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**11 - 18**of**18**### ◮ Analyzing theories, ◮ Verifying proofs, ◮ Assist tutoring,

, 2006

"... Abstraction with nouns and adjectives ..."

### 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

### (ULTRA group, Heriot-Watt University)

"... Abstract. In only few decades, computers have changed the way we approach documents. Throughout history, mathematicians and philosophers had clarified the relationship between mathematical thoughts and their textual and symbolic representations. We discuss here the consequences of computer-based for ..."

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Abstract. In only few decades, computers have changed the way we approach documents. Throughout history, mathematicians and philosophers had clarified the relationship between mathematical thoughts and their textual and symbolic representations. We discuss here the consequences of computer-based formalisation for mathematical authoring habits and we present an overview of our approach for computerising mathematical texts. 1.

### Digitised Mathematics:

, 2006

"... In only few decades, computers have changed the way we approach documents. Throughout history, mathematicians and philosophers had clarified the relationship between mathematical thoughts and their textual and symbolic representations. We discuss here the consequences of computerbased formalisation ..."

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In only few decades, computers have changed the way we approach documents. Throughout history, mathematicians and philosophers had clarified the relationship between mathematical thoughts and their textual and symbolic representations. We discuss here the consequences of computerbased formalisation for mathematical authoring habits and we present an overview of our approach for computerising mathematical texts. 1

### STUDIES IN LOGIC, GRAMMAR AND RHETORIC 10 (23) 2007 Gradual Computerisation/Formalisation of Mathematical Texts into Mizar

"... Abstract. We explain in this paper the gradual computerisation process of an ordinary mathematical text into more formal versions ending with a fully formalised Mizar text. The process is part of the MathLang–Mizar project and is divided into a number of steps (called aspects). The first three aspec ..."

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Abstract. We explain in this paper the gradual computerisation process of an ordinary mathematical text into more formal versions ending with a fully formalised Mizar text. The process is part of the MathLang–Mizar project and is divided into a number of steps (called aspects). The first three aspects (CGa, TSa and DRa) are the same for any MathLang–TP project where TP is any proof checker (e.g., Mizar, Coq, Isabelle, etc). These first three aspects are theoretically formalised and implemented and provide the mathematician and/or TP user with useful tools/automation. Using TSa, the mathematician edits his mathematical text just as he would use L ATEX, but at the same time he sees the mathematical text as it appears on his paper. TSa also gives the mathematician easy editing facilities to help assign to parts of the text, grammatical and mathematical roles and to relate different parts through a number of mathematical, rethorical and structural relations. MathLang would then automatically produce CGa and DRa versions of the text, checks its grammatical correctness and produce