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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 ..."
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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
Horizontal and Vertical Structuring of Typed Graph Transformation Systems
, 1996
"... this paper we concentrate on structuring and refinement concepts for graph transformation systems. Conceptually, we distinguish between two kinds of structuring. We speak of horizontal structuring if a large specification is obtained by combining and modifying smaller ones, possibly sharing some com ..."
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Cited by 27 (14 self)
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this paper we concentrate on structuring and refinement concepts for graph transformation systems. Conceptually, we distinguish between two kinds of structuring. We speak of horizontal structuring if a large specification is obtained by combining and modifying smaller ones, possibly sharing some common parts. Instead, if we consider the relationship between a more abstract and a more concrete version of the same specification, or between a specification and its implementation, we speak of vertical structuring.
Incompleteness of Behavioral Logics
, 2000
"... Incompleteness results for behavioral logics are investigated. We show that there is a basic finite behavioral specification for which the behavioral satisfaction problem is not recursively enumerable, which means that there are no automatic methods for proving all true statements; in particular, be ..."
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Cited by 25 (6 self)
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Incompleteness results for behavioral logics are investigated. We show that there is a basic finite behavioral specification for which the behavioral satisfaction problem is not recursively enumerable, which means that there are no automatic methods for proving all true statements; in particular, behavioral logics do not admit complete deduction systems. This holds for all of the behavioral logics of which we are aware. We also prove that the behavioral satisfaction problem is not corecursively enumerable, which means that there is no automatic way to refute false statements in behavioral logics. In fact we show stronger results, that all behavioral logics are # 0 2 hard, and that, for some data algebras, the complexity of behavioral satisfaction is not even arithmetic; matching upper bounds are established for some behavioral logics. In addition, we show for the fixeddata case that if operations mayhave more than one hidden argument, then final models need not exist, so that the coalgebraic flavor of behavioral logic is lost.
Categorybased Semantics for Equational and Constraint Logic Programming
, 1994
"... This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equation ..."
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Cited by 24 (10 self)
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This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equational deduction to an arbitrary category satisfying certain natural conditions; completeness is proved under a hypothesis of quantifier projectivity, using a semantic treatment that regards quantifiers as models rather than variables, and regards valuations as model morphisms rather than functions. This is used as a basis for a model theoretic categorybased approach to a paramodulationbased operational semantics for equational logic programming languages. Categorybased equational logic in conjunction with the theory of institutions is used to give mathematical foundations for modularisation in equational logic programming. We study the soundness and completeness problem for module imports i...
Hiding and Behaviour: an Institutional Approach
, 1994
"... Theories with hidden sorts provide a setting to study the idea of behaviour and behavioural equivalence of elements. But there are variants on the notion of theory: many sorted algebras, order sorted algebras and so on; we would like to use the theory of institutions to develop ideas of some general ..."
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Cited by 18 (3 self)
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Theories with hidden sorts provide a setting to study the idea of behaviour and behavioural equivalence of elements. But there are variants on the notion of theory: many sorted algebras, order sorted algebras and so on; we would like to use the theory of institutions to develop ideas of some generality. We formulate the notion of behavioural equivalence in a more abstract and categorical way, and we give a general explication of "hiding" in an institution. We use this show that both hidden many sorted algebras and hidden order sorted algebras yield institutions.
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.
An Overview of the Tatami Project
, 2000
"... This paper describes the Tatami project at UCSD, which is developing a system to support distributed cooperative software development over the web, and in particular, the validation of concurrent distributed software. The main components of our current prototype are a proof assistant, a generator fo ..."
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Cited by 13 (8 self)
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This paper describes the Tatami project at UCSD, which is developing a system to support distributed cooperative software development over the web, and in particular, the validation of concurrent distributed software. The main components of our current prototype are a proof assistant, a generator for documentation websites, a database, an equational proof engine, and a communication protocol to support distributed cooperative work. We believe behavioral specification and verification are important for software development, and for this purpose we use first order hidden logic with equational atoms. The paper also briefly describes some novel user interface design methods that have been developed and applied in the project
Circular Coinduction
 In International Joint Conference on Automated Reasoning
, 2000
"... Circular coinduction is a technique for behavioral reasoning that extends cobasis coinduction to specifications with circularities. Because behavioral satisfaction is not recursively enumerable, no algorithm can work for every behavioral statement. However, algorithms using circular coinduction can ..."
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Cited by 12 (5 self)
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Circular coinduction is a technique for behavioral reasoning that extends cobasis coinduction to specifications with circularities. Because behavioral satisfaction is not recursively enumerable, no algorithm can work for every behavioral statement. However, algorithms using circular coinduction can prove every practical behavioral result that we know. This paper proves the correctness of circular coinduction and some consequences.
A Hidden Herbrand Theorem: Combining the Object and Logic Paradigms
 Principles of Declarative Programming
, 1998
"... : The benefits of the object, logic (or relational), functional, and constraint paradigms ..."
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Cited by 11 (3 self)
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: The benefits of the object, logic (or relational), functional, and constraint paradigms
A Protocol for Distributed Cooperative Work
, 1999
"... After a brief review of hidden algebra, we give behavioral specifications for set theory and closure operators, and then use these to give a behavioral specification of an abstract protocol to support distributed cooperative work structured by dependencies in such a way as to form what we call a wea ..."
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Cited by 10 (6 self)
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After a brief review of hidden algebra, we give behavioral specifications for set theory and closure operators, and then use these to give a behavioral specification of an abstract protocol to support distributed cooperative work structured by dependencies in such a way as to form what we call a weak closure operator. We give some correctness proofs for this protocol, and then describe a concrete instance of it, called the tatami protocol, that supports distributed cooperative proving. Finally, we draw some methodological conclusions.