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Universal Coinductive Characterisations of Process Semantics [chapter]

David de Frutos Escrig, Carlos Gregorio Rodríguez
IFIP International Federation for Information Processing  
We present a theoretical framework which allows to define in a uniform way coinductive characterisations of nearly any semantic preorder or equivalence between processes, by means of simulations up-to  ...  the possibility of giving coinductive characterisations for all of them, or the existence of a canonical preorder inducing each of these equivalences.  ...  Once we had coinductive characterisations for many semantic equivalences we shifted the focus from equivalences to preorders.  ... 
doi:10.1007/978-0-387-09680-3_27 fatcat:mrymnggar5fhll7kbjoilb7efy

Coinductive Characterisations Reveal Nice Relations Between Preorders and Equivalences

David de Frutos Escrig, Carlos Gregorio Rodríguez, Miguel Palomino
2008 Electronical Notes in Theoretical Computer Science  
More important, we also present further generalisations of the result, since our coinductive characterisations are not only valid for the semantics coarser than the ready simulation.  ...  There are two ways to define a semantics for process algebras: either directly by means of an equivalence relation or by means of a preorder whose kernel is the desired equivalence.  ...  also shown the interest of having a uniform characterisation for process semantics, such as our coinductive characterisations, in order to prove general results on semantics.  ... 
doi:10.1016/j.entcs.2008.04.059 fatcat:jqksu7iv45boxcdlaq54i2qthy

Constrained Simulations, Nested Simulation Semantics and Counting Bisimulations

David de Frutos Escrig, Carlos Gregorio Rodríguez
2008 Electronical Notes in Theoretical Computer Science  
Finally, we conclude the study of the (generalised) nested semantics defining a generalisation of bisimulation relations, counting bisimulation, that allows us to define a characterisation of nested semantics  ...  This nested nature provides a fruitful framework for the study of the formal meaning and the properties of concurrent processes.  ...  Bisimilarity is a capital notion in process theory and it is the cornerstone for one of the targets of our work: providing coinductive characterisations of process semantics.  ... 
doi:10.1016/j.entcs.2008.03.074 fatcat:fhp7tktrsfdn5jcodzijm7zxhu

(Bi)simulations up-to characterise process semantics

David de Frutos Escrig, Carlos Gregorio Rodríguez
2009 Information and Computation  
We define (bi)simulations up-to a preorder and show how we can use them to provide a coinductive, (bi)simulation-like, characterisation of semantic (equivalences) preorders for processes.  ...  As an illustrative example of this technique, we generate an axiomatic characterisation of each of these canonical preorders, that is obtained simply by adding a single axiom to the axiomatization of the  ...  on the full universe of tests or formulae.  ... 
doi:10.1016/j.ic.2007.12.003 fatcat:jtgbwaht75cebfdh5tjy6td5yq

Coalgebraic Derivations in Logic Programming

Ekaterina Komendantskaya, John Power, Marc Herbstritt
2011 Annual Conference for Computer Science Logic  
We analyse this new algorithm in terms of the Theory of Observables, and we prove soundness, completeness, correctness and full abstraction results.  ...  Coalgebra may be used to provide semantics for SLD-derivations, both finite and infinite.  ...  We once again characterise coinductive derivations from the point of view of the Theory of Observables.  ... 
doi:10.4230/lipics.csl.2011.352 dblp:conf/csl/KomendantskayaP11 fatcat:6zun2z7hffaz3nsljdkmhxflkm

A Coinduction Principle for Recursive Data Types Based on Bisimulation

Marcelo P. Fiore
1996 Information and Computation  
By this we mean that the interpretations of IntStream, headS and tailS, say Z | , h and t, are characterised by the following universal property: for every set T equipped with a map article no. 0058 186  ...  semantics using the final coalgebra of the endofunctor Z_ : Set Ä Set where Z is the set of integers, _ is the cartesian-product functor, and Set is the category of small sets and functions.  ...  ACKNOWLEDGMENTS This work was done under the supervision of Gordon Plotkin and Barry Jay. I thank them both for their involvement and guidance.  ... 
doi:10.1006/inco.1996.0058 fatcat:4vyuqwsltrhmjouydkswa5kpxe

Coalgebraic Logic Programming: from Semantics to Implementation [article]

Ekaterina Komendantskaya, John Power, Martin Schmidt
2013 arXiv   pre-print
Here, we give a coherent semantics-led account of the issues, starting with abstract category theoretic semantics, developing coalgebra to characterise naturally arising trees, and proceeding towards implementation  ...  of a new dialect, CoALP, of logic programming, characterised by guarded lazy corecursion and parallelism.  ...  Stream can alternatively be given coalgebraic semantics [6, 9] or observational semantics [9, 14] . Coalgebraic semantics is, in general, well-suited to describing parallel processes [22, 43] .  ... 
arXiv:1312.6568v1 fatcat:euvpzzi5z5gnlpup5mqsudhhq4

Expressive Logics for Coinductive Predicates

Clemens Kupke, Jurriaan Rot, Michael Wagner
2020 Annual Conference for Computer Science Logic  
We formulate when a logic fully characterises a coinductive predicate on coalgebras, by providing suitable notions of adequacy and expressivity, and give sufficient conditions on the semantics.  ...  ACM Subject Classification Theory of computation → Modal and temporal logics; Theory of computation → Categorical semantics Acknowledgements We would like to thank Bart Jacobs for useful discussions and  ...  Coinductive predicates in a fibration. To characterise coinductive predicates, we make use of fibrations -this approach originates from the seminal work of Hermida and Jacobs [14] .  ... 
doi:10.4230/lipics.csl.2020.26 dblp:conf/csl/KupkeR20 fatcat:fxdsbiiedrgshgqbeyasc7gina

CoALP-Ty'16 [article]

Ekaterina Komendantskaya, František Farka
2016 arXiv   pre-print
This volume consists of extended abstracts describing current research in the following areas: Semantics: Lawvere theories and Coalgebra in Logic and Functional Programming Programming languages: Horn  ...  This volume constitutes the pre-proceedings of the Workshop on Coalgebra, Horn Clause Logic Programming and Types (CoALP-Ty'16), held on 28--29 November 2016 in Edinburgh as a mark of the end of the EPSRC  ...  This in turn gives us a universe of discourse for exploring other semantics and proof systems for mixed inductive-coinductive logic programs.  ... 
arXiv:1612.03032v1 fatcat:d6gug5imufgwbcslntnyts4nim

Coalgebraic logic programming: from Semantics to Implementation

Ekaterina Komendantskaya, John Power, Martin Schmidt
2014 Journal of Logic and Computation  
For example, in Stream, the goal stream(scons(x, scons(y,x))), if processed sequentially, leads to a failed derivation owing to ill-typing, whereas if proof search proceeds in a at Heriot-Watt University  ...  of a new dialect, CoALP, of logic programming, characterised by guarded lazy corecursion and parallelism. http://logcom.oxfordjournals.org/ Downloaded from 746 Coalgebraic logic programming abstract category  ...  Stream can alternatively be given coalgebraic semantics [6, 9] or observational semantics [9, 14] . Coalgebraic semantics is, in general, well-suited for describing parallel processes [22, 43] .  ... 
doi:10.1093/logcom/exu026 fatcat:32ofdknnjvfelbiod5pskrjhli

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

Coinductive Soundness of Corecursive Type Class Resolution [chapter]

František Farka, Ekaterina Komendantskaya, Kevin Hammond
2017 Lecture Notes in Computer Science  
This paper shows, for the first time, that corecursive type class resolution and its recent extensions are coinductively sound with respect to the greatest Herbrand models of logic programs and that they  ...  Horn clauses and first-order resolution are commonly used for the implementation of type classes in Haskell.  ...  Given a Herbrand universe U Σ we define the Herbrand base B Σ as the set of all atoms consisting only of ground terms in U Σ . Definition 2 (Semantic operator).  ... 
doi:10.1007/978-3-319-63139-4_18 fatcat:jmfbgvz36jgsfiaboiiox5bniy

On the origins of bisimulation and coinduction

Davide Sangiorgi
2009 ACM Transactions on Programming Languages and Systems  
ACKNOWLEDGMENT I am very grateful to the following people who helped me to find relevant papers and materials or helped me in tracing back bits of history: P. Aczel, G. Boudol, J. van  ...  By contrast, axioms of anti-foundation lead to the largest possible universe, i.e., a "coinductive universe".  ...  The former is an inductive definition of the universe, whereas the latter is a coinductive one.  ... 
doi:10.1145/1516507.1516510 fatcat:m5uvypq4xnbqxclecr3eadpwsu

Structural Resolution: a Framework for Coinductive Proof Search and Proof Construction in Horn Clause Logic [article]

Ekaterina Komendantskaya, Patricia Johann, Martin Schmidt
2017 arXiv   pre-print
In this paper, we prove soundness of structural resolution relative to Herbrand model semantics for productive inductive, coinductive, and mixed inductive-coinductive logic programs.  ...  One algorithm combines the method of loop detection with productive structural resolution, thus guaranteeing productivity of coinductive proofs for infinite rational terms.  ...  We particularly thank Vladimir Komendantskiy and Frantiŝek Farka, who at different times implemented prototypes of CoAlgebraic Logic Programming (CoALP) and S-Resolution: their input has been invaluable  ... 
arXiv:1511.07865v2 fatcat:6lqbu7vyqzegnchxtiws7ty3fu

Coinductive Interpreters for Process Calculi [chapter]

Luís Soares Barbosa, José Nuno Oliveira
2002 Lecture Notes in Computer Science  
This paper suggests functional programming languages with coinductive types as suitable devices for prototyping process calculi.  ...  The approach is illustrated by the detailed development in Charity of an interpreter for a family of process languages.  ...  Our semantic universe, however, is the final coalgebra for functor P(Ac(L) × Id), and, therefore, the dual final semantics approach will be followed up.  ... 
doi:10.1007/3-540-45788-7_11 fatcat:of35dr4robdcllnvuriyvhrz54
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