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An Algebra of Behavioural Types

António Ravara, Pedro Resende, Vasco T. Vasconcelos
2012 Information and Computation  
We propose a process algebra, the Algebra of Behavioural Types, as a language for typing concurrent objects.  ...  Moreover, a type provides an internal view of the objects that inhabits it: a synchronous one, since transitions correspond to message reception.  ...  Acknowledgments Special thanks to Gérard Boudol, Ilaria Castellani, Silvano Dal Zilio, and Massimo Merro, for fruitful discussions and careful reading of parts of this document.  ... 
doi:10.1016/j.ic.2011.12.005 fatcat:u4ske5sttrf35kmzmqellvuyye

Behavioural Categoricity of Abstract Data Type Specifications

P. Lescanne
1983 Computer journal  
Type Circular-List [Item] Operations INIT: (Item) -> Circular-List INSERT: (Item, Circular-List) -> Circular-List ROT: (Circular-List) -Circular-List WINDOW: (CircularJList) -» Item Axioms ROT(INIT(a))  ...  Acknowledgements I would like to thank Christine Choppy, Marie-Claude Gaudel, John Guttag, Sam Kamin, Srivas Mandayam, Jean-Luc Remy and Jeannette Wing who helped me to clarify my ideas on abstract data types  ...  In this note we want to present the concept of behavioural categoricity of an abstract data type specification.  ... 
doi:10.1093/comjnl/26.4.289 fatcat:xyu2vlaggndhxh2qz5ksht2dcm

Axisymmetric mean field dynamos with dynamic and algebraic α--quenchings [article]

Eurico Covas, Reza Tavakol, Andrew Tworkowski, Axel Brandenburg
1997 arXiv   pre-print
As regards differences, the important feature in the full sphere models is the occurrence of chaotic behaviour in the algebraic α--quenching models.  ...  Regarding similarities, both groups of models exhibit symmetric, antisymmetric and mixed modes of behaviour.  ...  This research also benefited from the EC Human Capital and Mobility (Networks) grant "Late type stars: activity, magnetism, turbulence" No. ERBCHRXCT940483.  ... 
arXiv:astro-ph/9709062v1 fatcat:a4aqmvs5pbem7gtbxymm66vgdm

Behavioural Equivalence and Indistinguishability in Higher-Order Typed Languages [chapter]

Shin-ya Katsumata
2003 Lecture Notes in Computer Science  
In the study of the simply typed lambda calculus, there is a well-known extension method using exponential relations (the following shows the case of binary relations between two combinatory algebras ¡  ...  We extend the study of the relationship between behavioural equivalence and the indistinguishability relation [4, 7] to the simply typed lambda calculus, where higher-order types are available.  ...  This work has been partly supported by an LFCS studentship.  ... 
doi:10.1007/978-3-540-40020-2_16 fatcat:i452jtfzbbet7e2nhh7loeonbe

Behavioural correctness of data representations

Oliver Schoett
1990 Science of Computer Programming  
't/crifying behavioural relations between data types directly can sometimes be dilkult, because it may require one to analyse the interaction of' the input and output operations of the data types.  ...  Correspondences and strong correspondences are relations between the carrier sets of the algebras (i.e., relating the values of the data types) that are "compatible" with the operations.  ...  The research was conducted at the University of Edinburgh on studentships from the Studienstiftung des deutschen Volkes and the University of Edinburgh.  ... 
doi:10.1016/0167-6423(90)90057-k fatcat:oan3652ikrcqhikaozfj4zbhoe

On behavioural abstraction and behavioural satisfaction in higher-order logic [chapter]

Martin Hofmann, Donald Sannella
1995 Lecture Notes in Computer Science  
A characterization of behavioural abstraction via behavioural satisfaction of formulae in which the equality symbol is interpreted as indistinguishability, due to Reichel and recently generalized to the  ...  The behavioural semantics of specifications with higher-order formulae as axioms is analyzed.  ...  Proof Method 7.8 is due to them, and they pointed out that a previous version of Proof Methods 7.12 and 7.14 were unnecessarily restrictive.  ... 
doi:10.1007/3-540-59293-8_199 fatcat:dqtudwjn2fhqfkma7z7qhyckg4

PROCESS ALGEBRAIC APPROACH TO HYBRID SYSTEMS

Ed Brinksma, Tomas Krilaviĉius, Yaroslav S. Usenko
2005 IFAC Proceedings Volumes  
In our contribution we present an extension of classical process algebra that is suitable for the modelling and analysis of continuous and hybrid dynamical systems.  ...  We believe that the basic tenets of process algebra are highly compatible with the behavioural approach to dynamical systems.  ...  In our contribution we present an extension of classical process algebra that is suitable for the modelling and analysis of continuous and hybrid dynamical systems that can be seen as a generalization  ... 
doi:10.3182/20050703-6-cz-1902.00338 fatcat:qhohdov6xndhrpt6ykclsmxoca

Page 1066 of Mathematical Reviews Vol. , Issue 91B [page]

1991 Mathematical Reviews  
Object types consist of an identification system, the object universe, and an instantiation system, describing the instances of the type.  ...  Summary: “A relation-sorted (algebraic) specification SPEC con- sists of a signature, a set of equations and an arbitrary relation p on the sorts.  ... 

Program specification and development in standard ML

Donald Sannella, Andrzej Tarlecki
1985 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages - POPL '85  
An attempt is made to apply ideas about algebraic specification in the context of a programming language.  ...  Acknowledgements The idea of adding axioms to a programming language  ...  this may be reduced to proving that any algebra satisfying the axioms of 9ii+, is behaviourally equivalent to an algebra satisfying the axioms of Bi. as in the previous case.  ... 
doi:10.1145/318593.318614 dblp:conf/popl/SannellaT85 fatcat:n2z6hiuhrzfn3nradboyuzg6na

Page 264 of Mathematical Reviews Vol. , Issue 85a [page]

1985 Mathematical Reviews  
But, for generalizing behavioural equivalence to parametrized data types also nonminimal algebras must be considered, and there the concepts differ from each other.  ...  Therefore the alge- braic concepts of abstract types are extended to partial algebras leading to ‘total’ homomorphisms for partial algebras.  ... 

Toward formal development of ML programs: Foundations and methodology [chapter]

Donald Sannella, Andrzej Tarlecki
1989 Lecture Notes in Computer Science  
For each of these three kinds of step, conditions are given which ensure the correctness of the result.  ...  A methodology is presented for the formal development of modular Standard ML programs from specifications.  ...  Only when a signature is used as an interface, is behavioural abstraction used to relax its interpretation by closing under behavioural equivalence with respect to an appropriate set of types, which thus  ... 
doi:10.1007/3-540-50940-2_48 fatcat:iekizpfyvzbdzpdwfeh57gj3si

On behavioural abstraction and behavioural satisfaction in higher-order logic

Martin Hofmann, Donald Sannella
1996 Theoretical Computer Science  
Definition 2.1 A signature Σ consists of a set B of base types and a set C of constants such that each c ∈ C has an arity n ≥ 0, an n-tuple of argument types b 1 , . . . , b n ∈ B and a result type b ∈  ...  Definition 2.2 The types over Σ are given by the following grammar: where b ∈ B. Types(Σ) denotes the set of all types over Σ.  ...  Acknowledgements: Thanks to Michel Bidoit and Rolf Hennicker for many very useful comments, including an explanation of how [BH95] relates to concepts and results in Sections 5 and 7.  ... 
doi:10.1016/0304-3975(96)00068-0 fatcat:3lxg2rwnpzaprnschtmvk7shu4

SMoLCS-driven concurrent calculi [chapter]

Egidio Astesiano, Gianna Reggio
1987 Lecture Notes in Computer Science  
an algebraic parameterized specification: for every choice of the parameters we fix one calculus in the family.  ...  The specification of a system is obtained as an instantiation of a parameterized data type, following a schema based on an operational intuition of a process as a labelled transition system and of a concurrent  ...  Many thanks also to Ombretta Arvigo for her patient Mac-typing and more generally for her cooperation at any time.  ... 
doi:10.1007/3-540-17660-8_55 fatcat:5mbcr3era5crrenqe2c6zgjjjy

Creation of a Self-Sustaining Token Economy

Oleksandr Letychevskyi
2022 The Journal of British Blockchain Association  
The system is supported by an algebraic server that leverages algebraic behaviour methods and an automatic proof system.  ...  The behaviour of each agent, namely, the investor, product users, and traders on an exchange, and a smart contract, which controls the interaction, are defined by the set of actions presented in behaviour  ...  The predicates and operations in the formula depend on the type of agent attribute. Let us consider the formal representation of tokenomics in the algebra of behaviours using a specific example.  ... 
doi:10.31585/jbba-5-1-(4)2022 fatcat:jqz6g6ksr5hqpewaqlou254ucq

Page 6065 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
The method used to define cdr for lists is extended to obtain the definition of an inverse for each argument of each constructor of an abstract data type.  ...  The main novel concept, which constitutes the core of this work, is that of behavioural coherence, which is essentially a property of preservation of behavioural structures.  ... 
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