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**11 - 14**of**14**### Computerising Mathematical Text with MathLang

"... Mathematical texts can be computerised in many ways that capture differing amounts of the mathematical meaning. At one end, there is document imaging, which captures the arrangement of black marks on paper, while at the other end there are proof assistants (e.g., Mizar, Isabelle, Coq, etc.), which c ..."

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Mathematical texts can be computerised in many ways that capture differing amounts of the mathematical meaning. At one end, there is document imaging, which captures the arrangement of black marks on paper, while at the other end there are proof assistants (e.g., Mizar, Isabelle, Coq, etc.), which capture the full mathematical meaning and have proofs expressed in a formal foundation of mathematics. In between, there are computer typesetting systems (e.g., LATEX and Presentation MathML) and semantically oriented systems (e.g., Content MathML, OpenMath, OMDoc, etc.). The MathLang project was initiated in 2000 by Fairouz Kamareddine and Joe Wells with the aim of developing an approach for computerising mathematical texts which is flexible enough to connect the different approaches to computerisation, which allows various degrees of formalisation, and which is compatible with different logical frameworks (e.g., set theory, category theory, type theory, etc.) and proof systems. The approach is embodied in a computer representation, which we call MathLang, and associated software tools, which are being developed by ongoing work. Four Ph.D. students (Manuel Maarek (2002/2007), Krzysztof Retel (since 2004), Robert Lamar (since 2006)), and Christoph Zengler (since 2008) and over a dozen master’s degree and undergraduate

### The MathLang Formalisation Path into Isabelle -- A Second-Year report

, 2003

"... A paper providing details of work accomplished during the second year of the PhD, and a plan for completion of dissertation in the final year. The objective of this PhD is to establish a path for conversion of mathematics from natural language to formalisation. This path is to be created in the cont ..."

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A paper providing details of work accomplished during the second year of the PhD, and a plan for completion of dissertation in the final year. The objective of this PhD is to establish a path for conversion of mathematics from natural language to formalisation. This path is to be created in the context of the mathematics computerisation framework. Furthermore, in this effort the end of the path is intended to be the language of the Isabelle proof assistant. To this end, we have made efforts and contributions including 1. a method for producing trees to aid analysis of MathLang annotations (as described in Section 2.1), 2. rules for converting MathLang annotations to code for the Isabelle proof assistant (see Section 2.2), and 3. a detailed analysis of the application of the Text and Symbol aspect of MathLang to a text from classical number theory (provided in Section