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Exploring Formalisation : A Primer in Human-Readable Mathematics in Lean 3 with Examples from Simplicial Topology
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ISBN: 9783031146497 9783031146480 9783031146503 Year: 2022 Publisher: Cham Springer International Publishing

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Abstract

This primer on mathematics formalisation provides a rapid, hands-on introduction to proof verification in Lean. After a quick introduction to Lean, the basic techniques of human-readable formalisation are introduced, illustrated by simple examples on maps, induction and real numbers. Subsequently, typical design options are discussed and brought to life through worked examples in the setting of simplicial complexes (a higher-dimensional generalisation of graph theory). Finally, the book demonstrates how current research in algebraic and geometric topology can be formalised by means of suitable abstraction layers. Informed by the author's recent teaching and research experience, this book allows students and researchers to quickly get started with formalising and checking their proofs. The core material of the book is accessible to mathematics students with basic programming skills. For the final chapter, familiarity with elementary category theory and algebraic topology is recommended.


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Machine translation
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ISSN: 09226567 15730573 Publisher: Dordrecht

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Abstract

Machine Translation publishes original research papers on all aspects of MT, and welcomes papers with a multilingual aspect from other areas of Computational Linguistics and Language Engineering, such as Computer-Assisted Translation, Multilingual Corpus Resources, Tools for translators, The role of technology in translator training, MT and language teaching, Evaluation, Description etc. Machine Translation regularly focuses on issues of special interest, features a regular Book Review section, and welcomes other contributions of interest to the wide readership of the journal, such as — text composition and generation, information retrieval, natural language interfaces, dialogue systems, message understanding systems, discourse phenomena, text mining, knowledge engineering, contrastive linguistics, morphology, syntax, semantics, pragmatics, computer-aided language instruction and learning software localization and internationalization.

Keywords

Translation science --- Computer. Automation --- Machine translating --- Computational linguistics --- Traduction automatique --- Linguistique informatique --- Periodicals. --- Périodiques --- Computational linguistics. --- Machine translating. --- #KVHA:Tijdschriften Vertaalwetenschap --- Periodicals --- Information Technology --- Artificial Intelligence --- Computer Architecture, Languages and Compilers --- General and Others --- Information Science and Systems --- Software Engineering --- Arts and Humanities --- Language & Linguistics --- Information Technology. --- Software Engineering. --- Automatic translating --- Computer translating --- Electronic translating --- Mechanical translating --- Automatic language processing --- Language and languages --- Language data processing --- Linguistics --- Natural language processing (Linguistics) --- Data processing --- #KVHA:Tijdschriften; Vertaalwetenschap --- Algorithms --- Applied linguistics --- Artificial intelligence --- Natural language generation (Computer science) --- Information theory --- Translating and interpreting --- Cross-language information retrieval --- Translating machines --- Mathematical linguistics --- Multilingual computing --- Tłumaczenie automatyczne --- linguistique. --- traduction automatique. --- mašīntulkošana --- tradução automática --- machine translation --- maskinöversättning --- strojno prevajanje --- strojový preklad --- traduzione automatica --- masintõlge --- strojový překlad --- koneellinen kääntäminen --- automatisk oversættelse --- përkthim automatik --- машинен превод --- automatische vertaling --- αυτόματη μετάφραση --- meaisínaistriúchán --- tłumaczenie automatyczne --- машинско превођење --- strojno prevođenje --- traduzzjoni awtomatika --- traducción automática --- машински превод --- traducere automată --- mašininis vertimas --- gépi fordítás --- automatische Übersetzung --- arvutipõhine tõlkesüsteem --- EUROTRA --- fordítói memória --- strojni prijevod --- počítačový překlad --- computerunterstützte Übersetzung --- računalno podržano prevođenje --- maschinelle Übersetzung --- computerised translation system --- automatinis vertimas --- datorizēta tulkošanas sistēma --- kompiuterizuota vertimo sistema --- számítógépes fordítás --- automaattinen kielenkääntöjärjestelmä --- počítačový systému prekladu --- računalni sustav za prevođenje --- sistem i komjuterizuar përkthimi --- edb-oversættelse --- автоматско преведување --- Sprachwissenschaft --- lingüística --- lingvistika --- lingwistika --- taalwetenschap --- keeleteadus --- linguística --- kielitiede --- nyelvészet --- teangeolaíocht --- językoznawstwo --- linguistikë --- лингвистика --- kalbotyra --- lingvistică --- jazykověda --- γλωσσολογία --- jezikoslovje --- lingvistik --- linguistica --- linguistics --- граматика --- etümoloogia --- nyelvtan --- spelluta --- γραμματική --- mondattan --- етимология --- lexicologia --- spraakkunst --- pronunciation --- pragmatika --- angewandte Sprachwissenschaft --- nauka o původu slov --- phonetics --- fonetiikka --- наука за јазикот --- morfologie --- правопис --- Etymologie --- pravopis --- Sprechtechnik --- prononciation --- fonētika --- etimologija --- grammatik --- Pragmalinguistik --- dějiny jazyka --- sprogvidenskab --- uttalslära --- ordboksvetenskap --- etymologia --- pisownia --- leksikologija --- leksikologji --- лексикологија --- gramatika --- fonetică --- προφορά --- etimología --- fonética --- λεξικολογία --- fonologie --- litriú --- betydelselära --- filologie --- sémantique --- Rechtschreibung --- Phonetik --- gramatică --- helyesírás --- gramática --- etimoloģija --- tartis --- Grammatik --- grammatika --- etymológia --- etymology --- grammar --- orthographe --- ääntäminen --- etymologi --- alaktan --- etimológia --- lexikológia --- hangtan --- ortografia --- Lexikologie --- syntax --- etimoloġija --- Sprachforschung --- lexicology --- kirjakuju --- Semantik --- szemantika --- semantik --- ortogrāfija --- grammatica --- φωνητική --- valodniecība --- semantiikka --- kielioppi --- leksikoloģija --- σημαντική --- ετυμολογία --- szókincstan --- oikeinkirjoitus --- fonetiek --- semantika --- sémantika --- keeletehnika --- Morphologie --- fonetikë --- lexikologi --- lexicología --- uttal --- beszédtechnika --- uitspraak --- jezikoslovlje --- spelling --- fonetik --- leksikoloogia --- mluvnice --- pronuncia --- semántica --- izgovor --- ljudlära --- semantica --- pronunciação --- semântica --- shqiptim --- pronúncia --- semantikë --- ορθογραφία --- phonétique --- matematická lingvistika --- étymologie --- stavemåde --- pronunciación --- výslovnosť --- etymologie --- taalkunde --- jazykozpyt --- udtale --- ortografía --- ortografie --- allmän språkvetenskap --- semantics --- semantiek --- fonetica --- etimologie --- linguïstiek --- rašyba --- Linguistik --- lessicologia --- leksikologi --- foneetika --- fonetika --- stavning --- gramatikë --- sanasto-oppi --- etimologia --- sanasaíocht --- semantică --- grammaire --- jelentéstan --- семантика --- morfológia --- aplikovaná lingvistika --- lexicologie

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