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Bounded Model Generation for Isabelle/HOL

Tjark Weber
2005 Electronical Notes in Theoretical Computer Science  
The algorithm has been implemented in the interactive theorem prover Isabelle/HOL, where it is used to automatically generate countermodels for non-theorems.  ...  A standard SAT solver can then be used to search for a satisfying assignment, and such an assignment can be transformed back into a model for the HOL formula.  ...  Acknowledgement The author would like to thank Martin Strecker, Tobias Nipkow and the anonymous referees for their valuable comments.  ... 
doi:10.1016/j.entcs.2004.10.027 fatcat:pg34wda2kvgb7co7i67hry2qgy

Cardinals in Isabelle/HOL [chapter]

Jasmin Christian Blanchette, Andrei Popescu, Dmitriy Traytel
2014 Lecture Notes in Computer Science  
We report on a formalization of ordinals and cardinals in Isabelle/HOL.  ...  We also discuss several applications of this general theory in formal developments.  ...  We present a formalization in Isabelle/HOL that provides such general-purpose theorems, as well as some more specialized results and applications.  ... 
doi:10.1007/978-3-319-08970-6_8 fatcat:iwslhjcasrakda4cz4dtfstsjm

From LCF to Isabelle/HOL

Lawrence C. Paulson, Tobias Nipkow, Makarius Wenzel
2019 Formal Aspects of Computing  
Here, we focus on Isabelle/HOL and its distinctive strengths.  ...  The resulting type, thm, From LCF to Isabelle/HOL 677  ...  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

Owicki/Gries in Isabelle/HOL [chapter]

Tobias Nipkow, Leonor Prensa Nieto
1999 Lecture Notes in Computer Science  
We present a formalization of the Gries/Owicki method for correctness proofs of concurrent imperative programs with shared variables in the theorem prover Isabelle/HOL.  ...  Acknowledgment We thank Javier Esparza, David von Oheimb, Cornelia Pusch and Markus Wenzel for the very helpful discussions, and two anonymous referees for their comments.  ...  Isabelle/HOL Isabelle [23, 12] is a generic interactive theorem prover and Isabelle/HOL is its instantiation for higher-order logic, which is very similar to Gordon's HOL system [10] .  ... 
doi:10.1007/978-3-540-49020-3_13 fatcat:6xjy7zmdvbcqfek5rrx2vkzhqy

Generating Verified LLVM from Isabelle/HOL

Peter Lammich, Michael Wagner
2019 International Conference on Interactive Theorem Proving  
We present a framework to generate verified LLVM programs from Isabelle/HOL.  ...  It is based on a code generator that generates LLVM text from a simplified fragment of LLVM, shallowly embedded into Isabelle/HOL.  ...  Haslbeck and Simon Wimmer for proofreading and useful suggestions.  ... 
doi:10.4230/lipics.itp.2019.22 dblp:conf/itp/Lammich19 fatcat:mska6m2pavc6jf2tl2hlumi2du

Nominal Techniques in Isabelle/HOL

Christian Urban
2008 Journal of automated reasoning  
The main technical novelty of this work is that it is compatible with the axiom of choice (unlike earlier nominal logic work by Pitts et al); thus we were able to implement all results in Isabelle/HOL  ...  Furthermore, we adapt work by Pitts providing a recursion combinator for the inductive set.  ...  Acknowledgements: I am very grateful to Andy Pitts and Michael Norrish for the many discussions with them on the subject of the paper.  ... 
doi:10.1007/s10817-008-9097-2 fatcat:cyhobuu5f5bcdg6a6gioymp4de

A Consistent Foundation for Isabelle/HOL [chapter]

Ondřej Kunčar, Andrei Popescu
2015 Lecture Notes in Computer Science  
The reason is that, in Isabelle/HOL, the theorems in D are not influenced by the others.  ...  the Isabelle/HOL problem under scrutiny, it is due to an error in the termination checker [8] .  ... 
doi:10.1007/978-3-319-22102-1_16 fatcat:z7znrl27rrchhaw6f4wqrfrura

Nominal Techniques in Isabelle/HOL [chapter]

Christian Urban, Christine Tasson
2005 Lecture Notes in Computer Science  
The main technical novelty of this work is that it is compatible with the axiom of choice (unlike earlier nominal logic work by Pitts et al); thus we were able to implement all results in Isabelle/HOL  ...  Furthermore, we adapt work by Pitts providing a recursion combinator for the inductive set.  ...  Acknowledgements: I am very grateful to Andy Pitts and Michael Norrish for the many discussions with them on the subject of the paper.  ... 
doi:10.1007/11532231_4 fatcat:rzfrcxaftjaeliscekxupkqv6a

A Consistent Foundation for Isabelle/HOL

Ondřej Kunčar, Andrei Popescu
2018 Journal of automated reasoning  
The reason is that, in Isabelle/HOL, the theorems in D are not influenced by the others.  ...  the Isabelle/HOL problem under scrutiny, it is due to an error in the termination checker [8] .  ... 
doi:10.1007/s10817-018-9454-8 fatcat:hwofbkfkh5e55hgziwrmnifu2y

A Verified Decision Procedure for Orders in Isabelle/HOL [article]

Lukas Stevens, Tobias Nipkow
2021 arXiv   pre-print
We formalise the procedure in Isabelle/HOL and provide a specification that is made executable using Isabelle's code generator.  ...  We present the first verified implementation of a decision procedure for the quantifier-free theory of partial and linear orders.  ...  Notation Isabelle/HOL conforms to everyday mathematical notation for the most part.  ... 
arXiv:2104.13117v2 fatcat:ufcpmxrtwjblxgmtykygprzrhu

LiFtEr: Language to Encode Induction Heuristics for Isabelle/HOL [article]

Yutaka Nagashima
2019 arXiv   pre-print
Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving.  ...  Isabelle experts know how to use these tools effectively; however, there is a little tool support for transferring this expert knowledge to a wider user audience.  ...  ., for example, verified the correctness of the seL4 micro-kernel in Isabelle/HOL [11] , whereas Leroy developed a certifying C compiler, CompCert, using Coq [15] .  ... 
arXiv:1906.08084v3 fatcat:uehy5lr3rnhgzfwon7bfbqz6o4

Fast Machine Words in Isabelle/HOL [chapter]

Andreas Lochbihler
2018 Lecture Notes in Computer Science  
This paper presents a library for Isabelle/HOL that links the existing formalisation of words to the machine words that the four target languages of Isabelle/HOL's code generator provide.  ...  The generated code is used for animating the formal specification [10, 38, 41, 45 ], validating the formal models [16, 18, 39], proving properties by evaluation [1, 21, 23, 48], and to obtain actual tools  ...  To that end, we have developed a general-purpose framework for Isabelle/HOL to run and test the generated code ( §5.1).  ... 
doi:10.1007/978-3-319-94821-8_23 fatcat:svckhxh7tfbe3g7ksn7w7ys55y

Imperative Functional Programming with Isabelle/HOL [chapter]

Lukas Bulwahn, Alexander Krauss, Florian Haftmann, Levent Erkök, John Matthews
2008 Lecture Notes in Computer Science  
We introduce a lightweight approach for reasoning about programs involving imperative data structures using the proof assistant Isabelle/HOL.  ...  The framework immediately allows for correct code generation to ML and Haskell.  ...  We would like to thank David Hardin, Joe Hurd, Matt Kaufmann, Dylan McNamee, Tobias Nipkow, Konrad Slind, and Tjark Weber for their useful discussions, encouragement and feedback on our work.  ... 
doi:10.1007/978-3-540-71067-7_14 fatcat:lcedkeoly5fzxol5ttbj6ezv24

Automatic Proof and Disproof in Isabelle/HOL [chapter]

Jasmin Christian Blanchette, Lukas Bulwahn, Tobias Nipkow
2011 Lecture Notes in Computer Science  
Isabelle/HOL is a popular interactive theorem prover based on higherorder logic. It owes its success to its ease of use and powerful automation.  ...  compiler as a fast evaluator for ground formulas, and its rival Nitpick is based on the model finder Kodkod, which performs a reduction to SAT.  ...  We thank Alexander Krauss, Mark Summerfield, and Thomas Türk for suggesting several textual improvements.  ... 
doi:10.1007/978-3-642-24364-6_2 fatcat:y4crzmmegfhybfp5xu2bwlxoae

Reconstructing veriT Proofs in Isabelle/HOL

Mathias Fleury, Hans-Jörg Schurr
2019 Electronic Proceedings in Theoretical Computer Science  
We present here a reconstruction procedure in the proof assistant Isabelle/HOL for proofs generated by the satisfiability modulo theories solver veriT which is part of the smt tactic.  ...  We thank Alex Brick, Daniel El Ouraoui, and Pascal Fontaine for suggesting many textual improvements.  ...  If the reconstruction is successful, the initial proof goal holds in the Isabelle/HOL logic.  ... 
doi:10.4204/eptcs.301.6 fatcat:cedffdxzcbaqjn5vwoloffrtgm
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