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Index

Ωmega XIII, 23, 25, 239, 285, 304,305, 307, 309–312, 387

λClam 239, 304, 307λµEµ– calculus, 160T -theorem 177dc:*– element, 322om:*– element, 324--> 8, 92, 214.rnc 232.rng 232<!-- 8, 92, 214&amp; 8&apos; 8&gt; 8&lt; 8&quot; 8OpenMath

– object, 108

639– ISO, 978601– ISO, 97

a– content dictionaries (OpenMath),

279abbreviation– namespace, 8, 231

Abelian– semigroup, 152about data– data, 84, 91, 97abstract 99– data– – type, 259– data type, 56, 155, 219– structure, 41– syntax, 41abstract– attribute value– – for type on omtext, 125Abstract Data Types– RNC Module ADT, 353– spec Module ADT, 84, 146, 155, 156,

218, 219, 333–335, 337ACL2 278action– attribute– – on dc:date, 99, 328, 329, 331– – on omlet, 206, 207, 329, 339active– document, 201ActiveMath XIII, 35, 65, 67, 74,

90, 95, 243, 244, 247, 266–273, 292,297

actual– parameter– – theory, 58actualization 56actuate

390 Index

– attribute, 206– – on omlet, 206acyclic 151adt– element, 138, 142, 156–158, 216, 315,

316, 321, 326, 328ADT (Abstract Data Types)– RNC Module, 353– spec Module, 84, 146, 155, 156, 218,

219, 333–335, 337advisor– thesis, 101against– attribute value– – for type on example, 44, 146agent– web, 5Alan– Bundy, 26Algebra– Fundamental Theorem of, 14Algebra 251algebra– system, 29algebraic– hierarchy, 174– specification, 23, 27, 55, 319all– attribute value– – for crossref-symbol on

presentation, 196α-conversion 119alphabet 148alternative– attribute value– – for type on omgroup, 329alternative– element, 145alternative– element, 145, 146, 320, 328Amaya 16analysis– formal, 310– natural language, 310Analytica 203analyzer 295anchor– named, 10Andrzej– Trybulec, 27animal 66annotation– semantic, 311

m:annotation– element, 115m:annotation-xml– element, 17, 115, 199answer– element, 210, 321ant– attribute value– – for role on dc:*, 101antecedent– bibliographic, 101– scientific, 101antithesis– attribute value– – for type on omtext, 125mq:anyorder– attribute, 255–257applet 205– Java, 207application 18, 108, 115– Xml, 6– web, 264– XML, 3, 14, 85, 214, 220application– attribute value– – for role on symbol, 137application/omdoc+xml 38applied– attribute value– – for role on presentation, 194, 330apply– element, 256m:apply– element, 17, 18, 115, 137, 194, 198,

238archiving– document, 35argument– element, 56, 156, 157, 320, 328arith1 28, 219arith1.ocd 20artefacts– electronic, 102artificial– intelligence, 286assertion 69, 159, 162, 304– level, 309assertion– element, 69, 70, 77, 139, 141, 142,

145–148, 161, 164, 165, 178, 184, 229,283, 314, 316, 320, 328, 340, 343

assertion– attribute

Index 391

– – on example, 47, 69, 147, 148– – on obligation, 178assertion-level proof– underspecification, 312assertional– element, 146, 147, 169, 171, 177assertions– type, 143assessment 209assistant– proof, 309– proof (automated), 75assoc– attribute value– – for fixity on presentation, 195assumption 162– local, 162assumption– attribute value– – for type on assertion, 143, 324assumption– element, 124, 144, 166, 315, 321ATP 278attribute 7– CSS, 86, 94, 96, 128, 322, 326, 348– default value, 229– node, 7– type, 9attribute– element, 191, 321, 328attribute-value– pair, 191attributes– attribute– – on use, 197, 331attribution– attribute value– – for role on symbol, 110, 137, 326attribution– attribute– – on cc:requirements, 103– attribute value, 137augmented 320aural 86aut– attribute value– – for role on dc:*, 101author 101automated– concept formation– – system, 75– deduction, 27, 319– proof

– – assistant, 75– theorem– – prover, 25, 75– – provers, 304automated theorem prover 30AutoMath 23axiom 23, 84, 125, 133, 162, 175, 218,

304– commutativity, 152– implicit, 139– inclusion, 179, 180, 183– system, 135axiom– attribute value– – for type on omtext, 40, 125, 324axiom– element, 67, 68, 138, 139, 146, 152,

158, 163–165, 321, 328axiom-inclusion– element, 176, 180, 184, 185, 216, 282,

283, 321, 325, 328, 341, 342axiominclusion– element, 185axiom inclusion 182axioms 139– Peano, 134, 135, 155

Bachus Naur Form notation 91background– scientific, 2backward– reasoning, 168balanced– bracketing– – structure, 6base– content dictionary, 154– knowledge, 163, 286– knowledge (mathematical ), 242– morphism, 176– URI, 151base– attribute– – on morphism, 61, 176Berners-Lee– Tim, 32Bibliographic– Record– – Schema, 248bibliographic– antecedent, 101binary– document model, 214

392 Index

binary– attribute value– – for format on data, 203binder– attribute value– – for role on symbol, 109, 137, 326binder– attribute value– – for role, 109binding 115, 119, 198– LaTeXML, 295– object, 137– operator, 109, 111binding– attribute value– – for role on presentation, 194, 330binding structure 18, 108binomial– coefficient, 197body 109bottom-up– proof– – step, 167bound– occurrence, 120– variable, 18, 108, 109, 119, 198box– layout, 86Boyer-Moore– corpus, 279bracket-style– attribute– – on presentation, 195– – on use, 197brackets– attribute value– – for crossref-symbol on

presentation, 196browser 5, 235– web (math-enabled), 264browsing 247BugZilla 224building blocks 83bullet– symbol, 94bulleted– list, 130Bundy– Alan, 26m:bvar– element, 18, 115, 120, 137, 194, 198by pointing– semantics, 19

byte array 111

C– programming– – language, 18calculus 309– λµEµ, 160– deduction (natural), 79– formal, 30– logical, 159– process, 286Carnegie Mellon University 65Cartesian– product, 43CAS 30, 262, 263, 265cascades– finite-state, 249Cascading– Style Sheet, 86cascading– style sheet, 320CASC competition 278Casl 23, 55, 155, 219, 281, 282, 285,

288catalog– XML, 9, 38, 225, 228Catholic– church, 121CC– license, 102– metadata, 102CC (Creative Commons Metadata)– spec Module, 84, 97, 102, 335–337cc: 38, 103cc:license– element, 102, 103cc:permissions– element, 39, 103cc:prohibitions– element, 39, 103cc:requirements– element, 39, 103CCaps 290, 303cd– attribute value– – for module on omdoc, 42cd– attribute– – on om:OMS, 31, 108, 119– – on OMS, 18, 43, 218– – on term, 128, 326cd*– attribute

Index 393

– – on theory, 50cd2omdoc.xsl 235CDATA 71– section, 8CDATA 203cdbase– attribute, 108, 109– – on om:OMOBJ, 19– – on om:theory, 149– – on OMS, 149– – on theory, 151, 153, 154, 326omcd:CDDefinition– element, 109omcd:CDName– element, 50cdreviewdate– attribute– – on theory, 154, 326cdrevision– attribute– – on theory, 153, 326cdstatus– attribute– – on theory, 153, 326omcd:CDURL– element, 50cdurl– attribute– – on theory, 154, 326cdversion– attribute– – on theory, 153, 326chain– local, 182, 184challenge problems– induction, 278, 279change– management, 182, 219, 258, 260– management of, 284changed 319chapter 22, 94character– hash, 10– lists of, 58character data– parsed, 91checking– proof, 30chemistry– vernacular, 122choice– element, 210, 321church

– Catholic, 121m:ci– element, 17, 115, 119, 120, 198, 238cite– attribute value– – for type on ref, 94Clam 278clarity– conceptual, XIIclass– CSS, 188– equivalence, 214class– attribute, 86, 87, 90, 94, 130, 188,

210, 320– – on dc:title, 71– – on omstyle, presentation, 188– – on phrase, 126, 189– – on presentation, 188, 194– – on ref, 71, 72, 96class definition– CSS, 71classical– first-order– – logic, 166classid– old attribute on code (deprecated in

OMDoc 1.2), 321, 328– old attribute on private (deprecated

in OMDoc 1.2), 330clause– copyleft, 39clb– attribute value– – for role on dc:*, 101client 264clipboard– system, 247closing– tag, 6, 39cmml– attribute value– – for format on use, 189CMP– element, 7, 39, 40, 44, 46, 93, 98, 99,

122, 123, 125, 126, 128, 129, 138,139, 146, 163, 164, 170, 177, 189,192, 204, 205, 209, 210, 216, 238,240, 243, 273, 280, 321, 322, 325,326, 328, 330, 331, 334, 335, 337, 338

omcd:CMP– element, 19, 20m:cn

394 Index

– element, 17, 115co-reference 17code– country, 122, 240– fragment, 70, 122code– element, 70, 71, 164, 189, 202–204,

206–208, 216, 321, 322, 328, 330, 342codebase– old attribute on code (deprecated in

OMDoc 1.2), 321, 328– old attribute on private (deprecated

in OMDoc 1.2), 330coefficient– binomial, 197collaborator 101Collection as Dublin Core Type 99Collection 100collection– multi-format, 208color– text, 86comma 196comment 92– persistent, 92– source, 92– XML, 8, 92, 214comment– attribute value– – for type on omtext, 92, 125commented– mathematical– – property, 19commercial use– attribute– – on cc:permission, 103communication 262, 309Communication Standard 242community 27, 319– mathematics (international), VIIIcommutativity– axiom, 152comorphism 287competency– element, 268complete– configuration, 259Complex Theories– RNC Module CTH, 355– spec Module CTH, 84, 173, 175, 177,

180, 182, 218, 219, 281, 288, 333, 335,336, 338

Component

– Presentation, 266– Tutorial, 266component– reuse, 281– shared, 281composition 176computation– request, 304computer– graphics, VII– science, 65computer-supported– education, 27, 319computer algebra VII– system, 19, 25, 29, 75, 111, 202, 203,

238, 304computer science– vernacular, 122concatenation– strings, 148concept 67, 69, 127, 136– extension, 67– mathematical, 136conceptual– clarity, XII– structure, 243conceptual clarity 83conclusion– attribute value– – for type on derive, 162– – for type on omtext, 125conclusion– element, 124, 144, 166, 315, 322, 329configuration– complete, 259– consistent, 259– management, 258Conjecture– Kepler’s, VIIconjecture 142– false, 148conjecture– attribute value– – for type on assertion, 143– – for type on omtext, 125, 324Connexions 257consequence 30– morphism, 282– relation, 30conservative 178– extension, 135, 145conservative– attribute value

Index 395

– – for conservativity, 178– – for definitional, 178conservativity 177conservativity– attribute, 178– – on axiom-inclusion, 321– – on imports, 177, 323– – on inclusion, 323– – on theory-inclusion, 327conservativity-just– attribute– – on axiom-inclusion, 321– – on imports, 177, 323– – on inclusion, 323– – on theory-inclusion, 327consistency 135, 175consistency– attribute– – on definition, 141– – on morphism, 175, 324consistent– configuration, 259Consortium– Web (World Wide), 6constant– attribute value– – for role on symbol, 137constitutive 133, 218– property, 20– theory element, 134constraint– solver, 75construct– programming, 263constructor 43, 56– symbol, 155, 156– term, 155constructor– element, 156, 157, 315, 322, 328Content– markup, 30content 89, 110– dictionary, 18, 107, 119, 127, 263– language, 304– management, 66– markup, 4, 28, 30, 31– navigation, 292– OMDoc, 66– search, 292– semantic, 310– structure, 126content dictionary 19, 21, 31, 42, 43,

108, 109, 116, 122, 235

– base, 154– format, 153– metadata, 153– OMDoc, 42, 153, 218– OpenMath, 153– status, 153– version number, 153Content in– PowerPoint, 290content OMDoc 217Content MathML 10, 15–19, 21,

27, 29, 31, 35, 40, 41, 107, 114–116,118–120, 124, 126, 127, 153, 189, 194,199, 235, 237, 238, 256, 296, 304,306, 319, 323

context 142, 168– dynamic, 263, 264– markup, 22, 28– mathematical, 126– mathematical (dynamic), 262– static, 263, 264context-free– grammar, 8, 227contradictory-axioms– attribute value– – for status on assertion, 144contrast– attribute value– – for type on omgroup, 329dc:contributor– element, 101dc:contributor– element, 98, 99, 104, 322, 329control– version, 258controlled– refinement, 242convention– structural, 2copyleft– clause, 39copyleft– attribute– – on cc:requirements, 103CoQ 239, 304, 307Core 309, 311, 312Core 309corollary 142corollary– attribute value– – for type on assertion, 143– – for type on omtext, 125, 324corpus

396 Index

– Boyer-Moore, 279– Dmac, 279correct 66correctness– management, 163counter-equivalent– attribute value– – for status on assertion, 144counter-example 69, 148counter-satisfiable– attribute value– – for status on assertion, 144counter-theorem– attribute value– – for status on assertion, 144country– code, 122, 240Course Capsules 298courseware 65CPoint 65, 242, 290–293, 298CPointAuthor 292, 293CPointBasic 293CPointGraphs 292CPointImport 293CPointNotes 293CPointStudent 293cr– attribute– – on element, 194, 323created– attribute value– – for action on dc:date, 99Creative Commons– Initiative, 92, 103– license, 38, 102– namespace, 38, 103– – URI, 103Creative Commons Metadata– spec Module CC, 84, 97, 102, 335–337dc:creator– element, 98, 99, 101, 104, 322cref– attribute– – on om:*, 324crid– attribute– – on element, 194, 323cross-reference 5, 17, 66, 96, 98, 112,

123, 125, 130, 162, 165, 194, 196,324, 330, 340

crossref-symbol– attribute– – on presentation, use, 196

– – on presentation, 197CSS– attribute, 86, 94, 96, 128, 322, 326,

348– class, 188– class definition, 71– directive, 86, 320– markup, 205– property, 96– style sheet, 86, 224CSS 6, 15, 16, 71, 86, 87, 90, 94, 96,

126, 128, 163, 188, 205, 320, 322,326, 340, 348

m:csymbol– element, 115, 116, 119, 126CTH (Complex Theories)– RNC Module, 355– spec Module, 84, 173, 175, 177, 180,

182, 218, 219, 281, 288, 333, 335, 336,338

Curry-Howard– isomorphism, 308cyclic 95

DAG 112, 123, 159, 162, 164, 165– explosion, 112data– about data, 84, 91, 97– table, 130data– attribute value– – for valuetype on param, 208data– element, 70, 203, 204, 206, 208, 216,

321, 322, 325, 328, 330, 341–343data– attribute– – on omlet, 205–207, 329Dataset as Dublin Core Type 99Dataset 38, 99, 100, 216, 217dataset– attribute value– – for type on omgroup (deprecated in

OMDoc 1.2), 93, 324data type– abstract, 56, 155, 219date– review, 154dc:date– element, 99, 104, 322, 328, 329, 331dateTime 99dc– attribute

Index 397

– – on action:date, 99DC (Dublin Core Metadata)– RNC Module, 350– spec Module, 84, 97, 98, 218, 220,

334, 335, 337, 338dc: 38, 98dc:*– element, 322dc:contributor– element, 101dc:contributor– element, 98, 99, 104, 322, 329dc:creator– element, 98, 99, 101, 104, 322dc:date– element, 99, 104, 322, 328, 329, 331dc:description– element, 42, 50, 99, 138, 216, 321,

322, 326, 328, 330dc:format– element, 100, 104dc:identifier– element, 100dc:language– element, 100, 104dc:publisher– element, 99, 322dc:relation– element, 100dc:rights– element, 100, 102, 104dc:source– element, 50, 100, 104dc:subject– element, 99, 138, 321, 322, 326dc:title– element, 71, 94, 98, 216, 326dc:type– element, 99, 100, 104, 216, 217dd– element, 130de 100, 122de-referencing 5decision– procedure, 25declaration 127– DOCTYPE, 229– document type, 9, 10, 229– local, 168– namespace, 7, 38, 85– namespace prefix, 42– prefix (namespace), 38, 85– symbol, 22, 139, 153

– term, 139, 327– type, 138decomposition 58, 183decomposition– element, 184, 185, 322, 327, 329, 331deduction– automated, 27, 319– natural, 170, 329default– namespace, 85default– attribute value– – for format on use, 189default value– attribute, 229defined– symbol, 139definiendum 135, 140definiens 135, 148, 171definiens– attribute value– – for role on term, 43, 128defining– occurrence, 119, 198definite– description– – operator, 60definition 23, 84, 125, 128, 133, 135,

148, 218, 304– document type, 42, 213, 227, 230– implicit, 135– inductive, 136– loose, 136– simple, 135definition– attribute value– – for type on omtext, 40, 125, 324definition– element, 42, 46, 47, 139–141, 145,

146, 149, 152, 163, 164, 171, 175,266, 314, 316, 322, 324, 328, 329, 331

definitional 177– form, 23– theory– – inclusion, 177definition by description 140definitionURL 115definitionURL– attribute– – on m:annotation, 115– – on m:ci, 120– – on m:csymbol, 116, 119, 126dependency

398 Index

– graph, 292deprecated 319derivative works– attribute– – on cc:permissions, 103derive– attribute value– – for type on omtext, 125derive– element, 70, 79, 161–166, 168, 314,

315, 329derived– inference– – rule, 171description– list, 130– logic, 286– service, 304dc:description– element, 42, 50, 99, 138, 216, 321,

322, 326, 328, 330Deskzilla 224development– graph, 58, 182, 219, 281, 282, 284– software (formal), 258, 281, 282– time, 281Development Graphs– spec Module DG, 84, 173, 182, 184,

218, 288, 334, 336– sped Module DG, 281DG (Development Graphs)– spec Module, 84, 173, 182, 184, 218,

288, 334, 336– sped Module, 281Dgrl 282, 284, 285di– element, 130dictionary– content, 18, 107, 119, 127, 263didactic– figure, 73, 74differential– equation, 14, 30difficulty– element, 268Digital– rights– – management, 102Digital Media in Education 290directed– acyclic– – graph, 112, 123, 159, 216directive

– CSS, 86, 320discharged-in– old attribute on hypothesis

(deprecated in OMDoc 1.2), 323, 329discourse– structure, 242discourse theory 133display– attribute value– – for action on omlet, 206, 207display:none– attribute value– – for style, 149dissemination– knowledge (mathematical), XIdistinction– presentation vs. content, 89distribution 39distribution– attribute– – on cc:permissions, 103distributivity 20m:divide– element, 17divisor– common (greatest), VIIdl– element, 122, 130Dmac– corpus, 279DOC (Document Structure)– RNC Module, 349– spec Module, 83, 84, 89, 122, 217,

218, 220, 335–338DocBook 220, 263DOCTYPE– declaration, 229DOCTYPE 228–231document– active, 201– archiving, 35– fragment, 97– hypertext, 5– individualized, 243– interactive, 243– knowledge-centered, 66, 240– library, 248– management, 6, 97– manager, 264– markup, 1– mathematical, 2, 21, 309– mathematical (formal), 310– mathematical (interactive), 262

Index 399

– mathematical (verified), 310– model, 214– multilingual, 240– narrative-structured, 66, 240– object model, 205, 213– preparation language, 242– retrieval, 35– reuse, 258– root, 7, 9, 83, 99, 218– server, 264– sharing, 258– source, 4– structure, 218, 260– structured, 261– target, 4– tree, 6– view, 248document-unique 9document model– binary, 214– structure (XML), 214– syntax (XML), 214document object– model, 18documents– annotated (semantically), 311– multilingual, 122Document Structure– RNC Module DOC, 349– spec Module DOC, 83, 84, 89, 122,

217, 218, 220, 335–338document type 228– declaration, 9, 10, 229– definition, 42, 213, 227, 230document type definition 8DOM 280– JAXP, 280domain– top-level, 103dominate 112DRM 102DSSSL 6dt– element, 130DTD 8, 39, 42, 86, 90, 120, 213, 224,

228, 229, 345– module, 230– normalization, 229– subset (internal), 229DTD Module– PF (Proofs and Arguments), 230DTD module 228Dublin Core 92, 299

– namespace, 38, 98– – URI, 98Dublin Core Metadata– RNC Module DC, 350– spec Module DC, 84, 97, 98, 218,

220, 334, 335, 337, 338DVI 4dynamic– context, 263, 264– – manager, 265– HTML, 205– mathematical– – context, 262

editing 247editor 101– invasive, 242– scientific, 309editorial– note, 293edt– attribute value– – for role on dc:*, 101education XII– computer-supported, 27, 319Educational OMDoc 219effect– element, 71, 204, 322effective– URI, 151elaboration– attribute value– – for type on omtext, 125electronic– artefacts, 102element 6– assertional, 146, 147, 169, 171, 177– empty, 7– module, 230– theory-constitutive, 134– token, 115– top-level, 90element– element, 190, 191, 194, 323, 327, 329,

339element– attribute– – on omstyle, 188– – on use, 197, 331elements– Euclid’s, XIEmacs 232, 242, 298–300, 309emacs 303

400 Index

embed– attribute value– – for show on omlet, 206emitter 295empty– element, 7– namespace, 85– string, 148en 100, 122en– attribute value– – for xml:lang, 122xml:en– attribute value– – for lang, 39encoding– UTF-8, 37encoding– attribute– – on m:annotation, 115– – on om:OMFOREIGN, 110endnote 130entailed-by– attribute– – on alternative, 145entailed-by-thm– attribute– – on alternative, 145entailment– system, 287entails– attribute– – on alternative, 145entails-thm– attribute– – on alternative, 145entity– mnemonic, 10– module inclusion, 230– parameter, 42, 228, 229– XML, 8, 9, 227entry– index, 130enumeration– attribute value– – for type on omgroup, 40, 94environment– development (proof), 25equation– differential, 14, 30– recursive, 140equivalence– class, 214

equivalent– attribute value– – for status on assertion, 144error– mathematical, 93– operator, 111– semantic, 111error– attribute value– – for role on symbol, 111, 137, 326escaping– XML, 8Euclid XIEuclid’s– elements, XIEuclid’s algorithm VIIevaluation– semantics, 312evidence– higher-level, 163evidence– attribute value– – for type on omtext, 125evolutionary– process, 282example 68, 84example– attribute value– – for type on omtext, 40, 44, 125example– element, 44, 47, 68–70, 146–148, 269,

322execute– attribute value– – for action on omlet, 206exercise 209exercise– element, 209, 210, 322, 323Exercises– RNC Module QUIZ, 359– rnc Module QUIZ, 346– spec Module QUIZ, 84, 209, 218, 219,

333, 335, 337exhaustivity 175exhaustivity– attribute– – on definition, 141– – on morphism, 175, 324exincl.xsl 236existence– attribute– – on definition, 140, 314– – on morphism, 175

Index 401

expansion 164– tree, 216experimental– attribute value– – for cdstatus on theory, 153explicit– namespace– – prefix, 114explosion– DAG, 112export– symbol, 137expres.xsl 236EXT (Extensions)– RNC Module, 356– rnc Module, 346– spec Module, 84, 122, 201, 218, 219,

334–337extension– concept, 67– conservative, 135, 145– conservative (principle of), 23Extensions– RNC Module EXT, 356– rnc Module EXT, 346– spec Module EXT, 84, 122, 201, 218,

219, 334–337external– mathematical– – service, 263– object, 205– subset, 229external– attribute value– – for original on data, 203, 322

factual– knowledge, 25false– conjecture, 148false– attribute value– – for verdict on answer, 210false-conjecture– attribute value– – for type on assertion, 143– – for type on omtext, 125, 324family– font, 86FAQ 223feature 110– symbol, 117field

– element, 268figure– didactic, 73, 74– rhetoric/didactic, 73, 74file– style, 4, 16finite-state– cascades, 249FireFox 77, 247, 250, 269first-order– logic, 30, 46, 123, 278– theorem– – prover, 77, 278fixity– attribute– – on presentation, use, 195– – on use, 197flatten 95FMP– element, 47, 70, 79, 93, 123–125, 127,

138, 140, 144, 163, 164, 166, 204,209, 210, 216, 242, 243, 321, 322, 329

omcd:FMP– element, 19, 20font– family, 86– variant, 86footnote 130footnote– attribute value– – for type on note, 131for– attribute value– – for type on example, 44, 146for– attribute, 341, 342– – on alternative, 145– – on assertion, 320– – on axiom, 68, 138, 321– – on decomposition, 184, 322, 329,

331– – on definition, 42, 139, 140, 314– – on example, 44, 69, 146– – on hint, 323– – on insort, 156– – on mc, 323– – on note, 131– – on omstyle, presentation, 188– – on omtext, 125, 329– – on path-just, 185, 325– – on presentation, 192, 194, 195– – on private, code, 202– – on private, 330

402 Index

– – on proof, 78, 161, 166, 314, 325– – on solution, 209– – on type, 139, 331foreign– namespace, 85form 3– definitional, 23formal– analysis, 310– calculus, 30– mathematical– – document, 310– – property, 19– mathematics, 30– parameter– – theory, 58– representation, 310– semantics, 310– software– – development, 258, 281, 282– system, 30formalism– grammar (normative), 228formalism– attribute– – on legacy, 120formalization 286format– content dictionary, 153– document (semantic), 311– frontend (human-oriented), 242– markup (semantic), 30– migration, 31dc:format– element, 100, 104format– attribute– – on data, 70, 203, 328, 330– – on legacy, 120– – on use, xslt, style, 189, 196– – on use, 238– old attribute on CMP (deprecated in

OMDoc 1.1), 328formula 107– mathematical, 14, 21formula– attribute value– – for type on assertion, 143– – for type on omtext, 125, 324formulae as– types, 21forward– reasoning, 167

Four-Colour– Theorem, VIIfr 100, 122fragment 229– code, 70, 122– document, 97– identifier, 10frame 86framework– logical, 21, 278free 155free– attribute value– – for type on adt, 156frequently– asked– – questions, 223from– attribute– – on axiom-inclusion, 180– – on imports, 42, 150– – on omtext, 125, 329– – on theory-inclusion, 178frozen– attribute value– – for action on dc:date, 99function 3, 14– partial, 157– predecessor, 56, 155, 156– recursive, 140, 155– successor, 155, 157– total, 157Fundamentals of Computer Science

65Fundamental Theorem of– Algebra, 14future-proof VIII

Godel’s– Incompleteness– – Theorem, VIIGAP 262gap– steps, 162gap– attribute value– – for type on derive, 162generated 155generated– attribute value– – for type on adt, 156generated-by– old attribute on alternative

(deprecated in OMDoc 1.1), 328

Index 403

– old attribute on assertion(deprecated in OMDoc 1.2), 328

– old attribute on axiom (deprecatedin OMDoc 1.2), 328

– old attribute on definition(deprecated in OMDoc 1.2), 329

– old attribute on symbol (deprecatedin OMDoc 1.2), 331

generated-from– attribute, 180, 341– – on alternative, 320– – on assertion, 142– – on axiom-inclusion, 321– – on axiom, 138, 158– – on decomposition, 322– – on example, 322– – on exercise, 322– – on hint, 323– – on mc, 323– – on omdoc, 324– – on omgroup, 324– – on omstyle, 324– – on omtext, 324– – on private, 321, 325– – on proofobject, 325– – on proof, 325– – on solution, 325– – on theory-inclusion, 327– – on type, 327generated-via– attribute, 180– – on adt, 321– – on alternative, 320– – on assertion, 320–322– – on axiom-inclusion, 321– – on decomposition, 322– – on example, 322– – on exercise, 322– – on hint, 323– – on mc, 323– – on omdoc, 324– – on omgroup, 324– – on omstyle, 324– – on omtext, 324– – on private, 321, 325– – on proofobject, 325– – on proof, 325– – on solution, 325– – on symbol, 326– – on theory-inclusion, 327– – on type, 327generator– model, 75

mq:generic– attribute, 255–257global 150, 180– link, 28, 282– theorem– – link, 283global– attribute value– – for scope on symbol, 137, 157– – for type on imports, 150, 180globals– attribute– – on axiom-inclusion, 185– – on path-just, 185glyph 137– mathematical, 293goal– learning, 266GoTo 292grammar– context-free, 8, 227graph 178– acyclic (directed), 112, 123, 159, 216– dependency, 292– development, 58, 182, 219, 281, 282,

284– theory, 178graphics– computer, VIIgreatest– common– – divisor, VIIgrounded 165group 14– multi-logic, 123, 138, 209– multi-system, 137– multilingual, 39, 40, 122, 123, 126,

138, 146, 163, 204, 209, 216, 240group 136, 151, 152group representation 30

hash– character, 10head– template, 192header– table, 130height– old attribute on omlet (deprecated

in OMDoc 1.2), 328–330HetCasl 288heterogeneous– specification, 286

404 Index

Hets 261, 285, 287–289hiding– attribute– – on morphism, 62, 176, 324hierarchy– algebraic, 174higher-level– evidence, 163– structure, 40higher-order– logic, 123, 282hint 209hint– element, 209, 210, 323Hol 23, 36home– theory, 134href– attribute– – on data, 203, 322, 328, 342– – on link, 130– – on om:OMR, 112– – on OMR, 47– – on ref, 343– old attribute on premise (deprecated

in OMDoc 1.1), 330xlink:href– attribute– – on in MathML, 17HTML– dynamic, 205HTML 5, 6, 10, 14, 15, 189, 190,

194, 196, 197, 205, 240, 252, 269,270, 272, 273

html– attribute value– – for format on legacy, 120– – for format on use, 189HTTP 75, 77human-oriented– frontend– – format, 242hyperlink 130hyperref.sty 196hypertext– document, 5Hypertext Markup Language 5hypothesis– inductive, 124, 163, 168hypothesis– attribute value– – for type on omtext, 125hypothesis

– element, 162, 163, 167, 323, 327, 329

icmap 270ICOM 279, 280ID– system, 224– type, 10, 27, 85, 86, 95, 319ID 9dc:id– attribute– – on xml:creator, 98– – on xml:subject, 326– – on xml:title, 326id– attribute, 86, 320– – on CMP, 328– – on decomposition, 329– – on FMP, 329– – on m:bvar, 120– – on om:*, 324– – on type, 331– – on with, 331– attribute (in MathML), 17– attribute (in OpenMath objects),

112xml:id– attribute, 7, 10, 85, 86, 124, 163, 188,

210, 320, 341– – on assertion, 142– – on code, 207– – on derive, 162, 166– – on description, 322– – on effect, 322– – on idx, 130– – on imports, 185, 323– – on inclusion, 323– – on input, 323, 325– – on legacy, 120– – on measure, 323– – on obligation, 324– – on omdoc, 38, 50, 90– – on omgroup, 40– – on omtext, 40, 96, 124– – on ordering, 324– – on phrase, 126– – on private, code, 202– – on proof, 161– – on ref, 94, 325– – on symbol, 325– – on term, 128– – on theory, 149, 151, 153, 326ID-type 10ide

Index 405

– element, 130Identifier– public, 9identifier 115– fragment, 10– public, 38, 225, 228– resource (uniform), 5– system, 225dc:identifier– element, 100idp– element, 130IDREF– type, 328IDREF 9idt– element, 130idx– element, 122, 130ignore– element, 92, 93, 95, 122IkeWiki 274, 275image/gif– attribute value– – for format on data, 203image/jpeg– attribute value– – for format on data, 203implicit– axiom, 139– definition, 135– knowledge, 290implicit– attribute value– – for type on definition, 47, 140import– local, 150imported– attribute value– – for action on dc:date, 99imports– element, 42, 43, 46, 58, 62, 150–152,

175–177, 180, 185, 282, 305, 323Imps 178, 305in-place– error– – markup, 93, 111in-the-large 285– structuring, 259– verification, 281, 285in-the-small 285– verification, 282, 285INCLUDE 231

include– attribute value– – for type on ref, 94, 95included– structurally, 177inclusion– axiom, 179, 180, 183– theory, 56–58, 173, 177, 179, 180,

182, 183– theory (definitional), 177– theory (local), 179, 180– theory (postulated), 177– theory (structural), 177inclusion– element, 58, 179, 323incomplete– proof, 162inconsistent 23, 134index– entry, 130– markup, 130– phrase, 130– text, 130index– attribute– – on ide, 130– – on in module RT, 131– – on phrase, 126individualized– document, 243induced-by– attribute, 339– – on obligation, 178induction– challenge problems, 278, 279– theorem prover, 278, 279– theorem provers, 278, 279inductive– definition, 136– hypothesis, 124, 163, 168– proof, 168– step, 168inductive– attribute value– – for type on definition, 140, 322inductive– attribute– – on assumption, 124, 321– – on hypothesis, 163inductively defined– set, 56inference– rule, 163, 164

406 Index

infix– attribute value– – for fixity on presentation, 195,

314infixl– attribute value– – for fixity on presentation, 195,

314infixr– attribute value– – for fixity on presentation, 195,

314informal– mathematics, 30information– retrieval, VII– set, 229– style, 188infoset 18inherit 175inheritance 218– relation, 151, 173– theory, 73inherited 150, 152inherits– attribute– – on metadata, 329Initiative– Creative Commons, 92, 103ink-on-paper 2, 3InKa 239, 278, 282, 304, 307input 71input– element, 71, 204, 207, 323in scope of– theory, 165insertion– set, 155insort– element, 156instance– schema, 232– theory, 56institution 287integer 111integration– protocol-based, 304– theory, 305– type, 284integrity condition 145intellectual– property, 102intelligence

– artificial, 286interactive– document, 243– mathematical– – document, 262interactivity 262interface 241– theory, 306interlingua 237, 304internal– subset, 42, 229– – DTD, 229international– mathematics– – community, VIIIinternationalization 240Internet– publication, 2MS Internet Explorer 235Internet Explorer 16, 77, 235interpretation– theory, 173interrelation– semantic, 258intersection– set, 124introduction– attribute value– – for type on omtext, 125intuitive– knowledge, 25inv 152invariant– under a document model X , 214invasive– editor, 242inverse– left, 181– right, 181“is a” relation 68Isabelle 23, 165ISBN 100ISO, 97– – norm, 100, 122, 240, 97– – norm, 38, 99, 334, 335isomorphism– Curry-Howard, 308ISSN 100itemize– attribute value– – for type on omgroup, 71, 94

Index 407

JAVA 280, 313Java 70, 204– applet, 207JavaScript 205JAXP– DOM, 280jEdit 272jEditOQMath 272, 273jurisdiction– attribute– – on cc:license, 103just-by– attribute– – on assertion, 142, 144, 320– – on type, 139, 327justification 163

K-14 15, 18, 114– mathematics, 116Kepler’s– Conjecture, VIIkey 110key– attribute value– – for role on presentation, 194, 330kind– old attribute on ref (deprecated in

OMDoc 1.2), 330– old attribute on symbol (deprecated

in OMDoc 1.1), 326Kindergarten 15, 114knowledge– base, 163, 286– factual, 25– implicit, 290– intuitive, 25– management, XII, 67– mathematical, VIII, XII, 1– presentation, 67– representation, 67knowledge-based– proof– – planning, 25knowledge-centered– document, 66, 240– view, 89knowledge-structured 89

labeled-dataset– attribute value– – for type on omgroup (deprecated in

OMDoc 1.2), 93, 324dc:lang

– attribute– – on xml:*, 101– – on xml:contributor, 99– – on xml:description, 99– – on xml:subject, 99– – on xml:title, 98xml:lang– attribute, 7, 122– – on CMP, 39, 122– – on description, 42– – on use, xslt, style, 189, 196language– content, 304– markup, 2– natural, 121– programming (C), 18– style sheet, 6dc:language– element, 100, 104language definition– theory, 238languages– multiple, 122, 240larg-group– old attribute on use (deprecated in

OMDoc 1.2), 327LATEX 4LaTeXML– binding, 295LaTeXML 295, 296Latin 121laymen 121layout– box, 86– schema, 17lbrack– attribute value– – for crossref-symbol on

presentation, 196lbrack– attribute– – on map, 191– – on presentation, use, 195–197– – on presentation, 314Learner– Model, 266learning 266– goal, 266left– inverse, 181– unit, 181legacy 120legacy

408 Index

– element, 40, 107, 120–122, 124, 164,170, 208, 323, 347

lemma 142lemma– attribute value– – for type on assertion, 143, 314– – for type on omtext, 40, 125, 324level– assertion, 309lexical– document– – model, 214li– element, 130library– document, 248libxml2 225license– CC, 102– Creative Commons, 38, 102cc:license– element, 102, 103lightweight– mechanism, VIIIline-feed 8lingua franca VIIIlink– global, 28, 282– local, 28, 282– simple, 130– theorem (global), 283link– element, 122, 130links– attribute– – on decomposition, 184– – on idp,ide, 130– – on idp, 130LISP 195lisp– attribute value– – for bracket-style on

presentation, 195list– bulleted, 130– description, 130– ordered, 130– semicolon-separated, 86– unordered, 130lists of– character, 58local 150, 152– assumption, 162

– chain, 182, 184– declaration, 168– import, 150– link, 28, 282– name, 85, 231– theory– – inclusion, 179, 180local– attribute value– – for original on data, 203, 322– – for scope on symbol, 137, 157– – for type on imports, 58, 150, 180local– attribute– – on path-just, 184locale (XSLT parameter) 240localization 240locator– resource (uniform), 5, 7logic– description, 286– first-order, 30, 46, 123, 278– first-order (classical), 166– higher-order, 123, 282– morphism, 308– propositional, 170– translation, 287logic– attribute– – on FMP, 123logical– calculus, 159– framework, 21, 278– system, 123logically– redundant, 218loose 155– definition, 136loose– attribute value– – for type on adt, 156

m: 114m:annotation– element, 115m:annotation-xml– element, 17, 115, 199m:apply– element, 17, 18, 115, 137, 194, 198,

238m:bvar– element, 18, 115, 120, 137, 194, 198m:ci

Index 409

– element, 17, 115, 119, 120, 198, 238m:cn– element, 17, 115m:csymbol– element, 115, 116, 119, 126m:divide– element, 17m:math– element, 107, 114, 120–122, 124, 164,

170, 323m:mathml– element, 208m:mfence– element, 15m:mfrac– element, 15m:mi– element, 15m:mn– element, 15m:mo– element, 15m:mover– element, 15m:mroot– element, 15m:mrow– element, 15m:mstyle– element, 15m:msub– element, 15m:msubsup– element, 15m:msup– element, 15m:munder– element, 15m:munderover– element, 15m:plus– element, 17m:semantics– element, 17, 115–117, 199machine-readable 18, 107macro– semantic, 296magma 47Makefiles 236Management– Knowledge (Mathematical), VIII,

241management

– change, 182, 219, 258, 260– configuration, 258– content, 66– correctness, 163– document, 6, 97– knowledge, XII, 67– knowledge (mathematical), XI, 182– rights, 92, 97– rights (Digital), 102management of– change, 284manager– context (dynamic), 265– context (static), 265– document, 264Mandelbrot– set, VIImap– element, 191, 323, 326, 327Maple™ 30, 249, 250, 304markup– Content, 30– content, 4, 28, 30, 31– context, 22, 28– CSS, 205– document, 1– error (in-place), 93, 111– index, 130– language, 2– multilingual (parallel), 126, 131– parallel, 17– presentation, 3– semantic, 30, 31, 290match– attribute, 192math– attribute value– – for bracket-style on

presentation, 195m:math– element, 107, 114, 120–122, 124, 164,

170, 323math– element, 256math-enabled– web– – browser, 264MathDox 243, 262–265Mathematica– notebook, 189Mathematica 203mathematica– attribute value

410 Index

– – for format on use, 189Mathematical– Knowledge– – Management, VIII, 241mathematical– assistant– – system, 25– concept, 136– context, 126– document, 2, 21, 309– error, 93– formula, 14, 21– glyph, 293– knowledge, VIII, XII, 1– – dissemination, XI– – management, XI, 182– – repository, 309– object, 14– practice, 309– proofs, 163– publication, 312– service, 75, 265, 304– software– – system, 2, 202– software bus, 75– statement, 21, 125, 126, 133, 180– symbol, 310– text, 99, 230, 310– text-editors, 309– theory, 22, 133, 282– vernacular, 30, 36, 45, 98, 121, 125,

128, 129, 159mathematical– knowledge– – base, 242Mathematical Objects– RNC Module MOBJ, 347– spec Module MOBJ, 84, 90, 107, 122,

217, 218, 220Mathematical Statements– RNC Module ST, 351– rnc Module ST, 345– spec Module ST, 84, 133, 149, 218,

333–338Mathematical Text– RNC Module MTXT, 348– spec Module MTXT, 84, 121, 122,

218, 220, 333–338Mathematica

® 14, 30, 189, 242,249, 250, 262, 298, 299, 301–304

mathematics XII– formal, 30– informal, 30

– K-14, 116mathematics library– digital (universal), VIIIMathML 1, 10, 14–21, 28, 32, 84–86,

107, 110, 114–117, 119, 120, 153, 189,194, 197, 198, 214, 227, 231, 240,242, 244, 247–249, 254, 256, 257, 269,270, 296, 301, 304, 348, 363, 364, 369

– content, 10, 15–19, 21, 27, 29, 31, 35,40, 41, 107, 114–116, 118–120, 124,126, 127, 153, 189, 194, 199, 235, 237,238, 256, 296, 304, 306, 319, 323

– presentation, 10, 15–17, 115, 119,189, 194, 197, 198, 227

MathML 197m:mathml– element, 208MathPlayer 16MathWeb XII, 75, 77, 223, 252, 280MathWeb-SB 26, 75, 77MathWeb-WS 75, 77, 79MathWeb OMDoc 219Maxima 249, 250, 269Maya XIII, 242, 281–285, 288MBase 35, 67, 77, 78, 242, 243, 252,

253, 280, 283, 304mc– element, 209, 210, 323measure– element, 141, 175, 323, 324, 329measure function 141mechanism– lightweight, VIIImembership– namespace, 7mental– representation, 137meta-data 36metadata 38, 50, 91, 97– CC, 102– content dictionary, 153metadata– element, 37, 40, 50, 71, 91, 92, 94,

97–100, 102, 104, 125, 138, 149, 203,216, 290, 321, 322, 325, 326, 328–330

method 163– proof, 163, 164, 178method– element, 79, 163–165, 315, 329, 330m:mfence– element, 15m:mfrac– element, 15

Index 411

m:mi– element, 15Microsoft– Internet Explorer, 16, 77, 235– Word, 3migration– format, 31MIME– type, 38, 100, 110, 203, 205, 206, 341misconception– element, 268Mizar 22, 23, 27, 36MMiSS 243, 258, 259, 261m:mn– element, 15mnemonic– entity, 10m:mo– element, 15MOBJ (Mathematical Objects)– RNC Module, 347– spec Module, 84, 90, 107, 122, 217,

218, 220mode– nXML, 232Model– Learner, 266model– document, 214– document (lexical), 214– document object, 18– generator, 75modularization 230module 83– DTD, 230– element, 230module– attribute– – on omdoc, 42module inclusion– entity, 230modules– attribute, 83, 90, 91, 217– – on omdoc, 38, 50, 91– – on omgroup, 324monograph 22monoid 60, 137monoid 152Moore’s Law VIImorphism 174– base, 176– consequence, 282– logic, 308

– theory, 173, 219morphism– element, 57, 61, 62, 175, 176, 178,

324motivation– attribute value– – for type on omtext, 125m:mover– element, 15MoWGLI 160mOZart 252Mozilla 16, 235, 242, 247, 249–251,

269MP3– recording, 102mq:anyorder– attribute, 255–257mq:generic– attribute, 255–257m:mroot– element, 15m:mrow– element, 15MS– Internet Explorer, 16, 77, 235m:mstyle– element, 15m:msub– element, 15m:msubsup– element, 15m:msup– element, 15MTXT (Mathematical Text)– RNC Module, 348– spec Module, 84, 121, 122, 218, 220,

333–338multi-format– collection, 208multi-logic– group, 123, 138, 209multi-system– group, 137multilingual 126, 139– document, 240– documents, 122– group, 39, 40, 122, 123, 126, 138, 146,

163, 204, 209, 216, 240– support, 122, 240– text, 218multiple– languages, 122, 240Multiple-choice exercise 210

412 Index

m:munder– element, 15m:munderover– element, 15

omcd:Name– element, 109name– local, 85, 231– qualified, 7, 8, 188, 190, 231– simple, 8, 9name– attribute– – on attribute, 191– – on constructor, 156– – on definition, 42– – on element, 190– – on om:OMS, 31, 108– – on om:OMV, om:OMS, 119– – on om:OMV, 109– – on OMS, 18, 43– – on OMV, 19, 42– – on param, 207, 208– – on recognizer, 157– – on selector, 157– – on sortdef, 156, 330– – on symbol, 42, 137, 138, 157, 314– – on term, 128, 326named– anchor, 10namespace 7, 122, 188, 190– abbreviation, 8, 231– Creative Commons, 38, 103– declaration, 7, 38, 85– default, 85– Dublin Core, 38, 98– empty, 85– foreign, 85– membership, 7– OMDoc, 38, 83– OpenMath, 38, 108– prefix, 85, 98, 103, 108, 114– – declaration, 38, 85– prefixed, 42– URI, 90, 231– XML, 7, 8, 230namespace-aware 114namespace prefix– declaration, 42narrative 125, 217– OMDoc, 66narrative– attribute value

– – for type on omgroup, 329narrative– attribute value– – for type on omgroup (deprecated in

OMDoc 1.2), 93narrative-centered 95– view, 89narrative-structured 89, 217– document, 66, 240M– structure, 243natural– deduction, 170, 329– – calculus, 79– – proof, 167– – style, 167– language, 121– number, 155natural language– analysis, 310navigation 293– content, 292nb2omdoc 301neut 152new– symbol, 135new– attribute value– – for show on omlet, 206nl 100, 122no– attribute value– – for crossref-symbol on

presentation, 196– – for inductive on hypothesis, 163– – for total on selector, 157, 330no-consequence– attribute value– – for status on assertion, 144node– attribute, 7– text, 7non-applied– occurrence, 199norm(ISO), 100, 122, 240(ISO), 38, 99, 334, 335normal form– ref, 95normalization– DTD, 229– URI, 151normalized 228

Index 413

normative– grammar– – formalism, 228– precedence, 9normed– attribute value– – for action on dc:date, 99notation 2– Polish, 108– prefix, 108note 130– editorial, 293note– element, 122, 130, 131notebook– Mathematica, 189NotebookML 301notice– attribute– – on cc:requirements, 103NqThm 278, 279ns– attribute– – on attribute, 191, 321– – on element, 190, 323NS.prefixed 231nsgmls 228, 299number 115– natural, 155– natural (positive), 156NuPrL 23, 36, 165nXML– mode, 232

o: 231object– OpenMath, 18, 108– binding, 137– external, 205– mathematical, 14– proof, 169, 170– symbol, 238object– attribute value– – for role on selector, 325– – for role on symbol, 137, 157– – for type on constructor, 322– – for type on recognizer, 325– – for valuetype on param, 208xhtml:object– element, 205, 206, 324object-oriented– programming, 66

object model– document, 205, 213obligation– proof, 178, 281–283obligation

– attribute value– – for type on assertion, 143– – for type on omtext, 324obligation

– element, 57, 178, 180, 182, 186, 216,324, 327–329

obsolete

– attribute value– – for cdstatus on theory, 153occurrence– bound, 120– defining, 119, 198– non-applied, 199official

– attribute value– – for cdstatus on theory, 153ol

– element, 122, 130om: 38, 108om:*

– element, 324om:OMA

– element, 18, 43, 108, 109, 112–114,194, 195, 238

om:OMATP

– element, 110om:OMATTR

– element, 110, 112, 116, 117, 119, 137,194, 198

om:OMB

– element, 111om:OMBIND

– element, 18, 108–110, 112, 119, 137,192, 194, 195, 198, 238

om:OMBVAR

– element, 18, 108–110, 119, 191, 192,198

om:OME

– element, 111om:OMF

– element, 111om:OMFOREIGN

– element, 110, 198, 324om:OMI

– element, 111om:OMOBJ

414 Index

– element, 7, 18, 42, 43, 46, 47, 107,108, 112, 120–122, 124, 164, 170, 208,216, 280, 323, 329, 330

om:OMR– element, 47, 112–114, 216, 324om:OMS– element, 7, 18, 42, 43, 108–110, 119,

128, 149, 153, 218om:OMSTR– element, 111, 329om:OMV– element, 18, 19, 42, 108, 109, 119,

238om:OMA– element, 18, 43, 108, 109, 112–114,

194, 195, 238om:OMATP– element, 110om:OMATTR– element, 110, 112, 116, 117, 119, 137,

194, 198om:OMB– element, 111om:OMBIND– element, 18, 108–110, 112, 119, 137,

192, 194, 195, 198, 238om:OMBVAR– element, 18, 108–110, 119, 191, 192,

198omcd:CDDefinition– element, 109omcd:CDName– element, 50omcd:CDURL– element, 50omcd:CMP– element, 19, 20omcd:FMP– element, 19, 20omcd:Name– element, 109OMDoc– content, 66– content dictionary, 42, 153, 218– namespace, 38, 83– – URI, 83– narrative, 66OMDoc VIII, XII, XIII, 1–3, 6, 7, 9,

10, 14, 18, 20, 23–38, 40, 42, 44, 47,49, 50, 52, 56–58, 61, 65–75, 77–79,81, 83–87, 90–104, 107–109, 111,114–117, 119–122, 124–131, 133, 134,136–140, 142, 143, 145–153, 155–157,

160–162, 164–166, 169–171, 173,175–182, 184, 185, 187–195, 198–206,208, 209, 211, 213–221, 223–225,227–232, 235–249, 251, 252, 261,263, 266–270, 272–283, 286, 288–290,292–295, 297–301, 303, 304, 306–308,312–316, 319, 320, 322, 324, 325,327–331, 333, 339, 342–349, 351, 353,354, 357, 361

OMDoc

– version 1.0, 112– version 1.1, 27, 86, 93, 112, 160, 235,

319, 320– version 1.2, 27, 38, 93, 98, 112, 230,

319, 320, 324– version 1, 27, 319omdoc

– element, 9, 39, 50, 83, 85, 90–92, 94,95, 99, 104, 217, 218, 232, 276, 324

omdoc-basic 42omdoc.cat 225omdoc.prefix 231omdoc1.1adapt1.2.xsl 235omdoc2html.xsl 240omdoc2pvs.xsl 238omdoc2share.xsl 240omdoc2sys.xsl 238omdoc2tex.xsl 240omdoc: 231OMDOM 213om:OME

– element, 111Ωmega 309om:OMF

– element, 111om:OMFOREIGN

– element, 110, 198, 324omgroup

– element, 40, 71, 90, 91, 93–95, 149,217, 290, 324, 329

om:OMI

– element, 111omlet

– element, 71, 122, 205–207, 230, 324,328–330, 339–341

om:OMOBJ

– element, 7, 18, 42, 43, 46, 47, 107,108, 112, 120–122, 124, 164, 170, 208,216, 280, 323, 329, 330

om:OMR

– element, 47, 112–114, 216, 324om:OMS

Index 415

– element, 7, 18, 42, 43, 108–110, 119,128, 149, 153, 218

om:OMSTR– element, 111, 329omstyle– element, 188–190, 193, 194, 216, 236,

324, 329, 331, 340omtext– element, 7, 39, 40, 43, 44, 71, 86, 92,

124–126, 148, 162, 216, 218, 266, 323,324, 329

om:OMV– element, 18, 19, 42, 108, 109, 119,

238onLoad– attribute value– – for action on omlet, 206onPresent– attribute value– – for action on omlet, 206onRequest– attribute value– – for action on omlet, 206ontologically– promiscuous, 308ontology 258op 152, 216Open eBook 101opening– tag, 6OpenMath– content dictionaries– – a, 279– namespace, 38, 108– – URI, 108OpenMath 1, 7, 8, 10, 14, 15, 17–21,

26–31, 33, 35, 38, 40–43, 47, 49, 50,52, 55, 84–86, 89, 92, 93, 107–114,116–120, 122–124, 127, 137, 153, 192,197, 198, 200, 214, 218, 219, 231, 235,237–239, 244, 249, 250, 254, 256, 262,263, 265, 269, 270, 272, 279, 280,299, 302–304, 306, 307, 314, 315, 323,324, 326, 330, 339, 348, 361, 385, 386

– object, 18OpenMath elements– extra attributes id and xref, 112OpenOffice 251operator– binding, 109, 111– description (definite), 60– error, 111OQMath 244, 272, 273

ordered– list, 130ordering 136, 141ordering– element, 141, 175, 324, 329original– attribute– – on data, 203, 322other– attribute value– – for action on omlet, 206– – for show on omlet, 206outfix– attribute value– – for fixity on presentation, 314output 71output– element, 71, 204, 325Owl 276Oz 252

p– element, 122, 129packing– sphere, VIIIpadding 86swim:page– element, 276pair 43– attribute-value, 191paragraph 94, 129parallel– markup, 17– multilingual– – markup, 126, 131param– element, 205, 207, 208parameter 55, 164, 240– XSLT, 240– entity, 42, 228, 229parameter– element, 329parameter entity 231– reference, 229parameters– attribute– – on adt, 156, 315, 321parametric– theory, 55parent– old attribute on presentation

(deprecated in OMDoc 1.2), 330parsed

416 Index

– character data, 91parser 71– validating, 8, 227– XML, 8, 92, 238– XML (validating), 9, 232partial– function, 157partial– attribute value, 330path-just– element, 184, 185, 321, 325pattern 140pattern– attribute value– – for type on definition, 141, 322– – for type on morphism, 175pattern– element, 330PDF 4, 269Peano– axioms, 134, 135, 155permission 39permissions 102cc:permissions– element, 39, 103permitted– attribute value, 103persistent– comment, 92PF (Proofs and Arguments)– DTD Module, 230– RNC Module, 354– rnc Module, 346– spec Module, 84, 159, 160, 218,

334–337phrase 126, 127– index, 130phrase– element, 87, 121, 122, 124, 126, 148,

189, 190, 321, 322, 325, 327physical– representation, 137pickling 252picture 102pixel-on-screen 3planning– proof (knowledge-based), 25plug-in 205, 206plus 28m:plus– element, 17pmml– attribute value

– – for format on legacy, 120– – for format on use, 189pointer 119, 120pointing– semantics by, 30Polish– notation, 108polynomial 30positioning 86positive– natural– – number, 156postfix– attribute value– – for fixity on presentation, 195,

314PostScript 4postulate– attribute value– – for type on assertion, 143– – for type on omtext, 125, 324postulated– theory– – inclusion, 177PowerPoint– Content in, 290PowerPoint 298MS PowerPoint 290–293PPT 290–293practice– mathematical, 309precedence– normative, 9precedence– attribute– – on map, 191– – on presentation, 195predecessor– function, 56, 155, 156predefined– symbol, 238predicate 157– recognizer, 157prefix– namespace, 85, 98, 103, 108, 114– namespace (explicit), 114– notation, 108prefix– attribute value– – for fixity on presentation, 195,

314prefixed– namespace, 42

Index 417

preloading– semantic, 296premise– element, 70, 79, 164–166, 330preparation language– document, 242PRES (Presentation)– RNC Module, 357– rnc Module, 345– spec Module, 84, 120, 187, 218, 333,

334, 336–338Presentation– Component, 266– RNC Module PRES, 357– rnc Module PRES, 345– spec Module PRES, 84, 120, 187,

218, 333, 334, 336–338presentation 89, 240, 290– knowledge, 67– markup, 3– proof, 163, 243– semantics-induced, 292– slides, 66presentation– element, 188, 192–195, 197, 198, 216,

235, 236, 238, 239, 314, 315, 325,330, 331, 343

Presentation MathML 10, 15–17,115, 119, 189, 194, 197, 198, 227

P.Rex 309primitive– symbol, 67, 68, 139principal– type, 139principle of– conservative– – extension, 23priority-union 104private– attribute value– – for cdstatus on theory, 153private– element, 67, 164, 202–204, 206, 208,

216, 322, 325, 327–330, 340, 342problem 142procedure– decision, 25process– calculus, 286– evolutionary, 282– reasoning, 116, 138processing instruction– style sheet, 87

processor– Xml, 6– XML, 225product– Cartesian, 43program 202programming– construct, 263– object-oriented, 66prohibited– attribute value, 103prohibitions 102cc:prohibitions– element, 39, 103Prolog 195promiscuous– ontologically, 308proof 133, 159, 178, 304– assistant, 309– checking, 30– deduction (natural), 167– development– – environment, 25– incomplete, 162– inductive, 168– method, 163, 164, 178– object, 169, 170– obligation, 178, 281–283– presentation, 163, 243– – system, 169, 202– sequent, 166– style (sequent), 167– verification, 30proof– attribute value– – for type on omtext, 125proof– element, 70, 78, 161–164, 166, 167,

169, 171, 184, 314, 316, 323, 325, 330proof-theoretic 307proof assistance– system, 309proofobject– element, 164, 169–171, 325, 330proofs– mathematical, 163proofs– attribute– – on assertion, 70, 328Proofs and Arguments– DTD Module PF, 230– RNC Module PF, 354– rnc Module PF, 346

418 Index

– spec Module PF, 84, 159, 160, 218,334–337

property– constitutive, 20– CSS, 96– intellectual, 102– mathematical (commented), 19– mathematical (formal), 19proposition– attribute value– – for type on assertion, 143– – for type on omtext, 125, 324propositional– logic, 170protocol-based– integration, 304ws:prove– element, 77prover– theorem, 202, 203– theorem (automated), 25, 75– theorem (first-order), 77, 278provers– theorem (automated), 304pto– attribute– – on data, 203, 321, 322, 325pto-version– attribute– – on data, 203, 321, 322, 325public– Identifier, 9– identifier, 38, 225, 228publication 309– Internet, 2– mathematical, 312dc:publisher– element, 99, 322Pvs 55, 238, 239, 304, 305, 307

QMath 242, 244–247, 249–251, 272,277

qmath– attribute value– – for format on legacy, 120qualified– name, 7, 8, 188, 190, 231questions– asked (frequently), 223QUIZ (Exercises)– RNC Module, 359– rnc Module, 346– spec Module, 84, 209, 218, 219, 333,

335, 337

rank– attribute– – on premise, 330rarg-group– old attribute on use (deprecated in

OMDoc 1.2), 327rbrack– attribute value– – for crossref-symbol on

presentation, 196rbrack– attribute– – on map, 191– – on presentation, use, 195–197– – on presentation, 314Rdf 74, 92, 104, 248, 274, 276reasoning– backward, 168– forward, 167– process, 116, 138– system, 75recognizer– predicate, 157recognizer– element, 157, 325, 328, 330recommendation 6, 14recording– MP3, 102recurse– element, 190, 191, 327, 330recursive– equation, 140– function, 140, 155recursive– attribute value– – for type on morphism, 175reducible– ref, 95reduction– ref, 95redundant– logically, 218ref– attribute value– – for valuetype on param, 208ref– element, 71, 73, 94–96, 122, 124, 216,

236, 325, 329, 330, 343ref-normal form 95ref-reducible 95ref-reduction 95ref-target– ref-target, 95

Index 419

ref-target 95ref-valid 95reference– parameter entity, 229– URI, 10, 42, 68, 90, 94, 115, 120, 130,

140, 142, 150, 176, 184, 185, 188, 189,202, 203, 206, 208

referencing 85refinement– controlled, 242reformulates– attribute– – on private, 67, 203, 325relation 43– “is a”, 68– consequence, 30– inheritance, 151, 173– inheritance (semantic), 297dc:relation– element, 100relative– URI, 151RelaxNG 8, 9, 224, 227, 228, 232,

345–348, 361, 363renaming– variable, 110, 119renumbering 4replace– attribute value– – for show on omlet, 206replaces– old attribute on private (deprecated

in OMDoc 1.2), 325, 330report-errors 236repository– knowledge (mathematical), 309representation– formal, 310– knowledge, 67– mental, 137– physical, 137– static, 311– theorem, 22representational– rigor, XIIreproduction 39reproduction– attribute– – on cc:permissions, 103requation– element, 140, 141, 175, 216, 324request– computation, 304

requirement– specification, 259, 281requirements 102cc:requirements– element, 39, 103requires– attribute– – on code, 71– – on private, code, 202– – on use, xslt, style, 189, 196resource description format 92retrieval– document, 35– information, VIIreuse– component, 281– document, 258– theory, 23review– date, 154review-on– attribute value– – for action on dc:date, 99revision 153rhetoric– role, 125rhetoric/didactic– figure, 73, 74Rich Text Structure– RNC Module RT, 356– spec Module RT, 84, 93, 121, 122,

128–131, 218, 220, 324, 334–338, 341,344

right– inverse, 181– unit, 181rights– management, 92, 97dc:rights– element, 100, 102, 104rigor– representational, XIIrigorous 121RNC 355RNC Module– ADT (Abstract Data Types), 353– CTH (Complex Theories), 355– DC (Dublin Core Metadata), 350– DOC (Document Structure), 349– EXT (Extensions), 356– MOBJ (Mathematical Objects), 347– MTXT (Mathematical Text), 348– PF (Proofs and Arguments), 354

420 Index

– PRES (Presentation), 357– QUIZ (Exercises), 359– RT (Rich Text Structure), 356– ST (Mathematical Statements), 351rnc Module– EXT (Extensions), 346– PF (Proofs and Arguments), 346– PRES (Presentation), 345– QUIZ (Exercises), 346– ST (Mathematical Statements), 345role 109– rhetoric, 125role– attribute, 98, 329– – on constructor, 322– – on dc:*, 101– – on presentation, 194, 330– – on recognizer, 325– – on selector, 325– – on sortdef, 326– – on symbol, 109, 110, 137, 157, 326– – on term, 43, 128root– document, 7, 9, 83, 99, 218row– table, 130rrl 278RT (Rich Text Structure)– RNC Module, 356– spec Module, 84, 93, 121, 122,

128–131, 218, 220, 324, 334–338, 341,344

rule– inference, 163, 164– inference (derived), 171RXP 228, 299

satisfiable– attribute value– – for status on assertion, 144Sax 280saxon 235Schema– Record (Bibliographic), 248schema 90, 224, 227, 232– instance, 232– layout, 17– XML, 8, 39, 86, 213, 228, 345xsi:schemaLocation– attribute– – on omdoc, 232Scheme 309scheme

– attribute– – on dc:identifier, 100science XII– computer, 65scientific– antecedent, 101– background, 2– editor, 309scope 165scope– attribute– – on symbol, 137, 157search– content, 292searching 247section 22, 94– CDATA, 8sectioning– attribute value– – for type on omgroup, 94see– attribute– – on idp,ide, 130seealso– attribute– – on idp,ide, 130select– attribute– – on attribute, 191, 321– – on map, 191– – on recurse, 191– – on value-of, 190selector– symbol, 155–157selector– element, 114, 157, 325, 326, 330selfinclusion– theory, 60, 62Semantic– Web, 286semantic– annotation, 311– authoring– – tool, 291– content, 310– document– – format, 311– error, 111– inheritance– – relation, 297– interrelation, 258– macro, 296– markup, 30, 31, 290

Index 421

– – format, 30– preloading, 296semantic-attribution– attribute value– – for role on symbol, 137, 326semantically– annotated– – documents, 311Semantic MediaWiki 275semantics– by pointing, 19– evaluation, 312– formal, 310m:semantics– element, 17, 115–117, 199semantics-induced– presentation, 292semantics by– pointing, 30semicolon-separated– list, 86semigroup 60– Abelian, 152semigroup 152Sentido 242, 246–251separator– attribute value– – for crossref-symbol on

presentation, 196separator– element, 191, 323separator– attribute– – on presentation, use, 196sequence– attribute value– – for type on omgroup, 93, 94, 329sequent 124, 329– proof, 166– style, 166– – proof, 167server– document, 264service– description, 304– mathematical, 75, 265, 304– mathematical (external), 263– web, 6set– inductively defined, 56– information, 229– insertion, 155– intersection, 124

– Mandelbrot, VII– theory, 304set 152setname1 117SGML 6, 228shared– component, 281sharing– document, 258– structure, 111, 112shorthand– xpointer, 10show– attribute, 206– – on omlet, 206side-effect 71Siette 268simple– definition, 135– link, 130– name, 8, 9simple– attribute value– – for type on definition, 46, 140,

141Simple Generalized Markup Language

6size– attribute– – on data, 203, 328slicing 40slide 66slide– attribute value– – for type on omgroup, 71slide presentation 66Soap 75–78software bus– mathematical, 75solution 209solution– element, 209, 210, 216, 325solver– constraint, 75sort 56, 138, 155, 156– symbol, 156sort– attribute value– – for role on selector, 326– – for role on symbol, 137, 157sort– attribute– – on argument, 328

422 Index

– old attribute on argument (depre-cated in OMDoc 1.2), 320

sort-by– attribute– – on idp, 130sortdef– element, 56, 156, 157, 216, 321, 326,

327, 330source 4– comment, 92– document, 4– theory, 56, 57, 150, 174, 177, 180dc:source– element, 50, 100, 104Spass 75–79specification 55, 219– algebraic, 23, 27, 55, 319– heterogeneous, 286– requirement, 259, 281– system, 281specifications– structured, 281spec Module– ADT (Abstract Data Types), 84,

146, 155, 156, 218, 219, 333–335, 337– CC (Creative Commons Metadata),

84, 97, 102, 335–337– CTH (Complex Theories), 84, 173,

175, 177, 180, 182, 218, 219, 281, 288,333, 335, 336, 338

– DC (Dublin Core Metadata), 84, 97,98, 218, 220, 334, 335, 337, 338

– DG (Development Graphs), 84, 173,182, 184, 218, 288, 334, 336

– DOC (Document Structure), 83, 84,89, 122, 217, 218, 220, 335–338

– EXT (Extensions), 84, 122, 201, 218,219, 334–337

– MOBJ (Mathematical Objects), 84,90, 107, 122, 217, 218, 220

– MTXT (Mathematical Text), 84,121, 122, 218, 220, 333–338

– PF (Proofs and Arguments), 84, 159,160, 218, 334–337

– PRES (Presentation), 84, 120, 187,218, 333, 334, 336–338

– QUIZ (Exercises), 84, 209, 218, 219,333, 335, 337

– RT (Rich Text Structure), 84, 93,121, 122, 128–131, 218, 220, 324,334–338, 341, 344

– ST (Mathematical Statements), 84,133, 149, 218, 333–338

sped Module– DG (Development Graphs), 281sphere– packing, VIIIST (Mathematical Statements)– RNC Module, 351– rnc Module, 345– spec Module, 84, 133, 149, 218,

333–338standalone– attribute– – on ?xml, 229start– tag, 38, 42state 263statement 128– mathematical, 21, 125, 126, 133, 180static– context, 263, 264– – manager, 265– representation, 311status– content dictionary, 153status– attribute– – on assertion, 142, 144, 320STEM XIIstep– inductive, 168– proof (bottom-up), 167– proof (top-down), 168steps– gap, 162strict 155string 111– empty, 148strings 148– concatenation, 148structural– convention, 2– theory– – inclusion, 177structurally– included, 177structure– abstract, 41– bracketing (balanced), 6– conceptual, 243– content, 126– discourse, 242– document, 218, 260– higher-level, 40– M, 243

Index 423

– sharing, 111, 112structured– document, 261– specifications, 281structuring– in-the-large, 259sts 117, 118style– deduction (natural), 167– file, 4, 16– information, 188– sequent, 166style– element, 189, 190, 192, 193, 196, 198,

326, 330, 331style– attribute, 86, 87, 90, 94, 130, 210,

320– – on definition, 149– – on omlet, 205– – on omtext, 86– – on phrase, 126– – on ref, 71, 96– – on with, 331– attribute (meaning changed in 1.2),

320– attribute (new meaning 1.2), 320Style Sheet– Cascading, 86style sheet 4, 6, 187, 224, 235– cascading, 320– CSS, 86, 224– language, 6– processing instruction, 87– XSL, 224Subversion 223dc:subject– element, 99, 138, 321, 322, 326subset– external, 229– internal, 42, 229successor– function, 155, 157support– multilingual, 122, 240svg 269svn 223, 224SWiM 274, 275, 277swim:page– element, 276symbol 18, 108, 115, 134, 136, 218– bullet, 94– constructor, 155, 156

– declaration, 22, 139, 153– defined, 139– export, 137– feature, 117– mathematical, 310– new, 135– object, 238– predefined, 238– primitive, 67, 68, 139– selector, 155–157– sort, 156symbol– element, 42, 43, 68, 110, 136–139,

143, 146, 152, 158, 163, 164, 191, 216,238, 239, 314, 316, 321–323, 326, 331

syntax– abstract, 41system– algebra, 29– assistant (mathematical), 25– axiom, 135– clipboard, 247– computer algebra, 19, 25, 29, 75, 111,

202, 203, 238, 304– concept formation (automated), 75– development (theory), 202– entailment, 287– formal, 30– ID, 224– identifier, 225– logical, 123– presentation (proof), 169, 202– proof assistance, 309– reasoning, 75– software (mathematical), 2, 202– specification, 281– type, 139– visualization, 304system– attribute– – on type, 139, 327

table 130– data, 130– header, 130– row, 130table– element, 122, 130tag– closing, 6, 39– opening, 6– start, 38, 42target 4, 95, 112

424 Index

– ref, 95– document, 4– theory, 57, 150, 174, 177, 180TargetLanguage 240tautologous-conclusion– attribute value– – for status on assertion, 144tautology– attribute value– – for status on assertion, 144taxonomy 66, 71td– element, 130teaching VIIItechnical– term, 127technology XIItemplate 187– xslt, 236– head, 192term– constructor, 155– declaration, 139, 327– technical, 127term– element, 43, 121, 122, 126–128, 326terminating– attribute– – on measure, 141– – on ordering, 324termination 136TeX– attribute value– – for format on legacy, 120– – for format on use, 189TEX 4, 14TEXmacs 309TexPoint 293Text as Dublin Core Type 99Text 38, 99, 100, 217text– color, 86– index, 130– mathematical, 99, 230, 310– multilingual, 218– node, 7text– element, 190, 191, 327, 331text-editors– mathematical, 309text/plain– attribute value– – for format on data, 203

textbook 22tgroup– element, 149, 326th– element, 130Theorem– Four-Colour, VII– Incompleteness (Godel’s), VIItheorem 23, 84, 128, 133, 142, 177,

178– prover, 202, 203– representation, 22theorem– attribute value– – for status on assertion, 144– – for type on assertion, 143– – for type on attribute, 148– – for type on omtext, 40, 125, 324Theorema 251theorem link 282theorem prover 30, 278– induction, 278, 279theorem provers– induction, 278, 279theory 55, 66, 142, 282– development– – system, 202– graph, 178– home, 134– inclusion, 56–58, 173, 177, 179, 180,

182, 183– inheritance, 73– in scope of, 165– instance, 56– integration, 305– interface, 306– interpretation, 173– language definition, 238– mathematical, 22, 133, 282– morphism, 173, 219– parameter (actual), 58– parameter (formal), 58– parametric, 55– reuse, 23– selfinclusion, 60, 62– set, 304– source, 56, 57, 150, 174, 177, 180– target, 57, 150, 174, 177, 180theory– element, 42, 50, 95, 134, 143, 146,

149–153, 156, 179, 238, 276, 297, 314,326, 327, 329, 330, 341

theory

Index 425

– attribute– – on alternative, 146, 320– – on assertion, 77, 142– – on axiom-inclusion, 321– – on decomposition, 322– – on example, 322– – on exercise, 322– – on hint, 323– – on mc, 323– – on omdoc, 324– – on omgroup, 149, 324– – on omtext, 324– – on presentation, 330– – on private, code, 202– – on private, 321, 325– – on proof, 161, 330– – on solution, 325– – on statement, 134, 152– – on theory-inclusion, 327– – on type, 143, 327– old attribute on presentation

(deprecated in OMDoc 1.2), 325theory-constitutive 139, 143, 156– element, 134theory- inclusion– element, 180theory-inclusion– element, 176, 178, 184, 185, 282, 283,

322, 327, 329, 331, 341, 342theory element– constitutive, 134thesis– advisor, 101thesis– attribute value– – for type on omtext, 125ths– attribute value– – for role on dc:*, 101Tim– Berners-Lee, 32time– development, 281timestamp– old attribute on axiom-inclusion

(deprecated in OMDoc 1.2), 328– old attribute on theory-inclusion

(deprecated in OMDoc 1.1), 331dc:title– element, 71, 94, 98, 216, 326to– attribute– – on axiom-inclusion, 180

– – on theory-inclusion, 178token– element, 115tool– authoring (semantic), 291toolbar 291top-down– proof– – step, 168top-level 149, 178, 184– domain, 103– element, 90total 158– function, 157total– attribute– – on selector, 157, 330– attribute value, 330TPS 239, 304, 305, 307TPTP 278tr– element, 130Tramp 79trang 232transcriber 101transition– attribute value– – for type on omtext, 125translation 131– logic, 287translation-equivalent 20translator 38, 101trc– attribute value– – for role on dc:*, 101tree 67, 159, 165– document, 6– expansion, 216trl– attribute value– – for role on dc:*, 101true– attribute value– – for verdict on answer, 210Trybulec– Andrzej, 27Turing 16Tutorial– Component, 266tutoring 309Twelf 23, 278type 116, 138, 156– assertions, 143

426 Index

– attribute, 9– data (abstract), 259– declaration, 138– ID, 10, 27, 85, 86, 95, 319– IDREF, 328– integration, 284– MIME, 38, 100, 110, 203, 205, 206,

341– principal, 139– system, 139type 117– attribute value– – for role on symbol, 137, 157dc:type– element, 99, 100, 104, 216, 217type– element, 137, 139, 143, 146, 157, 315,

320, 327, 331type– attribute, 94– – on adt, 156, 321– – on assertion, 142, 143, 229, 314,

328– – on attribute, 148– – on axiom, 138, 321– – on definition, 28, 46, 47, 139, 140– – on derive, 162– – on example, 44, 69, 146– – on ignore, 93– – on imports, 58, 150, 180– – on m:cn, 115– – on morphism, 175, 324– – on note, 130– – on omdoc, 91– – on omgroup, 40, 71, 93, 94, 329– – on omtext, 40, 92, 125, 126, 324,

329– – on phrase, 126– – on ref, 94, 95, 330– attribute (on MathML objects), 117– old attribute on code (deprecated in

OMDoc 1.1), 321, 325– old attribute on omlet (deprecated

in OMDoc 1.2), 329– old attribute on selector (depre-

cated in OMDoc 1.1), 330– old attribute on sortdef (deprecated

in OMDoc 1.2), 326types– formulae as, 21

ul– element, 122, 130

underspecification– assertion-level proof, 312Unicode 6, 214, 215Unicode 7, 9, 10, 15, 214, 227, 244,

250, 314uniform– resource– – identifier, 5– – locator, 5, 7uniqueness 85uniqueness– attribute– – on definition, 140– – on morphism, 175unit– left, 181– right, 181universal– digital– – mathematics library, VIIIUnix 225, 236unordered– list, 130unsatisfiable– attribute value– – for status on assertion, 144unsatisfiable-conclusion– attribute value– – for status on assertion, 144updated– attribute value– – for action on dc:date, 99URI 5, 9, 30, 38, 99, 100, 108, 109,

138, 139, 146, 151, 153, 228, 229– base, 151– effective, 151– namespace, 90, 231– namespace (Creative Commons), 103– namespace (Dublin Core), 98– namespace (OMDoc), 83– namespace (OpenMath), 108– normalization, 151– reference, 10, 42, 68, 90, 94, 115, 120,

130, 140, 142, 150, 176, 184, 185, 188,189, 202, 203, 206, 208

– relative, 151URL 5, 7, 224, 225use– element, 194–198, 238, 239, 314, 327,

331UTF-8– encoding, 37

valid

Index 427

– ref, 95validating– parser, 8, 227– XML– – parser, 9, 232validation 227validity 9, 227value 110, 140value– attribute– – on param, 208value-of– element, 190, 327, 331valuetype– attribute– – on param, 208variable 18, 108, 115– bound, 18, 108, 109, 119, 198– renaming, 110, 119variant 261– font, 86verbalizes– attribute– – on omtext, 126, 324– – on phrase, 126, 127, 148verdict– attribute– – on answer, 210verification– in-the-large, 281, 285– in-the-small, 282, 285– proof, 30verified– mathematical– – document, 310vernacular– chemistry, 122– computer science, 122– mathematical, 30, 36, 45, 98, 121,

125, 128, 129, 159version 153– control, 258version– attribute, 83– – on cc:license, 103– – on omdoc, 38, 90, 230version number– content dictionary, 153via– attribute– – on inclusion, 179via a morphism 174view

– document, 248– knowledge-centered, 89– narrative-centered, 89visualization– system, 304VSE-SL 281, 282

W3C 6, 14, 32, 75, 232Web– Semantic, 286– World Wide, 5, 13, 91web– agent, 5– application, 264– service, 6well-defined 135well-formed 229whitespace 8whitespace-separated list 138, 146who– attribute– – on dc:date, 99, 322, 329width– old attribute on omlet (deprecated

in OMDoc 1.2), 328–330Windows 225Wiris 269with– element, 331Wolfram Research 14Word– Microsoft, 3workflow 295World Wide– Web, 5, 13, 91– – Consortium, 6ws:prove– element, 77WYSIWYG 3, 309

xalan 235XHTML 129, 130, 206, 214, 220,

240, 242, 248, 249, 269xhtml:object– element, 205, 206, 324XLink 206, 227xlink 130xlink:href– attribute, 340XML– application, 3, 14, 85, 214, 220– catalog, 9, 38, 225, 228– comment, 8, 92, 214

428 Index

– entity, 8, 9, 227– escaping, 8– namespace, 7, 8, 230– parser, 8, 92, 238– processor, 225– schema, 8, 39, 86, 213, 228, 345– structure– – document model, 214– syntax– – document model, 214XML XII, 2, 3, 6–11, 14–16, 18–20,

26, 27, 34–39, 71, 75–77, 85–87, 90,92, 93, 98, 99, 108, 110–115, 119,120, 122, 134, 137, 151, 165, 187,190, 197, 201, 202, 213–216, 220, 224,225, 227–233, 235, 238, 246, 247, 252,255, 256, 262, 263, 272, 273, 278,294, 295, 301, 314, 319, 320, 324,327–329, 339, 340, 345, 356

XML-RPC 75, 220, 267xml:id– attribute, 7, 10, 85, 86, 124, 163, 188,

210, 320, 341– attribute (in module RT), 131– attribute (on Dublin Core elements),

322xml:lang– attribute, 7, 122XML CATALOG FILES 225xmllint 228, 232xmllint 225xmlns 7, 230, 231XPath 10, 190–192, 194, 247, 321,

340, 342XPointer 10xpointer– shorthand, 10xref– attribute, 112, 341– – on idx, 130– – on method, 79, 164, 329– – on omstyle, presentation, use,

xslt, style, 188– – on omstyle, presentation, 188,

324, 330– – on premise, 164, 330– – on presentation, 194– – on ref, 71, 94, 95XSL– style sheet, 224XSLT 10, 16, 85, 187, 189–194, 197,

198, 214, 231, 235–238, 240, 248, 270,320, 327, 331, 338

xslt– element, 189, 190, 192, 193, 196, 198,

327, 331xsltproc 225, 235

Yacas 249, 250, 269yes– attribute value– – for crossref-symbol on

presentation, 196, 197– – for cr on element, 194– – for inductive on hypothesis, 163– – for total on selector, 157, 330

zero 155