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Observational logic
 IN ALGEBRAIC METHODOLOGY AND SOFTWARE TECHNOLOGY (AMAST'98
, 1999
"... We present an institution of observational logic suited for statebased systems specifications. The institution is based on the notion of an observational signature (which incorporates the declaration of a distinguished set of observers) and on observational algebras whose operations are required ..."
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Cited by 52 (10 self)
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We present an institution of observational logic suited for statebased systems specifications. The institution is based on the notion of an observational signature (which incorporates the declaration of a distinguished set of observers) and on observational algebras whose operations are required to be compatible with the indistinguishability relation determined by the given observers. In particular, we introduce a homomorphism concept for observational algebras which adequately expresses observational relationships between algebras. Then we consider a flexible notion of observational signature morphism which guarantees the satisfaction condition of institutions w.r.t. observational satisfaction of arbitrary firstorder sentences. From the proof theoretical point of view we construct a sound and complete proof system for the observational consequence relation. Then we consider structured observational specifications and we provide a sound and complete proof system for such specifications by using a general, institutionindependent result of [6].
Modular Correctness Proofs of Behavioural Implementations
, 1995
"... . We introduce a concept of behavioural implementation for algebraic specifications which is based on an indistinguishability relation (called behavioural equality). The central objective of this work is the investigation of proof rules that first allow us to establish the correctness of behavioural ..."
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Cited by 30 (13 self)
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. We introduce a concept of behavioural implementation for algebraic specifications which is based on an indistinguishability relation (called behavioural equality). The central objective of this work is the investigation of proof rules that first allow us to establish the correctness of behavioural implementations in a modular (and stepwise) way and, moreover, are practicable enough to induce proof obligations that can be discharged with existing theorem provers. Under certain conditions our proof technique can also be applied for proving the correctness of implementations based on an abstraction equivalence between algebras in the sense of Sannella and Tarlecki. The whole approach is presented in the framework of total algebras and firstorder logic with equality. 1 Introduction Algebraic specification techniques allow one to formalize correctness notions for program development steps. Thereby an important role is played by observability concepts since it is often essential to abst...
Behavioural Satisfaction and Equivalence in Concrete Model Categories
, 1996
"... . We use the wellknown framework of concrete categories to show how much of standard universal algebra may be done in an abstract and still rather intuitive way. This is used to recast the unifying view of behavioural semantics of specications based on behavioural satisfaction and, respectively ..."
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Cited by 30 (9 self)
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. We use the wellknown framework of concrete categories to show how much of standard universal algebra may be done in an abstract and still rather intuitive way. This is used to recast the unifying view of behavioural semantics of specications based on behavioural satisfaction and, respectively, on behavioural equivalence of models abstracting away from many particular features of standard algebras. We also give an explicit representation of behavioural equivalence between models in terms of behavioural correspondences. 1 Introduction Behavioural semantics for specications plays a crucial role in the formalisation of the development process, where a specication need not be implemented exactly but only so that the required system behaviour is achieved  the idea goes back to [GGM76], [Hoa72]; see e.g. [ST95] for the context in which we view it now. There have been two basic approaches to behavioural semantics of speci cations. One introduces a new behavioural satisfaction o...
On Behavioural Abstraction and Behavioural Satisfaction in HigherOrder Logic
, 1996
"... The behavioural semantics of specifications with higherorder logical formulae as axioms is analyzed. A characterization of behavioural abstraction via behavioural satisfaction of formulae in which the equality symbol is interpreted as indistinguishability, which is due to Reichel and was recently g ..."
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Cited by 25 (5 self)
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The behavioural semantics of specifications with higherorder logical formulae as axioms is analyzed. A characterization of behavioural abstraction via behavioural satisfaction of formulae in which the equality symbol is interpreted as indistinguishability, which is due to Reichel and was recently generalized to the case of firstorder logic by Bidoit et al, is further generalized to this case. The fact that higherorder logic is powerful enough to express the indistinguishability relation is used to characterize behavioural satisfaction in terms of ordinary satisfaction, and to develop new methods for reasoning about specifications under behavioural semantics. 1 Introduction An important ingredient in the use of algebraic specifications to describe data abstractions is the concept of behavioural equivalence between algebras, which seems to appropriately capture the "black box" character of data abstractions, see e.g. [GGM76], [GM82], [ST87] and [ST95]. Roughly speaking (since there ...
Observational Proofs with Critical Contexts
 In Fundamental Approaches to Software Engineering
, 1998
"... Observability concepts contribute to a better understanding of software correctness. In order to prove observational properties, the concept of Context Induction has been developed by Hennicker [10]. We propose in this paper to embed Context Induction in the implicit induction framework of [8]. The ..."
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Cited by 24 (3 self)
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Observability concepts contribute to a better understanding of software correctness. In order to prove observational properties, the concept of Context Induction has been developed by Hennicker [10]. We propose in this paper to embed Context Induction in the implicit induction framework of [8]. The proof system we obtain applies to conditional specifications. It allows for many rewriting techniques and for the refutation of false observational conjectures. Under reasonable assumptions our method is refutationally complete, i.e. it can refute any conjecture which is not observationally valid. Moreover this proof system is operational: it has been implemented within the Spike prover and interesting computer experiments are reported.
Proving the Correctness of Behavioural Implementations
 Proc. AMAST '95, Springer LNCS 936
, 1995
"... . We introduce a concept of behavioural implementation for algebraic specifications which is based on an indistinguishability relation (called behavioural equality). The central objective of this work is the investigation of proof rules that first allow us to establish the correctness of behavioural ..."
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Cited by 12 (4 self)
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. We introduce a concept of behavioural implementation for algebraic specifications which is based on an indistinguishability relation (called behavioural equality). The central objective of this work is the investigation of proof rules that first allow us to establish the correctness of behavioural implementations in a modular way and moreover are practicable enough to induce proof obligations that can be discharged with existing theorem provers. Our proof technique can also be applied for proving abstractor implementations in the sense of Sannella and Tarlecki. 1 Introduction Algebraic specification techniques allow one to formalize correctness notions for program development steps. Thereby an important role is played by observability concepts since it is often essential to abstract from internal implementation details and to rely only on the observable behaviour of programs. Many approaches in the literature have considered behavioural concepts (cf. e.g. [GM 82], [R 87], [ST 88], ...
Proof Systems for Structured Specifications and Their Refinements
, 1999
"... Reasoning about specifications is one of the fundamental activities in the process of formal program development. This ranges from proving the consequences of a specification, during the prototyping or testing phase for a requirements speci cation, to proving the correctness of refinements (or imple ..."
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Cited by 12 (6 self)
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Reasoning about specifications is one of the fundamental activities in the process of formal program development. This ranges from proving the consequences of a specification, during the prototyping or testing phase for a requirements speci cation, to proving the correctness of refinements (or implementations) of specifications. The main proof techniques for algebraic specifications have their origin in equational Horn logic and term rewriting. These proof methods have been well studied in the case of nonstructured speci cations (see Chapters 9 and 10). For large systems of specifications built using the structuring operators of speci cation languages, relatively few proof techniques have been developed yet; for such proof systems, see [SB83, HST94, Wir91, Far92, Cen94, HWB97]. In this chapter we focus on proof systems designed particularly for modular specifications. The aim is to concentrate on the structuring concepts, while abstracting as much as possible from the par...
Testing from Structured Algebraic Specifications: The Oracle Problem
, 2000
"... To Herman and to my Parents. Work in the area of specificationbased testing has pointed out that testing can be effectively used to verify programs against formal specifications. The aim is to derive test information from formal specifications so that testing can be rigorously applied whenever full ..."
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Cited by 9 (2 self)
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To Herman and to my Parents. Work in the area of specificationbased testing has pointed out that testing can be effectively used to verify programs against formal specifications. The aim is to derive test information from formal specifications so that testing can be rigorously applied whenever full formal verification is not costeffective. However, there are still several obstacles to be overcome in order to establish testing as a standard in formal frameworks. Accurate interpretation of test results is an extremely critical one. This thesis is concerned with testing programs against structured algebraic specifications where axioms are expressed in firstorder logic with equations, the usual connectives and quantifiers. The main issue investigated is the socalled oracle problem, that is, whether a decision procedure can be defined for interpreting the results of tests according to a formal specification. In this context, testing consists in checking whether specification axioms are satisfied by programs. Consequently, tests exercise operations referred to by the axioms and oracles evaluate the axioms