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Faithfully Reflecting the Structure of Informal Mathematical Proofs into Formal Type Theories

G.I. Jojgov, R.P. Nederpelt, M. Scheffer
<span title="">2004</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
By using this intermediate version, the subsequent translation into a full-fledged type theory can be made such that the proof clearly reflects the structure of the original CML proof.  ...  In order to reduce the possibility of formalization errors and therefore increase the reliability of the translation of CML texts into type theories, we use a version of Nederpelt's formal language WTT  ...  In that sense the formal version reflects the structure of the original proof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2003.12.030">doi:10.1016/j.entcs.2003.12.030</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xzn2ocxvvbdp5ia76pwhdzuela">fatcat:xzn2ocxvvbdp5ia76pwhdzuela</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170929091806/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/77c/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMTU3MTA2NjEwNDAwMDE1NQ%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3e/98/3e981f55fcf518ad4adb1844ff8d2062bb7891b4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2003.12.030"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>

Page 884 of Mathematical Reviews Vol. , Issue 2000b [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
For deductions in an equational theory, the initial set of clauses is decomposed into the set of equations and the set of all remaining clauses.  ...  di- rectly reflect proof-strategic considerations.  ... 
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MathAbs

Muhammad Humayoun, Christophe Raffalli
<span title="">2010</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wknseg6ptbcjtieccaihkv7n54" style="color: black;">Proceedings of the 8th International Conference on Frontiers of Information Technology - FIT &#39;10</a> </i> &nbsp;
MathAbs (Mathematical Abstract language) is a system independent formal language for mathematical texts that can preserve its structure including the line of reasoning, proof steps and logical structure  ...  By system independent, we mean that its formalism is not based on any specific logic, theory or proof assistant.  ...  By "faithfully", we mean that the formal version of mathematics is as close as possible to the intentions expressed in the mathematical text.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1943628.1943665">doi:10.1145/1943628.1943665</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/fit/HumayounR10.html">dblp:conf/fit/HumayounR10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cuebsnwq7rgexcs3ngngdtsvzy">fatcat:cuebsnwq7rgexcs3ngngdtsvzy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706081931/http://www.lama.univ-savoie.fr/~humayoun/phd/pdf/FIT2010.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/aa/f1/aaf1ff5a874e2960f4407918fcd74198eea640f2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1943628.1943665"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Common Nouns as Types [chapter]

Zhaohui Luo
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
It is shown that, in order to faithfully interpret modified CNs as Σ-types so that the associated criteria of identity can be captured correctly, it is important to assume proof irrelevance in type theory  ...  When modern type theories are employed for formal semantics, common nouns (CNs) are interpreted as types, not as predicates.  ...  Thanks to Robin Adams, Stergios Chatzikyriakidis and members of the 'Type Theory and Applications' research group at RHUL for helpful discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-31262-5_12">doi:10.1007/978-3-642-31262-5_12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lko7tkgoivcbdahyhmaizvfknm">fatcat:lko7tkgoivcbdahyhmaizvfknm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705113405/http://www.cs.rhul.ac.uk/home/zhaohui/LACL12.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/43/3b/433ba557ac48eafca70f309f07f721ed7bfc170f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-31262-5_12"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Ontologies and languages for representing mathematical knowledge on the Semantic Web

Christoph Lange
<span title="">2013</span> <i title="IOS Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pcapks3huberdozbvfqowysuly" style="color: black;">Semantic Web Journal</a> </i> &nbsp;
metadata, and discussions about conceptualizations, formalizations, proofs, and (counter-)examples.  ...  Our review of vocabularies for representing these structures covers ontologies for mathematical problems, proofs, interlinked scientific publications, scientific discourse, as well as mathematical meta-data  ...  Later, the content is elaborated both into the formal and into the informal direction: A sloppy formula is written more rigorously, rigorous text is formalized in a certain mathematical foundation (meta-theory  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3233/sw-2012-0059">doi:10.3233/sw-2012-0059</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fmfywipm2bbunkqgbpxz54mcv4">fatcat:fmfywipm2bbunkqgbpxz54mcv4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829041355/http://www.semantic-web-journal.net/sites/default/files/swj122_3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bb/4d/bb4df86b6ee3f537c949315a3e2a6967d066c771.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3233/sw-2012-0059"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

The Rooster and the Butterflies [chapter]

Assia Mahboubi
<span title="">2013</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This purpose of this description is to discuss the representation of the elementary concepts of finite group theory inside type theory.  ...  The design choices underlying these representations were crucial to the successful formalization of a complete proof of the Odd Order Theorem with the Coq system.  ...  The author wishes to thank Y. Bertot, J. Carette, W. Farmer, G. Gonthier, L. Rideau and E. Tassi for their proofreading.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-39320-4_1">doi:10.1007/978-3-642-39320-4_1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jz33gwq7pze3zpr3u632kky3l4">fatcat:jz33gwq7pze3zpr3u632kky3l4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190227144145/http://pdfs.semanticscholar.org/821e/af5b8c0418ab72c6acdc85d6157fb7927f47.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/82/1e/821eaf5b8c0418ab72c6acdc85d6157fb7927f47.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-39320-4_1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Abstract State Machines 1988-1998: Commented ASM Bibliography [article]

Egon Boerger, James K. Huggins
<span title="1998-11-09">1998</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.  ...  elaborating the conjunctive component-as reflected by compilation of clause structure into WAM code-and the disjunctive component-as reflected by compilation of predicate structure into WAM code.  ...  A hierarchy of stepwise refined abstract machine models is developed, the ground version of which can be checked for whether it faithfully reflects the informally given problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/9811014v1">arXiv:cs/9811014v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w3vj5i7mzbccbcibroi7dkmhtq">fatcat:w3vj5i7mzbccbcibroi7dkmhtq</a> </span>
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A proposition is the (homotopy) type of its proofs [article]

Steve Awodey
<span title="2017-01-08">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
An introduction and survey of homotopy type theory in honor of W.W. Tait.  ...  The basis of homotopy type theory is an interpretation of the system of intensional type theory into abstract homotopy theory.  ...  a constructive foundation for mathematics and now has many applications in the theory of programming languages and formal proof verification, and homotopy theory, a branch of algebraic topology devoted  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1701.02024v1">arXiv:1701.02024v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f5yj6hfgcrfivj2ozxud2c6y74">fatcat:f5yj6hfgcrfivj2ozxud2c6y74</a> </span>
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Didactical Issues at the Interface of Mathematics and Computer Science [chapter]

Viviane Durand-Guerrier, Antoine Meyer, Simon Modeste
<span title="">2019</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4mntdwmqffcolpwqjiv465up3a" style="color: black;">The Mathematics Teacher in the Digital Era</a> </i> &nbsp;
We will elaborate on the links between the concepts of algorithm, proof, and program, and will argue for their significance in a general reflection on didactical issues in mathematics and computer science  ...  We make the hypothesis that, with the introduction of digital tools and computer science content in most curricula, significantly taking into account the epistemology of mathematics, computer science and  ...  In some sense, formalizing an algorithm into a program is an activity of the same nature as producing a formal proof from a standard mathematical proof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-28483-1_6">doi:10.1007/978-3-030-28483-1_6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cgtoxvtatfdipczdeyocpkav5y">fatcat:cgtoxvtatfdipczdeyocpkav5y</a> </span>
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A Logical Study of Some Common Principles of Inductive Definition and its Implications for Knowledge Representation [article]

Marc Denecker and Bart Bogaerts and Joost Vennekens
<span title="2017-02-15">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation  ...  We define a logic of definitions offering a uniform formal syntax to express definitions of the different sorts, and we define its semantics by a faithful formalization of the induction process.  ...  The correspondence between the mathematical objects of the informal definition and the structures of the formal definition, the question whether the formal definition faithfully expresses an informal definition  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1702.04551v1">arXiv:1702.04551v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e5jnp72zprespgmnfvvf7qcm3e">fatcat:e5jnp72zprespgmnfvvf7qcm3e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191018123731/https://arxiv.org/pdf/1702.04551v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ac/ed/aced1bb6db131280738cd12e012385995bcc917a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1702.04551v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Faithfully quadratic rings — a summary of results

M. Dickmann, F. Miraglia
<span title="">2016</span> <i title="Institute of Mathematics, Polish Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fw4xgzdadzetlaegr4yulpvxce" style="color: black;">Banach Center Publications</a> </i> &nbsp;
This is a summary of some of the main results in the monograph Faithfully Ordered Rings (Mem. Amer. Math.  ...  We achieve this by the use, in the ring context, of our abstract theory of quadratic forms, the theory of special groups, expounded in [DM1] 1 .  ...  Our proof of this property uses the theory of real semigroups, [DP] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4064/bc108-0-4">doi:10.4064/bc108-0-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bcxv6xlucna4rlgxvhxoa5qlrm">fatcat:bcxv6xlucna4rlgxvhxoa5qlrm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190426145814/https://www.impan.pl/shop/publication/transaction/download/product/91673?download.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fb/42/fb426a630546f39c6533ecfd09f01477674630ff.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4064/bc108-0-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

The Constructed Objectivity of Mathematics and the Cognitive Subject [chapter]

Giuseppe Longo
<span title="">2003</span> <i title="Springer Netherlands"> Quantum Mechanics, Mathematics, Cognition and Action </i> &nbsp;
it conceptually: geometric images and spaces, or the linguistic/algebraic structures of mathematics, set conceptual "contours" to relevant parts of the enormous amount of information that arrives upon  ...  And there begins the infinite regression of "relative consistency" results: if one wants to be sure that a given formal theory has a meaning (it is consistent), then one has to construct a  ...  In Type Theory we would say: only the type of a is used in the proof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/0-306-48144-8_14">doi:10.1007/0-306-48144-8_14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qakkkhjkkvgb5i2zlhdny4dqwy">fatcat:qakkkhjkkvgb5i2zlhdny4dqwy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706042117/http://www.di.ens.fr/users/longo/files/PhilosophyAndCognition/constr-obj.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/88/76/8876cebeee2fd67465b50d5a24e17e12f85e36e6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/0-306-48144-8_14"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Foundational Frameworks [chapter]

Geoffrey Hellman*
<span title="">2011</span> <i title="Springer Netherlands"> The Western Ontario Series in Philosophy of Science </i> &nbsp;
Finally, we sketch a variant of a modal-structural core system, incorporating elements of predicativism and the systems of reverse mathematics, and consider how it fares with respect to the desiderata  ...  After some metatheoretic preliminaries on questions of justification and rational reconstruction, we lay out some key desiderata for foundational frameworks for mathematics, some of which reflect recent  ...  There is nothing to prevent a modal-structural framework from demanding constructive proofs wherever they can be provided, including where possible proofs of (possible) existence of relevant types of structures  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-94-007-0431-2_1">doi:10.1007/978-94-007-0431-2_1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6jmyppvj4zd5zhisaeujmrwfiu">fatcat:6jmyppvj4zd5zhisaeujmrwfiu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100729021146/http://www.tc.umn.edu/~hellm001/Publications/FoundationalFrameworks.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c5/45/c545fe9cfd99f3c2ccdb57b7f4923e5e0bdce8ce.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-94-007-0431-2_1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Maude as a formal meta-tool [chapter]

M. Clavel, F. Durán, S. Eker, J. Meseguer, M. O. Stehr
<span title="">1999</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This paper explains how the reflective logical framework of rewriting logic can be used, in conjunction with an efficient reflective implementation such as the Maude language, to design formal meta-tools  ...  Given the different perspectives from which a complex software system has to be analyzed, the multiplicity of formalisms is unavoidable.  ...  We also thank our fellow Maude team members Grit Denker, Patrick Lincoln, Narciso Martí-Oliet and José Quesada for their contributions to the theory and practice of Maude, and Carolyn Talcott for many  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-48118-4_39">doi:10.1007/3-540-48118-4_39</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fefrfcvcafb2lih3jqxqudyacm">fatcat:fefrfcvcafb2lih3jqxqudyacm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180728130508/https://link.springer.com/content/pdf/10.1007%2F3-540-48118-4_39.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a4/2a/a42ab55155ba8af71fd1d65830bc74c6a295f0eb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-48118-4_39"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Mathematics in the Age of the Turing Machine [article]

Thomas Hales
<span title="2013-02-12">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.  ...  Although this research is still at an early stage, it suggests that the mechanical translation of mathematical prose into formal computer syntax that faithfully represents the semantics is a realistic  ...  Because of the need for type information, Ganesalingam raises questions about the suitability of Zermelo-Fraenkel set theory as the ultimate semantics of mathematics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1302.2898v1">arXiv:1302.2898v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ko2iqnfnq5dlbe6fwirbpvuswy">fatcat:ko2iqnfnq5dlbe6fwirbpvuswy</a> </span>
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