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<tr><td align="center" bgcolor="#8381de"><div class="skribetitle"><strong><big><big><big>7. R5Rs<br/>Scheme Revised(5) Report on the Algorithmic Language Scheme -- Formal syntax and semantics</big></big></big></strong></div><center>
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>Formal syntax and semantics</strong></font></th></tr>
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<tr><td valign="top" align="left">7.1</td><td colspan="4" width="100%"><a href="r5rs-10.html#Formal-syntax">Formal syntax</a></td></tr>
<tr><td></td><td valign="top" align="left">7.1.1</td><td colspan="3" width="100%"><a href="r5rs-10.html#Lexical-structure">Lexical structure</a></td></tr>
<tr><td></td><td valign="top" align="left">7.1.2</td><td colspan="3" width="100%"><a href="r5rs-10.html#External-representations">External representations</a></td></tr>
<tr><td></td><td valign="top" align="left">7.1.3</td><td colspan="3" width="100%"><a href="r5rs-10.html#Expressions">Expressions</a></td></tr>
<tr><td></td><td valign="top" align="left">7.1.4</td><td colspan="3" width="100%"><a href="r5rs-10.html#Quasiquotations">Quasiquotations</a></td></tr>
<tr><td></td><td valign="top" align="left">7.1.5</td><td colspan="3" width="100%"><a href="r5rs-10.html#Transformers">Transformers</a></td></tr>
<tr><td></td><td valign="top" align="left">7.1.6</td><td colspan="3" width="100%"><a href="r5rs-10.html#Programs-and-definitions">Programs and definitions</a></td></tr>
<tr><td valign="top" align="left">7.2</td><td colspan="4" width="100%"><a href="r5rs-10.html#Formal-semantics">Formal semantics</a></td></tr>
<tr><td valign="top" align="left">7.3</td><td colspan="4" width="100%"><a href="r5rs-10.html#Derived-expression-types">Derived expression types</a></td></tr>
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>Chapters</strong></font></th></tr>
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<tr><td valign="top" align="left"></td><td colspan="4" width="100%"><a href="r5rs-1.html#Summary">Summary</a></td></tr>
<tr><td valign="top" align="left"></td><td colspan="4" width="100%"><a href="r5rs-2.html#Introduction">Introduction</a></td></tr>
<tr><td valign="top" align="left"></td><td colspan="4" width="100%"><a href="r5rs-3.html#Table-of-contents">Table of contents</a></td></tr>
<tr><td valign="top" align="left">1</td><td colspan="4" width="100%"><a href="r5rs-4.html#Overview-of-Scheme">Overview of Scheme</a></td></tr>
<tr><td valign="top" align="left">2</td><td colspan="4" width="100%"><a href="r5rs-5.html#Lexical-conventions">Lexical conventions</a></td></tr>
<tr><td valign="top" align="left">3</td><td colspan="4" width="100%"><a href="r5rs-6.html#Basic-concepts">Basic concepts</a></td></tr>
<tr><td valign="top" align="left">4</td><td colspan="4" width="100%"><a href="r5rs-7.html#Expressions">Expressions</a></td></tr>
<tr><td valign="top" align="left">5</td><td colspan="4" width="100%"><a href="r5rs-8.html#Program-structure">Program structure</a></td></tr>
<tr><td valign="top" align="left">6</td><td colspan="4" width="100%"><a href="r5rs-9.html#Standard-procedures">Standard procedures</a></td></tr>
<tr><td valign="top" align="left">7</td><td colspan="4" width="100%"><a href="r5rs-10.html#Formal-syntax-and-semantics">Formal syntax and semantics</a></td></tr>
<tr><td valign="top" align="left">8</td><td colspan="4" width="100%"><a href="r5rs-11.html#Concepts">Concepts</a></td></tr>
<tr><td valign="top" align="left">9</td><td colspan="4" width="100%"><a href="r5rs-12.html#Variables-and-Procedures">Variables and Procedures</a></td></tr>
<tr><td valign="top" align="left"></td><td colspan="4" width="100%"><a href="r5rs-13.html#Notes">Notes</a></td></tr>
<tr><td valign="top" align="left"></td><td colspan="4" width="100%"><a href="r5rs-14.html#Additional-material">Additional material</a></td></tr>
<tr><td valign="top" align="left"></td><td colspan="4" width="100%"><a href="r5rs-15.html#Example">Example</a></td></tr>
<tr><td valign="top" align="left"></td><td colspan="4" width="100%"><a href="r5rs-16.html#Bibliography">Bibliography</a></td></tr>
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<td align="left" valign="top" class="skribe-body"><div class="skribe-body">
<a name="Formal-syntax-and-semantics" class="mark"></a>
This chapter provides formal descriptions of what has already been
described informally in previous chapters of this report.<br/><br/>
<!-- Formal syntax -->
<a name="Formal-syntax"></a>
<div class="section-atitle"><table width="100%"><tr><td bgcolor="#dedeff"><h3><font color="black">7.1 Formal syntax</font>
</h3></td></tr></table>
</div><div class="section">
<a name="Formal-syntax" class="mark"></a>
This section provides a formal syntax for Scheme written in an extended
BNF.<br/><br/>All spaces in the grammar are for legibility. Case is insignificant;
for example, <samp id='samp6767'
>#x1A</samp> and <samp id='samp6768'
>#X1a</samp> are equivalent. <empty>
stands for the empty string.<br/><br/>The following extensions to BNF are used to make the description more
concise: <thing>* means zero or more occurrences of
<thing>; and <thing>+ means at least one
<thing>.<br/><br/><!-- Lexical structure -->
<a name="Lexical-structure"></a>
<div class="subsection-atitle"><table width="100%"><tr><td bgcolor="#ffffff"><h3><font color="#8381de">7.1.1 Lexical structure</font>
</h3></td></tr></table>
</div><div class="subsection">
<a name="Lexical-structure" class="mark"></a>
This section describes how individual tokens (identifiers,
<a name="g6772" class="mark"></a>numbers, etc.) are formed from sequences of characters. The following
sections describe how expressions and programs are formed from sequences
of tokens.<br/><br/><Intertoken space> may occur on either side of any token, but not
within a token.<br/><br/>Tokens which require implicit termination (identifiers, numbers,
characters, and dot) may be terminated by any <delimiter>, but not
necessarily by anything else.<br/><br/>The following five characters are reserved for future extensions to the
language: <tt id='tt6777'
>[ ] { } |</tt><br/><br/><br/><center id='center6792'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ccccff"><pre class="prog" id='prog6790'
><tt id='tt6788'
><token> --> <identifier> | <boolean> | <number>
<a name="g6780" class="mark"></a> | <character> | <string>
| ( | ) | #( | <tt id='tt6782'
>'</tt> | <tt id='tt6783'
>`</tt> | , | ,@ | <strong id='bold6784'
>.</strong>
<delimiter> --> <whitespace> | ( | ) | " | ;
<whitespace> --> <space or newline>
<comment> --> ; <all subsequent characters up to a
line break>
<a name="g6786" class="mark"></a><atmosphere> --> <whitespace> | <comment>
<intertoken space> --> <atmosphere>*</tt><br/><br/>
</pre>
</td></tr>
</tbody></table></center>
<center id='center6811'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ccccff"><pre class="prog" id='prog6809'
><tt id='tt6808'
><identifier> --> <initial> <subsequent>*
| <peculiar identifier>
<initial> --> <letter> | <special initial>
<letter> --> a | b | c | ... | z<br/><br/><special initial> --> ! | $ | % | & | * | / | : | < | =
| > | ? | ^ | _ | ~
<subsequent> --> <initial> | <digit>
| <special subsequent>
<digit> --> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
<special subsequent> --> + | - | .: | @
<peculiar identifier> --> + | - | ...
<syntactic keyword> --> <expression keyword>
<a name="g6795" class="mark"></a><a name="g6798" class="mark"></a> | else | => | define
| unquote | unquote-splicing
<expression keyword> --> quote | lambda | if
| set! | begin | cond | and | or | case
| let | let* | letrec | do | delay
| quasiquote<br/><br/><strong id='bold6802'
><samp id='samp6801'
><variable> => <</samp></strong>any <identifier> that isn't
<a name="g6804" class="mark"></a> <strong id='bold6806'
> also a <syntactic keyword>></strong><br/><br/><boolean> --> #t | #f
<character> --> #\ <any character>
| #\ <character name>
<character name> --> space | newline
<string> --> " <string element>* "
<string element> --> <any character other than " or \>
| \" | \\ </tt>
</pre>
</td></tr>
</tbody></table></center>
<center id='center6815'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ccccff"><pre class="prog" id='prog6813'
><tt id='tt6812'
><number> --> <num 2>| <num 8>
| <num 10>| <num 16>
</tt>
</pre>
</td></tr>
</tbody></table></center>
The following rules for <num R>, <complex R>, <real
R>, <ureal R>, <uinteger R>, and <prefix R>
should be replicated for <strong id='bold6816'
>R = 2, 8, 10,</strong>
and 16. There are no rules for <decimal 2>, <decimal
8>, and <decimal 16>, which means that numbers containing
decimal points or exponents must be in decimal radix.
<center id='center6820'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ccccff"><pre class="prog" id='prog6818'
><tt id='tt6817'
><num R> --> <prefix R> <complex R>
<complex R> --> <real R> | <real R> @ <real R>
| <real R> + <ureal R> i | <real R> - <ureal R> i
| <real R> + i | <real R> - i
| + <ureal R> i | - <ureal R> i | + i | - i
<real R> --> <sign> <ureal R>
<ureal R> --> <uinteger R>
| <uinteger R> / <uinteger R>
| <decimal R>
<decimal 10> --> <uinteger 10> <suffix>
| . <digit 10>+ #* <suffix>
| <digit 10>+ . <digit 10>* #* <suffix>
| <digit 10>+ #+ . #* <suffix>
<uinteger R> --> <digit R>+ #*
<prefix R> --> <radix R> <exactness>
| <exactness> <radix R>
</tt>
</pre>
</td></tr>
</tbody></table></center>
<center id='center6834'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ccccff"><pre class="prog" id='prog6832'
><tt id='tt6831'
><suffix> --> <empty>
| <exponent marker> <sign> <digit 10>+
<exponent marker> --> e | s | f | d | l
<sign> --> <empty> | + | -
<exactness> --> <empty> | #i | #e
<a name="g6821" class="mark"></a><a name="g6823" class="mark"></a><radix 2> --> #b
<a name="g6825" class="mark"></a><radix 8> --> #o
<a name="g6827" class="mark"></a><radix 10> --> <empty> | #d
<radix 16> --> #x
<a name="g6829" class="mark"></a><digit 2> --> 0 | 1
<digit 8> --> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7
<digit 10> --> <digit>
<digit 16> --> <digit 10> | a | b | c | d | e | f </tt>
</pre>
</td></tr>
</tbody></table></center>
</div>
<!-- External representations -->
<a name="External-representations"></a>
<div class="subsection-atitle"><table width="100%"><tr><td bgcolor="#ffffff"><h3><font color="#8381de">7.1.2 External representations</font>
</h3></td></tr></table>
</div><div class="subsection">
<a name="External-representation" class="mark"></a>
<Datum> is what the <code id='code6835'
>read</code> procedure (section <a href="r5rs-9.html#Input" class="inbound">Input</a>)
<a name="g6837" class="mark"></a>successfully parses. Note that any string that parses as an
<expression> will also parse as a <datum>. <br/><br/><center id='center6843'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ccccff"><pre class="prog" id='prog6841'
><tt id='tt6840'
><datum> --> <simple datum> | <compound datum>
<simple datum> --> <boolean> | <number>
| <character> | <string> | <symbol>
<symbol> --> <identifier>
<compound datum> --> <list> | <vector>
<list> --> (<datum>*) | (<datum>+ .: <datum>)
| <abbreviation>
<abbreviation> --> <abbrev prefix> <datum>
<abbrev prefix> --> ' | ` | , | ,@
<vector> --> #(<datum>*) </tt>
</pre>
</td></tr>
</tbody></table></center>
</div>
<!-- Expressions -->
<a name="Expressions"></a>
<div class="subsection-atitle"><table width="100%"><tr><td bgcolor="#ffffff"><h3><font color="#8381de">7.1.3 Expressions</font>
</h3></td></tr></table>
</div><div class="subsection">
<a name="Expression" class="mark"></a>
<center id='center6856'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ccccff"><pre class="prog" id='prog6854'
><tt id='tt6853'
><expression> --> <variable>
| <literal>
| <procedure call>
| <lambda expression>
| <conditional>
| <assignment>
| <derived expression>
| <macro use>
| <macro block><br/><br/><literal> --> <quotation> | <self-evaluating>
<self-evaluating> --> <boolean> | <number>
| <character> | <string>
<quotation> --> '<datum> | (quote <datum>)
<procedure call> --> (<operator> <operand>*)
<operator> --> <expression>
<operand> --> <expression><br/><br/><lambda expression> --> (lambda <formals> <body>)
<formals> --> (<variable>*) | <variable>
| (<variable>+ .: <variable>)
<body> --> <definition>* <sequence>
<sequence> --> <command>* <expression>
<command> --> <expression><br/><br/><conditional> --> (if <test> <consequent> <alternate>)
<test> --> <expression>
<consequent> --> <expression>
<alternate> --> <expression> | <empty><br/><br/><assignment> --> (set! <variable> <expression>)<br/><br/><derived expression> -->
(cond <cond clause>+)
| (cond <cond clause>* (else <sequence>))
| (case <expression>
<case clause>+)
| (case <expression>
<case clause>*
(else <sequence>))
| (and <test>*)
| (or <test>*)
| (let (<binding spec>*) <body>)
| (let <variable> (<binding spec>*) <body>)
| (let* (<binding spec>*) <body>)
| (letrec (<binding spec>*) <body>)
| (begin <sequence>)
| (do (<iteration spec>*)
(<test> <do result>)
<command>*)
| (delay <expression>)
| <quasiquotation><br/><br/><cond clause> --> (<test> <sequence>)
| (<test>)
| (<test> => <recipient>)
<recipient> --> <expression>
<case clause> --> ((<datum>*) <sequence>)
<binding spec> --> (<variable> <expression>)
<iteration spec> --> (<variable> <init> <step>)
| (<variable> <init>)
<init> --> <expression>
<step> --> <expression>
<do result> --> <sequence> | <empty><br/><br/><macro use> --> (<keyword> <datum>*)
<keyword> --> <identifier><br/><br/><macro block> -->
(let-syntax (<syntax spec>*) <body>)
| (letrec-syntax (<syntax spec>*) <body>)
<syntax spec> --> (<keyword> <transformer spec>)<br/><br/></tt>
</pre>
</td></tr>
</tbody></table></center>
</div>
<!-- Quasiquotations -->
<a name="Quasiquotations"></a>
<div class="subsection-atitle"><table width="100%"><tr><td bgcolor="#ffffff"><h3><font color="#8381de">7.1.4 Quasiquotations</font>
</h3></td></tr></table>
</div><div class="subsection">
<a name="Quasiquotations" class="mark"></a>
The following grammar for quasiquote expressions is not context-free.
It is presented as a recipe for generating an infinite number of
production rules. Imagine a copy of the following rules for D = 1, 2,3, .... D keeps track of the nesting depth.<br/><br/><center id='center6861'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ccccff"><pre class="prog" id='prog6859'
><tt id='tt6858'
><quasiquotation> --> <quasiquotation 1>
<qq template 0> --> <expression>
<quasiquotation D> --> `<qq template D>
| (quasiquote <qq template D>)
<qq template D> --> <simple datum>
| <list qq template D>
| <vector qq template D>
| <unquotation D>
<list qq template D> --> (<qq template or splice D>*)
| (<qq template or splice D>+ .: <qq template D>)
| '<qq template D>
| <quasiquotation D+1>
<vector qq template D> --> #(<qq template or splice D>*)
<unquotation D> --> ,<qq template D-1>
| (unquote <qq template D-1>)
<qq template or splice D> --> <qq template D>
| <splicing unquotation D>
<splicing unquotation D> --> ,@<qq template D-1>
| (unquote-splicing <qq template D-1>) </tt>
</pre>
</td></tr>
</tbody></table></center>
In <quasiquotation>s, a <list qq template D> can sometimes
be confused with either an <unquotation D> or a <splicing
unquotation D>. The interpretation as an
<unquotation> or <splicing
unquotation D> takes precedence.<br/><br/></div>
<!-- Transformers -->
<a name="Transformers"></a>
<div class="subsection-atitle"><table width="100%"><tr><td bgcolor="#ffffff"><h3><font color="#8381de">7.1.5 Transformers</font>
</h3></td></tr></table>
</div><div class="subsection">
<a name="Transformers" class="mark"></a>
<center id='center6868'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ccccff"><pre class="prog" id='prog6866'
><tt id='tt6865'
><transformer spec> -->
(syntax-rules (<identifier>*) <syntax rule>*)
<syntax rule> --> (<pattern> <template>)
<pattern> --> <pattern identifier>
| (<pattern>*)
| (<pattern>+ . <pattern>)
| (<pattern>* <pattern> <ellipsis>)
| #(<pattern>*)
| #(<pattern>* <pattern> <ellipsis>)
| <pattern datum>
<pattern datum> --> <string>
| <character>
| <boolean>
| <number>
<template> --> <pattern identifier>
| (<template element>*)
| (<template element>+ . <template>)
| #(<template element>*)
| <template datum>
<template element> --> <template>
| <template> <ellipsis>
<template datum> --> <pattern datum>
<pattern identifier> --> <any identifier except <samp id='samp6863'
>...</samp>>
<ellipsis> --> <the identifier <samp id='samp6864'
>...</samp>>
</tt>
</pre>
</td></tr>
</tbody></table></center>
</div>
<!-- Programs and definitions -->
<a name="Programs-and-definitions"></a>
<div class="subsection-atitle"><table width="100%"><tr><td bgcolor="#ffffff"><h3><font color="#8381de">7.1.6 Programs and definitions</font>
</h3></td></tr></table>
</div><div class="subsection">
<a name="Programs-and-definitions" class="mark"></a>
<center id='center6872'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ccccff"><pre class="prog" id='prog6870'
><tt id='tt6869'
><program> --> <command or definition>*
<command or definition> --> <command>
| <definition>
| <syntax definition>
| (begin <command or definition>+)
<definition> --> (define <variable> <expression>)
| (define (<variable> <def formals>) <body>)
| (begin <definition>*)
<def formals> --> <variable>*
| <variable>* .: <variable>
<syntax definition> -->
(define-syntax <keyword> <transformer spec>)
</tt>
</pre>
</td></tr>
</tbody></table></center>
</div>
</div><br>
<!-- Formal semantics -->
<a name="Formal-semantics"></a>
<div class="section-atitle"><table width="100%"><tr><td bgcolor="#dedeff"><h3><font color="black">7.2 Formal semantics</font>
</h3></td></tr></table>
</div><div class="section">
<a name="Formal-semantics" class="mark"></a>
This section provides a formal denotational semantics for the primitive
expressions of Scheme and selected built-in procedures. The concepts
and notation used here are described in <span class="sc">[Stoy77]</span>.<br/><br/><font size="-1"><em id='emph6875'
>Note:</em> The formal semantics section was written in LaTeX which
is incompatible with TeXinfo. See the Formal semantics section of
the original document from which this was derived.
</font>
</div><br>
<!-- Derived expression types -->
<a name="Derived-expression-types"></a>
<div class="section-atitle"><table width="100%"><tr><td bgcolor="#dedeff"><h3><font color="black">7.3 Derived expression types</font>
</h3></td></tr></table>
</div><div class="section">
<a name="Derived-expression-type" class="mark"></a>
This section gives macro definitions for the derived expression types in
terms of the primitive expression types (literal, variable, call, <samp id='samp6877'
>lambda</samp>,
<samp id='samp6878'
>if</samp>, <samp id='samp6879'
>set!</samp>). See section <a href="r5rs-9.html#Control-features" class="inbound">Control features</a> for a possible
definition of <samp id='samp6880'
>delay</samp>.<br/><br/><center id='center6907'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ffffcc"><pre class="prog" id='prog6905'
>(<font color="#6959cf"><strong id='bold8175'
>define-syntax</strong></font> <font color="#6959cf"><strong id='bold8177'
>cond</strong></font>
(<strong id='bold8179'
>syntax-rules</strong> (else =>)
((<strong id='bold8180'
>cond</strong> (else result1 result2 ...))
(<strong id='bold8181'
>begin</strong> result1 result2 ...))
((<strong id='bold8182'
>cond</strong> (test => result))
(<strong id='bold8183'
>let</strong> ((temp test))
(<strong id='bold8184'
>if</strong> temp (result temp))))
((<strong id='bold8185'
>cond</strong> (test => result) clause1 clause2 ...)
(<strong id='bold8186'
>let</strong> ((temp test))
(<strong id='bold8187'
>if</strong> temp
(result temp)
(<strong id='bold8188'
>cond</strong> clause1 clause2 ...))))
((<strong id='bold8189'
>cond</strong> (test)) test)
((<strong id='bold8190'
>cond</strong> (test) clause1 clause2 ...)
(<strong id='bold8191'
>let</strong> ((temp test))
(<strong id='bold8192'
>if</strong> temp
temp
(<strong id='bold8193'
>cond</strong> clause1 clause2 ...))))
((<strong id='bold8194'
>cond</strong> (test result1 result2 ...))
(<strong id='bold8195'
>if</strong> test (<strong id='bold8196'
>begin</strong> result1 result2 ...)))
((<strong id='bold8197'
>cond</strong> (test result1 result2 ...)
clause1 clause2 ...)
(<strong id='bold8198'
>if</strong> test
(<strong id='bold8199'
>begin</strong> result1 result2 ...)
(<strong id='bold8200'
>cond</strong> clause1 clause2 ...)))))
</pre>
</td></tr>
</tbody></table></center>
<center id='center6924'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ffffcc"><pre class="prog" id='prog6922'
>(<font color="#6959cf"><strong id='bold8201'
>define-syntax</strong></font> <font color="#6959cf"><strong id='bold8203'
>case</strong></font>
(<strong id='bold8205'
>syntax-rules</strong> (else)
((<strong id='bold8206'
>case</strong> (key ...)
clauses ...)
(<strong id='bold8207'
>let</strong> ((atom-key (key ...)))
(<strong id='bold8208'
>case</strong> atom-key clauses ...)))
((<strong id='bold8209'
>case</strong> key
(else result1 result2 ...))
(<strong id='bold8210'
>begin</strong> result1 result2 ...))
((<strong id='bold8211'
>case</strong> key
((atoms ...) result1 result2 ...))
(<strong id='bold8212'
>if</strong> (memv key '(atoms ...))
(<strong id='bold8213'
>begin</strong> result1 result2 ...)))
((<strong id='bold8214'
>case</strong> key
((atoms ...) result1 result2 ...)
clause clauses ...)
(<strong id='bold8215'
>if</strong> (memv key '(atoms ...))
(<strong id='bold8216'
>begin</strong> result1 result2 ...)
(<strong id='bold8217'
>case</strong> key clause clauses ...)))))
</pre>
</td></tr>
</tbody></table></center>
<center id='center6930'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ffffcc"><pre class="prog" id='prog6928'
>(<font color="#6959cf"><strong id='bold8218'
>define-syntax</strong></font> <font color="#6959cf"><strong id='bold8220'
>and</strong></font>
(<strong id='bold8222'
>syntax-rules</strong> ()
((and) #t)
((and test) test)
((and test1 test2 ...)
(<strong id='bold8223'
>if</strong> test1 (and test2 ...) #f))))
</pre>
</td></tr>
</tbody></table></center>
<center id='center6937'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ffffcc"><pre class="prog" id='prog6935'
>(<font color="#6959cf"><strong id='bold8224'
>define-syntax</strong></font> <font color="#6959cf"><strong id='bold8226'
>or</strong></font>
(<strong id='bold8228'
>syntax-rules</strong> ()
((or) #f)
((or test) test)
((or test1 test2 ...)
(<strong id='bold8229'
>let</strong> ((x test1))
(<strong id='bold8230'
>if</strong> x x (or test2 ...))))))
</pre>
</td></tr>
</tbody></table></center>
<center id='center6947'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ffffcc"><pre class="prog" id='prog6945'
>(<font color="#6959cf"><strong id='bold8231'
>define-syntax</strong></font> <font color="#6959cf"><strong id='bold8233'
>let</strong></font>
(<strong id='bold8235'
>syntax-rules</strong> ()
((<strong id='bold8236'
>let</strong> ((name val) ...) body1 body2 ...)
((<strong id='bold8237'
>lambda</strong> (name ...) body1 body2 ...)
val ...))
((<strong id='bold8238'
>let</strong> tag ((name val) ...) body1 body2 ...)
((<strong id='bold8239'
>letrec</strong> ((tag (<strong id='bold8240'
>lambda</strong> (name ...)
body1 body2 ...)))
tag)
val ...))))
</pre>
</td></tr>
</tbody></table></center>
<center id='center6957'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ffffcc"><pre class="prog" id='prog6955'
>(<font color="#6959cf"><strong id='bold8241'
>define-syntax</strong></font> <font color="#6959cf"><strong id='bold8243'
>let*</strong></font>
(<strong id='bold8245'
>syntax-rules</strong> ()
((<strong id='bold8246'
>let*</strong> () body1 body2 ...)
(<strong id='bold8247'
>let</strong> () body1 body2 ...))
((<strong id='bold8248'
>let*</strong> ((name1 val1) (name2 val2) ...)
body1 body2 ...)
(<strong id='bold8249'
>let</strong> ((name1 val1))
(<strong id='bold8250'
>let*</strong> ((name2 val2) ...)
body1 body2 ...)))))
</pre>
</td></tr>
</tbody></table></center>
The following <samp id='samp6958'
>letrec</samp> macro uses the symbol <samp id='samp6959'
><undefined></samp>
in place of an expression which returns something that when stored in
a location makes it an error to try to obtain the value stored in the
location (no such expression is defined in Scheme).
A trick is used to generate the temporary names needed to avoid
specifying the order in which the values are evaluated.
This could also be accomplished by using an auxiliary macro.<br/><br/><center id='center6977'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ffffcc"><pre class="prog" id='prog6975'
>(<font color="#6959cf"><strong id='bold8251'
>define-syntax</strong></font> <font color="#6959cf"><strong id='bold8253'
>letrec</strong></font>
(<strong id='bold8255'
>syntax-rules</strong> ()
((<strong id='bold8256'
>letrec</strong> ((var1 init1) ...) body ...)
(<strong id='bold8257'
>letrec</strong> <font color="red">"generate temp names"</font>
(var1 ...)
()
((var1 init1) ...)
body ...))
((<strong id='bold8259'
>letrec</strong> <font color="red">"generate temp names"</font>
()
(temp1 ...)
((var1 init1) ...)
body ...)
(<strong id='bold8261'
>let</strong> ((var1 <undefined>) ...)
(<strong id='bold8262'
>let</strong> ((temp1 init1) ...)
(<strong id='bold8263'
>set!</strong> var1 temp1)
...
body ...)))
((<strong id='bold8264'
>letrec</strong> <font color="red">"generate temp names"</font>
(x y ...)
(temp ...)
((var1 init1) ...)
body ...)
(<strong id='bold8266'
>letrec</strong> <font color="red">"generate temp names"</font>
(y ...)
(newtemp temp ...)
((var1 init1) ...)
body ...))))
</pre>
</td></tr>
</tbody></table></center>
<center id='center6984'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ffffcc"><pre class="prog" id='prog6982'
>(<font color="#6959cf"><strong id='bold8268'
>define-syntax</strong></font> <font color="#6959cf"><strong id='bold8270'
>begin</strong></font>
(<strong id='bold8272'
>syntax-rules</strong> ()
((<strong id='bold8273'
>begin</strong> exp ...)
((<strong id='bold8274'
>lambda</strong> () exp ...)))))
</pre>
</td></tr>
</tbody></table></center>
The following alternative expansion for <samp id='samp6985'
>begin</samp> does not make use of
the ability to write more than one expression in the body of a lambda
expression. In any case, note that these rules apply only if the body
of the <samp id='samp6986'
>begin</samp> contains no definitions.<br/><br/><center id='center6996'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ffffcc"><pre class="prog" id='prog6994'
>(<font color="#6959cf"><strong id='bold8275'
>define-syntax</strong></font> <font color="#6959cf"><strong id='bold8277'
>begin</strong></font>
(<strong id='bold8279'
>syntax-rules</strong> ()
((<strong id='bold8280'
>begin</strong> exp)
exp)
((<strong id='bold8281'
>begin</strong> exp1 exp2 ...)
(<strong id='bold8282'
>let</strong> ((x exp1))
(<strong id='bold8283'
>begin</strong> exp2 ...)))))
</pre>
</td></tr>
</tbody></table></center>
The following definition
of <samp id='samp6997'
>do</samp> uses a trick to expand the variable clauses.
As with <samp id='samp6998'
>letrec</samp> above, an auxiliary macro would also work.
The expression <samp id='samp6999'
>(if #f #f)</samp> is used to obtain an unspecific
value.<br/><br/><center id='center7014'
><table cellspacing="0" class="color" cellpadding="0" width="95%"><tbody>
<tr><td bgcolor="#ffffcc"><pre class="prog" id='prog7012'
>(<font color="#6959cf"><strong id='bold8284'
>define-syntax</strong></font> <font color="#6959cf"><strong id='bold8286'
>do</strong></font>
(<strong id='bold8288'
>syntax-rules</strong> ()
((do ((var init step ...) ...)
(test expr ...)
command ...)
(<strong id='bold8289'
>letrec</strong>
((loop
(<strong id='bold8290'
>lambda</strong> (var ...)
(<strong id='bold8291'
>if</strong> test
(<strong id='bold8292'
>begin</strong>
(<strong id='bold8293'
>if</strong> #f #f)
expr ...)
(<strong id='bold8294'
>begin</strong>
command
...
(loop (do <font color="red">"step"</font> var step ...)
...))))))
(loop init ...)))
((do <font color="red">"step"</font> x)
x)
((do <font color="red">"step"</font> x y)
y)))
</pre>
</td></tr>
</tbody></table></center>
</div><br>
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</tr></table><div class="skribe-ending">
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