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21
Categorical Semantics Of Parallel Program Design
, 1997
"... We formalise, using Category Theory, modularisation techniques for parallel and distributed systems based on the notion of superposition, showing that parallel program design obeys the "universal laws" formulated by J.Goguen for General Systems Theory, as well as other algebraic propertie ..."
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Cited by 30 (10 self)
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We formalise, using Category Theory, modularisation techniques for parallel and distributed systems based on the notion of superposition, showing that parallel program design obeys the "universal laws" formulated by J.Goguen for General Systems Theory, as well as other algebraic properties of modularity formulated for Specification Theory. The resulting categorical formalisation unifies the different notions of superposition that have been proposed in the literature and clarifies their algebraic properties with respect to modularisation. It also suggests ways of extending or revising existing languages in order to provide higher levels of reusability, modularity and incrementality in system design. 1 Introduction The role of Category Theory in supporting the definition of 'scientific laws' of system modularisation and composition has been recognised since the early 70s when J.Goguen proposed the use of categorical techniques in General Systems Theory for unifying a variety of notion...
Categorybased Semantics for Equational and Constraint Logic Programming
, 1994
"... This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equation ..."
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Cited by 25 (10 self)
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This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equational deduction to an arbitrary category satisfying certain natural conditions; completeness is proved under a hypothesis of quantifier projectivity, using a semantic treatment that regards quantifiers as models rather than variables, and regards valuations as model morphisms rather than functions. This is used as a basis for a model theoretic categorybased approach to a paramodulationbased operational semantics for equational logic programming languages. Categorybased equational logic in conjunction with the theory of institutions is used to give mathematical foundations for modularisation in equational logic programming. We study the soundness and completeness problem for module imports i...
Object Interaction
, 1992
"... . Objects are presented as processes endowed with statedependent slots. Active objects have nonquiescent states. A morphism between two objects expresses that the source object is partof the target object, in such a way that the possible observations of the part, considered in isolation, are cons ..."
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Cited by 5 (2 self)
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. Objects are presented as processes endowed with statedependent slots. Active objects have nonquiescent states. A morphism between two objects expresses that the source object is partof the target object, in such a way that the possible observations of the part, considered in isolation, are constrained within the whole. Our semantic domain for objectoriented concepts includes a cocomplete category of objects where several kinds of dynamic interaction like event and memory sharing are reflected by colimits. 1 Introduction According to the objectoriented view [10]: (1) an object has an internal state that can be changed by certain actions (events) and observed through slots (attributes); and (2) an object displays behaviour (at any time some actions are possible and some are not). Therefore, an object is, basically, a process endowed with tracedependent slots. In [4,5] we find contributions to a semantic domain for objects dealing with aggregation of interacting objects as well as...
Tossing Algebraic Flowers down the Great Divide
 In People and Ideas in Theoretical Computer Science
, 1999
"... Data Types and Algebraic Semantics The history of programming languages, and to a large extent of software engineering as a whole, can be seen as a succession of ever more powerful abstraction mechanisms. The first stored program computers were programmed in binary, which soon gave way to assembly l ..."
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Data Types and Algebraic Semantics The history of programming languages, and to a large extent of software engineering as a whole, can be seen as a succession of ever more powerful abstraction mechanisms. The first stored program computers were programmed in binary, which soon gave way to assembly languages that allowed symbolic codes for operations and addresses. fortran began the spread of "high level" programming languages, though at the time it was strongly opposed by many assembly programmers; important features that developed later include blocks, recursive procedures, flexible types, classes, inheritance, modules, and genericity. Without going into the philosophical problems raised by abstraction (which in view of the discussion of realism in Section 4 may be considerable), it seems clear that the mathematics used to describe programming concepts should in general get more abstract as the programming concepts get more abstract. Nevertheless, there has been great resistance to u...
Composition of Reactive System Components
"... This paper will present the case for using a formal componentbased specification technique for reactive systems, such as the Object Calculus of Fiadeiro and Maibaum. The Object Calculus provides a modular, highly declarative and abstract specification language, suitable for refinement using modelb ..."
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This paper will present the case for using a formal componentbased specification technique for reactive systems, such as the Object Calculus of Fiadeiro and Maibaum. The Object Calculus provides a modular, highly declarative and abstract specification language, suitable for refinement using modelbased design notations such as B or VDM. In the Object Calculus, pre/post style specifications of the effect of actions can be given, together with temporal logic specifications of expected histories of behaviour of the system.
From Devs To Formal Methods: A Categorical Approach
"... The DEVS formalism developed by Zeigler and Sarjoughian is extended by the use of category theory. Several functors . . . ..."
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The DEVS formalism developed by Zeigler and Sarjoughian is extended by the use of category theory. Several functors . . .
Synthesising Interconnections
"... In the context of the modular and incremental development of complex systems, viewed as interconnections of interacting components, new dimensions and new problems arise in the calculation of programs from specifications. A particularly important aspect for extending existing methods to address comp ..."
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In the context of the modular and incremental development of complex systems, viewed as interconnections of interacting components, new dimensions and new problems arise in the calculation of programs from specifications. A particularly important aspect for extending existing methods to address composite systems is the ability, given programs that realise component specifications, to synthesise the interconnections between them in such a way that the system specification is realised. Taking our cue from earlier work on General Systems Theory (Goguen, 1973) and more recent work on parallel program design (Fiadeiro and Maibaum, 1996), we discuss, characterise and provide solutions for the synthesis of interconnections using a categorical framework in which components are modelled as objects (either specifications or programs) and morphisms are used to express interconnections between components. * This work was partially supported by the Esprit WG 8319 (MODELAGE), JNICT through contrac...
A Sheaf Semantics for Petri Nets
, 1993
"... : The semantics of Petri Nets are discussed within the "Objects are sheaves" paradigm. Transitions and places are represented as sheaves and nets are represented as diagrams of sheaves. Both an interleaving semantics, and a noninterleaving semantics are shown to arise as the limit of the ..."
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: The semantics of Petri Nets are discussed within the "Objects are sheaves" paradigm. Transitions and places are represented as sheaves and nets are represented as diagrams of sheaves. Both an interleaving semantics, and a noninterleaving semantics are shown to arise as the limit of the sheaf diagram representing the net. This work was supported by the Information Technology Promotion Agency, Japan, as part of the R & D of Basic Technology for Future Industries "New Models of Software Architecture" project sponsored by NEDO (New Energy and Industrial Technology Developments Organization). Printing: TKK Monistamo; Otaniemi 1993 Helsinki University of Technology Phone: 90 +3580 4511 Department of Computer Science Digital Systems Laboratory Telex: 125 161 htkk sf Otaniemi, Otakaari 1 Telefax: +3580465 077 SF02150 ESPOO, FINLAND Email: lab@hutds.hut.fi  1  1 Introduction Sheaf theory is a mathematical tool that has been successfully applied to the solution of difficult m...
Structured and Architectural Specifications of Concurrent Systems
"... We discuss the application of structured and architectural specifications of the Casl specification language in development of concurrent systems. In order to apply specification mechanisms of Casl we propose an institution for concurrent systems, based on firstorder lineartime temporal logic. We ..."
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We discuss the application of structured and architectural specifications of the Casl specification language in development of concurrent systems. In order to apply specification mechanisms of Casl we propose an institution for concurrent systems, based on firstorder lineartime temporal logic. We then study example structured and architectural specifications and observe that finalsemantics approach allows us to express properties of concurrent systems that cannot be stated directly in the logic we use. We exploit this fact by defining a new specificationbuilding operation specific for our institution. We also modify the semantics of architectural specifications to make them suitable for development of concurrent systems.
A critical look at design, verification, and validation of large scale simulations
"... Note to the Reader. I see six constituencies in CSE: computer, mathematical, and physical scientists; engineers; and technical and nontechnical managers. I have adopted a conversational tone to make this article as widely accessible as possible. Ihave also provided a Bibliography. ..."
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Note to the Reader. I see six constituencies in CSE: computer, mathematical, and physical scientists; engineers; and technical and nontechnical managers. I have adopted a conversational tone to make this article as widely accessible as possible. Ihave also provided a Bibliography.