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A Formalisation of the Normal Forms of Context-Free Grammars in HOL4 [chapter]

Aditi Barthwal, Michael Norrish
2010 Lecture Notes in Computer Science  
We describe the formalisation of the Chomsky and Greibach normal forms for context-free grammars (CFGs) using the HOL4 theorem prover.  ...  While both proofs are of similar length in their informal presentations, the mechanised proofs for Greibach normal form blow-up considerably.  ...  Acknowledgements NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre  ... 
doi:10.1007/978-3-642-15205-4_11 fatcat:bctvnjpsnbbbfcuvht2vylnorq

Mechanisation of PDA and Grammar Equivalence for Context-Free Languages [chapter]

Aditi Barthwal, Michael Norrish
2010 Lecture Notes in Computer Science  
We provide a formalisation of the theory of pushdown automata (PDAs) using the HOL4 theorem prover.  ...  The proofs blow up in size in way difficult to predict from examining original textbook presentations. Even a meticulous text proof has "intuitive" leaps that need to be identified and formalised.  ...  Constructing a PDA for a CFG Let G = (V, T, P, S) be a context-free grammar in Greibach normal form generating L.  ... 
doi:10.1007/978-3-642-13824-9_11 fatcat:dyxpnendozamvf7myuaunpig5u

Certified Normalization of Context-Free Grammars

Denis Firsov, Tarmo Uustalu
2015 Proceedings of the 2015 Conference on Certified Programs and Proofs - CPP '15  
Every context-free grammar can be transformed into an equivalent one in the Chomsky normal form by a sequence of four transformations.  ...  Also, we show that the right sequence of these transformations leads to a grammar in the Chomsky normal form (since each next transformation preserves the normality properties established by the previous  ...  Acknowledgement We thank our anonymous referees for the useful feedback.  ... 
doi:10.1145/2676724.2693177 dblp:conf/cpp/FirsovU15 fatcat:mnyovkgj6bgd5ckeebmwek6j2y

ISA semantics for ARMv8-a, RISC-v, and CHERI-MIPS

Alasdair Armstrong, Christopher Pulte, Shaked Flur, Ian Stark, Neel Krishnaswami, Peter Sewell, Thomas Bauereiss, Brian Campbell, Alastair Reid, Kathryn E. Gray, Robert M. Norton, Prashanth Mundkur (+2 others)
2019 Proceedings of the ACM on Programming Languages (PACMPL)  
To demonstrate the usability of the latter, we prove (in Isabelle) correctness of a purely functional characterisation of ARMv8-A address translation.  ...  In this paper, we present rigorous semantic models for the sequential behaviour of large parts of the mainstream ARMv8-A, RISC-V, and MIPS architectures, and the research CHERI-MIPS architecture, that  ...  The views, opinions, and/or findings contained in this paper are those of the authors and should not be interpreted as representing the official views or policies, either expressed or implied, of the Department  ... 
doi:10.1145/3290384 fatcat:v4zdb5cq7nbzzetgkitndrlcia

Programming and Proving with Classical Types [chapter]

Cristina Matache, Victor B. F. Gomes, Dominic P. Mulligan
2017 Lecture Notes in Computer Science  
In this work, we use the λµ-calculus as the foundation for a system of proof terms for classical first-order logic.  ...  We extend the language with polymorphic types, add a host of data types in 'direct style', and prove several metatheoretical properties.  ...  We thank the anonymous referees and Peter Sewell for their helpful comments.  ... 
doi:10.1007/978-3-319-71237-6_11 fatcat:2dz6qias4vbmpp3qggznclk3ee

Lem

Dominic P. Mulligan, Scott Owens, Kathryn E. Gray, Tom Ridge, Peter Sewell
2014 Proceedings of the 19th ACM SIGPLAN international conference on Functional programming - ICFP '14  
This requires a delicate balance of expressiveness, careful library design, and implementation of transformations -akin to compilation, but subject to the constraint of producing usable and human-readable  ...  The Lem design takes inspiration both from functional programming languages and from proof assistants, and Lem definitions are translatable into OCaml for testing, Coq, HOL4, and Isabelle/HOL for proof  ...  the users of Lem for their feedback.  ... 
doi:10.1145/2628136.2628143 dblp:conf/icfp/MulliganOGRS14 fatcat:jsndgoc5krcf7gd5scjm4h673u

Lem

Dominic P. Mulligan, Scott Owens, Kathryn E. Gray, Tom Ridge, Peter Sewell
2014 SIGPLAN notices  
This requires a delicate balance of expressiveness, careful library design, and implementation of transformations -akin to compilation, but subject to the constraint of producing usable and human-readable  ...  The Lem design takes inspiration both from functional programming languages and from proof assistants, and Lem definitions are translatable into OCaml for testing, Coq, HOL4, and Isabelle/HOL for proof  ...  the users of Lem for their feedback.  ... 
doi:10.1145/2692915.2628143 fatcat:hk5t5bloa5b6bjdcq3fw2jtmqu

Randomised Testing of a Microprocessor Model Using SMT-Solver State Generation [chapter]

Brian Campbell, Ian Stark
2014 Lecture Notes in Computer Science  
We validate a HOL4 model of the ARM Cortex-M0 microcontroller core by testing the model's behaviour on randomly chosen instructions against real chips from several manufacturers.  ...  give us sufficient confidence in the model.  ...  Our thanks go to Anthony Fox, Magnus Myreen, Peter Sewell and the other members of the REMS project for their assistance.  ... 
doi:10.1007/978-3-319-10702-8_13 fatcat:bc3g4oa63zcmrd7vkfq2pyklgq

Randomised testing of a microprocessor model using SMT-solver state generation

Brian Campbell, Ian Stark
2016 Science of Computer Programming  
We validate a HOL4 model of the ARM Cortex-M0 microcontroller core by testing the model's behaviour on randomly chosen instructions against real chips from several manufacturers.  ...  give us sufficient confidence in the model.  ...  Our thanks go to Anthony Fox, Magnus Myreen, Peter Sewell and the other members of the REMS project for their assistance.  ... 
doi:10.1016/j.scico.2015.10.012 fatcat:vr5jyfcjmbh6rniipte3ueab4u

Modelling Value-oriented Legal Reasoning in LogiKEy [article]

Christoph Benzmüller and David Fuenmayor and Bertram Lomfeld
2022 arXiv   pre-print
The logico-pluralist LogiKEy knowledge engineering methodology and framework is applied to the modelling of a theory of legal balancing in which legal knowledge (cases and laws) is encoded by utilising  ...  The theory obtained is then used to formalise, automatically evaluate, and reconstruct illustrative property law cases (involving appropriation of wild animals) within the Isabelle proof assistant system  ...  Acknowledgements We thank the unknown reviewers of our prior paper at the MLR 2020 workshop for their valuable comments and suggestions that have led to significant improvements of this article.  ... 
arXiv:2006.12789v5 fatcat:5hmrok7ls5c6riplcn3v5gvb34

General Bindings and Alpha-Equivalence in Nominal Isabelle

Christian Urban, Cezary Kaliszyk, Gilles Barthe
2012 Logical Methods in Computer Science  
Nominal Isabelle is a definitional extension of the Isabelle/HOL theorem prover.  ...  We also prove strong induction principles that have the usual variable convention already built in.  ...  Stephanie Weirich suggested to separate the subgrammars of kinds and types in our Core-Haskell example. Ramana Kumar and Andrei Popescu helped us with comments for an earlier version of this paper.  ... 
doi:10.2168/lmcs-8(2:14)2012 fatcat:elyvg7fhzjcnrbh6cba6n5j73u

Partiality and recursion in interactive theorem provers – an overview

ANA BOVE, ALEXANDER KRAUSS, MATTHIEU SOZEAU
2014 Mathematical Structures in Computer Science  
The use of interactive theorem provers to establish the correctness of critical parts of a software development or for formalizing mathematics is becoming more common and feasible in practice.  ...  However, most mature theorem provers lack a direct treatment of partial and general recursive functions; overcoming this weakness has been the objective of intensive research during the last decades.  ...  Moreover, the function is partial, as it terminates only on expressions in normal form.  ... 
doi:10.1017/s0960129514000115 fatcat:y3gdgilgd5bvlev3haw4l3fyxi

A formalisation of the theory of context-free languages in higher order logic [article]

Aditi Barthwal, University, The Australian National, University, The Australian National
2015
We present a formalisation of the theory of context-free languages using the HOL4 theorem prover.  ...  We have mechanised classical results involving context-free grammars and pushdown automata.  ...  Acknowledgements The Little Person and the Quest for the PhD  ... 
doi:10.25911/5d6e4c3c4b543 fatcat:a55lb5rvy5a5pc2nz4uroso3uy

Functional Representation of Prototypes in LVQ and Relevance Learning [chapter]

Friedrich Melchert, Udo Seiffert, Michael Biehl
2016 Advances in Intelligent Systems and Computing  
In addition to the regular research presentations, posters and demonstrations, we were happy to include several other elements in the program of BNAIC 2016, among which keynote presentations by Marc Cavazza  ...  Held yearly, the objective of BNAIC is to promote and disseminate recent research developments in Artificial Intelligence within Belgium, Luxembourg and the Netherlands.  ...  Acknowledgments The research reported has been performed in the context of the project 'Designing and Understanding Forensic Bayesian Networks with Arguments and Scenarios', funded in the NWO Forensic  ... 
doi:10.1007/978-3-319-28518-4_28 fatcat:uwxvq6txmrba3ajulmblafgh2a

LIPIcs, Volume 130, TYPES'18, Complete Volume [article]

Peter Dybjer, José Espírito Santo, Luís Pinto
2019
Acknowledgements This paper is dedicated to the memory of the late Martin Hofmann. Martin was one of the leading researchers in the field of functional programming and type theory.  ...  This article is based on his notes [6, 7], which is only one example of the inspiration he has given to many researchers. His tragic unexpected death was a deep loss for the community.  ...  This suggests a notion of normal form that is indexed by the set V of local variables of the enclosing context, whatever this is.  ... 
doi:10.4230/lipics.types.2018 fatcat:ewqkurxqlvhthh4gtzsr6wtaea
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