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The Isabelle/Naproche Natural Language Proof Assistant [chapter]

Adrian De Lon, Peter Koepke, Anton Lorenzen, Adrian Marti, Marcel Schütz, Makarius Wenzel
2021 Lecture Notes in Computer Science  
"Image missing" is included in the current version of the Isabelle/PIDE which allows comfortable editing and asynchronous proof-checking of ForTheL texts.  ...  The dialect of ForTheL can be typeset by "Image missing" into documents that approximate the language and appearance of ordinary mathematical texts.  ...  The Mizar language has been a role model for other proof languages. There are, e.g., "Mizar modes" for HOL [6, 25] and Coq [4] and the widely used Isar language for Isabelle [24, 22] .  ... 
doi:10.1007/978-3-030-79876-5_36 fatcat:2ox6tmqltvelpppwkrpketx46m

Calculational Reasoning Revisited An Isabelle/Isar Experience [chapter]

Gertrud Bauer, Markus Wenzel
2001 Lecture Notes in Computer Science  
language in a flexible and non-intrusive manner.  ...  We discuss the general concept of calculational reasoning within Isabelle/Isar, which provides a framework for high-level natural deduction proofs that may be written in a human-readable fashion.  ...  The Isabelle/Isar proof language The Isar proof language provides a general framework for human-readable natural deduction proofs [19, 20] ; its basic concepts are somewhat oriented towards the basic  ... 
doi:10.1007/3-540-44755-5_7 fatcat:i3vcqxol4ff4lkfweivxzmo2k4

From LCF to Isabelle/HOL

Lawrence C. Paulson, Tobias Nipkow, Makarius Wenzel
2019 Formal Aspects of Computing  
They include a highly readable structured language of proofs and a unique interactive development environment for editing live proof documents.  ...  Everything rests on the foundation conceived by Robin Milner for Edinburgh LCF: a proof kernel, using abstract types to ensure soundness and eliminate the need to store proofs.  ...  Acknowledgements We thank the referees, Jasmin Blanchette, Michael Norrish and Andrei Popescu for valuable comments on drafts of this paper.  ... 
doi:10.1007/s00165-019-00492-1 fatcat:rv5zmo22fjedvjxjz4lm22v6de

Isabelle/PIDE as Platform for Educational Tools

Makarius Wenzel, Burkhart Wolff
2012 Electronic Proceedings in Theoretical Computer Science  
The idea of "PIDE" (which means "Prover IDE") is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools.  ...  The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools.  ...  Unlike other systems in this category (notably Mizar [28] ), the Isar proof language is merely an application of a more general framework for structured logical environments: the notion of Isar proof  ... 
doi:10.4204/eptcs.79.9 fatcat:jovydhpwfzduxpk4heldyvp7du

An Isabelle Proof Method Language [chapter]

Daniel Matichuk, Makarius Wenzel, Toby Murray
2014 Lecture Notes in Computer Science  
In this paper we present Eisbach, a proof method language for Isabelle, which aims to fill this gap by incorporating Isar language elements, thus making it accessible to existing users.  ...  Isabelle's most popular language interface, Isar, is attractive for new users, and powerful in the hands of experts, but has previously lacked a means to write automated proof procedures.  ...  Thanks also to Peter Gammie, Magnus Myreen, and Thomas Sewell for feedback on drafts of this paper.  ... 
doi:10.1007/978-3-319-08970-6_25 fatcat:j32ukqtr35di5emlzbcpqlwta4

Interaction with Formal Mathematical Documents in Isabelle/PIDE [article]

Makarius Wenzel
2019 arXiv   pre-print
More recently, the scope of PIDE has widened towards languages that are not connected to logic and proof in Isabelle, but taken from a broader repertoire of mathematics on the computer.  ...  Isabelle/PIDE has emerged over more than 10 years as the standard Prover IDE for interactive theorem proving in Isabelle.  ...  A truly integrated development environment should do that automatically for the user, and treat Isabelle + AFP as one big mathematical document for editing (and browsing).  ... 
arXiv:1905.01735v1 fatcat:ixa3aawyubdg3liplcyow7iqwy

Making Isabelle Content Accessible in Knowledge Representation Formats [article]

Michael Kohlhase, Florian Rabe, Makarius Wenzel
2020 arXiv   pre-print
In the case of Isabelle, an export of the library into a FAIR (Findable, Accessible, Interoperable, and Reusable) knowledge exchange format was already envisioned by the authors in 1999 but had previously  ...  Such a systematic export of Isabelle content to a well-defined interchange format like OMDoc enables many applications such as dependency management, independent proof checking, or library search.  ...  In previous work, the authors have developed such a universal format [Koh06, RK13, KR16] for formal knowledge: OMDoc is an XML language geared towards making formula structure and context dependencies  ... 
arXiv:2005.08884v1 fatcat:tnzdgnb22zedvod3odyj6avqye

Asynchronous User Interaction and Tool Integration in Isabelle/PIDE [chapter]

Makarius Wenzel
2014 Lecture Notes in Computer Science  
Execution is implicit and managed by the prover on its own account in a timeless and stateless manner.  ...  Moreover, it is possible to integrate query operations via additional GUI panels with separate input and output (e.g. for Sledgehammer or findtheorems).  ...  The resulting application resembles Isabelle/jEdit, while the particular proof tools and logical foundations of the proof environment are quite different.  ... 
doi:10.1007/978-3-319-08970-6_33 fatcat:2jmq4mtazza67cx7rjrd3ndqra

Computerizing Mathematical Text with MathLang

Fairouz Kamareddine, J.B. Wells
2008 Electronical Notes in Theoretical Computer Science  
has only been done for Mizar and started for Isabelle).  ...  ., Mizar, Isabelle, Coq, etc.), which capture the full mathematical meaning and have proofs expressed in a formal foundation of mathematics.  ...  A Mizar document consists of an Environment-Declaration and a Text-Proper.  ... 
doi:10.1016/j.entcs.2008.03.063 fatcat:km2j4mpujfarpbhkxrn5evu7eq

A Qualitative Comparison of the Suitability of Four Theorem Provers for Basic Auction Theory [article]

Christoph Lange and Marco B. Caminati and Manfred Kerber and Till Mossakowski and Colin Rowat and Makarius Wenzel and Wolfgang Windsteiger
2013 arXiv   pre-print
We investigated the suitability of the Isabelle, Theorema, Mizar, and Hets/CASL/TPTP theorem provers for reproducing a key result of auction theory: Vickrey's 1961 theorem on the properties of second-price  ...  Based on our formalisation experience, taking an auction designer's perspective, we give recommendations on what system to use for formalising auctions, and outline further steps towards a complete auction  ...  The ideal theorem proving environment would feature a library as versatile as in Isabelle or Mizar, a prover as efficient as those of Isabelle or Mizar, giving error messages as informative as in Isabelle  ... 
arXiv:1303.4193v3 fatcat:qmiatmlwujcrlbrgfecu4dxbma

A Qualitative Comparison of the Suitability of Four Theorem Provers for Basic Auction Theory [chapter]

Christoph Lange, Marco B. Caminati, Manfred Kerber, Till Mossakowski, Colin Rowat, Makarius Wenzel, Wolfgang Windsteiger
2013 Lecture Notes in Computer Science  
We investigated the suitability of the Isabelle, Theorema, Mizar, and Hets/CASL/ TPTP theorem provers for reproducing a key result of auction theory: Vickrey's 1961 theorem on the properties of second-price  ...  Based on our formalisation experience, taking an auction designer's perspective, we give recommendations on what system to use for formalising auctions, and outline further steps towards a complete auction  ...  The ideal theorem proving environment would feature a library as versatile as in Isabelle or Mizar, a prover as efficient as those of Isabelle or Mizar, giving error messages as informative as in Isabelle  ... 
doi:10.1007/978-3-642-39320-4_13 fatcat:yndhv274j5gwlfni6kqvv2h5qa

History of Interactive Theorem Proving [chapter]

John Harrison, Josef Urban, Freek Wiedijk
2014 Handbook of the History of Logic  
ACKNOWLEDGEMENTS The authors are grateful to Jörg Siekmann for inviting them to prepare this chapter and for his patience in the face of our lengthy delays.  ...  The helpful review of the official reader Larry Paulson as well as useful comments from Mike Gordon, Tom Hales and J Moore, have significantly improved the eventual form of the chapter.  ...  An actual use of Mizar-PC was for teaching propositional logic in P lock and Warsaw. Mizar-QC 1977-1978 Mizar-QC added quantifiers to the language and proof rules for them.  ... 
doi:10.1016/b978-0-444-51624-4.50004-6 fatcat:sngnxnl3ivectj5taj3dgsaa7m

Four Decades of Mizar

Adam Grabowski, Artur Korniłowicz, Adam Naumowicz
2015 Journal of automated reasoning  
Mizar 1 is the name of both a formal language in which the mathematics is written, and of an entire software system that checks the texts for logical correctness and manages the data base of Mizar articles  ...  Various linguistic constructions have been introduced that made the Mizar language a more accurate reflection of the natural language of mathematics.  ...  To list the most important cases of Mizar's influence on other systems we can mention the Declare system developed by Syme [24] , the Mizar mode for HOL by Harrison [10] , the Isar language for Isabelle  ... 
doi:10.1007/s10817-015-9345-1 fatcat:wclwjz6eqzbvbis7w5tdolu5n4

Towards computer aided mathematics

Christoph Benzmüller
2006 Journal of Applied Logic  
Urban's article focuses on MIZARMODE, an Emacs-based authoring environment for the MIZAR system.  ...  More precisely, the authors present an integration of the human-oriented proof script language ISAR, the ISABELLE core proof assistant and the proof planner ISAPLANNER, which is a descendant of the Edinburgh  ... 
doi:10.1016/j.jal.2005.10.001 fatcat:gawws4hbbnappewt2z4dao5loq

Formalising Mathematics – in Praxis; A Mathematician's First Experiences with Isabelle/HOL and the Why and How of Getting Started

Angeliki Koutsoukou-Argyraki
2020 Jahresbericht der Deutschen Mathematiker-Vereinigung (Teubner)  
This is an account of a mathematician's first experiences with the proof assistant (interactive theorem prover) Isabelle/HOL, including a discussion on the rationale behind formalising mathematics and  ...  and potential of proof assistants for mathematics.  ...  as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.  ... 
doi:10.1365/s13291-020-00221-1 fatcat:pt4sfc3hlvfwlant3b4v2varwu
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