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Isabelle Import Infrastructure for the Mizar Mathematical Library [chapter]

Cezary Kaliszyk, Karol Pąk
2018 Lecture Notes in Computer Science  
We present an infrastructure that allows importing an initial part of the Mizar Mathematical Library into the Isabelle/Mizar object logic.  ...  The proof outlines are then imported by an Isabelle package, that translates particular Mizar directives to appropriate Isabelle meta-logic constructions.  ...  Mizar definitions need to be presented in a format that can be accepted by Isabelle.  ... 
doi:10.1007/978-3-319-96812-4_13 fatcat:puwm4uo5xjfxvniy5qn6t2ltou

Simple Dataset for Proof Method Recommendation in Isabelle/HOL (Dataset Description) [article]

Yutaka Nagashima
2020 arXiv   pre-print
In this data description, we present a simple dataset that contains data on over 400k proof method applications along with over 100 extracted features for each in a format that can be processed easily  ...  Our simple data format allows machine learning practitioners to try machine learning tools to predict proof methods in Isabelle/HOL without requiring domain expertise in logic.  ...  Conclusion and Related Work We presented our dataset for proof method recommendation in Isabelle/HOL.  ... 
arXiv:2004.10667v3 fatcat:yrd3dmroa5gojfrkg5noo2twty

Towards Evolutionary Theorem Proving for Isabelle/HOL [article]

Yutaka Nagashima
2019 arXiv   pre-print
In this abstract, we identify challenges in discovering heuristics for automatic proof search and propose our novel approach to improve heuristics of automatic proof search in Isabelle/HOL using evolutionary  ...  However, such existing proof corpora present only one way of proving conjectures, while there are often multiple equivalently effective ways to prove one conjecture.  ...  Nagashima et al. presented PSL, a proof strategy language [9] , for Isabelle/HOL.  ... 
arXiv:1904.08468v1 fatcat:2paxkdezfzholgv2bl64m5ld6y

Making Isabelle Content Accessible in Knowledge Representation Formats [article]

Michael Kohlhase, Florian Rabe, Makarius Wenzel
2020 arXiv   pre-print
Concretely we present an integration of PIDE and MMT that allows exporting all Isabelle libraries in OMDoc format.  ...  The libraries of proof assistants like Isabelle, Coq, HOL are notoriously difficult to interpret by external tools: de facto, only the prover itself can parse and process them adequately.  ...  We apply our approach to Isabelle [PNW19] : we present a definition of the Isabelle logical framework in Mmt and an export feature for Isabelle logics and libraries.  ... 
arXiv:2005.08884v1 fatcat:tnzdgnb22zedvod3odyj6avqye

Declarative Proof Translation (Short Paper)

Cezary Kaliszyk, Karol Pak, Michael Wagner
2019 International Conference on Interactive Theorem Proving  
This generates the corresponding theories with 15301 proof outlines accepted by the Isabelle proof checker.  ...  In this paper we discuss and classify the differences between them and propose efficient algorithms for declarative proof outline translation.  ...  Conclusion We proposed translation techniques for the various features present in declarative proof languages and we automatically translated the proof outlines from 200 articles of the MML to Isabelle  ... 
doi:10.4230/lipics.itp.2019.35 dblp:conf/itp/KaliszykP19 fatcat:ao67gqdgzvdvbofsklolkezq64

Making Isabelle Content Accessible in Knowledge Representation Formats

Michael Kohlhase, Florian Rabe, Makarius Wenzel, Assia Mahboubi, Marc Bezem
2020 Types for Proofs and Programs  
Concretely we present an integration of PIDE and Mmt that allows exporting all Isabelle libraries in OMDoc format.  ...  The libraries of proof assistants like Isabelle, Coq, HOL are notoriously difficult to interpret by external tools: de facto, only the prover itself can parse and process them adequately.  ...  We apply our approach to Isabelle [44] : we present a definition of the Isabelle logical framework in Mmt and an export feature for Isabelle logics and libraries.  ... 
doi:10.4230/lipics.types.2019.1 dblp:conf/types/KohlhaseRW19 fatcat:l35sk5hohjahdd54ylxkecxylm

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

Makarius Wenzel
2019 arXiv   pre-print
Isabelle/PIDE has emerged over more than 10 years as the standard Prover IDE for interactive theorem proving in Isabelle.  ...  The well-established Archive of Formal Proofs (AFP) testifies the success of such applications of formalized mathematics in Isabelle/HOL.  ...  Isabelle/PIDE as IDE for Interactive Proof Documents Isabelle is an interactive proof assistant (similar to Coq or HOL4), and PIDE is the Prover IDE framework for it.  ... 
arXiv:1905.01735v1 fatcat:ixa3aawyubdg3liplcyow7iqwy

A proof-centric approach to mathematical assistants

Lucas Dixon, Jacques Fleuriot
2006 Journal of Applied Logic  
We present an approach to mathematical assistants which uses readable, executable proof scripts as the central language for interaction.  ...  We argue that this synergy provides a flexible environment for the exploration, certification, and presentation of mathematical proof.  ...  Acknowledgements This research was funded by the EPSRC grant A Generic Approach to Proof Planning-GR/N37414/01.  ... 
doi:10.1016/j.jal.2005.10.007 fatcat:nmzu53bazfhvbfofhtl3muid34

NaDeA: A Natural Deduction Assistant with a Formalization in Isabelle [article]

Jørgen Villadsen, Alexander Birch Jensen, Anders Schlichtkrull
2015 arXiv   pre-print
We present a new software tool for teaching logic based on natural deduction. Its proof system is formalized in the proof assistant Isabelle such that its definition is very precise.  ...  and for other proof systems as well.  ...  Acknowledgements We would like to thank Stefan Berghofer for discussions about the formalization of natural deduction in Isabelle.  ... 
arXiv:1507.04002v1 fatcat:36chqozpcfg2jgb7xbs7dcfkwa

IsaPlanner: A Prototype Proof Planner in Isabelle [chapter]

Lucas Dixon, Jacques Fleuriot
2003 Lecture Notes in Computer Science  
IsaPlanner is a generic framework for proof planning in the interactive theorem prover Isabelle.  ...  This paper introduces our approach to proof planning, gives and overview of IsaPlanner, and presents one simple yet effective reasoning technique.  ...  We present IsaPlanner, a generic framework in Isabelle that interleaves proof planning with the proof plan's execution.  ... 
doi:10.1007/978-3-540-45085-6_22 fatcat:j5xdd5sgp5fo7lop4ubjykpgcy

Natural Deduction and the Isabelle Proof Assistant

Jørgen Villadsen, Andreas Halkjær From, Anders Schlichtkrull
2018 Electronic Proceedings in Theoretical Computer Science  
We describe our Natural Deduction Assistant (NaDeA) and the interfaces between the Isabelle proof assistant and NaDeA.  ...  In particular, we explain how NaDeA, using a generated prover that has been verified in Isabelle, provides feedback to the student, and also how NaDeA, for each formula proved by the student, provides  ...  Alexander Birch Jensen was the lead programmer for earlier versions of NaDeA and ProofJudge.  ... 
doi:10.4204/eptcs.267.9 fatcat:ehv2tosmcff2fnqer3frtc4toy

IsarMathLib - a Formalized Mathematics Library for Isabelle/ZF

Slawomir Kolodynski
2018 International Conference on Intelligent Computer Mathematics  
Isabelle [Isa1986] was chosen as the theorem proving environment for the project. There were several reasons for that.  ...  The second reason for the choice was Isabelle's declarative style Isar formal proof language that was "both like and unlike Mizar" [Wen2007].  ...  Some manual editing was usually necessary for the proofs to get successfully verified by Isabelle.  ... 
dblp:conf/mkm/Kolodynski18 fatcat:sewzfpcpvbd3vb5na7nxbdhklm

Homotopy Type Theory in Isabelle [article]

Joshua Chen
2021 arXiv   pre-print
This paper introduces Isabelle/HoTT, the first development of homotopy type theory in the Isabelle proof assistant.  ...  I also integrate the propositions-as-types paradigm with the declarative Isar proof language, providing an alternative to the tactic-based proofs of Coq and the proof terms of Agda.  ...  As a dependently typed Isabelle object logic which improves on Isabelle/CTT with necessary supporting infrastructure for type checking, term elaboration, proof term abstraction and tactics.  ... 
arXiv:2002.09282v2 fatcat:cgaeh2o2jrhlrb37ofqayl4pre

Natural Deduction Assistant (NaDeA)

Jørgen Villadsen, Andreas Halkjær From, Anders Schlichtkrull
2019 Electronic Proceedings in Theoretical Computer Science  
We present the Natural Deduction Assistant (NaDeA) and discuss its advantages and disadvantages as a tool for teaching logic.  ...  NaDeA is available online and is based on a formalization of natural deduction in the Isabelle proof assistant. We first provide concise formulations of the main formalization results.  ...  We also thank the anonymous reviewers for their comments.  ... 
doi:10.4204/eptcs.290.2 fatcat:2xp7xxowhbalvk6pxz4x56u24i

Reconstruction of Z3's Bit-Vector Proofs in HOL4 and Isabelle/HOL [chapter]

Sascha Böhme, Anthony C. J. Fox, Thomas Sewell, Tjark Weber
2011 Lecture Notes in Computer Science  
We present independent reconstruction of unsatisfiability proofs for bit-vector theories in the theorem provers HOL4 and Isabelle/HOL.  ...  We thereby obtain high correctness assurances for Z3's results, and increase the degree of proof automation for bit-vector problems in HOL4 and Isabelle/HOL.  ...  The authors are grateful to Nikolaj Bjørner and Leonardo de Moura for their help with Z3.  ... 
doi:10.1007/978-3-642-25379-9_15 fatcat:gesxkp2cm5girliosyngzyuwmi
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