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22
Introducing OBJ
, 1993
"... This is an introduction to the philosophy and use of OBJ, emphasizing its operational semantics, with aspects of its history and its logical semantics. Release 2 of OBJ3 is described in detail, with many examples. OBJ is a wide spectrum firstorder functional language that is rigorously based on ..."
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Cited by 120 (30 self)
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This is an introduction to the philosophy and use of OBJ, emphasizing its operational semantics, with aspects of its history and its logical semantics. Release 2 of OBJ3 is described in detail, with many examples. OBJ is a wide spectrum firstorder functional language that is rigorously based on (order sorted) equational logic and parameterized programming, supporting a declarative style that facilitates verification and allows OBJ to be used as a theorem prover.
A Hidden Agenda
 Theoretical Computer Science
, 2000
"... This paper publicly reveals, motivates, and surveys the results of an ambitious hidden agenda for applying algebra to software engineering. The paper reviews selected literature, introduces a new perspective on nondeterminism, and features powerful hidden coinduction techniques for proving behaviora ..."
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Cited by 110 (23 self)
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This paper publicly reveals, motivates, and surveys the results of an ambitious hidden agenda for applying algebra to software engineering. The paper reviews selected literature, introduces a new perspective on nondeterminism, and features powerful hidden coinduction techniques for proving behavioral properties of concurrent systems, especially renements; some proofs are given using OBJ3. We also discuss where modularization, bisimulation, transition systems and combinations of the object, logic, constraint and functional paradigms t into our hidden agenda. 1 Introduction Algebra can be useful in many dierent ways in software engineering, including specication, validation, language design, and underlying theory. Specication and validation can help in the practical production of reliable programs, advances in language design can help improve the state of the art, and theory can help with building new tools to increase automation, as well as with showing correctness of the whole e...
Proving Correctness Of Refinement And Implementation
, 1996
"... The notions of state and observable behaviour are fundamental to many areas of computer science. Hidden sorted algebra, an extension of many sorted algebra, captures these notions through hidden sorts and the behavioural satisfaction of equations. This makes it a powerful formalisation of abstract m ..."
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Cited by 29 (4 self)
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The notions of state and observable behaviour are fundamental to many areas of computer science. Hidden sorted algebra, an extension of many sorted algebra, captures these notions through hidden sorts and the behavioural satisfaction of equations. This makes it a powerful formalisation of abstract machines, and many results suggest that it is also suitable for the semantics of the object paradigm. Another extension of many sorted algebra, namely order sorted algebra, has proved useful in system specification and prototyping because of the way it handles subtypes and errors. The combination of these two algebraic approaches, hidden order sorted algebra, has also been proposed as a foundation for object paradigm, and has much promise as a foundation for Software Engineering. This paper extends recent work on hidden order sorted algebra by investigating the refinement and implementation of hidden order sorted specifications. We present definitions of refinement and implementation for suc...
Extra Theory Morphisms for Institutions: logical semantics for multiparadigm languages
, 1996
"... We extend the ordinary concept of theory morphism in institutions to extra theory morphisms. Extra theory morphism map theories belonging to different institutions across institution morphisms. We investigate the basic mathematical properties of extra theory morphisms supporting the semantics of log ..."
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Cited by 26 (7 self)
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We extend the ordinary concept of theory morphism in institutions to extra theory morphisms. Extra theory morphism map theories belonging to different institutions across institution morphisms. We investigate the basic mathematical properties of extra theory morphisms supporting the semantics of logical multiparadigm languages, especially structuring specifications (module systems) a la OBJClear. They include model reducts, free constructions (liberality), colimits, model amalgamation (exactness), and inclusion systems. We outline a general logical semantics for languages whose semantics satisfy certain "logical" principles by extending the institutional semantics developed within the ClearOBJ tradition. Finally, in the Appendix, we briefly illustrate it with the concrete example of CafeOBJ. Keywords Algebraic specification, Institutions, Theory morphism. AMS Classifications 68Q65, 18C10, 03G30, 08A70 2 1 Introduction Computing Motivation This work belongs to the research are...
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.
A Categorybased Equational Logic Semantics to Constraint Programming
 IN MAGNE HAVERAAEN, OLAF OWE, AND OLEJOHAN DAHL, EDITORS, RECENT TRENDS IN DATA TYPE SPECIFICATION
, 1996
"... This paper exploits the point of view of constraint programming as computation in a logical system, namely constraint logic. We define the basic ingredients of constraint logic, such as constraint models and generalised polynomials. We show that constraint logic is an institution, and we interna ..."
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Cited by 13 (4 self)
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This paper exploits the point of view of constraint programming as computation in a logical system, namely constraint logic. We define the basic ingredients of constraint logic, such as constraint models and generalised polynomials. We show that constraint logic is an institution, and we internalise the study of constraint logic to the framework of categorybased equational logic. By showing that constraint logic is a special case of categorybased equational logic, we integrate the constraint logic programming paradigm into equational logic programming. Results include a Herbrand theorem for constraint logic programming characterising Herbrand models as initial models in constraint logic.
Permissive Subsorted Partial Logic in CASL
, 1997
"... . This paper presents a permissive subsorted partial logic used in the CoFI Algebraic Specification Language. In contrast to other ordersorted logics, subsorting is not modeled by set inclusions, but by injective embeddings allowing for more general models in which subtypes can have different data t ..."
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Cited by 13 (8 self)
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. This paper presents a permissive subsorted partial logic used in the CoFI Algebraic Specification Language. In contrast to other ordersorted logics, subsorting is not modeled by set inclusions, but by injective embeddings allowing for more general models in which subtypes can have different data type representations. Furthermore, there are no restrictions like monotonicity, regularity or local filtration on signatures at all. Instead, the use of overloaded functions and predicates in formulae is required to be sufficiently disambiguated, such that all parses have the same semantics. An overload resolution algorithm is sketched. 1 Introduction During the past decades a large number of algebraic specification languages have been developed. The presence of so many similar specification languages with no common framework hinders the dissemination and application of research results in algebraic specification. In particular, it makes it difficult to produce educational material, to reus...
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
Logical Foundations of CafeOBJ
 Theoretical Computer Science
"... This paper surveys the logical and mathematical foundations of CafeOBJ, which is a successor of the famous algebraic specification language OBJ but adding several new primitive paradigms such as behavioural concurrent specification and rewriting logic. We first give a concise overview of CafeOBJ. T ..."
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Cited by 10 (1 self)
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This paper surveys the logical and mathematical foundations of CafeOBJ, which is a successor of the famous algebraic specification language OBJ but adding several new primitive paradigms such as behavioural concurrent specification and rewriting logic. We first give a concise overview of CafeOBJ. Then we focus on the actual logical foundations of the language at two different levels: basic specification and structured specification, including also the definition of the CafeOBJ institution. We survey some novel or more classical theoretical concepts supporting the logical foundations of CafeOBJ together with pointing to the main results but without giving proofs and without discussing all mathematical details. Novel theoretical concepts include the coherent hidden algebra formalism and its combination with rewriting logic, and Grothendieck (or fibred) institutions. However for proofs and for some of the mathematical details not discussed here we give pointers to relevant publications. ...