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Formal Interoperability
, 1998
"... this paper I briefly sketch recent work on metalogical foundations that seems promising as a conceptual basis on which to achieve the goal of formal interoperability. Specificaly, I will briefly discuss: ..."
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Cited by 13 (3 self)
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this paper I briefly sketch recent work on metalogical foundations that seems promising as a conceptual basis on which to achieve the goal of formal interoperability. Specificaly, I will briefly discuss:
Notes on Refinement, Interpolation and Uniformity.
"... The connection between some modularity properties and interpolation is revisited and restated in a general "logicindependent " framework. The presence of uniform interpolants is shown to assist in certain proof obligations, which suffice to establish the composition of refinements. The abs ..."
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Cited by 6 (5 self)
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The connection between some modularity properties and interpolation is revisited and restated in a general "logicindependent " framework. The presence of uniform interpolants is shown to assist in certain proof obligations, which suffice to establish the composition of refinements. The absence of the desirable interpolation properties from many logics that have been used in refinement, motivates a thorough investigation of methods to expand a specification formalism orthogonally, so that the critical uniform interpolants become available. A potential breakthrough is outlined in this paper. 1. A refinement paradigm Let us consider program development by means of stepwise refinements. One postulates some abstract data typelike specification 1 (ADT), suitable for the problem at hand, which has to be implemented on the available system. The end product consists of (the text of) an abstract program manipulating the postulated ADT, together with a suite of (texts of) modules implementin...
On a Generalised Modularisation Theorem
, 2000
"... The relation between a metalogical property of entailment (interpolation) and a structural property of categories of theory presentations (stability of faithful morphisms under pushouts) is studied in an abstract "general logic" framework. In particular, a known result for first order l ..."
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Cited by 1 (0 self)
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The relation between a metalogical property of entailment (interpolation) and a structural property of categories of theory presentations (stability of faithful morphisms under pushouts) is studied in an abstract "general logic" framework. In particular, a known result for first order logic (the "modularisation theorem"), stating that the stability of faithful morphisms under pushouts is equivalent to a specific form of interpolation, is generalised and reestablished. Furthermore, the stability under pushouts of the faithfulness of a given theory interpretation is shown to be equivalent to the existence of interpolants on specific loci of the underlying formalism. The latter neither assumes nor requires that the underlying logic possesses interpolation globally. 1 Introduction In this paper we revise, generalise and reestablish, in a notation independent framework, a strong relation between (a form of) interpolation [5, 20, 29, 1] and the stability of conservative extensio...
Integrating Heterogeneous Formalisms: Framework and Application
, 1999
"... In this paper we study the problem of integrating heterogeneous formal notations, emphasising the integration of the axiomatic (logical) semantics. We present a general method for integrating the consequence systems of interrelated heterogeneous formal notations and explain why and when the resultin ..."
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Cited by 1 (1 self)
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In this paper we study the problem of integrating heterogeneous formal notations, emphasising the integration of the axiomatic (logical) semantics. We present a general method for integrating the consequence systems of interrelated heterogeneous formal notations and explain why and when the resulting compound muiltilogical consequence system may need the additional support of structural (&quot;locality&quot;) axioms in order to incorporate the interrelations between the components. We illustrate the use of this method as a basis for the integration of VDM and B formalisms based on LPF and Classical logic.
Uniformity, Interpolation and Module specification in a Development Workspace
 the proceedings of the TFM'98 workshop
, 1997
"... . Interpolation and Schematic Reasoning are shown to underlie critical and somewhat complementary aspects of designing and (syntactically) manipulating specification modules. In addition, the presence of a Uniform presentation of interpolants facilitates the specification of modules. Also, the a ..."
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. Interpolation and Schematic Reasoning are shown to underlie critical and somewhat complementary aspects of designing and (syntactically) manipulating specification modules. In addition, the presence of a Uniform presentation of interpolants facilitates the specification of modules. Also, the ability to encapsulate and manipulate Uniform Schemata may assist us in reasoning with (abstractions of) hidden data. Unfortunately, most formalisms that have been used in fundamental approaches to software engineering lack uniform interpolation and do not directly support schematic reasoning. This paper reveals the critical role of uniform interpolants and uniform schemata from the perspective of modularity, and quotes a general construction indicating that a potentially large class of calculi can be extended conservatively so that a uniform presentation of the critical interpolants becomes available and the manipulation of uniform schemata is supported. 1 Introduction There is a ...
Modularity and Interpolation in a Development Workspace.
, 1997
"... The potential benefits of a uniform version of interpolation are hindered by its absence from many expressive logics. This motivates a thorough investigation of appropriate expansions of known entailments so that an easytoderive, uniform presentation of the interpolants is supported. This paper p ..."
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The potential benefits of a uniform version of interpolation are hindered by its absence from many expressive logics. This motivates a thorough investigation of appropriate expansions of known entailments so that an easytoderive, uniform presentation of the interpolants is supported. This paper presents the skeleton of a general construction and indicates that a potentially large class of entailments can be extended so that a uniform presentation of the interpolants is available. 1 Introduction There is a well established relation between interpolation [8] and modularity properties of refinements [23, 24, 29, 5, 32, 40, 39, 12, 11] and databases [25]. On the other hand, many logics that have been used in refinement or databases lack the desirable interpolation properties. To compensate for this inadequacy, several groups of researchers have proposed techniques to restrict these logics to fragments that have the desirable modularity properties. Some of these enterprises have focuse...
The VDM+B project: Objectives and Progress
"... Abstract. The VDM+B project is developing the formal underpinnings for an integration of VDM and B enabling their couse within one development. In this paper, we describe the objectives for the project, the approach being undertaken and the current status of the work. 1 ..."
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Abstract. The VDM+B project is developing the formal underpinnings for an integration of VDM and B enabling their couse within one development. In this paper, we describe the objectives for the project, the approach being undertaken and the current status of the work. 1
Hiding Information Via Abstraction (On the role of uniform interpolants in a Development Workspace)
"... . In this paper we analyse some fundamental interconnections between modularisation, (uniform) interpolants and information hiding and we explain how some compatible aspects of these concepts are combined in a notation independent method to establish the existence of a conservative extension J : ..."
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. In this paper we analyse some fundamental interconnections between modularisation, (uniform) interpolants and information hiding and we explain how some compatible aspects of these concepts are combined in a notation independent method to establish the existence of a conservative extension J :Espec!Edev of a frontend specification formalism Espec to a backend formalism Edev so that Edev accommodates sentences that act as uniform interpolants for entailments between Especsentences. The tuple hEspec ; J : Espec ! Edev i is called a Development Workspace (DW) and aims to support the management of Espec  specifications by associating the basic operations on them with Edevproof obligations. 1 Introduction In this paper we present and analyse how compatible realisations of general concepts, such as the (algebraic) information hiding operation, modularisation and (uniform) interpolation, blended together in a Development Workspace (DW) in order to generate E dev proof obli...
On Formal Specifications Parameterised By Diagrams
"... This paper presents an extension of previous work on the parameterisation of logical and algebraic specifications that leads to a novel formalisation of parameterisation which is (i) general enough to be independent of the specificities of the underlying formalism, and (ii) flexible enough to acc ..."
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This paper presents an extension of previous work on the parameterisation of logical and algebraic specifications that leads to a novel formalisation of parameterisation which is (i) general enough to be independent of the specificities of the underlying formalism, and (ii) flexible enough to accommodate the manipulation of complex parameterised specifications where the parameter is presented by means of a diagram of specifications and where parameterisations are instantiated along morphisms of specification diagrams. In addition, a unifying formalisation of parameterisation by means of a generic categorial encapsulation of the "is a part of " relation is obtained and a study of a mixed variance refinement of specification parameterised by diagrams is initiated. Keywords: formal specification, formal software development, software synthesis and composition, refinement and modularity, categorical models and methods, fibred categories. 1 Introduction One fundamental difference...
A Reflective Framework for Formal Interoperability
, 1998
"... In practice we find ourselves in constant need of moving back and forth between different formalizations capturing different aspects of a system. For example, in a large software system we typically have very different requirements, such as functional correctness, performance, realtime behavior, co ..."
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In practice we find ourselves in constant need of moving back and forth between different formalizations capturing different aspects of a system. For example, in a large software system we typically have very different requirements, such as functional correctness, performance, realtime behavior, concurrency, security, and fault tolerance, which correspond to different views of the system and that are typically expressed in different formal systems. Often these requirements affect each other, but it can be extremely difficult to reason about their mutual interaction, and no tools exist to support such reasoning. This situation is very unsatisfactory, and presents one of the biggest obstacles to the use of formal methods in software engineering because, given the complexity of large software systems, it is a fact of life that no single perspective, no single formalization or level of abstraction suffices to represent a system and reason about its behavior. We need (meta)formal methods and tools to achieve Formal Interoperability, that is, the capacity to move in a mathematically rigorous way across the different formalizations of a system, and to use in a rigorously integrated way the different tools supporting these formalizations. We will develop new, formal interoperability methodologies and generic metatools that are expected to achieve dramatic advances in software technology and formal methods: