XXX.PHO[P,JRA] - www.SailDart.org

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<COLUMN=370><FONT=0><FONT=11><SP><SP>CONTENTS<COLUMN=1342><FONT=0>
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<CR><LINESPACE 3>
<COLUMN=370><FONT=1><COLUMN=610>T<SP>A<SP>B<SP>L<SP>E<SP><SP><SP>O
  <SP>F<SP><SP><SP>C<SP>O<SP>N<SP>T<SP>E<SP>N<SP>T<SP>S<CR><LF>
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<CR><LF>
<CR><LF>
<COLUMN=370><FONT=1>PREFACE<COLUMN=1332>i<CR><LF>
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<COLUMN=370><FONT=1>CHAPTER<COLUMN=1259>PAGE<FONT=0><CR><LF>
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<COLUMN=370><FONT=0><COLUMN=406>1<COLUMN=454>SYMBOLIC<SP>EXPRESSIONS
  <COLUMN=1327>1<CR><LF>
<CR><LF>
<COLUMN=370><FONT=0><COLUMN=514>1.1<COLUMN=586>Introduction
  <COLUMN=754><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP>
  <SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.
  <SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP>
  <COLUMN=1317><SP>1<CR><LF>
<COLUMN=370><FONT=0><COLUMN=514>1.2<COLUMN=586>Weizenbaum<SP>example
  <COLUMN=862><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP>
  <SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.
  <SP><SP>.<SP><SP>.<SP><SP>.<SP><COLUMN=1317><SP>2<CR><LF>
<COLUMN=370><FONT=0><COLUMN=514>1.3<COLUMN=586>right<SP>indent<SP>example
  <COLUMN=862><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP>
  <SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.<SP><SP>.
  <SP><SP>.<SP><SP>.<SP><SP>.<SP><COLUMN=1317><SP>3<CR><LF>
<CR><LF>
<CR><LF>
<COLUMN=370><FONT=0><FONT=1>BIBLIOGRAPHY<COLUMN=1327>5<FONT=0><CR><LF>
<CR><LF>
<CR><LF>
<CR><LF>
<COLUMN=370><FONT=0><FONT=1>INDEX<COLUMN=1342><FONT=0><CR><LF>
<FF>
<COLUMN=370><FONT=0><FONT=11>1.<COLUMN=1024>Symbolic<SP>expressions
  <SP><SP><SP><SP><SP>1<FONT=0><CR><LF>
<CR><LF>
<CR><LF>
<CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=1169><FONT=1>CHAPTER<SP>1<FONT=0><CR><LF>
<CR><LF>
<CR><LF>
<CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=442><FONT=9>Symbolic<SP>Expressions
  <FONT=0><CR><LF>
<CR><LF>
<CR><LF>
<CR><LF>
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<CR><LF>
<CR><LF>
<CR><LF>
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<COLUMN=370><FONT=0><COLUMN=745><FONT=1>1.1<SP><SP>Introduction
  <FONT=0><CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0>If<COL INC 13>pressed<COL INC 13>for<COL INC 13>details
  <COL INC 13>we<COL INC 13>might<COL INC 13>attempt<COL INC 13>a
  <COL INC 13>more<COL INC 13>elaborate<COL INC 13>characterization<CR><LF>
<COLUMN=370><FONT=0>like<SP>the<SP>following:<CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=430><FONT=1>1.<FONT=0><SP><FONT=2>zero
  <FONT=0><SP>is<SP>an<SP>element<SP>of<SP><FONT=12>N<FONT=0>.<FONT=7>
  <SP>1<FONT=0><CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=430><FONT=1>3.<FONT=0><COL INC 22>The
  <COL INC 22>only<COL INC 22>elements<COL INC 22>of<COL INC 21>
  <FONT=12>N<FONT=0><COL INC 22>are<COL INC 22>those<COL INC 22>created
  <COL INC 22>by<COL INC 22>finitely<COL INC 21>many<CR><LF>
<COLUMN=370><FONT=0><COLUMN=430>applications<SP>of<SP>rules<SP>
  <FONT=1>1<FONT=0><SP>and<SP><FONT=1>2<FONT=0>.<CR><LINESPACE 3>
<COLUMN=370><FONT=0>Definition<COL INC 14><FONT=1>II<FONT=0>
  <COL INC 13>appears<COL INC 14>to<COL INC 13>be<COL INC 14>completely
  <COL INC 13>at<COL INC 14>the<COL INC 13>other<COL INC 14>end
  <COL INC 13>of<COL INC 14>the<COL INC 13>spectrum;<CR><LF>
<COLUMN=370><FONT=0>but<SP>unsatisfactory.<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=442>We<COL INC 14>shall<COL INC 14>refer
  <COL INC 14>to<COL INC 14>the<COL INC 14>digit<COL INC 14>representation
  <COL INC 14>as<COL INC 14><FONT=1>numerals<FONT=0><COL INC 15>and
  <COL INC 14>reserve<CR><LF>
<COLUMN=370><FONT=0>the<COL INC 17>Thus<COL INC 17>numerals
  <COL INC 17>denote,<COL INC 17>stand<COL INC 17>for,<COL INC 17>or
  <COL INC 17>represent<COL INC 17>the<COL INC 18>abstract<COL INC 17>objects
  <CR><LF>
<COLUMN=370><FONT=0>called<COL INC 17>natural<COL INC 16>numbers;
  <COL INC 17>and<COL INC 17>definition<COL INC 16><FONT=1>I<FONT=0>
  <COL INC 17>is<COL INC 17>better<COL INC 16>stated<COL INC 17>as:
  <COL INC 17>"a<COL INC 16>natural<CR><LF>
<COLUMN=370><FONT=0>number<CR><LF>
<CR><LF>
<CR><LF>
<CR><LF>
<CR><LF>
<CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0>________________<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=442><FONT=7><SP>1<FONT=0><SP>bite<SP>me,
  <SP>vip<SP>tabs!.<CR><LF>
<FF>
<COLUMN=370><FONT=0><FONT=11>2<SP><SP>Symbolic<SP>expressions
  <COLUMN=1303>1.1<FONT=0><CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=442>The<COL INC 18>basic<COL INC 18>content
  <COL INC 18>of<COL INC 18>an<COL INC 18>inductive<COL INC 18>definition
  <COL INC 18>of<COL INC 18>a<COL INC 18>set<COL INC 18>of<COL INC 18>objects
  <CR><LF>
<COLUMN=370><FONT=0>consists<SP>of<SP>three<SP>parts:<CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=490>(1)<COL INC 12>A<COL INC 12>description
  <COL INC 12>of<COL INC 12>an<COL INC 13>initial<COL INC 12>set
  <COL INC 12>of<COL INC 12>objects;<COL INC 12>the<COL INC 12>elements
  <COL INC 13>of<COL INC 12>this<CR><LF>
<COLUMN=370><FONT=0><COLUMN=490>set<COL INC 15>are<COL INC 16>the
  <COL INC 15>initial<COL INC 15>elements<COL INC 16>of<COL INC 15>the
  <COL INC 15>set<COL INC 16>we<COL INC 15>are<COL INC 15>describing
  <COL INC 16>in<COL INC 15>the<CR><LF>
<COLUMN=370><FONT=0><COLUMN=490>inductive<SP>definition.<CR>
  <LINESPACE 3>
<COLUMN=370><FONT=0><FONT=1>IND<FONT=0><CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=490>(2)<COL INC 11>Given<COL INC 11>the
  <COL INC 11>description<COL INC 11>of<COL INC 11>some<COL INC 11>existing
  <COL INC 11>elements<COL INC 11>in<COL INC 11>the<COL INC 12>set,
  <COL INC 11>we<CR><LF>
<COLUMN=370><FONT=0><COLUMN=490>are<SP>given<SP>a<SP>means<SP>of<SP>constructing
  <SP>more<SP>elements.<CR><LINESPACE 9>
<COLUMN=370><FONT=0><COLUMN=490>(3)<COL INC 12>A<COL INC 12>termination
  <COL INC 12>clause,<COL INC 12>saying<COL INC 12>that<COL INC 12>the
  <COL INC 12>only<COL INC 12>elements<COL INC 12>in<COL INC 12>the
  <COL INC 11>set<CR><LF>
<COLUMN=370><FONT=0><COLUMN=490>are<SP>those<SP>which<SP>gained<SP>admittance
  <SP>by<SP>either<SP>(1)<SP>or<SP>(2).<CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0>We<COL INC 25>can<COL INC 25>recast<COL INC 24>the
  <COL INC 25>positional<COL INC 25>notation<COL INC 24>description
  <COL INC 25>as<COL INC 25>an<COL INC 24>inductive<CR><LF>
<COLUMN=370><FONT=0>definition.<CR><LF>
<CR><LINESPACE 8>
<COLUMN=370><FONT=0><FONT=1>1.<FONT=0><SP><SP>A<SP>numeral<SP>is<SP>a
  <SP>digit<CR><LINESPACE 9>
<COLUMN=370><FONT=0><FONT=1>2.<FONT=0><SP><SP>If<SP><FONT=2>n<FONT=0>
  <SP>is<SP>a<SP>numeral<SP>then<SP><FONT=2>n<FONT=0><SP>followed<SP>by
  <SP>a<SP>digit<SP>is<SP>a<SP>numeral.<CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0>In<SP>words,<SP>"a<SP>numeral<SP>is<SP>a<SP>digit,
  <SP>or<SP>a<SP>numeral<SP>followed<SP>by<SP>a<SP>digit".<CR>
  <LINESPACE 20>
<COLUMN=370><FONT=0><LB>numeral<RB><COLUMN=538>::=<SP><LB>digit<RB><CR>
  <LINESPACE 9>
<COLUMN=370><FONT=0><LB>numeral<RB><COLUMN=538>::=<SP><LB>numeral<RB><LB>digit<RB><CR>
  <LINESPACE 3>
<COLUMN=370><FONT=0>As<SP>an<SP>abbreviation,<SP>the<SP><SP>two<SP>BNF
  <SP>equations<SP>may<SP>also<SP>be<SP>written:<CR><LINESPACE 3>
<COLUMN=370><FONT=0><LB>numeral<RB><COLUMN=538>::=<SP><LB>digit<RB><SP>|<SP><LB>numeral<RB><LB>digit<RB>.
  <CR><LINESPACE 20>
<COLUMN=370><FONT=0><COLUMN=442><LB>numeral<RB><COL INC 12>is<COL INC 11>the
  <COL INC 12>syntactic<COL INC 11>class<COL INC 12>of<COL INC 11>numerals
  <FONT=7><SP>2<FONT=0>.<COL INC 12><SP>When<COL INC 11>we<COL INC 12>are
  <COL INC 11>talking<CR><LF>
<COLUMN=370><FONT=0>about<SP>a<SP>syntactic<SP>class<SP>of<SP>objects
  <SP>we<SP>will<CR><LF>
<CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=681><FONT=1>1.2<SP><SP>Weizenbaum<SP>example
  <FONT=0><CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0>The<SP>flow<SP>of<SP>symbol<SP>table<SP>creation
  <SP>is:<CR><LINESPACE 20>
<COLUMN=370><FONT=0><COLUMN=418><COLUMN=454><FONT=2>f[2;3]
  <COLUMN=670><COLUMN=706>x<FONT=7>2<FONT=2><SP>+<SP>y<FONT=0><CR>
  <LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=418><COLUMN=454>E<FONT=3>0<FONT=0>
  <COLUMN=490><COLUMN=670><COLUMN=706>E<FONT=3>1<FONT=0><COLUMN=886>
  <COLUMN=946><COLUMN=982>E<FONT=3>0<FONT=0><CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=418><COLUMN=454>|<SP>/<COLUMN=490>
  <COLUMN=670>|<SP>E<FONT=3>0<FONT=0><COLUMN=886><COLUMN=946>
  <COLUMN=982>|<SP>/<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=418><COLUMN=454>______<SP>=<RB><COLUMN=670>______
  <COLUMN=886>=<RB><COLUMN=946>______<SP><SP>return<SP>with<SP>value<SP>
  <FONT=2>7<FONT=0>.<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=418><SP><FONT=2>f<COLUMN=454>|<SP>λ[[x;y]
  <SP>x<FONT=7>2<FONT=2><SP>+<SP>y]<FONT=0><COLUMN=670><FONT=2>x
  <COLUMN=706>|<SP>2<COLUMN=886><COLUMN=946>f<COLUMN=982>|<SP>λ[[x;y]
  <SP>...<SP>]<CR><LINESPACE 3>
<COLUMN=370><FONT=2><COLUMN=418><COLUMN=454><COLUMN=490><COLUMN=670>
  <SP>y<COLUMN=706>|<SP>3<FONT=0><CR><LINESPACE 20>
<COLUMN=370><FONT=0>Compare<SP>this<SP>sequence<SP>to<SP>the<SP>example
  <SP>on<SP>page<SP>.<CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0>________________<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=442><FONT=7><SP>2<FONT=0><COL INC 34>Note
  <COL INC 34>we<COL INC 33>could<COL INC 34>have<COL INC 34>written
  <COL INC 34><LB>numeral<RB><SP>::=<SP><LB>digit<RB><COL INC 33>and<CR><LF>
<COLUMN=370><FONT=0><LB>numeral<RB><SP>::=<SP><LB>digit<RB><LB>numeral<RB>,<COL INC 24>generating
  <COL INC 24>the<COL INC 23>same<COL INC 24>class,<COL INC 24>but
  <COL INC 24>in<COL INC 23>a<CR><LF>
<COLUMN=370><FONT=0>different<COL INC 12>order.<COL INC 12>Questions
  <COL INC 12>of<COL INC 12>syntax<COL INC 12>and<COL INC 12>grammars
  <COL INC 12>will<COL INC 12>not<COL INC 12>be<COL INC 12>stressed
  <COL INC 12>in<CR><LF>
<COLUMN=370><FONT=0>this<SP>book.<SP>See<SP>[Aho<SP>72].<CR><LF>
<FF>
<COLUMN=370><FONT=0><FONT=11>1.2<COLUMN=1024>Weizenbaum<SP>example
  <SP><SP><SP><SP><SP>3<FONT=0><CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=442>The<SP>sequence<SP>of<SP>tables<SP>corresponds
  <SP>to<SP>the<SP>evaluation<SP>sequence:<CR><LINESPACE 20>
<COLUMN=370><FONT=0><COLUMN=562><FONT=2>eval[<FONT=13>R<FONT=14>(<SP>
  <FONT=2>f[2;3]<SP><FONT=14>)<FONT=2>;<SP><FONT=13>R<FONT=14>(<SP>
  <FONT=2>{<LB>f<SP>,<SP>λ[[x;y]<SP>x<FONT=7>2<FONT=2><SP>+y]<RB>}<SP>
  <FONT=14>)<FONT=2>]<CR><LINESPACE 3>
<COLUMN=370><FONT=2><COLUMN=848>↓<CR><LINESPACE 3>
<COLUMN=370><FONT=2><COLUMN=849>7<FONT=0><CR><LF>
<CR><LF>
<CR><LINESPACE 20>
<COLUMN=370><FONT=0><COLUMN=686><FONT=1>1.3<SP><SP>right<SP>indent
  <SP>example<FONT=0><CR><LF>
<FF>
<COLUMN=370><FONT=0><FONT=11>4<SP><SP>Preface<COLUMN=1342><FONT=0>
  <CR><LF>
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<CR><LINESPACE 3>
<COLUMN=370><FONT=0><FONT=9>Preface<FONT=0><CR><LF>
<CR><LF>
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<CR><LINESPACE 3>
<COLUMN=370><FONT=5><COLUMN=442>"...<COL INC 15>it<COL INC 15>is
  <COL INC 15>important<COL INC 15>not<COL INC 15>to<COL INC 15>lose
  <COL INC 15>sight<COL INC 15>of<COL INC 15>the<COL INC 15>fact
  <COL INC 15>that<COL INC 15>there<COL INC 15>is<COL INC 14>a<CR><LF>
<COLUMN=370><FONT=5><COLUMN=442>difference<COL INC 28>then
  <COL INC 28>university<COL INC 27>education<COL INC 28>in<COL INC 28>this
  <COL INC 28>field<COL INC 27>should<CR><LF>
<COLUMN=370><FONT=5><COLUMN=442>emphasize<COL INC 32>enduring
  <COL INC 33>fundamental<COL INC 32>principles<COL INC 33>rather
  <COL INC 32>than<CR><LF>
<COLUMN=370><FONT=5><COLUMN=442>transient<SP>current<SP>technology."
  <CR><LF>
<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=442><COLUMN=627>Peter<SP>Wegner,<SP>
  <FONT=2>Three<SP>Computer<SP>Cultures<FONT=0><SP>[Weg<SP>70]<SP><SP>
  <SP><SP><SP><SP><SP><SP><CR><LF>
<CR><LF>
<CR><LINESPACE 8>
<COLUMN=370><FONT=0>This<SP>text<SP>is<SP>nominally<SP>about<SP>bloody
  <SP>crap.<CR><LF>
<FF>
<COLUMN=370><FONT=0><FONT=11><COLUMN=1109>BIBLIOGRPAHY<SP><SP><SP>
  <SP><SP>5<FONT=0><CR><LF>
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<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=442><FONT=9>Bibliography<FONT=0><CR><LF>
<CR><LF>
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<CR><LINESPACE 3>
<COLUMN=370><FONT=0>The<SP>basic<SP>form<SP>of<SP>an<SP>entry<SP>consists
  <SP>of<SP>three<SP>items:<CR><LINESPACE 3>
<COLUMN=370><FONT=0><COLUMN=430><FONT=1>1.<FONT=0><SP>A<SP>short<SP>name
  <SP>which<SP>is<SP>how<SP>the<SP>document<SP>is<SP>referenced<SP>in
  <SP>the<SP>text.<CR><LINESPACE 9>
<COLUMN=370><FONT=0><COLUMN=430><FONT=1>2.<FONT=0><SP>The<SP>full<SP>bibliographical
  <SP>reference.<CR><LINESPACE 9>
<COLUMN=370><FONT=0><COLUMN=430><FONT=1>3.<FONT=0><COL INC 10>A
  <COL INC 10>sequence<COL INC 10>of<COL INC 10>pages<COL INC 10>in
  <COL INC 10>the<COL INC 10>text<COL INC 10>which<COL INC 10>refer
  <COL INC 10>to<COL INC 10>this<COL INC 10>document.<COL INC 11>If
  <COL INC 10>the<CR><LF>
<COLUMN=370><FONT=0><COLUMN=430>document<COL INC 14>is<COL INC 14>not
  <COL INC 14>referenced<COL INC 14>the<COL INC 14>statement
  <COL INC 14><FONT=1>[<SP>norefs<SP>]<FONT=0><COL INC 15>appears
  <COL INC 14>instead;<CR><LF>
<COLUMN=370><FONT=0><COLUMN=430>these<COL INC 16>documents,
  <COL INC 16>while<COL INC 16>not<COL INC 16>referenced,<COL INC 16>are
  <COL INC 16>relevant<COL INC 16>to<COL INC 17>the<COL INC 16>material
  <CR><LF>
<COLUMN=370><FONT=0><COLUMN=430>covered<SP>in<SP>the<SP>text.<CR>
  <LINESPACE 20>
<COLUMN=370><FONT=0>[Aho<SP>72]<COLUMN=502>2<SP><FONT=1>[<FONT=0><CR><LF>
<FF>