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The Mathematical Vernacular
, 2000
"... A `mathematical vernacular' is a formal language for writing mathematical proofs which resembles the natural language from mathematical texts. Several systems (Hyperproof, Mizar, Isabelle/Isar) all basically have the same proof language. It consists of the combination of natural deduction with ..."
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A `mathematical vernacular' is a formal language for writing mathematical proofs which resembles the natural language from mathematical texts. Several systems (Hyperproof, Mizar, Isabelle/Isar) all basically have the same proof language. It consists of the combination of natural deduction
Translating Mathematical Vernacular into Knowledge Repositories
"... Abstract. Defining functions is a major topic when building mathematical repositories. Though relatively easy in mathematical vernacular, function definitions rise a number of questions and problems in fully formal languages (see [Dav03]). This becomes even more important for repositories in which p ..."
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Abstract. Defining functions is a major topic when building mathematical repositories. Though relatively easy in mathematical vernacular, function definitions rise a number of questions and problems in fully formal languages (see [Dav03]). This becomes even more important for repositories in which
Towards a formal mathematical vernacular
 Utrecht University
, 1992
"... Contemporary proof veri cators often use a command language to construct proofs. These commands are often called tactics. This new generation of theorem provers is a substantial improvement over earlier ones such asAUTOMATH. Based on experience with these new provers we feel the need to study these ..."
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these languages further, especially, because we think that these may be improved in their adequateness to express proofs closer to the established mathematical vernacular. We also feel that a systematic treatment of these vernaculars may lead to an improvement towards the automatic inference of trivial proof
Mathematical Vernacular and Conceptual Wellformedness in Mathematical Language
 Proceedings of the 2nd Inter. Conf. on Logical Aspects of Computational Linguistics, LNCS/LNAI 1582
, 1998
"... . This paper investigates the semantics of mathematical concepts in a type theoretic framework with coercive subtyping. The typetheoretic analysis provides a formal semantic basis in the design and implementation of Mathematical Vernacular (MV), a natural language suitable for interactive developmen ..."
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Cited by 14 (9 self)
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. This paper investigates the semantics of mathematical concepts in a type theoretic framework with coercive subtyping. The typetheoretic analysis provides a formal semantic basis in the design and implementation of Mathematical Vernacular (MV), a natural language suitable for interactive
Mathematical Vernacular in Type Theorybased Proof Assistants
 Workshop on User Interfaces in Theorem Proving
, 1998
"... In this paper we present the Durham Mathematical Vernacular (MV) project, discuss the general design of a prototype to support experimentation with issues of MV, explain current work on the prototype  specifically in the type theory basis of the work, and end with a brief discussion of methodology ..."
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Cited by 3 (2 self)
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In this paper we present the Durham Mathematical Vernacular (MV) project, discuss the general design of a prototype to support experimentation with issues of MV, explain current work on the prototype  specifically in the type theory basis of the work, and end with a brief discussion
Towards Mathematical Vernacular in a Mathematical Knowledge Base
, 1999
"... . In this paper we propose a methodology for developing representation formalisms for mathematical knowledge bases. We propose to equip knowledge bases with a hierarchy of logical systems that are linked by logic morphisms. These mappings relativize formulae and proofs and thus support translation o ..."
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 calculus with dependent sorts and labeled abstraction that is wellsuited both for formalizing mathematical practice and supporting efficient inference services. This "mathematical vernacular" is an extension of the sorted calculus from [Koh94] by records, dependent record sorts and selection
ComputerAssisted Reasoning with Natural Language: Implementing a Mathematical Vernacular
 In CLUK'98
, 1998
"... This paper presents the Durham Mathematical Vernacular (MV) project. The project aims to develop the technology for interactive tools based on proof checking with type theory, which allow mathematicians to develop mathematics in their usual vernacular. Its subgoals are to develop type theory techno ..."
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Cited by 1 (0 self)
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This paper presents the Durham Mathematical Vernacular (MV) project. The project aims to develop the technology for interactive tools based on proof checking with type theory, which allow mathematicians to develop mathematics in their usual vernacular. Its subgoals are to develop type theory
Vernacular Programming: General Recursion
"... This paper provides a mathematical analysis of the relationship between vernacular and formalised derivations of programs; in particular, when the vernacular derivations deploy general recursion. We introduce a calculus VPD to represent vernacular derivations and a constructive theory of operations ..."
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This paper provides a mathematical analysis of the relationship between vernacular and formalised derivations of programs; in particular, when the vernacular derivations deploy general recursion. We introduce a calculus VPD to represent vernacular derivations and a constructive theory of operations
Vernacular Mathematics, Discourse Representation, and Arbitrary Objects
, 1999
"... This paper discusses some of the issues that have to be addressed for a systematic treatment of vernacular mathematics. In vernacular proofs, variable letters are introduced and used in a way that does not conform to the usual interpretation offered for referring expressions in the formal semanti ..."
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This paper discusses some of the issues that have to be addressed for a systematic treatment of vernacular mathematics. In vernacular proofs, variable letters are introduced and used in a way that does not conform to the usual interpretation offered for referring expressions in the formal
Results 1  10
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39