Interactive Formal Specification for Mathematical Problems of Engineers
Abstract: The paper presents the second part of a precise description of the prototype that has been developed in the course of the ISAC project over the last two decades. This part describes the "specify-phase", while the first part describing the "solve-phase" is already published. In the specify-phase a student interactively constructs a formal specification. The ISAC prototype implements formal specifications as established in theoretical computer science, however, the input language for the construction avoids requiring users to have knowledge of logic; this makes the system useful for various engineering faculties (and also for high school). The paper discusses not only ISAC's design of the specify-phase in detail, but also gives a brief introduction to implementation with the aim of advertising the re-use of formal frameworks (inclusive respective front-ends) with their generic tools for language definition and their rich pool of software components for formal mathematics.
- Ralph-Johan Back & Joakim von Wright (1998): Refinement Calculus: A Systematic Introduction. Springer-Verlag. Graduate Texts in Computer Science, 10.1007/978-1-4612-1674-2.
- Christoph Benzmüller & David Fuenmayor (2021): Value-Oriented Legal Argumentation in Isabelle/HOL. In Liron Cohen & Cezary Kaliszyk, editors: 12th International Conference on Interactive Theorem Proving (ITP 2021), Leibniz International Proceedings in Informatics (LIPIcs) 193, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl, Germany, pp. 7:1–7:20, 10.4230/LIPIcs.ITP.2021.7.
- Bruno Buchberger (2023): Is ChatGPT Smarter Than Master’s Applicants? RISC Report Series 23-04, Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria. Available at https://www3.risc.jku.at/publications/download/risc_6684/23-04.pdf.
- Jasmin C.Blanchette: Hammering Away. A User’s Guide to Sledgehammer for Isabelle/HOL. contained in the Isabelle distribution. Available at http://isabelle.in.tum.de/doc/sledgehammer.pdf.
- Gabriella Daróczy & Walther Neuper (2013): Error-Patterns within “Next-Step-Guidance” in TP-based Educational Systems. In: eJMT, the Electronic Journal of Mathematics & Technology, 7, pp. 175–194. Available at https://php.radford.edu/~ejmt/ContentIndex.php#v7n2. Special Issue “TP-based Systems and Education”.
- In: 28th International Conference on Automated Deduction (CADE 28), Lecture Notes in Computer Science, Springer-Verlag, 10.1007/978-3-030-79876-5_36
- WTM Verlag, Münster.
- David Gries (1981): The science of programming. Texts and monographs in computer science, Springer-Verlag, 10.1007/978-1-4612-5983-1.
- Mateja Jamnik (2023): How Can We Make Trustworthy AI? In Marco Gaboardi & Femke van Raamsdonk, editors: 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023), Leibniz International Proceedings in Informatics (LIPIcs) 260, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl, Germany, pp. 2:1–2:1, 10.4230/LIPIcs.FSCD.2023.2.
- Franz Kober (2012): Logging of High-Level Steps in a Mechanized Math Assistant. Master’s thesis, IICM, Graz University of Technology. https://static.miraheze.org/isacwiki/e/e6/Fkober_bakk.pdf.
- In Pedro Quaresma, João Marcos & Walther Neuper, editors: Proceedings 11th International Workshop on Theorem Proving Components for Educational Software, Haifa, Israel, 11 August 2022, Electronic Proceedings in Theoretical Computer Science 375, Open Publishing Association, pp. 92–111, 10.4204/EPTCS.375.8.
- The MIT Press, Cambridge, London, 10.7551/mitpress/2319.001.0001.
- Walther Neuper (2012): Automated Generation of User Guidance by Combining Computation and Deduction. In Pedro Quaresma & Ralph-Johan Back, editors: Electronic Proceedings in Theoretical Computer Science, 79, Open Publishing Association, pp. 82–101, 10.4204/EPTCS.79.5.
- Walther Neuper (2019): Technologies for “Complete, Transparent & Interactive Models of Math” in Education. In Pedro Quaresma & Walther Neuper, editors: Proceedings 7th International Workshop on Theorem proving components for Educational software, Oxford, United Kingdom, 18 july 2018, Electronic Proceedings in Theoretical Computer Science 290, Open Publishing Association, pp. 76–95, 10.4204/EPTCS.290.6.
- Walther Neuper (2020): Lucas-Interpretation on Isabelle’s Functions. In Pedro Quaresma, Walther Neuper & João Marcos, editors: Proceedings 9th International Workshop on Theorem Proving Components for Educational Software (ThEdu’20), Paris, France, 29th June 2020, Electronic Proceedings in Theoretical Computer Science, 328, pp. 79–95, 10.4204/EPTCS.328.5.
- Walther Neuper & Christian Dürnsteiner (2007): Angewandte Mathematik und Fachtheorie mithilfe adaptierter Basis-Software. Technical Report 683, IMST – Innovationen Machen Schulen Top!, University of Klagenfurt, Institute of Instructional and School Development (IUS), 9010 Klagenfurt, Sterneckstrasse 15. Available at https://www.imst.ac.at/imst-wiki/images/f/f9/683_Kurzfassung_Neuper.pdf.
- Walther Neuper, Johannes Reitinger & Angelika Gründlinger (2008): Begreifen und Mechanisieren beim Algebra Einstieg. Technical Report 1063, IMST – Innovationen Machen Schulen Top!, University of Klagenfurt, Institute of Instructional and School Development (IUS), 9010 Klagenfurt, Sterneckstrasse 15. Available at https://www.imst.ac.at/imst-wiki/images/9/9d/1063_Langfassung_Reitinger.pdf.
- Walther Neuper et al. (2006): Angewandte Mathematik und Fachtheorie. Technical Report 357, IMST – Innovationen Machen Schulen Top!, University of Klagenfurt, Institute of Instructional and School Development (IUS), 9010 Klagenfurt, Sterneckstrasse 15. Available at http://imst.uni-klu.ac.at/imst-wiki/index.php/Angewandte_Mathematik_und_Fachtheorie.
- Lawrence C. Paulson, Tobias Nipkow & Makarius Wenzel (2019): From LCF to Isabelle/HOL. Formal Aspects of Computing 31, pp. 675–698, Springer, London, 10.1007/s00165-019-00492-1.
- Technical Report, Institute for Softwaretechnology, University of Technology. Available at https://static.miraheze.org/isacwiki/0/04/Isac-docu.pdf.
- Makarius Wenzel & Burkhart Wolff (2011): Isabelle/PIDE as Platform for Educational Tools. In Pedro Quaresma & Ralph-Johan Back, editors: Proceedings First Workshop on CTP Components for Educational Software, THedu’11, Wroclaw, Poland, 31th July 2011, EPTCS 79, pp. 143–153, 10.4204/EPTCS.79.9.
- Markus Wenzel (1999): Isar - a Generic Interpretative Approach to Readable Formal Proof Documents. In G. Dowek, A. Hirschowitz, C. Paulin & L. Thery, editors: Theorem Proving in Higher Order Logics, LNCS 1690, 12th International Conference TPHOLs’99, Springer, 10.1007/3-540-48256-3_12.
- W.Neuper, B.Stöger & M.Wenzel (2022): Towards Accessible Formal Mathematics with ISAC and Isabelle/VSCode. Isabelle Workshop 2022 https://sketis.net/isabelle/isabelle-workshop-2022. Accessed: 202-10-13.
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