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A Mechanised Proof System for Relation Algebra Using Display Logic [chapter]

Jeremy E. Dawson, Rajeev Goré
1998 Lecture Notes in Computer Science  
Our implementation is the rst mechanisation of any display calculus, but also provides a useful interactive proof assistant for relation algebra.  ...  We show how some relation algebraic theorems proved using our system can be put in the form of structural rules of Display Logic, facilitating later re-use.  ...  The second author is supported by the Australian Research Council via a Queen Elizabeth II Fellowship.  ... 
doi:10.1007/3-540-49545-2_18 fatcat:hrlp65zylraxxfgi5yoomcuvki

Mechanising the Alphabetised Relational Calculus

Gift Nuka, Jim Woodcock
2004 Electronical Notes in Theoretical Computer Science  
This allows us to use one of the standard theorem provers for Z, in order to provide mechanised support for reasoning about programs in the unifying theory.  ...  In this paper, we give a formal semantics of the alphabetised relational calculus, and use our definition to create a deep embedding of the calculus in Z.  ...  Acknowledgement The authors thank anonymous referees and Ana Cavalcanti for their helpful comments on this paper and Arther Hughes who read an earlier version of this paper.  ... 
doi:10.1016/j.entcs.2004.04.013 fatcat:re2vrz7moncyxhmrbasj2om7eu

A mechanisation of classical modal tense logics using isabelle [chapter]

Jeremy E Dawson, Rajeev Goré
1998 Lecture Notes in Computer Science  
The novelty of the implementation is that we use a Display Logic formalism of Kt as opposed to a traditional Gentzen system.  ...  We present an implementation of an interactive theorem prover for the basic tense logic Kt, and many of its extensions, using the generic proof assistant Isabelle.  ...  Display calculi exist for Linear, Relevant, BCK, Lambek and other substructural logics Gor98, Res98] , for the logic of Relation Algebras Gor97], and even for nominal tense logics DG98].  ... 
doi:10.1007/bfb0095045 fatcat:4k2tnchesnfv3mz3ysa5q76kbm

Preface

A. Bundy
2005 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
One contribution of 13 to a Discussion Meeting Issue 'The nature of mathematical proof'.  ...  Also, some mathematicians have found computer systems to be a useful experimental tool, which can do not just numeric calculations, but also symbolic, algebraic manipulation and graphical display of the  ...  In particular, he contrasts preferences for mechanised versus non-mechanised proof and formal versus rigorous proofs.  ... 
doi:10.1098/rsta.2005.1660 fatcat:7a5xjkcvlrbhvl7vp52oe7euvu

Cut-free display calculi for relation algebras [chapter]

Rajeev Goré
1997 Lecture Notes in Computer Science  
We extend Belnap's Display Logic to give a cut-free Gentzen-style calculus for relation algebras.  ...  It also appears to be the rst purely propositional Gentzen-style calculus for relation algebras.  ...  Acknowledgments: Thanks to Lev Gordeev, Wolfgang Heinle, Greg Restall and Timothy Surendonk for many helpful discussions.  ... 
doi:10.1007/3-540-63172-0_40 fatcat:3ctbkynpw5cyph6sjwgqajvwvm

Can Refinement be Automated?

Peter Höfner, Georg Struth
2008 Electronical Notes in Theoretical Computer Science  
Our novel approach mechanises a refinement calculus based on Kleene algebras in an off the shelf resolution and paramodulation theorem prover and a counterexample checker with heuristics for hypothesis  ...  The proofs are supported by a toolkit of meaningful refinement laws that has also been verified and that, for the first time, allows the refinement of programs and software systems, and the verification  ...  We are most grateful to Mark Schaefer for placing his powerful PC at our disposal for proof search. With our own slow machines we would possibly not have met the deadline.  ... 
doi:10.1016/j.entcs.2008.02.021 fatcat:tqtg3hmpmzgchbeyngwupaza7y

A New Machine-checked Proof of Strong Normalisation for Display Logic

Jeremy E. Dawson, Rajeev Goré
2003 Electronical Notes in Theoretical Computer Science  
We use a deep embedding of the display calculus for relation algebras δRA in the logical framework Isabelle/HOL to formalise a new, machine-checked, proof of strong normalisation and cut-elimination for  ...  We believe this is the first full formalisation of a strong normalisation result for a sequent system using a logical framework.  ...  A Deep Embedding of δRA in Isabelle/HOL The following grammar defines the syntax of relation algebras: A B ::= p i | | ⊥ | ¬A | A ∧ B | A ∨ B | 1 | 0 | A | A + B | A • B A display calculus for relation  ... 
doi:10.1016/s1571-0661(04)81004-1 fatcat:5l76ya3mojdy5ksahru2vvutdm

Mechanising Hankin and Barendregt using the Gordon-Melham axioms

Michael Norrish
2003 Proceedings of the 2003 workshop on Mechanized reasoning about languages with variable binding - MERLIN '03  
Using these as a foundation, I mechanised the proofs from Chapters 2 and 3 of Hankin [5] (equational theory and reduction theory), followed by most of Chapter 11 of Barendregt [2] (residuals, finiteness  ...  I describe the mechanisation in HOL of some basic λ-calculus theory, using the axioms proposed by Gordon and Melham [4].  ...  I came to the mechanisation with some experience of confluence proofs in other systems, but no knowledge of any of the λ-calculus proofs except of Church-Rosser for β-reduction.  ... 
doi:10.1145/976571.976577 dblp:conf/icfp/Norrish03 fatcat:y4nugdgk5ff4tahj6homx7ti4u

Checking SysML Models for Co-simulation [chapter]

Nuno Amálio, Richard Payne, Ana Cavalcanti, Jim Woodcock
2016 Lecture Notes in Computer Science  
Verification of these properties involves theorem proving and model-checking using: Fragmenta, a formal theory for representing typed visual models, with its mechanisation in the Isabelle/HOL proof assistant  ...  proving and model-checking; our verification and transformation workbench for typed visual models based on Fragmenta and Isabelle; an approach to detect algebraic loops using CSP and FDR3; and a comparison  ...  Thanks are due to Etienne Brosse, who implemented the INTO-SysML profile in the Modelio tool, and Bernhard Thiele, who provided useful feeedback on the work presented here.  ... 
doi:10.1007/978-3-319-47846-3_28 fatcat:mn2zw4xvu5aabgdj6iscnhmnfm

Mechanising λ-calculus using a classical first order theory of terms with permutations

Michael Norrish
2006 Higher-Order and Symbolic Computation  
The issues in mechanising pen-and-paper proofs are discussed; in particular, those difficulties arising from the sources' use of the Barendregt Variable Convention.  ...  This paper describes the mechanisation in HOL of some basic λ-calculus theory.  ...  Acknowledgements I would like to thank Andy Pitts for many useful discussions about recursion, Christian Urban for many useful discussions about BVC-compatible induction principles, and René Vestergaard  ... 
doi:10.1007/s10990-006-8745-7 fatcat:u5jw53nhljcj5cd4tpkmmrclpu

Substructural logics on display

R Gore
1998 Logic Journal of the IGPL  
Using a refinement of the display property, you can pick and choose from these possibilities to construct a display calculus for your needs. their particular viewpoint, to varying degrees of success.  ...  The Display Logic of Nuel Belnap is a general Gentzen-style proof theoretical framework designed to capture many different logics in one uniform setting.  ...  Ono [59] gives a sequent system for Girard's exponentials together with associated algebraic semantics. MacCaull [48] has given a semantics for this system using binary Kripke relations.  ... 
doi:10.1093/jigpal/6.3.451 fatcat:erqlhxit7fe25a4gmybgimeuzy

Technologies for "Complete, Transparent & Interactive Models of Math" in Education

Walther Neuper
2019 Electronic Proceedings in Theoretical Computer Science  
Interaction uses several layers of formal languages: the language of terms, of specifications, of proofs and of program language, which are connected by Lucas-Interpretation providing "next-step-guidance  ...  Respective concepts and technologies have been clarified to an extent, which calls for cooperation with educational sciences in order to optimise the new generation's impact on educational practice.  ...  A few decades ago integration, for instance, was a task for demanded experts using Bronstein [3] and other tables, today everyone uses computer algebra for such tasks.  ... 
doi:10.4204/eptcs.290.6 fatcat:rdkwwdqubvd4jpp3xwgddmfyma

Integration of Formal Proof into Unified Assurance Cases with Isabelle/SACM [article]

Simon Foster, Yakoub Nemouchi, Mario Gleirscher, Ran Wei, Tim Kelly
2020 arXiv   pre-print
We thus show that Isabelle is a suitable platform for critical systems assurance.  ...  To validate our approach, we present a substantial case study based on the Tokeneer secure entry system benchmark.  ...  Finally, we create an artifact relation that gives the provenance for the proof of FSFR1.  ... 
arXiv:2009.12154v1 fatcat:fqnawy4s3rafteg3gfihj7ohgq

Isabelle/SACM: Computer-Assisted Assurance Cases with Integrated Formal Methods [chapter]

Yakoub Nemouchi, Simon Foster, Mario Gleirscher, Tim Kelly
2019 Lecture Notes in Computer Science  
In this paper, we contribute a formal machine-checked interactive language for the computer-assisted construction of ACs called Isabelle/SACM.  ...  To validate Isabelle/SACM, we present a novel formalisation of the Tokeneer benchmark, verify its security requirements, and form a mechanised AC that combines the resulting formal and informal artifacts  ...  Tokeneer is therefore a successful example of using FMs to assure a system against CC.  ... 
doi:10.1007/978-3-030-34968-4_21 fatcat:f4yorb4dongwvkf72u3saaxl7a

Mechanical verification of refactorings

Nik Sultana, Simon Thompson
2008 Proceedings of the 2008 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation - PEPM '08  
For a refactoring to be correct the refactored program must be identical in behaviour to the original program.  ...  proofs.  ...  financial support provided to the first author by the Computing Laboratory and by the Malta Government Scholarship Scheme through award MGSS/2006/007; the second author acknowledges the support of the EPSRC for  ... 
doi:10.1145/1328408.1328417 dblp:conf/pepm/SultanaT08 fatcat:5ygcrbwngrethdlgc7iqte6ugm
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