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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 ..."
Abstract

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
Proof of Correctness of Object Representations
"... This paper presents an algebraic account of implementation that is applicable to the object paradigm. The key to its applicability is the notion of state: objects have local states that are observable only through their outputs. That is, objects may be viewed as abstract machines with hidden local s ..."
Abstract

Cited by 27 (14 self)
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This paper presents an algebraic account of implementation that is applicable to the object paradigm. The key to its applicability is the notion of state: objects have local states that are observable only through their outputs. That is, objects may be viewed as abstract machines with hidden local state (as in [9]). Consequently, a correct implementation need only have the required visible behaviour. We use hidden order sorted algebra to formalise the object paradigm [4, 5, 8]. Advantages of an algebraic approach include a high level of intellectual rigour, a large body of supporting mathematics, and simple, efficient proofs using only equational logic. A wide variety of extensions to equational logic have been developed to treat various programming features, while preserving its essential simplicity. For example, order sorted equational logic uses a notion of subsort to treat computations that may raise exceptions or fail to terminate. Hidden sorted logic extends standard equational logic to capture an important distinction between immutable data types, such as booleans and integers, and mutable objects, such as program variables and database entities. The terms abstract data types and abstract object classes refer to these two kinds of entity. The former represent `visible' data values; the latter represent data stored in a hidden state. In hidden sorted equational logic, an equation of hidden sort need not be satisfied in the usual sense, but only up to observability, in that only its visible consequences need hold. Thus, hidden sorted logic allows greater freedom in implementations. The simplicity of the underlying logic is important, because we want a tractable