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Little Theories
 Automated DeductionCADE11, volume 607 of Lecture Notes in Computer Science
, 1992
"... In the "little theories" version of the axiomatic method, different portions of mathematics are developed in various different formal axiomatic theories. Axiomatic theories may be related by inclusion or by theory interpretation. We argue that the little theories approach is a desirable way to forma ..."
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Cited by 48 (15 self)
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In the "little theories" version of the axiomatic method, different portions of mathematics are developed in various different formal axiomatic theories. Axiomatic theories may be related by inclusion or by theory interpretation. We argue that the little theories approach is a desirable way to formalize mathematics, and we describe how imps, an Interactive Mathematical Proof System, supports it.
(ML)²: A formal language for KADS models of expertise
, 1993
"... This paper reports on an investigation into a formal language for specifying kads models of expertise. After arguing the need for and the use of such formal representations, we discuss each of the layers of a kads model of expertise in the subsequent sections, and define the formal constructions tha ..."
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Cited by 35 (9 self)
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This paper reports on an investigation into a formal language for specifying kads models of expertise. After arguing the need for and the use of such formal representations, we discuss each of the layers of a kads model of expertise in the subsequent sections, and define the formal constructions that we use to represent the kads entities at every layer: ordersorted logic at the domain layer, metalogic at the inference layer, and dynamiclogic at the task layer. All these constructions together make up (ml) 2 , the language that we use to represent models of expertise. We illustrate the use of (ml) 2 in a small example model. We conclude by describing our experience to date with constructing such formal models in (ml) 2 , and by discussing some open problems that remain for future work. 1 Introduction One of the central concerns of "knowledge engineering" is the construction of a model of some problem solving behaviour. This model should eventually lead to the construction of a...
Logical Systems for Structured Specifications
, 2000
"... We study proof systems for reasoning about logical consequences and refinement of structured specifications, based on similar systems proposed earlier in the literature [ST 88, Wir 91]. Following Goguen and Burstall, the notion of an underlying logical system over which we build specifications is fo ..."
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Cited by 35 (1 self)
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We study proof systems for reasoning about logical consequences and refinement of structured specifications, based on similar systems proposed earlier in the literature [ST 88, Wir 91]. Following Goguen and Burstall, the notion of an underlying logical system over which we build specifications is formalized as an institution and extended to a more general notion, called (D, T )institution. We show that under simple assumptions (essentially: amalgamation and interpolation) the proposed proof systems are sound and complete. The completeness proofs are inspired by proofs due to M. V. Cengarle (see [Cen 94]) for specifications in firstorder logic and the logical systems for reasoning about them. We then propose a methodology for reusing proof systems built over institutions rich enough to satisfy the properties required for the completeness results for specifications built over poorer institutions where these properties need not hold.
Formal program development in Extended ML for the working programmer
, 1991
"... Extended ML is a framework for the formal development of programs in the Standard ML programming language from highlevel specifications of their required input/output behaviour. It strongly supports the development of modular programs consisting of an interconnected collection of generic and reusab ..."
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Cited by 34 (10 self)
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Extended ML is a framework for the formal development of programs in the Standard ML programming language from highlevel specifications of their required input/output behaviour. It strongly supports the development of modular programs consisting of an interconnected collection of generic and reusable units. The Extended ML framework includes a methodology for formal program development which establishes a number of ways of proceeding from a given specification of a programming task towards a program. Each such step gives rise to one or more proof obligations which must be proved in order to establish the correctness of that step. This paper is intended as a useroriented summary of the Extended ML language and methodology. Theoretical technicalities are avoided whenever possible, with emphasis placed on the practical aspects of formal program development. An extended example of a complete program development in Extended ML is included.
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.
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...
Structured theory presentations and logic representations
 ANNALS OF PURE AND APPLIED LOGIC
, 1994
"... The purpose of a logical framework such as LF is to provide a language for defining logical systems suitable for use in a logicindependent proof development environment. All inferential activity in an object logic (in particular, proof search) is to be conducted in the logical framework via the ..."
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Cited by 14 (2 self)
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The purpose of a logical framework such as LF is to provide a language for defining logical systems suitable for use in a logicindependent proof development environment. All inferential activity in an object logic (in particular, proof search) is to be conducted in the logical framework via the representation of that logic in the framework. An important tool for controlling search in an object logic, the need for which is motivated by the difficulty of reasoning about large and complex systems, is the use of structured theory presentations. In this paper a rudimentary language of structured theory presentations is presented, and the use of this structure in proof search for an arbitrary object logic is explored. The behaviour of structured theory presentations under representation in a logical framework is studied, focusing on the problem of "lifting" presentations from the object logic to the metalogic of the framework. The topic of imposing structure on logic presentations...
Proof Systems for Structured Specifications and Their Refinements
, 1999
"... Reasoning about specifications is one of the fundamental activities in the process of formal program development. This ranges from proving the consequences of a specification, during the prototyping or testing phase for a requirements speci cation, to proving the correctness of refinements (or imple ..."
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Cited by 12 (5 self)
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Reasoning about specifications is one of the fundamental activities in the process of formal program development. This ranges from proving the consequences of a specification, during the prototyping or testing phase for a requirements speci cation, to proving the correctness of refinements (or implementations) of specifications. The main proof techniques for algebraic specifications have their origin in equational Horn logic and term rewriting. These proof methods have been well studied in the case of nonstructured speci cations (see Chapters 9 and 10). For large systems of specifications built using the structuring operators of speci cation languages, relatively few proof techniques have been developed yet; for such proof systems, see [SB83, HST94, Wir91, Far92, Cen94, HWB97]. In this chapter we focus on proof systems designed particularly for modular specifications. The aim is to concentrate on the structuring concepts, while abstracting as much as possible from the par...
Structuring Specifications intheLarge and intheSmall: HigherOrder Functions, Dependent Types and Inheritance in SPECTRAL
 PROC. COLLOQ. ON COMBINING PARADIGMS FOR SOFTWARE DEVELOPMENT, JOINT CONF. ON THEORY AND PRACTICE OF SOFTWARE DEVELOPMENT (TAPSOFT
"... ..."
A new semantics for Clear
"... Summary. A semantics for the Clear specification language is given. The language of set theory is employed to present constructions corresponding to Clear's specificationcombining operations, which are then used as the basis for a denotational semantics. This is in contrast to Burstall and Goguen's ..."
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Cited by 7 (1 self)
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Summary. A semantics for the Clear specification language is given. The language of set theory is employed to present constructions corresponding to Clear's specificationcombining operations, which are then used as the basis for a denotational semantics. This is in contrast to Burstall and Goguen's 1980 semantics which described the meanings of these operations