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Isabelle as Document-oriented Proof Assistant
- CONFERENCE ON INTELLIGENT COMPUTER MATHEMATICS / MATHEMATICAL KNOWLEDGE MANAGEMENT (CICM/MKM 2011), LNAI 6824, SPRINGER. AVAILABLE AT HTTP://DX.DOI.ORG/10.1007/ 978-3-642-22673-1_17. M. WENZEL 15
"... Proof assistants in the LCF tradition, such as Coq, Isabelle, and the HOL family, are notorious for old-fashioned command-line interaction with input and output of plain text. Established prover interfaces like Proof General merely add a thin layer on top of the read-eval-print loop in the backgroun ..."
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Cited by 13 (8 self)
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Proof assistants in the LCF tradition, such as Coq, Isabelle, and the HOL family, are notorious for old-fashioned command-line interaction with input and output of plain text. Established prover interfaces like Proof General merely add a thin layer on top of the read-eval-print loop in the background. More sophisticated mathematical editors, Web-services, Wiki-servers for mathematical content do exist, but any project that aims at fully formal proof-checking struggles with recurrent prob-lems posed by ancient prover engines. Taking the perspective of Isabelle, we discuss common problems and solutions that have emerged in the past few years, to fit the prover smoothly into a document-oriented environment with rich semantic annotations for formal sources. For example, this enables a conventional editor frame-work to present formal content provided by the prover, without having to understand logic itself (or reimplement a prover). This can be achieved with minimal changes on the editor and prover side, but the combination is able to support the usual metaphors of squiggly underline, tooltips, popups etc. that are now commonplace in browsers or IDEs. Many of these document-oriented traits of current Isabelle are sufficiently general to be transferred to other provers. If such principles are becoming routinely available in LCF-style provers, building combined mathematical assistants should become more feasible.
Towards Improving Interactive Mathematical Authoring by Ontology-driven 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 text-editors the author can directly use the natural language and formula notation she is used to. In the new documentcentric paradi ..."
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Cited by 7 (0 self)
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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 text-editors 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 ontology-driven management of change can improve the process of interactive mathematical authoring.
Authoring verified documents by interactive proof construction and verification in text-editors
- LECTURE NOTES IN COMPUTER SCIENCE VOLUME 5144
, 2008
"... Aiming at a document-centric approach to formalizing and verifying mathematics and software we integrated the proof assistance system ΩMEGA with the standard scientific text-editor TEXMACS. The author writes her mathematical document entirely inside the text-editor in a controlled language with for ..."
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Aiming at a document-centric approach to formalizing and verifying mathematics and software we integrated the proof assistance system ΩMEGA with the standard scientific text-editor TEXMACS. The author writes her mathematical document entirely inside the text-editor 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 real-time 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 in-complete or underspecified proof steps, it tries to automatically repair them. For collaborative authoring we propose to manage partially or fully verified docu-ments together with its justifications and notational information centrally in a mathematics repository using an extension of OMDOC.
Towards community of practice support for interactive mathematical authoring
- In Müller [Mül07a
"... In order to foster the use of proof assistance systems, we integrated the proof assistance system ΩMEGA with the standard scientific text-editor TEXMACS using the mediator PLATΩ. We aim at a document-centric approach to formalizing and verifying mathematics and soft-ware. Assisted by the proof assis ..."
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In order to foster the use of proof assistance systems, we integrated the proof assistance system ΩMEGA with the standard scientific text-editor TEXMACS using the mediator PLATΩ. We aim at a document-centric approach to formalizing and verifying mathematics and soft-ware. Assisted by the proof assistance system, the author writes her document entirely inside the text-editor in a language she is used to, that is a mixture of natural language and formu-las in LATEX style. We developed a basic mechanism that allows the author to define her own notation inside a document in a natural way, and use it to parse the formulas written by the author as well as to render the formulas generated by the proof assistance system. This paper examines how the mediator PLATΩ can be extended to identify, analyze and support communities of practice based on the notation practice of individual authors. 1
Managing proof documents for asynchronous processing
- In User Interfaces for Theorem Provers (UITPs 2008), volume 226 of ENTCS
, 2009
"... Asynchronous proof processing is a recent approach at improving the usability and performance of interactive theorem provers. It builds on a simple metaphor: the user edits a proof document while the prover checks its consistency in the background without explicit requests from the user. This paper ..."
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Asynchronous proof processing is a recent approach at improving the usability and performance of interactive theorem provers. It builds on a simple metaphor: the user edits a proof document while the prover checks its consistency in the background without explicit requests from the user. This paper presents a software architecture for asynchronous proof processing. Its foundation is a novel state model for commands that synchronizes the possibly parallel accesses of the user interface and prover. The state model is complemented by a communication protocol that places minimal requirements on the prover. The model also allows asynchronous processing to be emulated by existing linear-processing proof engines, such that the migration to the new communication protocol is simplified. A prototype implementation that works with the current development version of Isabelle is presented.
Organization, Transformation, and Propagation of Mathematical Knowledge in Ωmega
"... 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 thi ..."
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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 knowledge-based 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 non-monotonically 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.
• Idea: Script buffer [3, 1]
"... • UI keeps proof script for batch replay • Linear processing, commands become “locked” • Focus on mechanics of proving – user-friendly? H. Gast Asynchronous Proof Document Management (UITP ’08, 22.8.2008) 2Document-Centered View • Metaphor “proof document” • User edits human-readble a proof document ..."
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• UI keeps proof script for batch replay • Linear processing, commands become “locked” • Focus on mechanics of proving – user-friendly? H. Gast Asynchronous Proof Document Management (UITP ’08, 22.8.2008) 2Document-Centered View • Metaphor “proof document” • User edits human-readble a proof document • Prover checks the consistency • Assisted authoring [2] • Isar as human-readable proof language [8] • Backflow: Assistance by prover for editing • Processing linear • PlatΩ approach [6] • Near-natural, text-book style input language • Front-end 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]
User Interfaces for Theorem Provers: Necessary Nuisance or
"... Abstract: This note considers the design of user interfaces for interactive theorem provers. The basic rules of interface design are reviewed, and their applicability to theorem provers is discussed, leading to considerations about the particular chal-lenges of interface design for theorem provers. ..."
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Abstract: This note considers the design of user interfaces for interactive theorem provers. The basic rules of interface design are reviewed, and their applicability to theorem provers is discussed, leading to considerations about the particular chal-lenges of interface design for theorem provers. A short overview and classification of existing interfaces is given, followed by suggestions of possible future work in the area.
