLibrary">Not included in this library</a></h2>
|
|
<p>
|
|
The following items are not in this library:
|
|
<ul>
|
|
<li>Sort routines
|
|
<li>Destructuring/pattern-matching macro
|
|
<li>Tree-processing routines
|
|
</ul>
|
|
<p>
|
|
They should have their own <abbr title="Scheme Request for Implementation">SRFI</abbr> specs.
|
|
<p>
|
|
|
|
|
|
<!--========================================================================-->
|
|
<h1><a name="TheProcedures">The procedures</a></h1>
|
|
<p>
|
|
|
|
In a Scheme system that has a module or package system, these procedures
|
|
should be contained in a module named "list-lib".
|
|
|
|
The templates given below obey the following conventions for procedure formals:
|
|
<table>
|
|
<tr valign=baseline><th align=left> <var>list</var>
|
|
<td> A proper (finite, nil-terminated) list
|
|
<tr valign=baseline><th align=left> <var>clist</var>
|
|
<td> A proper or circular list
|
|
<tr valign=baseline><th align=left> <var>flist</var>
|
|
<td> A finite (proper or dotted) list
|
|
<tr valign=baseline><th align=left> <var>pair</var>
|
|
<td> A pair
|
|
<tr valign=baseline>
|
|
<th align=left> <var>x</var>, <var>y</var>, <var>d</var>, <var>a</var>
|
|
<td> Any value
|
|
<tr valign=baseline><th align=left> <var>object</var>, <var>value</var>
|
|
<td> Any value
|
|
<tr valign=baseline><th align=left> <var>n</var>, <var>i</var>
|
|
<td> A natural number (an integer >= 0)
|
|
<tr valign=baseline><th align=left> <var>proc</var>
|
|
<td> A procedure
|
|
<tr valign=baseline><th align=left> <var>pred</var>
|
|
<td> A procedure whose return value is treated as a boolean
|
|
<tr valign=baseline><th align=left> <var>=</var>
|
|
<td> A boolean procedure taking two arguments
|
|
</table>
|
|
|
|
<p>
|
|
It is an error to pass a circular or dotted list to a procedure not
|
|
defined to accept such an argument.
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="Constructors">Constructors</a></h2>
|
|
<p>
|
|
|
|
<dl>
|
|
|
|
<!--
|
|
==== cons
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="cons"></a>
|
|
<code class=proc-def>cons</code> <var>a d -> pair</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>]
|
|
The primitive constructor. Returns a newly allocated pair whose car is
|
|
<var>a</var> and whose cdr is <var>d</var>.
|
|
The pair is guaranteed to be different (in the sense of <code>eqv?</code>)
|
|
from every existing object.
|
|
<pre class=code-example>
|
|
(cons 'a '()) => (a)
|
|
(cons '(a) '(b c d)) => ((a) b c d)
|
|
(cons "a" '(b c)) => ("a" b c)
|
|
(cons 'a 3) => (a . 3)
|
|
(cons '(a b) 'c) => ((a b) . c)
|
|
</pre>
|
|
|
|
<!--
|
|
==== list
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="list"></a>
|
|
<code class=proc-def>list</code> <var>object ... -> list</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>]
|
|
Returns a newly allocated list of its arguments.
|
|
<pre class=code-example>
|
|
(list 'a (+ 3 4) 'c) => (a 7 c)
|
|
(list) => ()
|
|
</pre>
|
|
|
|
<!--
|
|
==== xcons
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="xcons"></a>
|
|
<code class=proc-def>xcons</code> <var>d a -> pair</var>
|
|
<dd class=proc-def>
|
|
<pre>
|
|
(lambda (d a) (cons a d))
|
|
</pre>
|
|
Of utility only as a value to be conveniently passed to higher-order
|
|
procedures.
|
|
|
|
<pre class=code-example>
|
|
(xcons '(b c) 'a) => (a b c)
|
|
</pre>
|
|
|
|
The name stands for "eXchanged CONS."
|
|
|
|
<!--
|
|
==== cons*
|
|
============================================================================-->
|
|
<a name="cons*"></a>
|
|
<dt class=proc-def><code class=proc-def>cons*</code><var> elt<sub>1</sub> elt<sub>2</sub> ... -> object</var>
|
|
<dd class=proc-def>
|
|
|
|
Like <code>list</code>,
|
|
but the last argument provides the tail of the constructed list,
|
|
returning
|
|
<div class=indent><code>
|
|
(cons <var>elt<sub>1</sub></var> (cons <var>elt<sub>2</sub></var> (cons ... <var>elt<sub>n</sub></var>)))
|
|
</code></div>
|
|
This function is called <code>list*</code> in <a href="#CommonLisp">Common Lisp</a> and about
|
|
half of the Schemes that provide it,
|
|
and <code>cons*</code> in the other half.
|
|
<pre class=code-example>
|
|
(cons* 1 2 3 4) => (1 2 3 . 4)
|
|
(cons* 1) => 1
|
|
</pre>
|
|
|
|
<!--
|
|
==== make-list
|
|
============================================================================-->
|
|
<a name="make-list"></a>
|
|
<dt class=proc-def> <code class=proc-def>make-list</code> <var>n [fill] -> list</var>
|
|
<dd class=proc-def>
|
|
Returns an <var>n</var>-element list,
|
|
whose elements are all the value <var>fill</var>.
|
|
If the <var>fill</var> argument is not given, the elements of the list may
|
|
be arbitrary values.
|
|
<pre class=code-example>
|
|
(make-list 4 'c) => (c c c c)
|
|
</pre>
|
|
|
|
<!--
|
|
==== list-tabulate
|
|
============================================================================-->
|
|
<a name="list-tabulate"></a>
|
|
<dt class=proc-def><code class=proc-def>list-tabulate</code><var> n init-proc -> list</var>
|
|
<dd class=proc-def>
|
|
Returns an <var>n</var>-element list. Element <var>i</var> of the list, where 0 <= <var>i</var> < <var>n</var>,
|
|
is produced by <code>(<var>init-proc</var> <var>i</var>)</code>. No guarantee is made about the dynamic
|
|
order in which <var>init-proc</var> is applied to these indices.
|
|
|
|
<pre class=code-example>
|
|
(list-tabulate 4 values) => (0 1 2 3)
|
|
</pre>
|
|
|
|
<!--
|
|
==== list-copy
|
|
============================================================================-->
|
|
<a name="list-copy"></a>
|
|
<dt class=proc-def><code class=proc-def>list-copy</code><var> flist -> flist</var>
|
|
<dd class=proc-def>
|
|
Copies the spine of the argument.
|
|
|
|
<!--
|
|
==== circular-list
|
|
============================================================================-->
|
|
<a name="circular-list"></a>
|
|
<dt class=proc-def><code class=proc-def>circular-list</code><var> elt<sub>1</sub> elt<sub>2</sub> ... -> list</var>
|
|
<dd class=proc-def>
|
|
Constructs a circular list of the elements.
|
|
<pre class=code-example>
|
|
(circular-list 'z 'q) => (z q z q z q ...)
|
|
</pre>
|
|
|
|
<!--
|
|
==== iota
|
|
============================================================================-->
|
|
<a name="iota"></a>
|
|
<dt class=proc-def><code class=proc-def>iota</code><var> count [start step] -> list</var>
|
|
<dd class=proc-def>
|
|
Returns a list containing the elements
|
|
<pre class=code-example>
|
|
(<var>start</var> <var>start</var>+<var>step</var> ... <var>start</var>+(<var>count</var>-1)*<var>step</var>)
|
|
</pre>
|
|
The <var>start</var> and <var>step</var> parameters default to 0 and 1, respectively.
|
|
This procedure takes its name from the APL primitive.
|
|
|
|
<pre class=code-example>
|
|
(iota 5) => (0 1 2 3 4)
|
|
(iota 5 0 -0.1) => (0 -0.1 -0.2 -0.3 -0.4)
|
|
</pre>
|
|
</dl>
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="Predicates">Predicates</a></h2>
|
|
<p>
|
|
Note: the predicates <code>proper-list?</code>, <code>circular-list?</code>, and <code>dotted-list?</code>
|
|
partition the entire universe of Scheme values.
|
|
|
|
<dl>
|
|
<!--
|
|
==== proper-list?
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<code class=proc-def>proper-list?</code><var> x -> boolean</var>
|
|
<a name="proper-list-p"></a>
|
|
<dd class=proc-def>
|
|
Returns true iff <var>x</var> is a proper list -- a finite, nil-terminated list.
|
|
<p>
|
|
More carefully: The empty list is a proper list. A pair whose cdr is a
|
|
proper list is also a proper list:
|
|
<pre>
|
|
<proper-list> ::= () (Empty proper list)
|
|
| (cons <x> <proper-list>) (Proper-list pair)
|
|
</pre>
|
|
Note that this definition rules out circular lists. This
|
|
function is required to detect this case and return false.
|
|
<p>
|
|
Nil-terminated lists are called "proper" lists by <abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr> and <a href="#CommonLisp">Common Lisp</a>.
|
|
The opposite of proper is improper.
|
|
<p>
|
|
<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr> binds this function to the variable <code>list?</code>.
|
|
<p>
|
|
<pre>
|
|
(not (proper-list? <var>x</var>)) = (or (dotted-list? <var>x</var>) (circular-list? <var>x</var>))
|
|
</pre>
|
|
|
|
<!--
|
|
==== circular-list?
|
|
============================================================================-->
|
|
<a name="circular-list-p"></a>
|
|
<dt class=proc-def><code class=proc-def>circular-list?</code><var> x -> boolean</var>
|
|
<dd class=proc-def>
|
|
True if <var>x</var> is a circular list. A circular list is a value such that
|
|
for every <var>n</var> >= 0, cdr<sup><var>n</var></sup>(<var>x</var>) is a pair.
|
|
<p>
|
|
Terminology: The opposite of circular is finite.
|
|
<pre>
|
|
(not (circular-list? <var>x</var>)) = (or (proper-list? <var>x</var>) (dotted-list? <var>x</var>))
|
|
</pre>
|
|
|
|
<!--
|
|
==== dotted-list?
|
|
============================================================================-->
|
|
<a name="dotted-list-p"></a>
|
|
<dt class=proc-def><code class=proc-def>dotted-list?</code><var> x -> boolean</var>
|
|
<dd class=proc-def>
|
|
True if <var>x</var> is a finite, non-nil-terminated list. That is, there exists
|
|
an <var>n</var> >= 0 such that cdr<sup><var>n</var></sup>(<var>x</var>) is neither a pair nor ().
|
|
This includes
|
|
non-pair, non-() values (<em>e.g.</em> symbols, numbers),
|
|
which are considered to be dotted lists of length 0.
|
|
<pre>
|
|
(not (dotted-list? <var>x</var>)) = (or (proper-list? <var>x</var>) (circular-list? <var>x</var>))
|
|
</pre>
|
|
|
|
<!--
|
|
==== pair?
|
|
============================================================================-->
|
|
<a name="pair-p"></a>
|
|
<dt class=proc-def><code class=proc-def>pair?</code><var> object -> boolean</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>]
|
|
Returns #t if <var>object</var> is a pair; otherwise, #f.
|
|
<pre class=code-example>
|
|
(pair? '(a . b)) => #t
|
|
(pair? '(a b c)) => #t
|
|
(pair? '()) => #f
|
|
(pair? '#(a b)) => #f
|
|
(pair? 7) => #f
|
|
(pair? 'a) => #f
|
|
</pre>
|
|
|
|
<!--
|
|
==== null?
|
|
============================================================================-->
|
|
<a name="null-p"></a>
|
|
<dt class=proc-def><code class=proc-def>null?</code><var> object -> boolean</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>]
|
|
Returns #t if <var>object</var> is the empty list; otherwise, #f.
|
|
|
|
<!--
|
|
==== null-list?
|
|
============================================================================-->
|
|
<a name="null-list-p"></a>
|
|
<dt class=proc-def><code class=proc-def>null-list?</code><var> list -> boolean</var>
|
|
<dd class=proc-def>
|
|
<var>List</var> is a proper or circular list. This procedure returns true if
|
|
the argument is the empty list (), and false otherwise. It is an
|
|
error to pass this procedure a value which is not a proper or
|
|
circular list.
|
|
|
|
This procedure is recommended as the termination condition for
|
|
list-processing procedures that are not defined on dotted lists.
|
|
|
|
<!--
|
|
==== not-pair?
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="not-pair-p"></a>
|
|
<code class=proc-def>not-pair?</code><var> x -> boolean</var>
|
|
<dd class=proc-def>
|
|
<pre>(lambda (x) (not (pair? x)))</pre>
|
|
Provided as a procedure as it can be useful as the termination condition
|
|
for list-processing procedures that wish to handle all finite lists,
|
|
both proper and dotted.
|
|
|
|
<!--
|
|
==== list=
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="list="></a>
|
|
<code class=proc-def>list=</code><var> elt= list<sub>1</sub> ... -> boolean</var>
|
|
<dd class=proc-def>
|
|
Determines list equality, given an element-equality procedure.
|
|
Proper list <var>A</var> equals proper list <var>B</var>
|
|
if they are of the same length,
|
|
and their corresponding elements are equal,
|
|
as determined by <var>elt=</var>.
|
|
If the element-comparison procedure's first argument is
|
|
from <var>list<sub>i</sub></var>,
|
|
then its second argument is from <var>list<sub>i+1</sub></var>,
|
|
<em>i.e.</em> it is always called as
|
|
<code>(<var>elt=</var> <var>a</var> <var>b</var>)</code>
|
|
for <var>a</var> an element of list <var>A</var>,
|
|
and <var>b</var> an element of list <var>B</var>.
|
|
<p>
|
|
In the <var>n</var>-ary case,
|
|
every <var>list<sub>i</sub></var> is compared to
|
|
<var>list<sub>i+1</sub></var>
|
|
(as opposed, for example, to comparing
|
|
<var>list<sub>1</sub></var> to every <var>list<sub>i</sub></var>,
|
|
for <var>i</var>>1).
|
|
If there are no list arguments at all,
|
|
<code>list=</code> simply returns true.
|
|
<p>
|
|
It is an error to apply <code>list=</code> to anything except proper lists.
|
|
While
|
|
implementations may choose to extend it to circular lists, note that it
|
|
cannot reasonably be extended to dotted lists, as it provides no way to
|
|
specify an equality procedure for comparing the list terminators.
|
|
<p>
|
|
Note that the dynamic order in which the <var>elt=</var> procedure is
|
|
applied to pairs of elements is not specified.
|
|
For example, if <code>list=</code> is applied
|
|
to three lists, <var>A</var>, <var>B</var>, and <var>C</var>,
|
|
it may first completely compare <var>A</var> to <var>B</var>,
|
|
then compare <var>B</var> to <var>C</var>,
|
|
or it may compare the first elements of <var>A</var> and <var>B</var>,
|
|
then the first elements of <var>B</var> and <var>C</var>,
|
|
then the second elements of <var>A</var> and <var>B</var>, and so forth.
|
|
<p>
|
|
The equality procedure must be consistent with <code>eq?</code>.
|
|
That is, it must be the case that
|
|
<div class=indent>
|
|
<code>(eq? <var>x</var> <var>y</var>)</code> => <code>(<var>elt=</var> <var>x</var> <var>y</var>)</code>.
|
|
</div>
|
|
Note that this implies that two lists which are <code>eq?</code>
|
|
are always <var>list=</var>, as well; implementations may exploit this
|
|
fact to "short-cut" the element-by-element comparisons.
|
|
<pre class=code-example>
|
|
(list= eq?) => #t ; Trivial cases
|
|
(list= eq? '(a)) => #t
|
|
</pre>
|
|
|
|
</dl>
|
|
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="Selectors">Selectors</a></h2>
|
|
<dl>
|
|
|
|
<!--
|
|
==== car cdr
|
|
============================================================================-->
|
|
<a name="car"></a>
|
|
<a name="cdr"></a>
|
|
<dt class=proc-def1><code class=proc-def>car</code><var> pair -> value</var>
|
|
<dt class=proc-defn><code class=proc-def>cdr</code><var> pair -> value</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>]
|
|
These functions return the contents of the car and cdr field of their
|
|
argument, respectively.
|
|
Note that it is an error to apply them to the empty list.
|
|
<pre class=code-example>
|
|
(car '(a b c)) => a (cdr '(a b c)) => (b c)
|
|
(car '((a) b c d)) => (a) (cdr '((a) b c d)) => (b c d)
|
|
(car '(1 . 2)) => 1 (cdr '(1 . 2)) => 2
|
|
(car '()) => *error* (cdr '()) => *error*
|
|
</pre>
|
|
|
|
|
|
|
|
<!--
|
|
==== caar cadr ... cdddar cddddr
|
|
============================================================================-->
|
|
<a name="caar"></a>
|
|
<a name="cadr"></a>
|
|
<a name="cdddar"></a>
|
|
<a name="cddddr"></a>
|
|
<dt class=proc-def1><code class=proc-def>caar</code><var> pair -> value</var>
|
|
<dt class=proc-defi><code class=proc-def>cadr</code><var> pair -> value</var>
|
|
<dt class=proc-defi><code class=proc-def>:</code>
|
|
<dt class=proc-defi><code class=proc-def>cdddar</code><var> pair -> value</var>
|
|
<dt class=proc-defn><code class=proc-def>cddddr</code><var> pair -> value</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>]
|
|
These procedures are compositions of <code>car</code> and <code>cdr</code>,
|
|
where for example <code>caddr</code> could be defined by
|
|
<pre class=code-example>
|
|
(define caddr (lambda (x) (car (cdr (cdr x))))).
|
|
</pre>
|
|
Arbitrary compositions, up to four deep, are provided. There are
|
|
twenty-eight of these procedures in all.
|
|
|
|
<!--
|
|
==== list-ref
|
|
============================================================================-->
|
|
<a name="list-ref"></a>
|
|
<dt class=proc-def><code class=proc-def>list-ref</code><var> clist i -> value</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>]
|
|
Returns the <var>i</var><sup>th</sup> element of <var>clist</var>.
|
|
(This is the same as the car of
|
|
<code>(drop <var>clist</var> <var>i</var>)</code>.)
|
|
It is an error if <var>i</var> >= <var>n</var>,
|
|
where <var>n</var> is the length of <var>clist</var>.
|
|
<pre class=code-example>
|
|
(list-ref '(a b c d) 2) => c
|
|
</pre>
|
|
|
|
<!--
|
|
==== tenth
|
|
==== ninth
|
|
==== eighth
|
|
==== seventh
|
|
==== sixth
|
|
==== fifth
|
|
==== fourth
|
|
==== third
|
|
==== second
|
|
==== first
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="first"></a>
|
|
<code class=proc-def>first </code><var>pair -> object </var>
|
|
<dt class=proc-defi>
|
|
<a name="second"></a>
|
|
<code class=proc-def>second </code><var>pair -> object </var>
|
|
<dt class=proc-defi>
|
|
<a name="third"></a>
|
|
<code class=proc-def>third </code><var>pair -> object </var>
|
|
<dt class=proc-defi>
|
|
<a name="fourth"></a>
|
|
<code class=proc-def>fourth </code><var>pair -> object </var>
|
|
<dt class=proc-defi>
|
|
<a name="fifth"></a>
|
|
<code class=proc-def>fifth </code><var>pair -> object </var>
|
|
<dt class=proc-defi>
|
|
<a name="sixth"></a>
|
|
<code class=proc-def>sixth </code><var>pair -> object </var>
|
|
<dt class=proc-defi>
|
|
<a name="seventh"></a>
|
|
<code class=proc-def>seventh </code><var>pair -> object </var>
|
|
<dt class=proc-defi>
|
|
<a name="eighth"></a>
|
|
<code class=proc-def>eighth </code><var>pair -> object </var>
|
|
<dt class=proc-defi>
|
|
<a name="ninth"></a>
|
|
<code class=proc-def>ninth </code><var>pair -> object </var>
|
|
<dt class=proc-defn>
|
|
<a name="tenth"></a>
|
|
<code class=proc-def>tenth </code><var>pair -> object </var>
|
|
<dd class=proc-def>
|
|
Synonyms for <code>car</code>, <code>cadr</code>, <code>caddr</code>, ...
|
|
|
|
<pre class=code-example>
|
|
(third '(a b c d e)) => c
|
|
</pre>
|
|
|
|
<!--
|
|
==== car+cdr
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="car+cdr"></a>
|
|
<code class=proc-def>car+cdr</code><var> pair -> [x y]</var>
|
|
<dd class=proc-def>
|
|
The fundamental pair deconstructor:
|
|
<pre class=code-example>
|
|
(lambda (p) (values (car p) (cdr p)))
|
|
</pre>
|
|
This can, of course, be implemented more efficiently by a compiler.
|
|
|
|
<!--
|
|
==== drop
|
|
==== take
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="take"></a>
|
|
<code class=proc-def>take</code><var> x i -> list</var>
|
|
<dt class=proc-defn>
|
|
<a name="drop"></a>
|
|
<code class=proc-def>drop</code><var> x i -> object</var>
|
|
<dd class=proc-def>
|
|
<code>take</code> returns the first <var>i</var> elements of list <var>x</var>.<br>
|
|
<code>drop</code> returns all but the first <var>i</var> elements of list <var>x</var>.
|
|
<pre class=code-example>
|
|
(take '(a b c d e) 2) => (a b)
|
|
(drop '(a b c d e) 2) => (c d e)
|
|
</pre>
|
|
<var>x</var> may be any value -- a proper, circular, or dotted list:
|
|
<pre class=code-example>
|
|
(take '(1 2 3 . d) 2) => (1 2)
|
|
(drop '(1 2 3 . d) 2) => (3 . d)
|
|
(take '(1 2 3 . d) 3) => (1 2 3)
|
|
(drop '(1 2 3 . d) 3) => d
|
|
</pre>
|
|
For a legal <var>i</var>, <code>take</code> and <code>drop</code> partition the list in a manner which
|
|
can be inverted with <code>append</code>:
|
|
<pre class=code-example>
|
|
(append (take <var>x</var> <var>i</var>) (drop <var>x</var> <var>i</var>)) = <var>x</var>
|
|
</pre>
|
|
<code>drop</code> is exactly equivalent to performing <var>i</var> cdr operations on <var>x</var>;
|
|
the returned value shares a common tail with <var>x</var>.
|
|
|
|
If the argument is a list of non-zero length, <code>take</code> is guaranteed to
|
|
return a freshly-allocated list, even in the case where the entire
|
|
list is taken, <em>e.g.</em> <code>(take lis (length lis))</code>.
|
|
|
|
<!--
|
|
==== drop-right
|
|
==== take-right
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="take-right"></a>
|
|
<code class=proc-def>take-right</code><var> flist i -> object</var>
|
|
<dt class=proc-defn>
|
|
<a name="drop-right"></a>
|
|
<code class=proc-def>drop-right</code><var> flist i -> list</var>
|
|
<dd class=proc-def>
|
|
<code>take-right</code> returns the last <var>i</var> elements of <var>flist</var>.<br>
|
|
<code>drop-right</code> returns all but the last <var>i</var> elements of <var>flist</var>.
|
|
<pre class=code-example>
|
|
(take-right '(a b c d e) 2) => (d e)
|
|
(drop-right '(a b c d e) 2) => (a b c)
|
|
</pre>
|
|
The returned list may share a common tail with the argument list.
|
|
<p>
|
|
<var>flist</var> may be any finite list, either proper or dotted:
|
|
<pre class=code-example>
|
|
(take-right '(1 2 3 . d) 2) => (2 3 . d)
|
|
(drop-right '(1 2 3 . d) 2) => (1)
|
|
(take-right '(1 2 3 . d) 0) => d
|
|
(drop-right '(1 2 3 . d) 0) => (1 2 3)
|
|
</pre>
|
|
For a legal <var>i</var>, <code>take-right</code> and <code>drop-right</code> partition the list in a manner
|
|
which can be inverted with <code>append</code>:
|
|
<pre class=code-example>
|
|
(append (take <var>flist</var> <var>i</var>) (drop <var>flist</var> <var>i</var>)) = <var>flist</var>
|
|
</pre>
|
|
<code>take-right</code>'s return value is guaranteed to share a common tail with <var>flist</var>.
|
|
|
|
If the argument is a list of non-zero length, <code>drop-right</code> is guaranteed to
|
|
return a freshly-allocated list, even in the case where nothing is
|
|
dropped, <em>e.g.</em> <code>(drop-right lis 0)</code>.
|
|
|
|
<!--
|
|
==== drop-right!
|
|
==== take!
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="take!"></a>
|
|
<code class=proc-def>take!</code><var> x i -> list</var>
|
|
<dt class=proc-defn>
|
|
<a name="drop-right!"></a>
|
|
<code class=proc-def>drop-right!</code><var> flist i -> list</var>
|
|
<dd class=proc-def>
|
|
<code>take!</code> and <code>drop-right!</code> are "linear-update" variants of <code>take</code> and
|
|
<code>drop-right</code>: the procedure is allowed, but not required, to alter the
|
|
argument list to produce the result.
|
|
<p>
|
|
If <var>x</var> is circular, <code>take!</code> may return a shorter-than-expected list:
|
|
<pre class=code-example>
|
|
(take! (circular-list 1 3 5) 8) => (1 3)
|
|
(take! (circular-list 1 3 5) 8) => (1 3 5 1 3 5 1 3)
|
|
</pre>
|
|
|
|
|
|
<!--
|
|
==== last-pair
|
|
==== last
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="last"></a>
|
|
<code class=proc-def>last</code><var> pair -> object</var>
|
|
<dt class=proc-defn>
|
|
<a name="last-pair"></a>
|
|
<code class=proc-def>last-pair</code><var> pair -> pair</var>
|
|
<dd class=proc-def>
|
|
<code>last</code> returns the last element of the non-empty,
|
|
finite list <var>pair</var>.
|
|
<code>last-pair</code> returns the last pair in the non-empty,
|
|
finite list <var>pair</var>.
|
|
|
|
<pre class=code-example>
|
|
(last '(a b c)) => c
|
|
(last-pair '(a b c)) => (c)
|
|
</pre>
|
|
|
|
</dl>
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="Miscellaneous">Miscellaneous: length, append, reverse, zip & count</a></h2>
|
|
|
|
<dl>
|
|
<!--
|
|
==== length+
|
|
==== length
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="length"></a>
|
|
<code class=proc-def>length </code><var>list -> integer</var>
|
|
<dt class=proc-defn>
|
|
<a name="length+"></a>
|
|
<code class=proc-def>length+ </code><var>clist -> integer or #f</var>
|
|
<dd class=proc-def>
|
|
Both <code>length</code> and <code>length+</code> return the length of the argument.
|
|
It is an error to pass a value to <code>length</code> which is not a proper
|
|
list (finite and nil-terminated). In particular, this means an
|
|
implementation may diverge or signal an error when <code>length</code> is
|
|
applied to a circular list.
|
|
<p>
|
|
<code>length+</code>, on the other hand, returns <code>#F</code> when applied to a circular
|
|
list.
|
|
<p>
|
|
The length of a proper list is a non-negative integer <var>n</var> such that <code>cdr</code>
|
|
applied <var>n</var> times to the list produces the empty list.
|
|
|
|
|
|
<!--
|
|
==== append append!
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="append"></a>
|
|
<code class=proc-def>append </code><var> list<sub>1</sub> ... -> list</var>
|
|
<dt class=proc-defn>
|
|
<a name="append!"></a>
|
|
<code class=proc-def>append!</code><var> list<sub>1</sub> ... -> list</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>]
|
|
<code>append</code> returns a list consisting of the elements
|
|
of <var>list<sub>1</sub></var>
|
|
followed by the elements of the other list parameters.
|
|
<pre class=code-example>
|
|
(append '(x) '(y)) => (x y)
|
|
(append '(a) '(b c d)) => (a b c d)
|
|
(append '(a (b)) '((c))) => (a (b) (c))
|
|
</pre>
|
|
The resulting list is always newly allocated, except that it
|
|
shares structure with the final <var>list<sub>i</sub></var> argument.
|
|
This last argument may be any value at all;
|
|
an improper list results if it is not
|
|
a proper list. All other arguments must be proper lists.
|
|
<pre class=code-example>
|
|
(append '(a b) '(c . d)) => (a b c . d)
|
|
(append '() 'a) => a
|
|
(append '(x y)) => (x y)
|
|
(append) => ()
|
|
</pre>
|
|
|
|
<code>append!</code> is the "linear-update" variant of <code>append</code>
|
|
-- it is allowed, but not required, to alter cons cells in the argument
|
|
lists to construct the result list.
|
|
The last argument is never altered; the result
|
|
list shares structure with this parameter.
|
|
|
|
<!--
|
|
==== reverse reverse!
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="reverse"></a>
|
|
<code class=proc-def>reverse </code><var> list -> list</var>
|
|
<dt class=proc-defn>
|
|
<a name="reverse!"></a>
|
|
<code class=proc-def>reverse!</code><var> list -> list</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>]
|
|
|
|
<code>reverse</code> returns a newly allocated list consisting of
|
|
the elements of <var>list</var> in reverse order.
|
|
<pre class=code-example>
|
|
(reverse '(a b c)) => (c b a)
|
|
(reverse '(a (b c) d (e (f))))
|
|
=> ((e (f)) d (b c) a)
|
|
</pre>
|
|
<code>reverse!</code> is the linear-update variant of <code>reverse</code>.
|
|
It is permitted, but not required, to alter the argument's cons cells
|
|
to produce the reversed list.
|
|
|
|
|
|
<!--
|
|
==== append-reverse!
|
|
==== append-reverse
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="append-reverse"></a>
|
|
<code class=proc-def>append-reverse </code><var>rev-head tail -> list</var>
|
|
<dt class=proc-defn>
|
|
<a name="append-reverse!"></a>
|
|
<code class=proc-def>append-reverse! </code><var>rev-head tail -> list</var>
|
|
<dd class=proc-def>
|
|
<code>append-reverse</code> returns
|
|
<code>(append (reverse <var>rev-head</var>) <var>tail</var>)</code>.
|
|
It is provided because it is a common operation -- a common
|
|
list-processing style calls for this exact operation to transfer values
|
|
accumulated in reverse order onto the front of another list, and because
|
|
the implementation is significantly more efficient than the simple
|
|
composition it replaces. (But note that this pattern of iterative
|
|
computation followed by a reverse can frequently be rewritten as a
|
|
recursion, dispensing with the <code>reverse</code> and <code>append-reverse</code> steps, and
|
|
shifting temporary, intermediate storage from the heap to the stack,
|
|
which is typically a win for reasons of cache locality and eager storage
|
|
reclamation.)
|
|
<p>
|
|
<code>append-reverse!</code> is just the linear-update variant -- it is allowed, but
|
|
not required, to alter <var>rev-head</var>'s cons cells to construct the result.
|
|
|
|
<!--
|
|
==== zip
|
|
============================================================================-->
|
|
<a name="zip"></a>
|
|
<dt class=proc-def><code class=proc-def>zip</code> <var>clist<sub>1</sub> clist<sub>2</sub> ... -> list</var>
|
|
<dd class=proc-def>
|
|
<pre>(lambda lists (apply map list lists))
|
|
</pre>
|
|
If <code>zip</code> is passed <var>n</var> lists, it returns a list as long as the shortest
|
|
of these lists, each element of which is an <var>n</var>-element list comprised
|
|
of the corresponding elements from the parameter lists.
|
|
|
|
<pre class=code-example>
|
|
(zip '(one two three)
|
|
'(1 2 3)
|
|
'(odd even odd even odd even odd even))
|
|
=> ((one 1 odd) (two 2 even) (three 3 odd))
|
|
|
|
(zip '(1 2 3)) => ((1) (2) (3))
|
|
</pre>
|
|
At least one of the argument lists must be finite:
|
|
<pre class=code-example>
|
|
(zip '(3 1 4 1) (circular-list #f #t))
|
|
=> ((3 #f) (1 #t) (4 #f) (1 #t))
|
|
</pre>
|
|
|
|
<!--
|
|
==== unzip5
|
|
==== unzip4
|
|
==== unzip3
|
|
==== unzip2
|
|
==== unzip1
|
|
============================================================================-->
|
|
<a name="unzip1"></a>
|
|
<dt class=proc-def1> <code class=proc-def>unzip1</code><var> list -> list</var>
|
|
<a name="unzip2"></a>
|
|
<dt class=proc-defi> <code class=proc-def>unzip2</code><var> list -> [list list]</var>
|
|
<a name="unzip3"></a>
|
|
<dt class=proc-defi> <code class=proc-def>unzip3</code><var> list -> [list list list]</var>
|
|
<a name="unzip4"></a>
|
|
<dt class=proc-defi> <code class=proc-def>unzip4</code><var> list -> [list list list list]</var>
|
|
<a name="unzip5"></a>
|
|
<dt class=proc-defn> <code class=proc-def>unzip5</code><var> list -> [list list list list list]</var>
|
|
<dd class=proc-def>
|
|
<code>unzip1</code> takes a list of lists,
|
|
where every list must contain at least one element,
|
|
and returns a list containing the initial element of each such list.
|
|
That is, it returns <code>(map car lists)</code>.
|
|
<code>unzip2</code> takes a list of lists, where every list must contain at least
|
|
two elements, and returns two values: a list of the first elements,
|
|
and a list of the second elements. <code>unzip3</code> does the same for the first
|
|
three elements of the lists, and so forth.
|
|
|
|
<pre class=code-example>
|
|
(unzip2 '((1 one) (2 two) (3 three))) =>
|
|
(1 2 3)
|
|
(one two three)
|
|
</pre>
|
|
|
|
<!--
|
|
==== count
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="count"></a>
|
|
<code class=proc-def>count</code><var> pred clist<sub>1</sub> clist<sub>2</sub> -> integer</var>
|
|
<dd class=proc-def>
|
|
<var>pred</var> is a procedure taking as many arguments as there
|
|
are lists and returning a single value. It is applied
|
|
element-wise to the elements of the <var>list</var>s, and a count is
|
|
tallied of the number of elements that produce a true value. This count
|
|
is returned. <code>count</code> is "iterative" in that it is guaranteed
|
|
to apply <var>pred</var> to the <var>list</var> elements in a
|
|
left-to-right order.
|
|
The counting stops when the shortest list expires.
|
|
<pre class=code-example>
|
|
(count even? '(3 1 4 1 5 9 2 5 6)) => 3
|
|
(count < '(1 2 4 8) '(2 4 6 8 10 12 14 16)) => 3
|
|
</pre>
|
|
At least one of the argument lists must be finite:
|
|
<pre class=code-example>
|
|
(count < '(3 1 4 1) (circular-list 1 10)) => 2
|
|
</pre>
|
|
|
|
</dl>
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="FoldUnfoldMap">Fold, unfold & map</a></h2>
|
|
<dl>
|
|
<!--
|
|
==== fold
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="fold"></a>
|
|
<code class=proc-def>fold</code><var> kons knil clist<sub>1</sub> clist<sub>2</sub> ... -> value</var>
|
|
<dd class=proc-def>
|
|
The fundamental list iterator.
|
|
<p>
|
|
First, consider the single list-parameter case. If <var>clist<sub>1</sub></var> = (<var>e<sub>1</sub></var> <var>e<sub>2</sub></var> ... <var>e<sub>n</sub></var>),
|
|
then this procedure returns
|
|
<div class=indent>
|
|
<code>(<var>kons</var> <var>e<sub>n</sub></var> ... (<var>kons</var> <var>e<sub>2</sub></var> (<var>kons</var> <var>e<sub>1</sub></var> <var>knil</var>)) ... )</code>
|
|
</div>
|
|
That is, it obeys the (tail) recursion
|
|
<pre class=code-example>
|
|
(fold <var>kons</var> <var>knil</var> <var>lis</var>) = (fold <var>kons</var> (<var>kons</var> (car <var>lis</var>) <var>knil</var>) (cdr <var>lis</var>))
|
|
(fold <var>kons</var> <var>knil</var> '()) = <var>knil</var>
|
|
</pre>
|
|
|
|
Examples:
|
|
<pre class=code-example>
|
|
(fold + 0 lis) ; Add up the elements of LIS.
|
|
|
|
(fold cons '() lis) ; Reverse LIS.
|
|
|
|
(fold cons tail rev-head) ; See APPEND-REVERSE.
|
|
|
|
;; How many symbols in LIS?
|
|
(fold (lambda (x count) (if (symbol? x) (+ count 1) count))
|
|
0
|
|
lis)
|
|
|
|
;; Length of the longest string in LIS:
|
|
(fold (lambda (s max-len) (max max-len (string-length s)))
|
|
0
|
|
lis)
|
|
</pre>
|
|
|
|
If <var>n</var> list arguments are provided, then the <var>kons</var> function must take
|
|
<var>n</var>+1 parameters: one element from each list, and the "seed" or fold
|
|
state, which is initially <var>knil</var>. The fold operation terminates when
|
|
the shortest list runs out of values:
|
|
<pre class=code-example>
|
|
(fold cons* '() '(a b c) '(1 2 3 4 5)) => (c 3 b 2 a 1)
|
|
</pre>
|
|
At least one of the list arguments must be finite.
|
|
|
|
<!--
|
|
==== fold-right
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="fold-right"></a>
|
|
<code class=proc-def>fold-right</code><var> kons knil clist<sub>1</sub> clist<sub>2</sub> ... -> value</var>
|
|
<dd class=proc-def>
|
|
The fundamental list recursion operator.
|
|
<p>
|
|
First, consider the single list-parameter case. If <var>clist<sub>1</sub></var> = <code>(<var>e<sub>1</sub></var> <var>e<sub>2</sub></var> ... <var>e<sub>n</sub></var>)</code>,
|
|
then this procedure returns
|
|
<div class=indent><code>
|
|
(<var>kons</var> <var>e<sub>1</sub></var> (<var>kons</var> <var>e<sub>2</sub></var> ... (<var>kons</var> <var>e<sub>n</sub></var> <var>knil</var>)))
|
|
</code></div>
|
|
That is, it obeys the recursion
|
|
<pre class=code-example>
|
|
(fold-right <var>kons</var> <var>knil</var> <var>lis</var>) = (<var>kons</var> (car <var>lis</var>) (fold-right <var>kons</var> <var>knil</var> (cdr <var>lis</var>)))
|
|
(fold-right <var>kons</var> <var>knil</var> '()) = <var>knil</var>
|
|
</pre>
|
|
|
|
Examples:
|
|
<pre class=code-example>
|
|
(fold-right cons '() lis) ; Copy LIS.
|
|
|
|
;; Filter the even numbers out of LIS.
|
|
(fold-right (lambda (x l) (if (even? x) (cons x l) l)) '() lis))
|
|
</pre>
|
|
|
|
If <var>n</var> list arguments are provided, then the <var>kons</var> function must take
|
|
<var>n</var>+1 parameters: one element from each list, and the "seed" or fold
|
|
state, which is initially <var>knil</var>. The fold operation terminates when
|
|
the shortest list runs out of values:
|
|
<pre class=code-example>
|
|
(fold-right cons* '() '(a b c) '(1 2 3 4 5)) => (a 1 b 2 c 3)
|
|
</pre>
|
|
At least one of the list arguments must be finite.
|
|
|
|
<!--
|
|
==== pair-fold
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="pair-fold"></a>
|
|
<code class=proc-def>pair-fold</code><var> kons knil clist<sub>1</sub> clist<sub>2</sub> ... -> value</var>
|
|
<dd class=proc-def>
|
|
Analogous to <code>fold</code>, but <var>kons</var> is applied to successive sublists of the
|
|
lists, rather than successive elements -- that is, <var>kons</var> is applied to the
|
|
pairs making up the lists, giving this (tail) recursion:
|
|
<pre class=code-example>
|
|
(pair-fold <var>kons</var> <var>knil</var> <var>lis</var>) = (let ((tail (cdr <var>lis</var>)))
|
|
(pair-fold <var>kons</var> (<var>kons</var> <var>lis</var> <var>knil</var>) tail))
|
|
(pair-fold <var>kons</var> <var>knil</var> <code>'()</code>) = <var>knil</var>
|
|
</pre>
|
|
For finite lists, the <var>kons</var> function may reliably apply
|
|
<code>set-cdr!</code> to the pairs it is given
|
|
without altering the sequence of execution.
|
|
<p>
|
|
Example:
|
|
<pre class=code-example>
|
|
;;; Destructively reverse a list.
|
|
(pair-fold (lambda (pair tail) (set-cdr! pair tail) pair) '() lis))
|
|
</pre>
|
|
|
|
At least one of the list arguments must be finite.
|
|
|
|
|
|
<!--
|
|
==== pair-fold-right
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="pair-fold-right"></a>
|
|
<code class=proc-def>pair-fold-right</code><var> kons knil clist<sub>1</sub> clist<sub>2</sub> ... -> value</var>
|
|
<dd class=proc-def>
|
|
Holds the same relationship with <code>fold-right</code> that <code>pair-fold</code> holds with <code>fold</code>.
|
|
Obeys the recursion
|
|
<pre class=code-example>
|
|
(pair-fold-right <var>kons</var> <var>knil</var> <var>lis</var>) =
|
|
(<var>kons</var> <var>lis</var> (pair-fold-right <var>kons</var> <var>knil</var> (cdr <var>lis</var>)))
|
|
(pair-fold-right <var>kons</var> <var>knil</var> <code>'()</code>) = <var>knil</var>
|
|
</pre>
|
|
|
|
Example:
|
|
<pre class=code-example>
|
|
(pair-fold-right cons '() '(a b c)) => ((a b c) (b c) (c))
|
|
</pre>
|
|
|
|
At least one of the list arguments must be finite.
|
|
|
|
<!--
|
|
==== reduce
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="reduce"></a>
|
|
<code class=proc-def>reduce</code><var> f ridentity list -> value</var>
|
|
<dd class=proc-def>
|
|
<code>reduce</code> is a variant of <code>fold</code>.
|
|
<p>
|
|
<var>ridentity</var> should be a "right identity" of the procedure <var>f</var> -- that is,
|
|
for any value <var>x</var> acceptable to <var>f</var>,
|
|
<pre class=code-example>
|
|
(<var>f</var> <var>x</var> <var>ridentity</var>) = <var>x</var>
|
|
</pre>
|
|
|
|
<code>reduce</code> has the following definition:
|
|
<div class=indent>
|
|
If <var>list</var> = (), return <var>ridentity</var>;<br>
|
|
Otherwise, return <code>(fold <var>f</var> (car <var>list</var>) (cdr <var>list</var>))</code>.
|
|
</div>
|
|
...in other words, we compute
|
|
<code>(fold <var>f</var> <var>ridentity</var> <var>list</var>)</code>.
|
|
<p>
|
|
Note that <var>ridentity</var> is used <em>only</em> in the empty-list case.
|
|
You typically use <code>reduce</code> when applying <var>f</var> is expensive and you'd
|
|
like to avoid the extra application incurred when <code>fold</code> applies
|
|
<var>f</var> to the head of <var>list</var> and the identity value,
|
|
redundantly producing the same value passed in to <var>f</var>.
|
|
For example, if <var>f</var> involves searching a file directory or
|
|
performing a database query, this can be significant.
|
|
In general, however, <code>fold</code> is useful in many contexts where <code>reduce</code> is not
|
|
(consider the examples given in the <code>fold</code> definition -- only one of the
|
|
five folds uses a function with a right identity.
|
|
The other four may not be performed with <code>reduce</code>).
|
|
|
|
<p>
|
|
Note: MIT Scheme and Haskell flip F's arg order for their <code>reduce</code> and
|
|
<code>fold</code> functions.
|
|
|
|
<!--
|
|
==== reduce-right
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="reduce-right"></a>
|
|
<code class=proc-def>reduce-right</code><var> f ridentity list -> value</var>
|
|
<dd class=proc-def>
|
|
<code>reduce-right</code> is the fold-right variant of <code>reduce</code>.
|
|
It obeys the following definition:
|
|
<pre class=code-example>
|
|
(reduce-right <var>f</var> <var>ridentity</var> '()) = <var>ridentity</var>
|
|
(reduce-right <var>f</var> <var>ridentity</var> '(<var>e<sub>1</sub></var>)) = (<var>f</var> <var>e<sub>1</sub></var> <var>ridentity</var>) = <var>e<sub>1</sub></var>
|
|
(reduce-right <var>f</var> <var>ridentity</var> '(<var>e<sub>1</sub></var> <var>e<sub>2</sub></var> ...)) =
|
|
(<var>f</var> <var>e<sub>1</sub></var> (reduce <var>f</var> <var>ridentity</var> (<var>e<sub>2</sub></var> ...)))
|
|
</pre>
|
|
...in other words, we compute
|
|
<code>(fold-right <var>f</var> <var>ridentity</var> <var>list</var>)</code>.
|
|
|
|
<!--
|
|
==== unfold
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="unfold"></a>
|
|
<code class=proc-def>unfold</code><var> p f g seed [tail] -> list</var>
|
|
<dd class=proc-def>
|
|
<code>unfold</code> constructs a list with the following loop:
|
|
<pre class=code-example>
|
|
(let lp ((seed seed) (lis tail))
|
|
(if (p seed) lis
|
|
(lp (g seed)
|
|
(cons (f seed) lis))))
|
|
</pre>
|
|
<dl>
|
|
<dt> <var>p</var> <dd> Determines when to stop unfolding.
|
|
<dt> <var>f</var> <dd> Maps each seed value to the corresponding list element.
|
|
<dt> <var>g</var> <dd> Maps each seed value to next seed value.
|
|
<dt> <var>seed</var> <dd> The "state" value for the unfold.
|
|
<dt> <var>tail</var> <dd> list terminator; defaults to <code>'()</code>.
|
|
</dl>
|
|
<p>
|
|
<code>unfold</code> is the fundamental iterative list constructor,
|
|
just as <code>fold</code> is the
|
|
fundamental iterative list consumer.
|
|
While <code>unfold</code> may seem a bit abstract
|
|
to novice functional programmers, it can be used in a number of ways:
|
|
<pre class=code-example>
|
|
;; List of squares: 1^2 ... 10^2
|
|
(unfold zero?
|
|
(lambda (x) (* x x))
|
|
(lambda (x) (- x 1))
|
|
10)
|
|
|
|
;; Reverse a proper list.
|
|
(unfold null-list? car cdr lis)
|
|
|
|
;; Read current input port into a list of values.
|
|
(unfold eof-object? values (lambda (x) (read)) (read))
|
|
|
|
;; (append-reverse rev-head tail)
|
|
(unfold null-list? car cdr rev-head tail)
|
|
</pre>
|
|
|
|
Interested functional programmers may enjoy noting that
|
|
<code>fold</code> and <code>unfold</code>
|
|
are in some sense inverses.
|
|
That is, given operations <var>knull?</var>, <var>kar</var>,
|
|
<var>kdr</var>, <var>kons</var>, and <var>knil</var> satisfying
|
|
<div class=indent>
|
|
<code>(<var>kons</var> (<var>kar</var> <var>x</var>) (<var>kdr</var> <var>x</var>))</code> = <code>x</code>
|
|
and
|
|
<code>(<var>knull?</var> <var>knil</var>)</code> = <code>#t</code>
|
|
</div>
|
|
then
|
|
<div class=indent>
|
|
<code>(fold <var>kons</var> <var>knil</var> (unfold <var>knull?</var> <var>kar</var> <var>kdr</var> <var>x</var>))</code> = <var>x</var>
|
|
</div>
|
|
and
|
|
<div class=indent>
|
|
<code>(unfold <var>knull?</var> <var>kar</var> <var>kdr</var> (fold <var>kons</var> <var>knil</var> <var>x</var>))</code> = <var>x</var>.
|
|
</div>
|
|
|
|
This combinator presumably has some pretentious mathematical name;
|
|
interested readers are invited to communicate it to the author.
|
|
|
|
|
|
<!--
|
|
==== unfold-right
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="unfold-right"></a>
|
|
<code class=proc-def>unfold-right</code><var> p f g seed [tail-gen] -> list</var>
|
|
<dd class=proc-def>
|
|
<code>unfold</code> is best described by its basic recursion:
|
|
<pre class=code-example>
|
|
(unfold-right <var>p</var> <var>f</var> <var>g</var> <var>seed</var>) =
|
|
(if (<var>p</var> <var>seed</var>) (<var>tail-gen</var> <var>seed</var>)
|
|
(cons (<var>f</var> <var>seed</var>)
|
|
(unfold-right <var>p</var> <var>f</var> <var>g</var> (<var>g</var> <var>seed</var>))))
|
|
</pre>
|
|
<dl>
|
|
<dt> <var>p</var> <dd> Determines when to stop unfolding.
|
|
<dt> <var>f</var> <dd> Maps each seed value to the corresponding list element.
|
|
<dt> <var>g</var> <dd> Maps each seed value to next seed value.
|
|
<dt> <var>seed</var> <dd> The "state" value for the unfold.
|
|
<dt> <var>tail-gen</var> <dd> Creates the tail of the list;
|
|
defaults to <code>(lambda (x) '())</code>
|
|
</dl>
|
|
<p>
|
|
<code>unfold-right</code> is the fundamental recursive list constructor,
|
|
just as <code>fold-right</code> is
|
|
the fundamental recursive list consumer.
|
|
While <code>unfold-right</code> may seem a bit abstract
|
|
to novice functional programmers, it can be used in a number of ways:
|
|
|
|
<pre class=code-example>
|
|
;; List of squares: 1^2 ... 10^2
|
|
(unfold-right (lambda (x) (> x 10))
|
|
(lambda (x) (* x x))
|
|
(lambda (x) (+ x 1))
|
|
1)
|
|
|
|
(unfold-right null-list? car cdr lis) ; Copy a proper list.
|
|
|
|
;; Read current input port into a list of values.
|
|
(unfold-right eof-object? values (lambda (x) (read)) (read))
|
|
|
|
;; Copy a possibly non-proper list:
|
|
(unfold-right not-pair? car cdr lis
|
|
values)
|
|
|
|
;; Append HEAD onto TAIL:
|
|
(unfold-right null-list? car cdr head
|
|
(lambda (x) tail))
|
|
</pre>
|
|
|
|
Interested functional programmers may enjoy noting that
|
|
<code>fold-right</code> and <code>unfold-right</code>
|
|
are in some sense inverses.
|
|
That is, given operations <var>knull?</var>, <var>kar</var>,
|
|
<var>kdr</var>, <var>kons</var>, and <var>knil</var> satisfying
|
|
<div class=indent>
|
|
<code>(<var>kons</var> (<var>kar</var> <var>x</var>) (<var>kdr</var> <var>x</var>))</code> = <code>x</code>
|
|
and
|
|
<code>(<var>knull?</var> <var>knil</var>)</code> = <code>#t</code>
|
|
</div>
|
|
then
|
|
<div class=indent>
|
|
<code>(fold-right <var>kons</var> <var>knil</var> (unfold-right <var>knull?</var> <var>kar</var> <var>kdr</var> <var>x</var>))</code> = <var>x</var>
|
|
</div>
|
|
and
|
|
<div class=indent>
|
|
<code>(unfold-right <var>knull?</var> <var>kar</var> <var>kdr</var> (fold-right <var>kons</var> <var>knil</var> <var>x</var>))</code> = <var>x</var>.
|
|
</div>
|
|
|
|
This combinator sometimes is called an "anamorphism;" when an
|
|
explicit <var>tail-gen</var> procedure is supplied, it is called an
|
|
"apomorphism."
|
|
|
|
|
|
<!--
|
|
==== map
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="map"></a>
|
|
<code class=proc-def>map</code><var> proc clist<sub>1</sub> clist<sub>2</sub> ... -> list</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>+]
|
|
|
|
<var>proc</var> is a procedure taking as many arguments
|
|
as there are list arguments and returning a single value.
|
|
<code>map</code> applies <var>proc</var> element-wise to the elements
|
|
of the lists and returns a list of the results,
|
|
in order.
|
|
The dynamic order in which <var>proc</var>
|
|
is applied to the elements of the lists is unspecified.
|
|
|
|
<pre class=code-example>
|
|
(map cadr '((a b) (d e) (g h))) => (b e h)
|
|
|
|
(map (lambda (n) (expt n n))
|
|
'(1 2 3 4 5))
|
|
=> (1 4 27 256 3125)
|
|
|
|
(map + '(1 2 3) '(4 5 6)) => (5 7 9)
|
|
|
|
(let ((count 0))
|
|
(map (lambda (ignored)
|
|
(set! count (+ count 1))
|
|
count)
|
|
'(a b))) => (1 2) <em>or</em> (2 1)
|
|
</pre>
|
|
|
|
This procedure is extended from its
|
|
<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>
|
|
specification to allow the arguments to be of unequal length;
|
|
it terminates when the shortest list runs out.
|
|
<p>
|
|
At least one of the argument lists must be finite:
|
|
<pre class=code-example>
|
|
(map + '(3 1 4 1) (circular-list 1 0)) => (4 1 5 1)
|
|
</pre>
|
|
|
|
<!--
|
|
==== for-each
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="for-each"></a>
|
|
<code class=proc-def>for-each</code><var> proc clist<sub>1</sub> clist<sub>2</sub> ... -> unspecified</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>+]
|
|
|
|
The arguments to <code>for-each</code> are like the arguments to
|
|
<code>map</code>, but
|
|
<code>for-each</code> calls <var>proc</var> for its side effects rather
|
|
than for its values.
|
|
Unlike <code>map</code>, <code>for-each</code> is guaranteed to call
|
|
<var>proc</var> on the elements of the lists in order from the first
|
|
element(s) to the last,
|
|
and the value returned by <code>for-each</code> is unspecified.
|
|
<pre class=code-example>
|
|
(let ((v (make-vector 5)))
|
|
(for-each (lambda (i)
|
|
(vector-set! v i (* i i)))
|
|
'(0 1 2 3 4))
|
|
v) => #(0 1 4 9 16)
|
|
</pre>
|
|
|
|
This procedure is extended from its
|
|
<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>
|
|
specification to allow the arguments to be of unequal length;
|
|
it terminates when the shortest list runs out.
|
|
<p>
|
|
At least one of the argument lists must be finite.
|
|
|
|
<!--
|
|
==== append-map!
|
|
==== append-map
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="append-map"></a>
|
|
<code class=proc-def>append-map </code><var>f clist<sub>1</sub> clist<sub>2</sub> ... -> value</var>
|
|
<dt class=proc-defn>
|
|
<a name="append-map!"></a>
|
|
<code class=proc-def>append-map! </code><var>f clist<sub>1</sub> clist<sub>2</sub> ... -> value</var>
|
|
<dd class=proc-def>
|
|
Equivalent to
|
|
<div class=indent><code>
|
|
(apply append (map <var>f</var> <var>clist<sub>1</sub></var> <var>clist<sub>2</sub></var> ...))
|
|
</code></div>
|
|
and
|
|
<div class=indent><code>
|
|
(apply append! (map <var>f</var> <var>clist<sub>1</sub></var> <var>clist<sub>2</sub></var> ...))
|
|
</code></div>
|
|
|
|
Map <var>f</var> over the elements of the lists, just as in the <code>map</code> function.
|
|
However, the results of the applications are appended together to
|
|
make the final result. <code>append-map</code> uses <code>append</code> to append the results
|
|
together; <code>append-map!</code> uses <code>append!</code>.
|
|
<p>
|
|
The dynamic order in which the various applications of <var>f</var> are made is
|
|
not specified.
|
|
<p>
|
|
Example:
|
|
<pre class=code-example>
|
|
(append-map! (lambda (x) (list x (- x))) '(1 3 8))
|
|
=> (1 -1 3 -3 8 -8)
|
|
</pre>
|
|
|
|
At least one of the list arguments must be finite.
|
|
|
|
<!--
|
|
==== map!
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="map!"></a>
|
|
<code class=proc-def>map!</code><var> f list<sub>1</sub> clist<sub>2</sub> ... -> list</var>
|
|
<dd class=proc-def>
|
|
Linear-update variant of <code>map</code> -- <code>map!</code> is allowed, but not required, to
|
|
alter the cons cells of <var>list<sub>1</sub></var> to construct the result list.
|
|
<p>
|
|
The dynamic order in which the various applications of <var>f</var> are made is
|
|
not specified.
|
|
|
|
In the n-ary case, <var>clist<sub>2</sub></var>, <var>clist<sub>3</sub></var>, ... must have at least as many
|
|
elements as <var>list<sub>1</sub></var>.
|
|
|
|
<!--
|
|
==== map-in-order
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="map-in-order"></a>
|
|
<code class=proc-def>map-in-order </code><var>f</var> <var>clist<sub>1</sub> clist<sub>2</sub> ... -> list</var>
|
|
<dd class=proc-def>
|
|
A variant of the <code>map</code> procedure that guarantees to apply <var>f</var> across
|
|
the elements of the <var>list<sub>i</sub></var> arguments in a left-to-right order. This
|
|
is useful for mapping procedures that both have side effects and
|
|
return useful values.
|
|
<p>
|
|
At least one of the list arguments must be finite.
|
|
|
|
<!--
|
|
==== pair-for-each
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="pair-for-each"></a>
|
|
<code class=proc-def>pair-for-each </code><var>f clist<sub>1</sub> clist<sub>2</sub> ... -> unspecific</var>
|
|
<dd class=proc-def>
|
|
Like <code>for-each</code>, but <var>f</var> is applied to successive sublists of the argument
|
|
lists. That is, <var>f</var> is applied to the cons cells of the lists, rather
|
|
than the lists' elements. These applications occur in left-to-right
|
|
order.
|
|
<p>
|
|
The <var>f</var> procedure may reliably apply <code>set-cdr!</code> to the pairs it is given
|
|
without altering the sequence of execution.
|
|
|
|
<pre class=code-example>
|
|
(pair-for-each (lambda (pair) (display pair) (newline)) '(a b c)) ==>
|
|
(a b c)
|
|
(b c)
|
|
(c)
|
|
</pre>
|
|
|
|
At least one of the list arguments must be finite.
|
|
|
|
<!--
|
|
==== filter-map
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="filter-map"></a>
|
|
<code class=proc-def>filter-map</code><var> f clist<sub>1</sub> clist<sub>2</sub> ... -> list</var>
|
|
<dd class=proc-def>
|
|
Like <code>map</code>, but only true values are saved.
|
|
<pre class=code-example>
|
|
(filter-map (lambda (x) (and (number? x) (* x x))) '(a 1 b 3 c 7))
|
|
=> (1 9 49)
|
|
</pre>
|
|
The dynamic order in which the various applications of <var>f</var> are made is
|
|
not specified.
|
|
<p>
|
|
At least one of the list arguments must be finite.
|
|
</dl>
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="FilteringPartitioning">Filtering & partitioning</a></h2>
|
|
<dl>
|
|
|
|
<!--
|
|
==== filter
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="filter"></a>
|
|
<code class=proc-def>filter</code><var> pred list -> list</var>
|
|
<dd class=proc-def>
|
|
Return all the elements of <var>list</var> that satisfy predicate <var>pred</var>.
|
|
The list is not disordered -- elements that appear in the result list
|
|
occur in the same order as they occur in the argument list.
|
|
The returned list may share a common tail with the argument list.
|
|
The dynamic order in which the various applications of <var>pred</var> are made is
|
|
not specified.
|
|
|
|
<pre class=code-example>
|
|
(filter even? '(0 7 8 8 43 -4)) => (0 8 8 -4)
|
|
</pre>
|
|
|
|
<!--
|
|
==== partition
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="partition"></a>
|
|
<code class=proc-def>partition</code><var> pred list -> [list list]</var>
|
|
<dd class=proc-def>
|
|
Partitions the elements of <var>list</var> with predicate <var>pred</var>, and returns two
|
|
values: the list of in-elements and the list of out-elements.
|
|
The list is not disordered -- elements occur in the result lists
|
|
in the same order as they occur in the argument list.
|
|
The dynamic order in which the various applications of <var>pred</var> are made is
|
|
not specified. One of the returned lists may share a common tail with the
|
|
argument list.
|
|
|
|
<pre class=code-example>
|
|
(partition symbol? '(one 2 3 four five 6)) =>
|
|
(one four five)
|
|
(2 3 6)
|
|
</pre>
|
|
|
|
<!--
|
|
==== remove
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="remove"></a>
|
|
<code class=proc-def>remove</code><var> pred list -> list</var>
|
|
<dd class=proc-def>
|
|
Returns <var>list</var> without the elements that satisfy predicate <var>pred</var>:
|
|
<pre class=code-example>
|
|
(lambda (pred list) (filter (lambda (x) (not (pred x))) list))
|
|
</pre>
|
|
The list is not disordered -- elements that appear in the result list
|
|
occur in the same order as they occur in the argument list.
|
|
The returned list may share a common tail with the argument list.
|
|
The dynamic order in which the various applications of <var>pred</var> are made is
|
|
not specified.
|
|
|
|
<pre class=code-example>
|
|
(remove even? '(0 7 8 8 43 -4)) => (7 43)
|
|
</pre>
|
|
|
|
<!--
|
|
==== remove!
|
|
==== partition!
|
|
==== filter!
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="filter!"></a>
|
|
<code class=proc-def>filter! </code><var>pred list -> list</var>
|
|
<dt class=proc-defi>
|
|
<a name="partition!"></a>
|
|
<code class=proc-def>partition! </code><var>pred list -> [list list]</var>
|
|
<dt class=proc-defn>
|
|
<a name="remove!"></a>
|
|
<code class=proc-def>remove! </code><var>pred list -> list</var>
|
|
<dd class=proc-def>
|
|
Linear-update variants of <code>filter</code>, <code>partition</code> and <code>remove</code>.
|
|
These procedures are allowed, but not required, to alter the cons cells
|
|
in the argument list to construct the result lists.
|
|
|
|
</dl>
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="Searching">Searching</a></h2>
|
|
<p>
|
|
|
|
The following procedures all search lists for a leftmost element satisfying
|
|
some criteria. This means they do not always examine the entire list; thus,
|
|
there is no efficient way for them to reliably detect and signal an error when
|
|
passed a dotted or circular list. Here are the general rules describing how
|
|
these procedures work when applied to different kinds of lists:
|
|
|
|
<dl>
|
|
<dt> Proper lists:
|
|
<dd> The standard, canonical behavior happens in this case.
|
|
|
|
<dt> Dotted lists:
|
|
<dd> It is an error to pass these procedures a dotted list
|
|
that does not contain an element satisfying the search
|
|
criteria. That is, it is an error if the procedure has
|
|
to search all the way to the end of the dotted list.
|
|
However, this <abbr title="Scheme Request for Implementation">SRFI</abbr> does <em>not</em> specify anything at all
|
|
about the behavior of these procedures when passed a
|
|
dotted list containing an element satisfying the search
|
|
criteria. It may finish successfully, signal an error,
|
|
or perform some third action. Different implementations
|
|
may provide different functionality in this case; code
|
|
which is compliant with this <abbr title="Scheme Request for Implementation">SRFI</abbr> may not rely on any
|
|
particular behavior. Future <abbr title="Scheme Request for Implementation">SRFI</abbr>'s may refine SRFI-1
|
|
to define specific behavior in this case.
|
|
<p>
|
|
In brief, SRFI-1 compliant code may not pass a dotted
|
|
list argument to these procedures.
|
|
|
|
<dt> Circular lists:
|
|
<dd> It is an error to pass these procedures a circular list
|
|
that does not contain an element satisfying the search
|
|
criteria. Note that the procedure is not required to
|
|
detect this case; it may simply diverge. It is, however,
|
|
acceptable to search a circular list <em>if the search is
|
|
successful</em> -- that is, if the list contains an element
|
|
satisfying the search criteria.
|
|
</dl>
|
|
<p>
|
|
Here are some examples, using the <code>find</code> and <code>any</code> procedures as canonical
|
|
representatives:
|
|
<pre class=code-example>
|
|
;; Proper list -- success
|
|
(find even? '(1 2 3)) => 2
|
|
(any even? '(1 2 3)) => #t
|
|
|
|
;; proper list -- failure
|
|
(find even? '(1 7 3)) => #f
|
|
(any even? '(1 7 3)) => #f
|
|
|
|
;; Failure is error on a dotted list.
|
|
(find even? '(1 3 . x)) => error
|
|
(any even? '(1 3 . x)) => error
|
|
|
|
;; The dotted list contains an element satisfying the search.
|
|
;; This case is not specified -- it could be success, an error,
|
|
;; or some third possibility.
|
|
(find even? '(1 2 . x)) => error/undefined
|
|
(any even? '(1 2 . x)) => error/undefined ; success, error or other.
|
|
|
|
;; circular list -- success
|
|
(find even? (circular-list 1 6 3)) => 6
|
|
(any even? (circular-list 1 6 3)) => #t
|
|
|
|
;; circular list -- failure is error. Procedure may diverge.
|
|
(find even? (circular-list 1 3)) => error
|
|
(any even? (circular-list 1 3)) => error
|
|
</pre>
|
|
|
|
<dl>
|
|
<!--
|
|
==== find
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="find"></a>
|
|
<code class=proc-def>find</code><var> pred clist -> value</var>
|
|
<dd class=proc-def>
|
|
Return the first element of <var>clist</var> that satisfies predicate <var>pred</var>;
|
|
false if no element does.
|
|
|
|
<pre class=code-example>
|
|
(find even? '(3 1 4 1 5 9)) => 4
|
|
</pre>
|
|
|
|
Note that <code>find</code> has an ambiguity in its lookup semantics -- if <code>find</code>
|
|
returns <code>#f</code>, you cannot tell (in general) if it found a <code>#f</code> element
|
|
that satisfied <var>pred</var>, or if it did not find any element at all. In
|
|
many situations, this ambiguity cannot arise -- either the list being
|
|
searched is known not to contain any <code>#f</code> elements, or the list is
|
|
guaranteed to have an element satisfying <var>pred</var>. However, in cases
|
|
where this ambiguity can arise, you should use <code>find-tail</code> instead of
|
|
<code>find</code> -- <code>find-tail</code> has no such ambiguity:
|
|
<pre class=code-example>
|
|
(cond ((find-tail pred lis) => (lambda (pair) ...)) ; Handle (CAR PAIR)
|
|
(else ...)) ; Search failed.
|
|
</pre>
|
|
|
|
<!--
|
|
==== find-tail
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="find-tail"></a>
|
|
<code class=proc-def>find-tail</code><var> pred clist -> pair or false</var>
|
|
<dd class=proc-def>
|
|
Return the first pair of <var>clist</var> whose car satisfies <var>pred</var>. If no pair does,
|
|
return false.
|
|
<p>
|
|
<code>find-tail</code> can be viewed as a general-predicate variant of the <code>member</code>
|
|
function.
|
|
<p>
|
|
Examples:
|
|
<pre class=code-example>
|
|
(find-tail even? '(3 1 37 -8 -5 0 0)) => (-8 -5 0 0)
|
|
(find-tail even? '(3 1 37 -5)) => #f
|
|
|
|
;; MEMBER X LIS:
|
|
(find-tail (lambda (elt) (equal? x elt)) lis)
|
|
</pre>
|
|
|
|
In the circular-list case, this procedure "rotates" the list.
|
|
|
|
<!--
|
|
==== any
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="any"></a>
|
|
<code class=proc-def>any</code><var> pred clist<sub>1</sub> clist<sub>2</sub> ... -> value</var>
|
|
<dd class=proc-def>
|
|
Applies the predicate across the lists, returning true if the predicate
|
|
returns true on any application.
|
|
<p>
|
|
If there are <var>n</var> list arguments <var>clist<sub>1</sub></var> ... <var>clist<sub>n</sub></var>, then <var>pred</var> must be a
|
|
procedure taking <var>n</var> arguments and returning a boolean result.
|
|
<p>
|
|
<code>any</code> applies <var>pred</var> to the first elements of the <var>clist<sub>i</sub></var> parameters.
|
|
If this application returns a true value, <code>any</code> immediately returns
|
|
that value. Otherwise, it iterates, applying <var>pred</var> to the second
|
|
elements of the <var>clist<sub>i</sub></var> parameters, then the third, and so forth.
|
|
The iteration stops when a true value is produced or one of the lists runs
|
|
out of values; in
|
|
the latter case, <code>any</code> returns <code>#f</code>.
|
|
The application of <var>pred</var> to the last element of the
|
|
lists is a tail call.
|
|
<p>
|
|
Note the difference between <code>find</code> and <code>any</code> -- <code>find</code> returns the element
|
|
that satisfied the predicate; <code>any</code> returns the true value that the
|
|
predicate produced.
|
|
<p>
|
|
Like <code>every</code>, <code>any</code>'s name does not end with a question mark -- this is to
|
|
indicate that it does not return a simple boolean (<code>#t</code> or <code>#f</code>), but a
|
|
general value.
|
|
|
|
<pre class=code-example>
|
|
(any integer? '(a 3 b 2.7)) => #t
|
|
(any integer? '(a 3.1 b 2.7)) => #f
|
|
(any < '(3 1 4 1 5)
|
|
'(2 7 1 8 2)) => #t
|
|
</pre>
|
|
|
|
<!--
|
|
==== every
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="every"></a>
|
|
<code class=proc-def>every</code><var> pred clist<sub>1</sub> clist<sub>2</sub> ... -> value</var>
|
|
<dd class=proc-def>
|
|
Applies the predicate across the lists, returning true if the predicate
|
|
returns true on every application.
|
|
<p>
|
|
If there are <var>n</var> list arguments <var>clist<sub>1</sub></var> ... <var>clist<sub>n</sub></var>, then <var>pred</var> must be a
|
|
procedure taking <var>n</var> arguments and returning a boolean result.
|
|
<p>
|
|
<code>every</code> applies <var>pred</var> to the first elements of the <var>clist<sub>i</sub></var> parameters.
|
|
If this application returns false, <code>every</code> immediately returns false.
|
|
Otherwise, it iterates, applying <var>pred</var> to the second elements of the
|
|
<var>clist<sub>i</sub></var> parameters, then the third, and so forth. The iteration stops
|
|
when a false value is produced or one of the lists runs out of values.
|
|
In the latter case, <code>every</code> returns
|
|
the true value produced by its final application of <var>pred</var>.
|
|
The application of <var>pred</var> to the last element of the lists
|
|
is a tail call.
|
|
<p>
|
|
If one of the <var>clist<sub>i</sub></var> has no elements, <code>every</code> simply returns <code>#t</code>.
|
|
<p>
|
|
Like <code>any</code>, <code>every</code>'s name does not end with a question mark -- this is to
|
|
indicate that it does not return a simple boolean (<code>#t</code> or <code>#f</code>), but a
|
|
general value.
|
|
|
|
<!--
|
|
==== list-index
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="list-index"></a>
|
|
<code class=proc-def>list-index</code><var> pred clist<sub>1</sub> clist<sub>2</sub> ... -> integer or false</var>
|
|
<dd class=proc-def>
|
|
Return the index of the leftmost element that satisfies <var>pred</var>.
|
|
<p>
|
|
If there are <var>n</var> list arguments <var>clist<sub>1</sub></var> ... <var>clist<sub>n</sub></var>, then <var>pred</var> must be a
|
|
function taking <var>n</var> arguments and returning a boolean result.
|
|
<p>
|
|
<code>list-index</code> applies <var>pred</var> to the first elements of the <var>clist<sub>i</sub></var> parameters.
|
|
If this application returns true, <code>list-index</code> immediately returns zero.
|
|
Otherwise, it iterates, applying <var>pred</var> to the second elements of the
|
|
<var>clist<sub>i</sub></var> parameters, then the third, and so forth. When it finds a tuple of
|
|
list elements that cause <var>pred</var> to return true, it stops and returns the
|
|
zero-based index of that position in the lists.
|
|
<p>
|
|
The iteration stops when one of the lists runs out of values; in this
|
|
case, <code>list-index</code> returns <code>#f</code>.
|
|
|
|
<pre class=code-example>
|
|
(list-index even? '(3 1 4 1 5 9)) => 2
|
|
(list-index < '(3 1 4 1 5 9 2 5 6) '(2 7 1 8 2)) => 1
|
|
(list-index = '(3 1 4 1 5 9 2 5 6) '(2 7 1 8 2)) => #f
|
|
</pre>
|
|
|
|
<!--
|
|
==== member memq memv
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="member"></a>
|
|
<code class=proc-def>member</code><var> x list [=] -> list</var>
|
|
<dt class=proc-defi>
|
|
<a name="memq"></a>
|
|
<code class=proc-def>memq</code><var> x list -> list</var>
|
|
<dt class=proc-defn>
|
|
<a name="memv"></a>
|
|
<code class=proc-def>memv</code><var> x list -> list</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>+]
|
|
|
|
These procedures return the first sublist of <var>list</var> whose car is
|
|
<var>x</var>, where the sublists of <var>list</var> are the
|
|
non-empty lists returned by
|
|
<code>(drop <var>list</var> <var>i</var>)</code>
|
|
for <var>i</var> less than the length of <var>list</var>.
|
|
If <var>x</var> does
|
|
not occur in <var>list</var>, then <code>#f</code> is returned.
|
|
<code>memq</code> uses <code>eq?</code> to compare <var>x</var>
|
|
with the elements of <var>list</var>,
|
|
while <code>memv</code> uses <code>eqv?</code>, and
|
|
<code>member</code> uses <code>equal?</code>.
|
|
|
|
<pre class=code-example>
|
|
(memq 'a '(a b c)) => (a b c)
|
|
(memq 'b '(a b c)) => (b c)
|
|
(memq 'a '(b c d)) => #f
|
|
(memq (list 'a) '(b (a) c)) => #f
|
|
(member (list 'a)
|
|
'(b (a) c)) => ((a) c)
|
|
(memq 101 '(100 101 102)) => *unspecified*
|
|
(memv 101 '(100 101 102)) => (101 102)
|
|
</pre>
|
|
|
|
<code>member</code> is extended from its
|
|
<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>
|
|
definition to allow the client to pass in
|
|
an optional equality procedure <var>=</var> used to compare keys.
|
|
|
|
<p>
|
|
The comparison procedure is used to compare the elements <var>e<sub>i</sub></var> of <var>list</var>
|
|
to the key <var>x</var> in this way:
|
|
<div class=indent><code>
|
|
(= <var>x</var> <var>e<sub>i</sub></var>) ; list is (E1 ... En)
|
|
</code></div>
|
|
That is, the first argument is always <var>x</var>, and the second argument is
|
|
one of the list elements. Thus one can reliably find the first element
|
|
of <var>list</var> that is greater than five with
|
|
<code>(member 5 <var>list</var> <)</code>
|
|
|
|
<p>
|
|
Note that fully general list searching may be performed with
|
|
the <code>find-tail</code> and <code>find</code> procedures, <em>e.g.</em>
|
|
<pre class=code-example>
|
|
(find-tail even? list) ; Find the first elt with an even key.
|
|
</pre>
|
|
|
|
</dl>
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="Deletion">Deletion</a></h2>
|
|
<p>
|
|
|
|
<dl>
|
|
<!--
|
|
==== delete!
|
|
==== delete
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="delete"></a>
|
|
<code class=proc-def>delete </code><var>x list [=] -> list</var>
|
|
<dt class=proc-defn>
|
|
<a name="delete!"></a>
|
|
<code class=proc-def>delete! </code><var>x list [=] -> list</var>
|
|
<dd class=proc-def>
|
|
<code>delete</code> uses the comparison procedure =, which defaults to <code>equal?</code>, to find
|
|
all elements of <var>list</var> that are equal to <var>x</var>, and deletes them from <var>list</var>. The
|
|
dynamic order in which the various applications of <var>=</var> are made is not
|
|
specified.
|
|
|
|
<p>
|
|
The list is not disordered -- elements that appear in the result list
|
|
occur in the same order as they occur in the argument list.
|
|
The result may share a common tail with the argument list.
|
|
|
|
<p>
|
|
Note that fully general element deletion can be performed with the <code>remove</code>
|
|
and <code>remove!</code> procedures, <em>e.g.</em>:
|
|
<pre class=code-example>
|
|
;; Delete all the even elements from LIS:
|
|
(remove even? lis)
|
|
</pre>
|
|
|
|
The comparison procedure is used in this way:
|
|
<code>(= <var>x</var> <var>e<sub>i</sub></var>)</code>.
|
|
That is, <var>x</var> is always the first argument,
|
|
and a list element is always the
|
|
second argument. The comparison procedure will be used to compare each
|
|
element of <var>list</var> exactly once; the order in which it is applied to the
|
|
various <var>e<sub>i</sub></var> is not specified. Thus, one can reliably remove all the
|
|
numbers greater than five from a list with
|
|
<code>(delete 5 list <)</code>
|
|
|
|
<p>
|
|
<code>delete!</code> is the linear-update variant of <code>delete</code>.
|
|
It is allowed, but not required, to alter the cons cells in
|
|
its argument list to construct the result.
|
|
|
|
<!--
|
|
==== delete-duplicates!
|
|
==== delete-duplicates
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="delete-duplicates"></a>
|
|
<code class=proc-def>delete-duplicates </code><var>list [=] -> list</var>
|
|
<dt class=proc-defn>
|
|
<a name="delete-duplicates!"></a>
|
|
<code class=proc-def>delete-duplicates! </code><var>list [=] -> list</var>
|
|
<dd class=proc-def>
|
|
<code>delete-duplicates</code> removes duplicate elements from the
|
|
list argument.
|
|
If there are multiple equal elements in the argument list, the result list
|
|
only contains the first or leftmost of these elements in the result.
|
|
The order of these surviving elements is the same as in the original
|
|
list -- <code>delete-duplicates</code> does not disorder the list (hence it is useful
|
|
for "cleaning up" association lists).
|
|
<p>
|
|
The <var>=</var> parameter is used to compare the elements of the list; it defaults
|
|
to <code>equal?</code>. If <var>x</var> comes before <var>y</var> in <var>list</var>, then the comparison is performed
|
|
<code>(= <var>x</var> <var>y</var>)</code>.
|
|
The comparison procedure will be used to compare each pair of elements in
|
|
<var>list</var> no more than once;
|
|
the order in which it is applied to the various pairs is not specified.
|
|
<p>
|
|
Implementations of <code>delete-duplicates</code>
|
|
are allowed to share common tails
|
|
between argument and result lists -- for example, if the list argument
|
|
contains only unique elements, it may simply return exactly
|
|
this list.
|
|
<p>
|
|
Be aware that, in general, <code>delete-duplicates</code>
|
|
runs in time O(n<sup>2</sup>) for <var>n</var>-element lists.
|
|
Uniquifying long lists can be accomplished in O(n lg n) time by sorting
|
|
the list to bring equal elements together, then using a linear-time
|
|
algorithm to remove equal elements. Alternatively, one can use algorithms
|
|
based on element-marking, with linear-time results.
|
|
|
|
<p>
|
|
<code>delete-duplicates!</code> is the linear-update variant of <code>delete-duplicates</code>; it
|
|
is allowed, but not required, to alter the cons cells in its argument
|
|
list to construct the result.
|
|
<pre class=code-example>
|
|
(delete-duplicates '(a b a c a b c z)) => (a b c z)
|
|
|
|
;; Clean up an alist:
|
|
(delete-duplicates '((a . 3) (b . 7) (a . 9) (c . 1))
|
|
(lambda (x y) (eq? (car x) (car y))))
|
|
=> ((a . 3) (b . 7) (c . 1))
|
|
</pre>
|
|
</dl>
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="AssociationLists">Association lists</a></h2>
|
|
<p>
|
|
An "association list" (or "alist") is a list of pairs. The car of each pair
|
|
contains a key value, and the cdr contains the associated data value. They can
|
|
be used to construct simple look-up tables in Scheme. Note that association
|
|
lists are probably inappropriate for performance-critical use on large data;
|
|
in these cases, hash tables or some other alternative should be employed.
|
|
|
|
<dl>
|
|
<!--
|
|
==== assoc assq assv
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="assoc"></a>
|
|
<code class=proc-def>assoc</code><var> key alist [=] -> pair or #f</var>
|
|
<dt class=proc-defi>
|
|
<a name="assq"></a>
|
|
<code class=proc-def>assq</code><var> key alist -> pair or #f</var>
|
|
<dt class=proc-defn>
|
|
<a name="assv"></a>
|
|
<code class=proc-def>assv</code><var> key alist -> pair or #f</var>
|
|
<dd class=proc-def>
|
|
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>+]
|
|
<var>alist</var> must be an association list -- a list of pairs.
|
|
These procedures
|
|
find the first pair in <var>alist</var> whose car field is <var>key</var>,
|
|
and returns that pair.
|
|
If no pair in <var>alist</var> has <var>key</var> as its car,
|
|
then <code>#f</code> is returned.
|
|
<code>assq</code> uses <code>eq?</code> to compare <var>key</var>
|
|
with the car fields of the pairs in <var>alist</var>,
|
|
while <code>assv</code> uses <code>eqv?</code>
|
|
and <code>assoc</code> uses <code>equal?</code>.
|
|
<pre class=code-example>
|
|
(define e '((a 1) (b 2) (c 3)))
|
|
(assq 'a e) => (a 1)
|
|
(assq 'b e) => (b 2)
|
|
(assq 'd e) => #f
|
|
(assq (list 'a) '(((a)) ((b)) ((c)))) => #f
|
|
(assoc (list 'a) '(((a)) ((b)) ((c)))) => ((a))
|
|
(assq 5 '((2 3) (5 7) (11 13))) => *unspecified*
|
|
(assv 5 '((2 3) (5 7) (11 13))) => (5 7)
|
|
</pre>
|
|
|
|
<code>assoc</code> is extended from its
|
|
<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>
|
|
definition to allow the client to pass in
|
|
an optional equality procedure <var>=</var> used to compare keys.
|
|
|
|
<p>
|
|
The comparison procedure is used to compare the elements <var>e<sub>i</sub></var> of <var>list</var>
|
|
to the <var>key</var> parameter in this way:
|
|
<div class=indent><code>
|
|
(= <var>key</var> (car <var>e<sub>i</sub></var>)) ; list is (E1 ... En)
|
|
</code></div>
|
|
That is, the first argument is always <var>key</var>,
|
|
and the second argument is one of the list elements.
|
|
Thus one can reliably find the first entry
|
|
of <var>alist</var> whose key is greater than five with
|
|
<code>(assoc 5 <var>alist</var> <)</code>
|
|
|
|
<p>
|
|
Note that fully general alist searching may be performed with
|
|
the <code>find-tail</code> and <code>find</code> procedures, <em>e.g.</em>
|
|
<pre class=code-example>
|
|
;; Look up the first association in <var>alist</var> with an even key:
|
|
(find (lambda (a) (even? (car a))) alist)
|
|
</pre>
|
|
|
|
|
|
<!--
|
|
==== alist-cons
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="alist-cons"></a>
|
|
<code class=proc-def>alist-cons</code><var> key datum alist -> alist</var>
|
|
<dd class=proc-def>
|
|
<pre>
|
|
(lambda (key datum alist) (cons (cons key datum) alist))
|
|
</pre>
|
|
Cons a new alist entry mapping <var>key</var> -> <var>datum</var> onto <var>alist</var>.
|
|
|
|
<!--
|
|
==== alist-copy
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="alist-copy"></a>
|
|
<code class=proc-def>alist-copy</code><var> alist -> alist</var>
|
|
<dd class=proc-def>
|
|
Make a fresh copy of <var>alist</var>. This means copying each pair that
|
|
forms an association as well as the spine of the list, <em>i.e.</em>
|
|
<pre>
|
|
(lambda (a) (map (lambda (elt) (cons (car elt) (cdr elt))) a))
|
|
</pre>
|
|
|
|
<!--
|
|
==== alist-delete!
|
|
==== alist-delete
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="alist-delete"></a>
|
|
<code class=proc-def>alist-delete </code><var>key alist [=] -> alist</var>
|
|
<dt class=proc-defn>
|
|
<a name="alist-delete!"></a>
|
|
<code class=proc-def>alist-delete! </code><var>key alist [=] -> alist</var>
|
|
<dd class=proc-def>
|
|
<code>alist-delete</code> deletes all associations from <var>alist</var> with the given <var>key</var>,
|
|
using key-comparison procedure =, which defaults to <code>equal?</code>.
|
|
The dynamic order in which the various applications of <var>=</var> are made is not
|
|
specified.
|
|
<p>
|
|
Return values may share common tails with the <var>alist</var> argument.
|
|
The alist is not disordered -- elements that appear in the result alist
|
|
occur in the same order as they occur in the argument alist.
|
|
<p>
|
|
The comparison procedure is used to compare the element keys <var>k<sub>i</sub></var> of <var>alist</var>'s
|
|
entries to the <var>key</var> parameter in this way:
|
|
<code>(= <var>key</var> <var>k<sub>i</sub></var>)</code>.
|
|
Thus, one can reliably remove all entries of <var>alist</var> whose key is greater
|
|
than five with
|
|
<code>(alist-delete 5 <var>alist</var> <)</code>
|
|
<p>
|
|
<code>alist-delete!</code> is the linear-update variant of <code>alist-delete</code>.
|
|
It is allowed, but not required,
|
|
to alter cons cells from the <var>alist</var> parameter to construct the result.
|
|
|
|
</dl>
|
|
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="SetOperationsOnLists">Set operations on lists</a></h2>
|
|
<p>
|
|
These procedures implement operations on sets represented as lists of elements.
|
|
They all take an <var>=</var> argument used to compare elements of lists.
|
|
This equality procedure is required to be consistent with <code>eq?</code>.
|
|
That is, it must be the case that
|
|
<div class=indent>
|
|
<code>(eq? <var>x</var> <var>y</var>)</code> => <code>(<var>=</var> <var>x</var> <var>y</var>)</code>.
|
|
</div>
|
|
Note that this implies, in turn, that two lists that are <code>eq?</code> are
|
|
also set-equal by any legal comparison procedure. This allows for
|
|
constant-time determination of set operations on <code>eq?</code> lists.
|
|
|
|
<p>
|
|
Be aware that these procedures typically run in time
|
|
O(<var>n</var> * <var>m</var>)
|
|
for <var>n</var>- and <var>m</var>-element list arguments.
|
|
Performance-critical applications
|
|
operating upon large sets will probably wish to use other data
|
|
structures and algorithms.
|
|
|
|
<dl>
|
|
<!--
|
|
==== lset<=
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="lset<="></a>
|
|
<code class=proc-def>lset<=</code><var> = list<sub>1</sub> ... -> boolean</var>
|
|
<dd class=proc-def>
|
|
Returns true iff every <var>list<sub>i</sub></var> is a subset of <var>list<sub>i+1</sub></var>, using <var>=</var> for
|
|
the element-equality procedure.
|
|
List <var>A</var> is a subset of list <var>B</var> if every
|
|
element in <var>A</var> is equal to some element of <var>B</var>.
|
|
When performing an element comparison,
|
|
the <var>=</var> procedure's first argument is an element
|
|
of <var>A</var>; its second, an element of <var>B</var>.
|
|
<pre class=code-example>
|
|
(lset<= eq? '(a) '(a b a) '(a b c c)) => #t
|
|
|
|
(lset<= eq?) => #t ; Trivial cases
|
|
(lset<= eq? '(a)) => #t
|
|
</pre>
|
|
|
|
<!--
|
|
==== lset=
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="lset="></a>
|
|
<code class=proc-def>lset=</code><var> = list<sub>1</sub> list<sub>2</sub> ... -> boolean</var>
|
|
<dd class=proc-def>
|
|
Returns true iff every <var>list<sub>i</sub></var> is set-equal to <var>list<sub>i+1</sub></var>, using <var>=</var> for
|
|
the element-equality procedure. "Set-equal" simply means that
|
|
<var>list<sub>i</sub></var> is a subset of <var>list<sub>i+1</sub></var>, and <var>list<sub>i+1</sub></var> is a subset of <var>list<sub>i</sub></var>.
|
|
The <var>=</var> procedure's first argument is an element of <var>list<sub>i</sub></var>; its second is an element of
|
|
<var>list<sub>i+1</sub></var>.
|
|
<pre class=code-example>
|
|
(lset= eq? '(b e a) '(a e b) '(e e b a)) => #t
|
|
|
|
(lset= eq?) => #t ; Trivial cases
|
|
(lset= eq? '(a)) => #t
|
|
</pre>
|
|
|
|
<!--
|
|
==== lset-adjoin
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="lset-adjoin"></a>
|
|
<code class=proc-def>lset-adjoin</code><var> = list elt<sub>1</sub> ... -> list</var>
|
|
<dd class=proc-def>
|
|
Adds the <var>elt<sub>i</sub></var> elements not already in the list parameter to the
|
|
result list. The result shares a common tail with the list parameter.
|
|
The new elements are added to the front of the list, but no guarantees
|
|
are made about their order. The <var>=</var> parameter is an equality procedure
|
|
used to determine if an <var>elt<sub>i</sub></var> is already a member of <var>list</var>. Its first
|
|
argument is an element of <var>list</var>; its second is one of the <var>elt<sub>i</sub></var>.
|
|
<p>
|
|
The list parameter is always a suffix of the result -- even if the list
|
|
parameter contains repeated elements, these are not reduced.
|
|
<pre class=code-example>
|
|
(lset-adjoin eq? '(a b c d c e) 'a 'e 'i 'o 'u) => (u o i a b c d c e)
|
|
</pre>
|
|
|
|
<!--
|
|
==== lset-union
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="lset-union"></a>
|
|
<code class=proc-def>lset-union</code><var> = list<sub>1</sub> ... -> list</var>
|
|
<dd class=proc-def>
|
|
Returns the union of the lists, using <var>=</var> for the element-equality
|
|
procedure.
|
|
<p>
|
|
The union of lists <var>A</var> and <var>B</var> is constructed as follows:
|
|
<ul>
|
|
<li> If <var>A</var> is the empty list,
|
|
the answer is <var>B</var> (or a copy of <var>B</var>).
|
|
<li> Otherwise, the result is initialised to be list <var>A</var>
|
|
(or a copy of <var>A</var>).
|
|
<li> Proceed through the elements of list <var>B</var>
|
|
in a left-to-right order.
|
|
If <var>b</var> is such an element of <var>B</var>,
|
|
compare every element <var>r</var> of the current result list
|
|
to <var>b</var>:
|
|
<code>(= <var>r</var> <var>b</var>)</code>.
|
|
If all comparisons fail,
|
|
<var>b</var> is consed onto the front of the result.
|
|
</ul>
|
|
However, there is no guarantee that = will be applied to every pair
|
|
of arguments from <var>A</var> and <var>B</var>.
|
|
In particular, if <var>A</var> is <code>eq</code>? to <var>B</var>,
|
|
the operation may immediately terminate.
|
|
|
|
<p>
|
|
In the n-ary case, the two-argument list-union operation is simply
|
|
folded across the argument lists.
|
|
|
|
<pre class=code-example>
|
|
(lset-union eq? '(a b c d e) '(a e i o u)) =>
|
|
(u o i a b c d e)
|
|
|
|
;; Repeated elements in LIST1 are preserved.
|
|
(lset-union eq? '(a a c) '(x a x)) => (x a a c)
|
|
|
|
;; Trivial cases
|
|
(lset-union eq?) => ()
|
|
(lset-union eq? '(a b c)) => (a b c)
|
|
</pre>
|
|
|
|
<!--
|
|
==== lset-intersection
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="lset-intersection"></a>
|
|
<code class=proc-def>lset-intersection</code><var> = list<sub>1</sub> list<sub>2</sub> ... -> list</var>
|
|
<dd class=proc-def>
|
|
Returns the intersection of the lists,
|
|
using <var>=</var> for the element-equality procedure.
|
|
<p>
|
|
The intersection of lists <var>A</var> and <var>B</var>
|
|
is comprised of every element of <var>A</var> that is <var>=</var>
|
|
to some element of <var>B</var>:
|
|
<code>(<var>=</var> <var>a</var> <var>b</var>)</code>,
|
|
for <var>a</var> in <var>A</var>, and <var>b</var> in <var>B</var>.
|
|
Note this implies that an element which appears in <var>B</var>
|
|
and multiple times in list <var>A</var>
|
|
will also appear multiple times in the result.
|
|
<p>
|
|
The order in which elements appear in the result is the same as
|
|
they appear in <var>list<sub>1</sub></var> --
|
|
that is, <code>lset-intersection</code> essentially filters
|
|
<var>list<sub>1</sub></var>,
|
|
without disarranging element order.
|
|
The result may
|
|
share a common tail with <var>list<sub>1</sub></var>.
|
|
<p>
|
|
In the n-ary case, the two-argument list-intersection operation is simply
|
|
folded across the argument lists. However, the dynamic order in which the
|
|
applications of <var>=</var> are made is not specified.
|
|
The procedure may check an
|
|
element of <var>list<sub>1</sub></var> for membership
|
|
in every other list before proceeding to
|
|
consider the next element of <var>list<sub>1</sub></var>,
|
|
or it may completely intersect <var>list<sub>1</sub></var>
|
|
and <var>list<sub>2</sub></var>
|
|
before proceeding to <var>list<sub>3</sub></var>,
|
|
or it may go about its work in some third order.
|
|
|
|
<pre class=code-example>
|
|
(lset-intersection eq? '(a b c d e) '(a e i o u)) => (a e)
|
|
|
|
;; Repeated elements in LIST1 are preserved.
|
|
(lset-intersection eq? '(a x y a) '(x a x z)) => '(a x a)
|
|
|
|
(lset-intersection eq? '(a b c)) => (a b c) ; Trivial case
|
|
</pre>
|
|
|
|
<!--
|
|
==== lset-difference
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="lset-difference"></a>
|
|
<code class=proc-def>lset-difference</code><var> = list<sub>1</sub> list<sub>2</sub> ... -> list</var>
|
|
<dd class=proc-def>
|
|
Returns the difference of the lists, using <var>=</var> for the element-equality
|
|
procedure -- all the elements of <var>list<sub>1</sub></var> that are not
|
|
<var>=</var> to any element from one of the
|
|
other <var>list<sub>i</sub></var> parameters.
|
|
<p>
|
|
The <var>=</var> procedure's first argument is
|
|
always an element of <var>list<sub>1</sub></var>;
|
|
its second is an element of one of the other <var>list<sub>i</sub></var>.
|
|
Elements that are repeated multiple times in the
|
|
<var>list<sub>1</sub></var> parameter
|
|
will occur multiple times in the result.
|
|
|
|
The order in which elements appear in the result is the same as
|
|
they appear in <var>list<sub>1</sub></var> --
|
|
that is, <code>lset-difference</code> essentially
|
|
filters <var>list<sub>1</sub></var>, without disarranging element order.
|
|
The result may share a common tail with <var>list<sub>1</sub></var>.
|
|
|
|
The dynamic order in which the applications of <var>=</var> are made is not
|
|
specified.
|
|
The procedure may check an element of <var>list<sub>1</sub></var>
|
|
for membership in every other list before proceeding to consider the
|
|
next element of <var>list<sub>1</sub></var>,
|
|
or it may completely compute the difference of
|
|
<var>list<sub>1</sub></var> and <var>list<sub>2</sub></var> before
|
|
proceeding to <var>list<sub>3</sub></var>,
|
|
or it may go about its work in some third order.
|
|
|
|
<pre class=code-example>
|
|
(lset-difference eq? '(a b c d e) '(a e i o u)) => (b c d)
|
|
|
|
(lset-difference eq? '(a b c)) => (a b c) ; Trivial case
|
|
</pre>
|
|
|
|
<!--
|
|
==== lset-xor
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="lset-xor"></a>
|
|
<code class=proc-def>lset-xor</code><var> = list<sub>1</sub> ... -> list</var>
|
|
<dd class=proc-def>
|
|
Returns the exclusive-or of the sets,
|
|
using <var>=</var> for the element-equality procedure.
|
|
If there are exactly two lists, this is all the elements
|
|
that appear in exactly one of the two lists. The operation is associative,
|
|
and thus extends to the n-ary case -- the elements that appear in an
|
|
odd number of the lists. The result may share a common tail with any of
|
|
the <var>list<sub>i</sub></var> parameters.
|
|
<p>
|
|
More precisely, for two lists <var>A</var> and <var>B</var>,
|
|
<var>A</var> xor <var>B</var> is a list of
|
|
<ul>
|
|
<li> every element <var>a</var> of <var>A</var>
|
|
such that there is no element <var>b</var> of <var>B</var>
|
|
such that <code>(<var>=</var> <var>a</var> <var>b</var>)</code>, and
|
|
<li> every element <var>b</var> of <var>B</var>
|
|
such that there is no element <var>a</var> of <var>A</var>
|
|
such that <code>(<var>=</var> <var>b</var> <var>a</var>)</code>.
|
|
</ul>
|
|
However, an implementation is allowed to assume that <var>=</var> is
|
|
symmetric -- that is, that
|
|
<div class=indent>
|
|
<code>(<var>=</var> <var>a</var> <var>b</var>)</code> =>
|
|
<code>(<var>=</var> <var>b</var> <var>a</var>)</code>.
|
|
</div>
|
|
This means, for example, that if a comparison
|
|
<code>(<var>=</var> <var>a</var> <var>b</var>)</code> produces
|
|
true for some <var>a</var> in <var>A</var>
|
|
and <var>b</var> in <var>B</var>,
|
|
both <var>a</var> and <var>b</var> may be removed from
|
|
inclusion in the result.
|
|
<p>
|
|
In the n-ary case, the binary-xor operation is simply folded across
|
|
the lists.
|
|
|
|
<pre class=code-example>
|
|
(lset-xor eq? '(a b c d e) '(a e i o u)) => (d c b i o u)
|
|
|
|
;; Trivial cases.
|
|
(lset-xor eq?) => ()
|
|
(lset-xor eq? '(a b c d e)) => (a b c d e)
|
|
</pre>
|
|
|
|
|
|
<!--
|
|
==== lset-diff+intersection
|
|
============================================================================-->
|
|
<dt class=proc-def>
|
|
<a name="lset-diff+intersection"></a>
|
|
<code class=proc-def>lset-diff+intersection</code><var> = list<sub>1</sub> list<sub>2</sub> ... -> [list list]</var>
|
|
<dd class=proc-def>
|
|
Returns two values -- the difference and the intersection of the lists.
|
|
Is equivalent to
|
|
<pre class=code-example>
|
|
(values (lset-difference <var>=</var> <var>list<sub>1</sub></var> <var>list<sub>2</sub></var> ...)
|
|
(lset-intersection <var>=</var> <var>list<sub>1</sub></var>
|
|
(lset-union <var>=</var> <var>list<sub>2</sub></var> ...)))
|
|
</pre>
|
|
but can be implemented more efficiently.
|
|
<p>
|
|
The <var>=</var> procedure's first argument is an element of <var>list<sub>1</sub></var>; its second
|
|
is an element of one of the other <var>list<sub>i</sub></var>.
|
|
<p>
|
|
Either of the answer lists may share a
|
|
common tail with <var>list<sub>1</sub></var>.
|
|
This operation essentially partitions <var>list<sub>1</sub></var>.
|
|
|
|
<!--
|
|
==== lset-diff+intersection!
|
|
==== lset-xor!
|
|
==== lset-difference!
|
|
==== lset-intersection!
|
|
==== lset-union!
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="lset-union!"></a>
|
|
<code class=proc-def>lset-union! </code><var>= list<sub>1</sub> ... -> list</var>
|
|
<dt class=proc-defi>
|
|
<a name="lset-intersection!"></a>
|
|
<code class=proc-def>lset-intersection! </code><var>= list<sub>1</sub> list<sub>2</sub> ... -> list</var>
|
|
<dt class=proc-defi>
|
|
<a name="lset-difference!"></a>
|
|
<code class=proc-def>lset-difference! </code><var>= list<sub>1</sub> list<sub>2</sub> ... -> list</var>
|
|
<dt class=proc-defi>
|
|
<a name="lset-xor!"></a>
|
|
<code class=proc-def>lset-xor! </code><var>= list<sub>1</sub> ... -> list</var>
|
|
<dt class=proc-defn>
|
|
<a name="lset-diff+intersection!"></a>
|
|
<code class=proc-def>lset-diff+intersection! </code><var>= list<sub>1</sub> list<sub>2</sub> ... -> [list list]</var>
|
|
<dd class=proc-def>
|
|
These are linear-update variants. They are allowed, but not required,
|
|
to use the cons cells in their first list parameter to construct their
|
|
answer. <code>lset-union!</code> is permitted to recycle cons cells from <em>any</em>
|
|
of its list arguments.
|
|
</dl>
|
|
|
|
<!--========================================================================-->
|
|
<h2><a name="PrimitiveSideEffects">Primitive side-effects</a></h2>
|
|
<p>
|
|
These two procedures are the primitive,
|
|
<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>
|
|
side-effect operations on pairs.
|
|
|
|
<dl>
|
|
<!--
|
|
==== set-car!
|
|
============================================================================-->
|
|
<dt class=proc-def1>
|
|
<a name="set-car!"></a>
|
|
<code class=proc-def>set-car!</code><var> pair object -> unspecified</var>
|
|
<dt class=proc-defn>
|
|
<a name="set-cdr!"></a>
|
|
<code class=proc-def>set-cdr!</code><var> pair object -> unspecified</var>
|
|
<dd class=proc-def>
|
|
[<abbr title="Revised^5 Report on Scheme"><a href="#R5RS">R5RS</a></abbr>]
|
|
These procedures store <var>object</var> in the car and cdr field
|
|
of <var>pair</var>, respectively.
|
|
The value returned is unspecified.
|
|
<pre class=code-example>
|
|
(define (f) (list 'not-a-constant-list))
|
|
(define (g) '(constant-list))
|
|
(set-car! (f) 3) => *unspecified*
|
|
(set-car! (g) 3) => *error*
|
|
</pre>
|
|
</dl>
|
|
|
|
<!--========================================================================-->
|
|
<h1><a name="Acknowledgements">Acknowledgements</a></h1>
|
|
<p>
|
|
The design of this library benefited greatly from the feedback provided during
|
|
the <abbr title="Scheme Request for Implementation">SRFI</abbr> discussion phase. Among those contributing thoughtful commentary and
|
|
suggestions, both on the mailing list and by private discussion, were Mike
|
|
Ashley, Darius Bacon, Alan Bawden, Phil Bewig, Jim Blandy, Dan Bornstein, Per
|
|
Bothner, Anthony Carrico, Doug Currie, Kent Dybvig, Sergei Egorov, Doug Evans,
|
|
Marc Feeley, Matthias Felleisen, Will Fitzgerald, Matthew Flatt, Dan Friedman,
|
|
Lars Thomas Hansen, Brian Harvey, Erik Hilsdale, Wolfgang Hukriede, Richard
|
|
Kelsey, Donovan Kolbly, Shriram Krishnamurthi, Dave Mason, Jussi Piitulainen,
|
|
David Pokorny, Duncan Smith, Mike Sperber, Maciej Stachowiak, Harvey J. Stein,
|
|
John David Stone, and Joerg F. Wittenberger. I am grateful to them for their
|
|
assistance.
|
|
<p>
|
|
I am also grateful the authors, implementors and documentors of all the systems
|
|
mentioned in the introduction. Aubrey Jaffer and Kent Pitman should be noted
|
|
for their work in producing Web-accessible versions of the R5RS and
|
|
<a href="#CommonLisp">Common Lisp</a> spec, which was a tremendous aid.
|
|
<p>
|
|
This is not to imply that these individuals necessarily endorse the final
|
|
results, of course.
|
|
|
|
|
|
<!--========================================================================-->
|
|
<h1><a name="ReferencesLinks">References & links</a></h1>
|
|
<p>
|
|
|
|
<dl>
|
|
<dt class=biblio>This document, in HTML:
|
|
<dd><a href="http://srfi.schemers.org/srfi-1/srfi-1.html">
|
|
http://srfi.schemers.org/srfi-1/srfi-1.html</a>
|
|
|
|
<br><a class=draft
|
|
href="ftp://ftp.ai.mit.edu/people/shivers/srfi/srfi-1/srfi-1.html">
|
|
ftp://ftp.ai.mit.edu/people/shivers/srfi/srfi-1/srfi-1.html (draft)</a>
|
|
|
|
<dt class=biblio>This document, in simple text format:
|
|
<dd><a href="http://srfi.schemers.org/srfi-1/srfi-1.txt">
|
|
http://srfi.schemers.org/srfi-1/srfi-1.txt</a>
|
|
|
|
<br><a class=draft
|
|
href="ftp://ftp.ai.mit.edu/people/shivers/srfi/srfi-1/srfi-1.txt">
|
|
ftp://ftp.ai.mit.edu/people/shivers/srfi/srfi-1/srfi-1.txt (draft)</a>
|
|
|
|
<dt class=biblio>Source code for the reference implementation:
|
|
<dd><a HREF="http://srfi.schemers.org/srfi-1/srfi-1-reference.scm">
|
|
http://srfi.schemers.org/srfi-1/srfi-1-reference.scm</a>
|
|
|
|
<br><a class=draft
|
|
href="ftp://ftp.ai.mit.edu/people/shivers/srfi/srfi-1/srfi-1-reference.scm">
|
|
ftp://ftp.ai.mit.edu/people/shivers/srfi/srfi-1/srfi-1-reference.scm (draft)</a>
|
|
|
|
<dt class=biblio>Archive of SRFI-1 discussion-list email:
|
|
<dd><a href="http://srfi.schemers.org/srfi-1/mail-archive/maillist.html">
|
|
http://srfi.schemers.org/srfi-1/mail-archive/maillist.html</a>
|
|
|
|
<dt class=biblio>SRFI web site:
|
|
<dd><a href="http://srfi.schemers.org/">
|
|
http://srfi.schemers.org/</a>
|
|
</dl>
|
|
|
|
<p>
|
|
|
|
<dl>
|
|
<dt class=biblio><strong><a name="CommonLisp">[CommonLisp]</a></strong></dt>
|
|
<dd><em>Common Lisp: the Language</em><br>
|
|
Guy L. Steele Jr. (editor).<br>
|
|
Digital Press, Maynard, Mass., second edition 1990.<br>
|
|
Available at <a href="http://www.elwood.com/alu/table/references.htm#cltl2">
|
|
http://www.elwood.com/alu/table/references.htm#cltl2</a>.
|
|
<p>
|
|
|
|
The Common Lisp "HyperSpec," produced by Kent Pitman, is essentially
|
|
the ANSI spec for Common Lisp:
|
|
<a href="http://www.harlequin.com/education/books/HyperSpec/">
|
|
http://www.harlequin.com/education/books/HyperSpec/</a>.
|
|
|
|
<dt class=biblio><strong><a name="R5RS">[R5RS]</a></strong></dt>
|
|
<dd>Revised<sup>5</sup> report on the algorithmic language Scheme.<br>
|
|
R. Kelsey, W. Clinger, J. Rees (editors). <br>
|
|
Higher-Order and Symbolic Computation, Vol. 11, No. 1, September, 1998. <br>
|
|
and ACM SIGPLAN Notices, Vol. 33, No. 9, October, 1998. <br>
|
|
Available at <a href="http://www.schemers.org/Documents/Standards/">
|
|
http://www.schemers.org/Documents/Standards/</a>.
|
|
|
|
</dl>
|
|
|
|
|
|
|
|
<!--========================================================================-->
|
|
<h1><a name="Copyright">Copyright</a></h1>
|
|
<p>
|
|
|
|
Certain portions of this document -- the specific, marked segments of text
|
|
describing the R5RS procedures -- were adapted with permission from the R5RS
|
|
report.
|
|
<p>
|
|
|
|
All other text is copyright (C) Olin Shivers (1998, 1999).
|
|
All Rights Reserved.
|
|
<p>
|
|
This document and translations of it may be copied and furnished to
|
|
others, and derivative works that comment on or otherwise explain it
|
|
or assist in its implementation may be prepared, copied, published and
|
|
distributed, in whole or in part, without restriction of any kind,
|
|
provided that the above copyright notice and this paragraph are
|
|
included on all such copies and derivative works. However, this
|
|
document itself may not be modified in any way, such as by removing
|
|
the copyright notice or references to the Scheme Request For
|
|
Implementation process or editors, except as needed for the purpose of
|
|
developing <abbr title="Scheme Request for Implementation">SRFI</abbr>s in which case the procedures for copyrights defined
|
|
in the <abbr title="Scheme Request for Implementation">SRFI</abbr> process must be followed, or as required to translate it
|
|
into languages other than English.
|
|
<p>
|
|
The limited permissions granted above are perpetual and will not be
|
|
revoked by the authors or their successors or assigns.
|
|
<p>
|
|
This document and the information contained herein is provided on an
|
|
"AS IS" basis and THE AUTHOR AND THE <abbr title="Scheme Request for Implementation">SRFI</abbr> EDITORS DISCLAIM ALL
|
|
WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY
|
|
WARRANTY THAT THE USE OF THE INFORMATION HEREIN WILL NOT INFRINGE ANY
|
|
RIGHTS OR ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
|
|
PARTICULAR PURPOSE.
|
|
|
|
</body>
|
|
</html>
|