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M.: Authoring verified documents by interactive proof construction and verification in texteditors
 Lecture Notes in Computer Science Volume 5144
, 2008
"... Abstract. Aiming at a documentcentric approach to formalizing and verifying mathematics and software we integrated the proof assistance system ΩMEGA with the standard scientific texteditor TEXMACS. The author writes her mathematical document entirely inside the texteditor in a controlled language ..."
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Abstract. Aiming at a documentcentric approach to formalizing and verifying mathematics and software we integrated the proof assistance system ΩMEGA with the standard scientific texteditor TEXMACS. The author writes her mathematical document entirely inside the texteditor in a controlled language with formulas in LATEX style. The notation specified in such a document is used for both parsing and rendering formulas in the document. To make this approach effectively usable as a realtime application we present an efficient hybrid parsing technique that is able to deal with the scalability problem resulting from modifying or extending notation dynamically. Furthermore, we present incremental methods to quickly verify constructed or modified proof steps by ΩMEGA. If the system detects incomplete or underspecified proof steps, it tries to automatically repair them. For collaborative authoring we propose to manage partially or fully verified documents together with its justifications and notational information centrally in a mathematics repository using an extension of OMDOC. 1
Organization, Transformation, and Propagation of Mathematical Knowledge in Ωmega
"... Abstract. Mathematical assistance systems and proof assistance systems in general have traditionally been developed as large, monolithic systems which are often hard to maintain and extend. In this article we propose a component network architecture as a means to design and implement such systems. U ..."
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Abstract. Mathematical assistance systems and proof assistance systems in general have traditionally been developed as large, monolithic systems which are often hard to maintain and extend. In this article we propose a component network architecture as a means to design and implement such systems. Under this view a mathematical assistance system is an integrated knowledgebased system composed as a network of individual, specialized components. These components manipulate and mutually exchange different kinds of mathematical knowledge encoded within different document formats. Consequently, several units of mathematical knowledge coexist throughout the system within these components and this knowledge changes nonmonotonically over time. Our approach has resulted in a lean and maintainable system code and makes the system open for extensions. Moreover, it naturally decomposes the global and complex reasoning and truth maintenance task into local reasoning and truth maintenance tasks inside the system components. The interplay between neighboring components in the network is thereby realized by nonmonotonic updates over agreed interface representations encoding different kinds of mathematical knowledge. 1.
• Idea: Script buffer [3, 1]
"... • UI keeps proof script for batch replay • Linear processing, commands become “locked” • Focus on mechanics of proving – userfriendly? H. Gast Asynchronous Proof Document Management (UITP ’08, 22.8.2008) 2DocumentCentered View • Metaphor “proof document” • User edits humanreadble a proof document ..."
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• UI keeps proof script for batch replay • Linear processing, commands become “locked” • Focus on mechanics of proving – userfriendly? H. Gast Asynchronous Proof Document Management (UITP ’08, 22.8.2008) 2DocumentCentered View • Metaphor “proof document” • User edits humanreadble a proof document • Prover checks the consistency • Assisted authoring [2] • Isar as humanreadable proof language [8] • Backflow: Assistance by prover for editing • Processing linear • PlatΩ approach [6] • Nearnatural, textbook style input language • Frontend parses structure & computes structural diff • Triggers necessary (re)checking by Ωmega prover H. Gast Asynchronous Proof Document Management (UITP ’08, 22.8.2008) 3Asynchronous Proof Processing [7]
Towards Improving Interactive Mathematical Authoring by Ontologydriven Management of Change
"... The interactive use of mathematical assistance systems requires an intensive training in their input and command language. With the integration into scientific WYSIWYG texteditors the author can directly use the natural language and formula notation she is used to. In the new documentcentric paradi ..."
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The interactive use of mathematical assistance systems requires an intensive training in their input and command language. With the integration into scientific WYSIWYG texteditors the author can directly use the natural language and formula notation she is used to. In the new documentcentric paradigm changes to the document are transformed by a mediator into commands for the mathematical assistance system. This paper describes how ontologydriven management of change can improve the process of interactive mathematical authoring. 1