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31
Circular Coinductive Rewriting
 In Proceedings of Automated Software Engineering 2000
, 2000
"... Circular coinductive rewriting is a new method for proving behavioral properties, that combines behavioral rewriting with circular coinduction. This method is implemented in our new BOBJ behavioral specification and computation system, which is used in examples throughout this paper. These examples ..."
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Cited by 46 (11 self)
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Circular coinductive rewriting is a new method for proving behavioral properties, that combines behavioral rewriting with circular coinduction. This method is implemented in our new BOBJ behavioral specification and computation system, which is used in examples throughout this paper. These examples demonstrate the surprising power of circular coinductive rewriting. The paper also sketches the underlying hidden algebraic theory and briefly describes BOBJ and some of its algorithms.
Hiding More of Hidden Algebra
 FM'99  Formal Methods
, 1999
"... This paper generalizes the hidden algebra approach to allow: (P1) operations with multiple hidden arguments, and (P2) defining behavioral equivalence with a subset of operations, in addition to the already present (P3) builtin data types, (P4) nondeterminism, (P5) concurrency, and (P6) noncongruen ..."
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Cited by 42 (15 self)
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This paper generalizes the hidden algebra approach to allow: (P1) operations with multiple hidden arguments, and (P2) defining behavioral equivalence with a subset of operations, in addition to the already present (P3) builtin data types, (P4) nondeterminism, (P5) concurrency, and (P6) noncongruent operations. All important results generalize, but more elegant formulations use the new institution in Section 5. Behavioral satisfaction appeared 1981 in [20], hidden algebra 1989 in [9], multiple hidden arguments 1992 in [1], congruent and behavioral operations in [1, 18], behavioral equivalence defined by a subset of operations in [1], and noncongruent operations in [5]; all this was previously integrated in [21], but this paper gives new examples, institutions, and results relating hidden algebra to information hiding. We assume familiarity with basics of algebraic specification, e.g., [11, 13].
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...
Hidden Congruent Deduction
 Automated Deduction in Classical and NonClassical Logics
, 1998
"... This paper presents some techniques of this kind in the area called hidden algebra, clustered around the central notion of coinduction. We believe hidden algebra is the natural next step in the evolution of algebraic semantics and its first order proof technology. Hidden algebra originated in [7], a ..."
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Cited by 27 (18 self)
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This paper presents some techniques of this kind in the area called hidden algebra, clustered around the central notion of coinduction. We believe hidden algebra is the natural next step in the evolution of algebraic semantics and its first order proof technology. Hidden algebra originated in [7], and was developed further in [8, 10, 3, 12, 5] among other places; the most comprehensive survey currently available is [12]
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.
Hidden Coinduction: Behavioral Correctness Proofs for Objects
 Mathematical Structures in Computer Science
, 1999
"... This paper unveils and motivates an ambitious programme of hidden algebraic research in software engineering, beginning with our general goals, continuing with an overview of results, and including some future plans. The main contribution is powerful hidden coinduction techniques for proving behavio ..."
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Cited by 24 (8 self)
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This paper unveils and motivates an ambitious programme of hidden algebraic research in software engineering, beginning with our general goals, continuing with an overview of results, and including some future plans. The main contribution is powerful hidden coinduction techniques for proving behavioral correctness of concurrent systems; several mechanical proofs are given using OBJ3. We also show how modularization, bisimulation, transition systems, concurrency and combinations of the functional, constraint, logic and object paradigms fit into hidden algebra. 1. Introduction
Extended ML: Past, present and future
 PROC. 7TH WORKSHOP ON SPECIFICATION OF ABSTRACT DATA TYPES, WUSTERHAUSEN. SPRINGER LNCS 534
, 1991
"... An overview of past, present and future work on the Extended ML formal program development framework is given, with emphasis on two topics of current active research: the semantics of the Extended ML specification language, and tools to support formal program development. ..."
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Cited by 22 (8 self)
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An overview of past, present and future work on the Extended ML formal program development framework is given, with emphasis on two topics of current active research: the semantics of the Extended ML specification language, and tools to support formal program development.
Conditional Circular Coinductive Rewriting with Case Analysis
, 2002
"... We argue for an algorithmic approach to behavioral proofs, review the hidden algebra approach, develop circular coinductive rewriting for conditional goals, extend it with case analysis, and give some examples. ..."
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Cited by 18 (1 self)
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We argue for an algorithmic approach to behavioral proofs, review the hidden algebra approach, develop circular coinductive rewriting for conditional goals, extend it with case analysis, and give some examples.
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...