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Coinduction for preordered algebra

Răzvan Diaconescu
2011 Information and Computation  
We extend the coinduction proof method for behavioural equivalence to coinduction for proving behavioural transitions.  ...  , which is the algebraic framework for behavioural specification.  ...  Acknowledgments The author thanks both anonymous referees for their comments that have helped improve the presentation of this work.  ... 
doi:10.1016/j.ic.2010.11.001 fatcat:c5vcbhq4izb2re6m2knh5w3aam

Coinductive Logic Programming [chapter]

Luke Simon, Ajay Mallya, Ajay Bansal, Gopal Gupta
2006 Lecture Notes in Computer Science  
As Logtalk uses as a back-end compiler a compatible Prolog system, we discuss the status of key Prolog features for an efficient and usable implementation of coinduction.  ...  We describe the implementation of coinductive logic programming found in Logtalk, discussing its features and limitations.  ...  We thank Gopal Gupta, Feliks Kluźniak, Neda Saeedloei, Brian DeVries, and Kyle Marple for helpful discussions on coinduction during a sabbatical visit to U.T.Dallas and for most of the coinduction examples  ... 
doi:10.1007/11799573_25 fatcat:y2kxgo26uvdzvpqp5w5kwyg7n4

Behaviour-refinement of coalgebraic specifications with coinductive correctness proofs [chapter]

Bart Jacobs
1997 Lecture Notes in Computer Science  
The coalgebraic approach allows us to use coinductive proof methods in establishing re nements (via (bi)simulations). This is illustrated in several examples.  ...  It tells us when objects in a \concrete" class behave exactly like (or: simulate) objects in an \abstract" class.  ...  Bisimilarity corresponds to behavioural satisfaction in hidden-sorted algebra, see e.g. 7, 2]. Therefore, coinduction can also be used as a proof-technique in hidden sorted algebra, see 7] .  ... 
doi:10.1007/bfb0030641 fatcat:4qszl64icngajisapdbjm6jqgu

On the origins of bisimulation and coinduction

Davide Sangiorgi
2009 ACM Transactions on Programming Languages and Systems  
The main objective of the paper is indeed to advocate the proof technique and to suggest the name coinduction for it.  ...  What excites him is the coinductive proof technique for bisimilarity.  ... 
doi:10.1145/1516507.1516510 fatcat:m5uvypq4xnbqxclecr3eadpwsu

Permutations in Coinductive Graph Representation [chapter]

Celia Picard, Ralph Matthes
2012 Lecture Notes in Computer Science  
In the proof assistant Coq, one can model certain classes of graphs by coinductive types.  ...  Still, a formal development has been carried out in Coq, by using its built-in language for proof automation.  ...  Acknowledgements We warmly thank our reviewers for their attentive reading and interesting propositions and challenges.  ... 
doi:10.1007/978-3-642-32784-1_12 fatcat:hbbdp67j4jhanonj52iaetitjq

A hidden agenda

Joseph Goguen, Grant Malcolm
2000 Theoretical Computer Science  
The paper reviews selected literature, introduces a new perspective on nondeterminism, and features powerful hidden coinduction techniques for proving behavioral properties of concurrent systems, especially  ...  reÿnements; some proofs are given using OBJ3.  ...  ., the CEC under ESPRIT-2 BRA Working Groups 6071, IS-CORE (Information Systems COrrectness and REusability) and 6112, COMPASS (COMPrehensive Algebraic Approach to System Speciÿcation and development),  ... 
doi:10.1016/s0304-3975(99)00275-3 fatcat:z6ivbv4ssfcdpck5whjx3e5zvm

Concurrency Theory: A Historical Perspective on Coinduction and Process Calculi [chapter]

Jos C.M. Baeten, Davide Sangiorgi
2014 Handbook of the History of Logic  
Acknowledgements The authors are grateful to Luca Aceto and Rob van Glabbeek for comments on an earlier draft of the paper.  ...  The main objective of the paper is indeed to advocate the proof technique and to suggest the name coinduction for it.  ...  Here, emphasis is put on proof methods to prove programs correct.  ... 
doi:10.1016/b978-0-444-51624-4.50009-5 fatcat:o4fvjxxppvf2pkpjkcpj3erfym

A hidden Herbrand theorem: combining the object and logic paradigms

Joseph Goguen, Grant Malcolm, Tom Kemp
2002 The Journal of Logic and Algebraic Programming  
We call this novel programming paradigm active constraint object programming, suggest some applications for it, and show that it is computationally feasible by reducing it to familiar problems over term  ...  The benefits of the object, logic (or relational), functional, and constraint paradigms can be obtained from our previous combination of the object and functional paradigms in hidden algebra, by combining  ...  largely conducted between 1994 and 1996, with partial support from the UK Science and Engineering Research Council, the European Union under ESPRIT-2 BRA Working Groups 6071, IS-CORE (Information Systems COrrectness  ... 
doi:10.1016/s1567-8326(01)00011-x fatcat:vi5x3k3vl5bcfdisiybnfggmbq

Flexible Coinduction

FRANCESCO DAGNINO
2021
This flexible interpretation nicely subsumes standard inductive and coinductive ones and is naturally associated with a proof principle, which smoothly extends the usual coinduction principle.  ...  To this end, we consider the restriction of the flexible coinductive interpretation to regular derivations, analysing again both proof-theoretic and fixed point semant [...]  ...  Note that, θ i θ 1 θ 2 , for all i = 1, 2, by de nition.  ... 
doi:10.15167/dagnino-francesco_phd2021-01-13 fatcat:p6mrh2y7p5hm5gy4jbhaa3qjl4

Foreword

J. P. Bahsoun, J. L. Fiadeiro, D. Galmiche
1999 Mathematical Structures in Computer Science  
Another proposal for such a framework to deal with concurrent object-oriented features for software development can be based on algebra, mainly hidden sorted algebra, which can be seen as an evolution  ...  Its objective was to provide an integrated forum for the presentation of research and the exchange of ideas and experiences in the topics concerned with proofs, concurrency and object-oriented programming  ...  Foreword 226 paper entitled Hidden coinduction: behavioural correctness proofs for objects focuses on semi-mechanical proof techniques for hidden algebra, as a way of proving behavioural properties of  ... 
doi:10.1017/s0960129599002753 fatcat:7xh2n46uu5gz3cbvfnm3jefhli

Towards a Protocol Algebra Based on Algebraic Specifications [chapter]

Iakovos Ouranos, Petros Stefaneas
2014 Studies in Computational Intelligence  
The proposed protocol algebra is inspired by the module algebra and the hierarchical object composition technique.  ...  We sketch some first steps towards the definition of a protocol algebra based on the framework of behavioural algebraic specification.  ...  The correctness of the coinduction method follows from the fundamental result characterizing the behavioral equivalence as the largest hidden congruence.  ... 
doi:10.1007/978-3-319-00948-3_6 fatcat:2xwcxryhlncxpcqeosievtnxu4

Verifying behavioural specifications in CafeOBJ environment [chapter]

Akira Mori, Kokichi Futatsugi
1999 Lecture Notes in Computer Science  
The refinement proof based on behavioural coinduction is given for the first example, and the coherence proof based on invariance is given for the second.  ...  In this paper, we present techniques for automated verification of behavioural specifications using hidden algebra.  ...  Joseph Goguen for his pioneering work in algebraic specification theory and for creating a new exciting field of study for us.  ... 
doi:10.1007/3-540-48118-4_36 fatcat:t6h4vbxn2rcpniite4xvrstjre

Page 4351 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
coinduction: behavioural correctness proofs for objects.  ...  The main contribution is powerful hidden coinduction techniques for proving behavioural correctness of concurrent sys- tems, and several mechanical proofs are given using OBJ3.  ... 

Component-based algebraic specification and verification in cafeOBJ [chapter]

R.ăzvan Diaconescu, Kokichi Futatsugi, Shusaku Iida
1999 Lecture Notes in Computer Science  
We first give an overview of the main features of CafeOBJ, including its logical foundations, and then we focus on the behavioural specification paradigm in CafeOBJ, surveying the object-oriented CafeOBJ  ...  The last part of this paper further focuses on a component-based behavioural specification and verification methodology which features high reusability of both specification code and verification proof  ...  This means that behavioural proofs for the bank account system are almost automatic, without having to go through the usual coinduction process.  ... 
doi:10.1007/3-540-48118-4_37 fatcat:whjv72oylvf5rps33rxxin52ki

Objects as Abstract Machines [chapter]

Simone Veglioni
1997 IFIP Advances in Information and Communication Technology  
As an alternative model for objects behaviour, Malcolm 1997) by providing an observational semantic and interaction mechanisms.  ...  Keywords abstract machine, behavioural equivalence, hidden algebra, OBJ, algebraic specification.  ...  ACKNOWLEDGEMENTS I would like to express my gratitude to my supervisor Grant Malcolm for his constant help, and to Rocco de Nicola for many helpful discussions.  ... 
doi:10.1007/978-0-387-35261-9_19 fatcat:u7v46ogarfcmdbexzqoi4llhhu
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