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Observational logic
 In Algebraic Methodology and Software Technology (AMAST'98
, 1999
"... Abstract. 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 r ..."
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Cited by 53 (10 self)
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Abstract. 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]. 1
Behavioural Theories and The Proof of Behavioural Properties
, 1996
"... Behavioural theories are a generalization of firstorder theories where the equality predicate symbol is interpreted by a behavioural equality of objects (and not by their identity). In this paper we first consider arbitrary behavioural equalities determined by some (partial) congruence relation and ..."
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Cited by 33 (8 self)
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Behavioural theories are a generalization of firstorder theories where the equality predicate symbol is interpreted by a behavioural equality of objects (and not by their identity). In this paper we first consider arbitrary behavioural equalities determined by some (partial) congruence relation and we show how to reduce the behavioural theory of any class of algebras to (a subset of) the standard theory of some corresponding class of algebras. This reduction is the basis of a method for proving behavioural theorems whenever an axiomatization of the behavioural equality is provided. Then we focus on the important special case of (partial) observational equalities where two elements are observationally equal if they cannot be distinguished by observable computations over some set of input values. We provide general conditions under which an obvious infinite axiomatization of the observational equality can be replaced by a finitary one and we provide methodological guidelines for finding such...
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...
Observational Specifications and the Indistinguishability Assumption
 Theoretical Computer Science
, 1995
"... To establish the correctness of some software w.r.t. its formal specification is widely recognized as a difficult task. A first simplification is obtained when the semantics of an algebraic specification is defined as the class of all algebras which correspond to the correct realizations of the spec ..."
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Cited by 17 (0 self)
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To establish the correctness of some software w.r.t. its formal specification is widely recognized as a difficult task. A first simplification is obtained when the semantics of an algebraic specification is defined as the class of all algebras which correspond to the correct realizations of the specification. A software is then declared correct if it corresponds to some algebra of this class. We approach this goal by defining an observational satisfaction relation which is less restrictive than the usual satisfaction relation. Based on this notion we provide an institution for observational specifications. The idea is that the validity of an equational axiom should depend on an observational equality, instead of the usual equality. We show that it is not reasonable to expect an observational equality to be a congruence. We define an observational algebra as an algebra equipped with an observational equality which is an equivalence relation but not necessarily a congruence. We assume th...
Proving Behavioural Theorems with Standard FirstOrder Logic
 In Proc. of ALP'94
, 1994
"... . Behavioural logic is a generalization of firstorder logic where the equality predicate is interpreted by a behavioural equality of objects (and not by their identity). We establish simple and general su#cient conditions under which the behavioural validity of some firstorder formula with respect ..."
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Cited by 15 (5 self)
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. Behavioural logic is a generalization of firstorder logic where the equality predicate is interpreted by a behavioural equality of objects (and not by their identity). We establish simple and general su#cient conditions under which the behavioural validity of some firstorder formula with respect to a given firstorder specification is equivalent to the standard validity of the same formula in a suitably enriched specification. As a consequence any proof system for firstorder logic can be used to prove the behavioural validity of firstorder formulas. 1 Introduction Observability plays a prominent role in formal software development, since it provides a suitable basis for defining adequate correctness concepts. For instance, for proving the correctness of a program with respect to a given specification, many examples show that it is essential to abstract from internal implementation details and to rely only on the observable behaviour of the program. A similar situation is the not...
A General Framework for Modular Implementations of Modular System Specifications
, 1993
"... . We investigate the impact of modularity on the semantics and on the implementation of software specifications. Based on the stratified loose semantics approach we develop a suitable specification framework which meets our basic requirements: the independent construction of implementations for the ..."
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Cited by 13 (6 self)
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. We investigate the impact of modularity on the semantics and on the implementation of software specifications. Based on the stratified loose semantics approach we develop a suitable specification framework which meets our basic requirements: the independent construction of implementations for the single constituent parts (modules) of a system specification and the encapsulated development of each implementation part using the principle of stepwise refinement. Our paper is not aimed at providing an elaborated specification language but rather to concentrate on the modularity issues of system development. Hence, only few but powerful constructs are provided which can be seen as a kernel for further extensions. In particular, we will show that implementation and parameterization can be handled within a uniform concept and we will prove compatibility theorems like the horizontal composition property. All constructs are defined on top of a very general logical framework thus being applica...
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], ...
A Behavioural Algebraic Framework for Modular System Design with Reuse
"... . A formal framework for the design of modular software systems is presented which incorporates the idea of reusing software components in new applications. The approach is based on structured algebraic specifications with behavioural semantics. In a first step, syntax and semantics of structured be ..."
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Cited by 9 (2 self)
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. A formal framework for the design of modular software systems is presented which incorporates the idea of reusing software components in new applications. The approach is based on structured algebraic specifications with behavioural semantics. In a first step, syntax and semantics of structured behavioural specifications are introduced. Then, in order to provide a clean interconnection mechanism for specifications, behavioural specifications with import interfaces are considered and their composition with respect to the behavioural requirements of the import interface is defined. In the next step, a simple implementation notion for behavioural specifications with import interface is presented which is compatible with the composition of specifications. Hence it is guaranteed that separately developed implementations of parts of an abstract system specification can be automatically composed to a globally correct system implementation. This is a particular important requirement for the ...
Towards an Adequate Notion of Observation
 ESOP '92, 4th European Symposium on Programming
, 1992
"... One can attempt to solve the problem of establishing the correctness of some software w.r.t. a formal specification at the semantical level. For this purpose, the semantics of an algebraic specification should be the class of all algebras which correspond to the correct realizations of the specifica ..."
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Cited by 7 (2 self)
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One can attempt to solve the problem of establishing the correctness of some software w.r.t. a formal specification at the semantical level. For this purpose, the semantics of an algebraic specification should be the class of all algebras which correspond to the correct realizations of the specification. We approach this goal by defining an observational satisfaction relation which is less restrictive than the usual satisfaction relation. The idea is that the validity of an equational axiom should depend on an observational equality, instead of the usual equality. We show that it is not reasonable to expect an observational equality to be a congruence, hence we define an observational algebra as an algebra equipped with an observational equality which is an equivalence relation but not necessarily a congruence. Since terms may represent computations, our notion of observation depends on a set of observable terms. From a careful case study it follows that this requires to take into acco...
A Model Inference System for Generic Specification with Application to Code Sharing
 In Proc. of TAPSOFT95, Col. on Formal Approaches in Software Engineering, LNCS 915
, 1995
"... . This paper presents a model inference system to control instantiation of generic modules. Generic parameters are specified by properties which represent classes of modules sharing some common features. Just as type checking consists in verifying that an expression is well typed, model checking all ..."
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Cited by 4 (3 self)
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. This paper presents a model inference system to control instantiation of generic modules. Generic parameters are specified by properties which represent classes of modules sharing some common features. Just as type checking consists in verifying that an expression is well typed, model checking allows to detect whether a (possibly generic) instantiation of a generic module is valid, i.e. whether the instantiation module is a model of the parameterizing property. Equality of instances can be derived from a canonical representation of modules. At last, we show how the code of generic modules can be shared for all instances of modules. 1 Introduction Genericity is a useful feature for specification languages, and for programming languages alike, because it allows to reuse already written packages by instantiating them on various ways, thus limits the risk of bugs and reduces software costs. When a generic module is instantiated and imported into another module, one has to check that the...