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196
Testing Equivalences for Processes
 Theoretical Computer Science
, 1984
"... Abstract. Given a set of processes and a set of tests on these processes we show how to define in a natural way three different eyuitalences on processes. ThesP equivalences are applied to a particular language CCS. We give associated complete proof systems and fully abstract models. These models ha ..."
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Cited by 438 (27 self)
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Abstract. Given a set of processes and a set of tests on these processes we show how to define in a natural way three different eyuitalences on processes. ThesP equivalences are applied to a particular language CCS. We give associated complete proof systems and fully abstract models. These models have a simple representation in terms of trees.
A new approach to abstract syntax with variable binding
 Formal Aspects of Computing
, 2002
"... Abstract. The permutation model of set theory with atoms (FMsets), devised by Fraenkel and Mostowski in the 1930s, supports notions of ‘nameabstraction ’ and ‘fresh name ’ that provide a new way to represent, compute with, and reason about the syntax of formal systems involving variablebinding op ..."
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Cited by 226 (48 self)
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Abstract. The permutation model of set theory with atoms (FMsets), devised by Fraenkel and Mostowski in the 1930s, supports notions of ‘nameabstraction ’ and ‘fresh name ’ that provide a new way to represent, compute with, and reason about the syntax of formal systems involving variablebinding operations. Inductively defined FMsets involving the nameabstraction set former (together with Cartesian product and disjoint union) can correctly encode syntax modulo renaming of bound variables. In this way, the standard theory of algebraic data types can be extended to encompass signatures involving binding operators. In particular, there is an associated notion of structural recursion for defining syntaxmanipulating functions (such as capture avoiding substitution, set of free variables, etc.) and a notion of proof by structural induction, both of which remain pleasingly close to informal practice in computer science. 1.
A New Approach to Abstract Syntax Involving Binders
 In 14th Annual Symposium on Logic in Computer Science
, 1999
"... Syntax Involving Binders Murdoch Gabbay Cambridge University DPMMS Cambridge CB2 1SB, UK M.J.Gabbay@cantab.com Andrew Pitts Cambridge University Computer Laboratory Cambridge CB2 3QG, UK ap@cl.cam.ac.uk Abstract The FraenkelMostowski permutation model of set theory with atoms (FMsets) ..."
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Cited by 153 (15 self)
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Syntax Involving Binders Murdoch Gabbay Cambridge University DPMMS Cambridge CB2 1SB, UK M.J.Gabbay@cantab.com Andrew Pitts Cambridge University Computer Laboratory Cambridge CB2 3QG, UK ap@cl.cam.ac.uk Abstract The FraenkelMostowski permutation model of set theory with atoms (FMsets) can serve as the semantic basis of metalogics for specifying and reasoning about formal systems involving name binding, ffconversion, capture avoiding substitution, and so on. We show that in FMset theory one can express statements quantifying over `fresh' names and we use this to give a novel settheoretic interpretation of name abstraction. Inductively defined FMsets involving this nameabstraction set former (together with cartesian product and disjoint union) can correctly encode objectlevel syntax modulo ffconversion. In this way, the standard theory of algebraic data types can be extended to encompass signatures involving binding operators. In particular, there is an associated n...
Categorical Logic
 A CHAPTER IN THE FORTHCOMING VOLUME VI OF HANDBOOK OF LOGIC IN COMPUTER SCIENCE
, 1995
"... ..."
On Observational Equivalence and Algebraic Specification
, 1987
"... The properties of a simple and natural notion of observational equivalence of algebras and the corresponding specificationbuilding operation are studied. We begin with a defmition of observational equivalence which is adequate to handle reachable algebras only, and show how to extend it to cope wit ..."
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Cited by 68 (15 self)
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The properties of a simple and natural notion of observational equivalence of algebras and the corresponding specificationbuilding operation are studied. We begin with a defmition of observational equivalence which is adequate to handle reachable algebras only, and show how to extend it to cope with unreachable algebras and also how it may be generalised to make sense under an arbitrary institution. Behavioural equivalence is treated as an important special case of observational equivalence, and its central role in program development is shown by means of an example.
The Tile Model
 PROOF, LANGUAGE AND INTERACTION: ESSAYS IN HONOUR OF ROBIN MILNER
, 1996
"... In this paper we introduce a model for a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting, in particular from the rewriting logic framework [Mes92], and of concurrency theory: among the ..."
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Cited by 66 (24 self)
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In this paper we introduce a model for a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting, in particular from the rewriting logic framework [Mes92], and of concurrency theory: among the others, the structured operational semantics [Plo81], the context systems [LX90] and the structured transition systems [CM92] approaches. Our model recollects many properties of these sources: first, it provides a compositional way to describe both the states and the sequences of transitions performed by a given system, stressing their distributed nature. Second, a suitable notion of typed proof allows to take into account also those formalisms relying on the notions of synchronization and sideeffects to determine the actual behaviour of a system. Finally, an equivalence relation over sequences of transitions is defined, equipping the system under analysis with a concurrent semantics, ...
Specification and verification challenges for sequential objectoriented programs
 UNDER CONSIDERATION FOR PUBLICATION IN FORMAL ASPECTS OF COMPUTING
"... The state of knowledge in how to specify sequential programs in objectoriented languages such as Java and C# and the state of the art in automated verification tools for such programs have made measurable progress in the last several years. This paper describes several remaining challenges and app ..."
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Cited by 59 (5 self)
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The state of knowledge in how to specify sequential programs in objectoriented languages such as Java and C# and the state of the art in automated verification tools for such programs have made measurable progress in the last several years. This paper describes several remaining challenges and approaches to their solution.
The rewriting logic semantics project
 University of Illinois at UrbanaChampaign
, 2005
"... Rewriting logic is a flexible and expressive logical framework that unifies algebraic denotational semantics and structural operational semantics (SOS) in a novel way, avoiding their respective limitations and allowing succinct semantic definitions. The fact that a rewrite logic theory’s axioms incl ..."
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Cited by 47 (13 self)
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Rewriting logic is a flexible and expressive logical framework that unifies algebraic denotational semantics and structural operational semantics (SOS) in a novel way, avoiding their respective limitations and allowing succinct semantic definitions. The fact that a rewrite logic theory’s axioms include both equations and rewrite rules provides a useful “abstraction dial ” to find the right balance between abstraction and computational observability in semantic definitions. Such semantic definitions are directly executable as interpreters in a rewriting logic language such as Maude, whose generic formal tools can be used to endow those interpreters with powerful program analysis capabilities. Key words: Semantics and analysis of programming languages, rewriting logic 1
Constructing Specification Morphisms
 Journal of Symbolic Computation
, 1993
"... This paper is part of a broader research program to explore a mechanizable model of software development based on algebraic specifications and specification morphisms. An algebraic specification (or simply a specification) defines a language and constrains its possible meanings via axioms and infere ..."
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Cited by 43 (7 self)
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This paper is part of a broader research program to explore a mechanizable model of software development based on algebraic specifications and specification morphisms. An algebraic specification (or simply a specification) defines a language and constrains its possible meanings via axioms and inference rules. Specifications can be used to express many kinds of softwarerelated artifacts, including domain models (Srinivas(1991)), formal requirements (Astesiano and Wirsing (1987), Ehrig and Mahr (1990), Partsch (1990), Sannella and Tarlecki (1985)), programming languages (Broy et al. (1987), Goguen and Winkler (1988), Hoare (1989)), abstract data types (Goguen et al. (1978), Guttag and Horning (1978)), and abstract algorithms (Smith and Lowry (1990)). There has been much work on operations for constructing larger specifications from smaller specifications (Astesiano and Wirsing (1987), Burstall and Goguen (1977), Sannella and Tarlecki (1988)). A specification morphism translates the language of one specification into the language of another specification in a way that preserves theorems. Specification morphisms underlie several aspects of software development, including specification refine