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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 66 (17 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.
Toward formal development of ML programs: foundations and methodology
, 1989
"... A formal methodology is presented for the systematic evolution of modular Standard ML programs from specifications by means of verified refinement steps, in the framework of the Extended ML specification language. Program development proceeds via a sequence of design (modular decomposition), codi ..."
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Cited by 51 (20 self)
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A formal methodology is presented for the systematic evolution of modular Standard ML programs from specifications by means of verified refinement steps, in the framework of the Extended ML specification language. Program development proceeds via a sequence of design (modular decomposition), coding and refinement steps. For each of these three kinds of steps, conditions are given which ensure the correctness of the result. These conditions seem to be as weak as possible under the constraint of being expressible as "local" interface matching requirements. Interfaces are only required to match up to behavioural equivalence, which is seen as vital to the use of data abstraction in program development. Copyright c fl 1989 by D. Sannella and A. Tarlecki. All rights reserved. An extended abstract of this paper will appear in Proc. Colloq. on Current Issues in Programming Languages, Joint Conf. on Theory and Practice of Software Development (TAPSOFT), Barcelona, Springer LNCS (1989)....
Extended ML: an institutionindependent framework for formal program development
 PROC. WORKSHOP ON CATEGORY THEORY AND COMPUTER PROGRAMMING
, 1986
"... The Extended ML specification language provides a framework for the formal stepwise development of modular programs in the Standard ML programming language from specifications. The object of this paper is to equip Extended ML with a semantics which is completely independent of the logical system use ..."
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Cited by 19 (10 self)
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The Extended ML specification language provides a framework for the formal stepwise development of modular programs in the Standard ML programming language from specifications. The object of this paper is to equip Extended ML with a semantics which is completely independent of the logical system used to write specifications, building on Goguen and Burstall's work on the notion of an institution as a formalisation of the concept of a logical system. One advantage of this is that it permits freedom in the choice of the logic used in writing specifications; an intriguing sideeffect is that it enables Extended ML to be used to develop programs in languages other than Standard ML since we view programs as simply Extended ML specifications which happen to include only "executable" axioms. The semantics of Extended ML is defined in terms of the primitive specificationbuilding operations of the ASL kernel specification language which itself has an institutionindependent semantics. It is no...
Notes on Refinement, Interpolation and Uniformity.
"... The connection between some modularity properties and interpolation is revisited and restated in a general "logicindependent " framework. The presence of uniform interpolants is shown to assist in certain proof obligations, which suffice to establish the composition of refinements. The absence of th ..."
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Cited by 6 (5 self)
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The connection between some modularity properties and interpolation is revisited and restated in a general "logicindependent " framework. The presence of uniform interpolants is shown to assist in certain proof obligations, which suffice to establish the composition of refinements. The absence of the desirable interpolation properties from many logics that have been used in refinement, motivates a thorough investigation of methods to expand a specification formalism orthogonally, so that the critical uniform interpolants become available. A potential breakthrough is outlined in this paper. 1. A refinement paradigm Let us consider program development by means of stepwise refinements. One postulates some abstract data typelike specification 1 (ADT), suitable for the problem at hand, which has to be implemented on the available system. The end product consists of (the text of) an abstract program manipulating the postulated ADT, together with a suite of (texts of) modules implementin...
A Kernel Specification Formalism with HigherOrder Parameterisation
 PROC. 7TH INTL. WORKSHOP ON SPECIFICATION OF ABSTRACT DATA TYPES, WUSTERHAUSEN. SPRINGER LNCS 534
, 1991
"... A specification formalism with parameterisation of an arbitrary order is presented. It is given a denotationalstyle semantics, accompanied by an inference system for proving that an object satisfies a specification. The inference system incorporates, but is not limited to, a clearly identified t ..."
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Cited by 6 (2 self)
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A specification formalism with parameterisation of an arbitrary order is presented. It is given a denotationalstyle semantics, accompanied by an inference system for proving that an object satisfies a specification. The inference system incorporates, but is not limited to, a clearly identified typechecking component. Special effort is made to carefully distinguish between parameterised specifications, which denote functions yielding classes of objects, and specifications of parameterised objects, which denote classes of functions yielding objects. To deal with both of these in a uniform framework, it was convenient to view specifications, which specify objects, as objects themselves, and to introduce a notion of a specification of specifications. The formalism includes the basic specificationbuilding operations of the ASL specification language. This choice, however, is orthogonal to the new ideas presented. The formalism is also institutionindependent, although this iss...
On a Generalised Modularisation Theorem
, 2000
"... The relation between a metalogical property of entailment (interpolation) and a structural property of categories of theory presentations (stability of faithful morphisms under pushouts) is studied in an abstract "general logic" framework. In particular, a known result for first order logic (the ..."
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Cited by 1 (0 self)
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The relation between a metalogical property of entailment (interpolation) and a structural property of categories of theory presentations (stability of faithful morphisms under pushouts) is studied in an abstract "general logic" framework. In particular, a known result for first order logic (the "modularisation theorem"), stating that the stability of faithful morphisms under pushouts is equivalent to a specific form of interpolation, is generalised and reestablished. Furthermore, the stability under pushouts of the faithfulness of a given theory interpretation is shown to be equivalent to the existence of interpolants on specific loci of the underlying formalism. The latter neither assumes nor requires that the underlying logic possesses interpolation globally. 1 Introduction In this paper we revise, generalise and reestablish, in a notation independent framework, a strong relation between (a form of) interpolation [5, 20, 29, 1] and the stability of conservative extensio...
ON OBSERVATIONAL EQUIVALENCE AND ALGEBRAIC SPECIFICATION Extended abstract i
"... The properties of a simple and natural notion of observational equivalence of algebras and the corresponding specificationbuilding operation (observational abstraction) are studied. We begin with a definition of observational equivalence which is adequate to handle reachable algebras only, and show ..."
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The properties of a simple and natural notion of observational equivalence of algebras and the corresponding specificationbuilding operation (observational abstraction) are studied. We begin with a definition 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. 1