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On the Insufficiency of Ontologies: Problems in Knowledge Sharing and Alternative Solutions
"... One of the benefits of formally represented knowledge lies in its potential to be shared. Ontologies have been proposed as the ultimate solution to problems in knowledge sharing. However even when an agreed correspondence between ontologies is reached that is not the end of the problems in knowledge ..."
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One of the benefits of formally represented knowledge lies in its potential to be shared. Ontologies have been proposed as the ultimate solution to problems in knowledge sharing. However even when an agreed correspondence between ontologies is reached that is not the end of the problems in knowledge sharing. In this paper we explore a number of realistic knowledgesharing situations and their related problems for which ontologies fall short in providing a solution. For each situation we propose and analyse alternative solutions.
A formalism for higherorder composition languages that satisfies the churchrosser property
, 2006
"... personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires pri ..."
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Cited by 8 (6 self)
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personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission.
A Model for Formal Parametric Polymorphism: A PER Interpretation for System R
, 1995
"... System R is an extension of system F that formalizes Reynolds' notion of relational parametricity. In system R, considerably more lambdaterms can be proved equal than in system F: for example, the encoded weak products of F are strong products in R. Also, many "theorems for free" à la Wadler can be ..."
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Cited by 6 (0 self)
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System R is an extension of system F that formalizes Reynolds' notion of relational parametricity. In system R, considerably more lambdaterms can be proved equal than in system F: for example, the encoded weak products of F are strong products in R. Also, many "theorems for free" à la Wadler can be proved formally in R. In this paper we describe a semantics for system R. As a first step, we give a precise and general reconstruction of the per model of system F of Bainbridge et al., presenting it as a categorical model in the sense of Seely. Then we interpret system R in this model.
Compiler Construction Using Scheme
 In Functional programming languages in education (FPLE), LNCS 1022
, 1995
"... This paper describes a course in compiler design that focuses on the Scheme implementation of a Scheme compiler that generates native assembly code for a real architecture. The course is suitable for advanced undergraduate and beginning graduate students. It is intended both to provide a general kno ..."
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Cited by 5 (0 self)
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This paper describes a course in compiler design that focuses on the Scheme implementation of a Scheme compiler that generates native assembly code for a real architecture. The course is suitable for advanced undergraduate and beginning graduate students. It is intended both to provide a general knowledge about compiler design and implementation and to serve as a springboard to more advanced courses. Although this paper concentrates on the implementation of a compiler, an outline for an advanced topics course that builds upon the compiler is also presented.
Computably based locally compact spaces
, 2003
"... ASD (Abstract Stone Duality) is a reaxiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated lambdacalculus. In this paper, this is shown to be equivalen ..."
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Cited by 5 (3 self)
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ASD (Abstract Stone Duality) is a reaxiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated lambdacalculus. In this paper, this is shown to be equivalent to a notion of computable basis for locally compact sober spaces or locales, involving a family of open subspaces and accompanying family of compact ones. This generalises Smyth’s effectively given domains and Jung’s Strong proximity lattices. Part of the data for a basis is the inclusion relation of compact subspaces within open ones, which is formulated in locale theory as the waybelow relation on a continuous lattice. The finitary properties of this relation are characterised here, including the Wilker condition for the cover of a compact space by two open ones. The real line is used as a running example, being closely related to Scott’s domain of intervals. ASD does not use the category of sets, but the full subcategory of overt discrete objects plays this role; it is an arithmetic universe (pretopos with lists). In particular, we use this subcategory to translate computable bases for classical spaces into objects in the ASD calculus.
Extensional rewriting with sums
 In TLCA
, 2007
"... Abstract. Inspired by recent work on normalisation by evaluation for sums, we propose a normalising and confluent extensional rewriting theory for the simplytyped λcalculus extended with sum types. As a corollary of confluence we obtain decidability for the extensional equational theory of simply ..."
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Cited by 5 (3 self)
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Abstract. Inspired by recent work on normalisation by evaluation for sums, we propose a normalising and confluent extensional rewriting theory for the simplytyped λcalculus extended with sum types. As a corollary of confluence we obtain decidability for the extensional equational theory of simplytyped λcalculus extended with sum types. Unlike previous decidability results, which rely on advanced rewriting techniques or advanced category theory, we only use standard techniques. 1
A lambda calculus for real analysis
, 2005
"... Abstract Stone Duality is a revolutionary theory that works directly with computable continuous functions, without using set theory, infinitary lattice theory or a prior theory of discrete computation. Every expression in the calculus denotes both a continuous function and a program, but the reasoni ..."
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Cited by 4 (0 self)
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Abstract Stone Duality is a revolutionary theory that works directly with computable continuous functions, without using set theory, infinitary lattice theory or a prior theory of discrete computation. Every expression in the calculus denotes both a continuous function and a program, but the reasoning looks remarkably like a sanitised form of that in classical topology. This paper is an introduction to ASD for the general mathematician, and applies it to elementary real analysis. It culminates in the Intermediate Value Theorem, i.e. the solution of equations fx = 0 for continuous f: R → R. As is well known from both numerical and constructive considerations, the equation cannot be solved if f “hovers ” near 0, whilst tangential solutions will never be found. In ASD, both of these failures and the general method of finding solutions of the equation when they exist are explained by the new concept of “overtness”. The zeroes are captured, not as a set, but by highertype operators � and ♦ that remain (Scott) continuous across singularities of a parametric equation. Expressing topology in terms of continuous functions rather than sets of points leads to
A Calculus of Refinements: its class of models
, 1992
"... The Calculus of Refinements (COR) presented here takes this idea of types as specifications and subtyping as refinement and pushes it to an extreme. Types and values are no longer distinguished; in COR we consider a unique hierarchy of objects. A good way to deal with the hierarchy of objects is to ..."
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Cited by 2 (2 self)
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The Calculus of Refinements (COR) presented here takes this idea of types as specifications and subtyping as refinement and pushes it to an extreme. Types and values are no longer distinguished; in COR we consider a unique hierarchy of objects. A good way to deal with the hierarchy of objects is to structure it as a complete lattice. And if functions are to be considered as first class citizens in the hierarchy then the lattice must be reflexive: it must have the space of functions (some of them) as a sublattice. To represent reflexive lattices, the most simple language is an extension of the calculus with lattice operators: this is the language of COR. The aim of this communication is to show that the results about the soundness and the completeness of calculus can be extended without problems to COR. 1 Introduction Data and its classification into types are kept separated and used distinctively in most programming languages. Types are mainly used as a discipline that contributes ...