E. A. Ashcroft, A. A. Faustini, R. Jagannathan, and W. W. Wadge. Multidimensional programming. Oxford University Press, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....suggested) is the quantification over the subscript of the next i operator. This would allow many useful programs to be coded in a compact way. Another interesting extension to Cactus is the addition of multiple time dimensions. Multidimensional programming is a promising new area of research [30, 31] but had mainly been explored so far for linear time dimensions. Recent work however [22, 20] has demonstrated that multidimensional branching time languages provide an effective means for implementing higherorder functional languages. We believe than an investigation of multidimensional Cactus ....

E. A. Ashcroft, A. A. Faustini, R. Jagannathan, and W. W. Wadge. Multidimensional programming. Oxford University Press, 1995.

....MXML document each information piece may be qualified by a context specifier denoting the world in which the information piece holds. There is a number of alternative worlds for a document, generated by the dimensions used in that document. The idea of applying dimensions to languages is not new [2, 5]. GLU [2] is a programming language based on the notion of multiple dimensions and ISE [7] is a multidimensional version of Perl. Our work was influenced by Intensional HTML (IHTML) 8] a Web authoring language that allows a single Web page to have different variations and to dynamically adapt ....

....each information piece may be qualified by a context specifier denoting the world in which the information piece holds. There is a number of alternative worlds for a document, generated by the dimensions used in that document. The idea of applying dimensions to languages is not new [2, 5] GLU [2] is a programming language based on the notion of multiple dimensions and ISE [7] is a multidimensional version of Perl. Our work was influenced by Intensional HTML (IHTML) 8] a Web authoring language that allows a single Web page to have different variations and to dynamically adapt itself to a ....

E. A. Ashcroft, A. A. Faustini, R. Jagannathan, and W. W. Wadge. Multidimensional programming. Oxford University Press, 1995.

....way, and (c) duplication of information: information that is common can be duplicated, which is undesirable. In this paper we introduce multidimensional semistructured data and an extension of OEM called multidimensional OEM, that incorporate ideas from multidimensional programming languages [3] and associate data with dimensions, in order to tackle the aforementioned problems. We show how multidimensional OEM can be reduced to OEM under a speci c world. As an example application of multidimensional OEM, we consider the problem of representing histories of changes in an OEM database. ....

E. A. Ashcroft, A. A. Faustini, R. Jagannathan, and W. W. Wadge. Multidimensional Programming. Oxford University Press, 1995.

....MXML document each information piece may be quali ed by a context speci er denoting the world in which the information piece holds. There is a number of alternative worlds for a document, generated by the dimensions used in that document. The idea of applying dimensions to languages is not new [2, 5]. GLU [2] is a programming language based on the notion of multiple dimensions and ISE [7] is a multidimensional version of Perl. Our work was in uenced by Intensional HTML (IHTML) 8] a Web authoring language that allows a single Web page to have di erent variations and to dynamically adapt ....

....each information piece may be quali ed by a context speci er denoting the world in which the information piece holds. There is a number of alternative worlds for a document, generated by the dimensions used in that document. The idea of applying dimensions to languages is not new [2, 5] GLU [2] is a programming language based on the notion of multiple dimensions and ISE [7] is a multidimensional version of Perl. Our work was in uenced by Intensional HTML (IHTML) 8] a Web authoring language that allows a single Web page to have di erent variations and to dynamically adapt itself to a ....

E. A. Ashcroft, A. A. Faustini, R. Jagannathan, and W. W. Wadge. Multidimensional programming. Oxford University Press, 1995.

....project Executable Intensional Languages and Intelligent Applications in Multimedia, Hypermedia and Virtual Reality of ENE 99, contract no 99E 265. In this paper we propose a solution to the above problem, based on ideas that originate from the area of multidimensional programming languages [4, 14]. More speci cally, we propose the language Multidimensional XML (MXML) which extends traditional XML with the capability of representing context dependent information in a compact way. The development of MXML was in uenced by the ideas behind the design of Intensional HTML [20, 8, 7] In ....

....free grammar for XML documents, or as a kind of schema for XML data. A document may refer to a DTD to which it conforms. 2.2 Multidimensional Formalisms The idea of dimension enabled languages is not new. Possibly the rst multidimensional programming language is the (functional) language GLU [3, 4]. GLU allows the user to declare dimensions, and to de ne multidimensional entities that vary across these dimensions. So, a two dimensional entity can be thought as an in nite table, a three dimensional one as a cube extending in nitely across the three dimensions, and so on. One can perform ....

E. A. Ashcroft, A. A. Faustini, R. Jagannathan, and W. W. Wadge. Multidimensional programming. Oxford University Press, 1995.

.... several underlying structures sets as in SETL [37] bags in Gamma [7] relations (set of tuples) in SQL , the array structure is one of the most popular: vectors (e.g. in LISP) nested vectors (in NESL [6] 81 2 [15, 30] and multidimensional arrays (HPF [34] MOA [20] Indexical Lucid [1]) Typical operations on collections structured as arrays are maps (point wise application of functions) reductions, scans [5] and various permutations or rearranging operations. Managing an array as a whole offers an abstract and semantically clean programming model, which can be embedded ....

....the explicit numerical resolution of the parabolic partial differential equation governing the heat diffusion in a thin uniform rod. 10 Conclusion This paper reports some efforts to extend the concept of collection. There is a number of researches to extend the concept of array: Indexical Lucid [1], LPARX [25] Infidel [38] AMR [3] These approaches consider more general shapes for arrays than n dimensional bounding box, but always rely on grids (that is, a point is indexed by a tuple of integers) This forbids for example the natural representation of a tree or a triangular lattice. ....

Ashcroft, E. A., Faustini, A., Jagannathan, R., and Wadge, W. Multidimensional Programming. Oxford University Press, February 1995. ISBN 0-19-507597-8.

.... Since its conception various implementations of Lucid have been written (see [75] and [188] and one such implementation pLucid Lucid over the algebra of POP 2 taken from [51] has been used experimentally for software design (see [221] Recently work on GLU (Granular Lucid) has appeared in [11]. 9.4.4 Lucid Syntax. The RS Flip Flop can be described in Lucid as follows: flipflop(In1, In2) Out1, Out2) where Out1 = true fby (In1 nor Out2) Out2 = false fby (In2 nor Out1) 9.5 LUSTRE LUSTRE (see [53] is a synchronous dataflow language related to Lucid. Like Lucid it is based on the ....

E A Ashcroft, A A Faustini, R Jagannathan, and W W Wadge. Multidimensional Programming. Oxford University Press, 1995.

....an equivalence between the class of D0L Systems and a particular construction of programs in the 81 2 declarative data parallel language. 1 Introduction 81 2 is a declarative data parallel language aimed at the simulation of dynamical systems. Its main structure is the fabric which is a stream [1, 2, 3] of collections [4] The stream aspect of the fabric is used to describe the time axis of the simulation whereas the collection aspect of the fabric describe the space axis of the simulation. Because of space restrictions, we will not detail the 81 2 language here. The reader should refer to the ....

E. Ashcroft, A. Faustini, R. Jagannatha, and W. Wadge. Multidimensional Programming. Oxford University Press, February 1995. ISBN 0-19-507597-8.

.... nnf1; 1; 1g = f1; 2; 3g. Reductions and scans can be performed in O(log 2 (n) steps on SIMD architecture, where n is the number of elements in the collection, if the number of PEs is greater than n. The Concept of Stream in 81 2. Streams in 81 2 are infinite series of values as in LUCID [9]. Streams in 81 2 are computed in a strict ascending order, and at a given instant of the computation, there is always only one value (the current value) of the stream stored in the memory. No dynamic allocation of memory nor garbage collector is required. Two streams may have different clocks, ....

E. Ashcroft, A. Faustini, R. Jagannatha, and W. Wadge. Multidimensional Programming. Oxford University Press, February 1995. ISBN 0-19-507597-8.

....definition of webs supports implicit control parallelism. Usual structures of collections are sets (SETL [SDDS86] bags (Gamma [BCLM88] relations (set of tuples, e.g. in SQL) vectors ( LISP) nested vectors (NESL [Ble93] 81 2) and multidimensional arrays (HPF, MOA [HM91] new Lucid [AFJW95] Typical operations on collections structured as arrays are point wise applied scalar functions, reductions, scans and various permutations or rearranging operations that can be interpreted as communication operations in a data parallel implementation. Recursive definitions of ....

....sets of bounded rectangular regions in Z n . This library will be used for the implementation of abelian fields. It is itself based on AVTL [Sch95] a portable MPI [For94] based parallel vector template library. There is a small number of research efforts to extend the concept of array: Lucid [AFJW95] LPARKX [KB94] Infidel [Sem94] AMR [BLQ92] They all consider more general shapes for arrays than n dimensional bounding box, but always rely on grids (that is, a point is indexed by a tuple of integer) This forbids for example the natural representation of a tree or a triangular lattice. ....

E. Ashcroft, A. Faustini, R. Jagannatha, and W. Wadge. Multidimensional Programming. Oxford University Press, February 1995. ISBN 0-19-507597-8.

....collections. Collections have been advocated as a good support for data parallelism [3] Usual structures of aggregation are sets (SETL [4] bags (Gamma [5] relations (set of tuples, e.g. in SQL) vectors ( LISP) nested vectors (NESL [6] and multidimensional arrays (HPF, MOA [7] new Lucid [8]) Typical operations on arrays as collections are pointwise applied scalar functions, reductions, scans and various permutations or rearranging operations that can be interpreted as communication operations in a data parallel implementation. Nowadays, simulation of large dynamical systems ....

....of sets of bounded rectangular regions in Z n . This library will be used for the implementation of abelian fields. It is itself based on AVTL [13] a portable MPI [14] based parallel vector template library. There is a small number of research efforts to extend the concept of array: Lucid [8], LPARKX [15] Infidel [16] AMR [17] They all consider more general shapes for arrays but always rely on grids (that is, a point is indexed by a tuple of integer) This forbidd for example the natural representation of a tree or a triangular lattice. In field definitions, the decomposition of ....

E. Ashcroft, A. Faustini, R. Jagannatha, and W. Wadge. Multidimensional Programming. Oxford University Press, February 1995. ISBN 0-19-507597-8.

....that will not produce any value and correspond to deadlock tasks are detected (this is probably a programmer error) The task sequencing graph being an approximation of the real dependency graph, it is possible that we might detect as incorrect, programs that have a defined value. For example: T [2] = fT: 1 ; 0g (T: 1 refers to the second element of T ) The sequencing of T totally depends on itself because so does T: i (i can be a value computed at run time) This program results in a sequencing graph with a total cycle whereas the semantics of the language gives the obvious solution ....

E. Ashcroft, A. Faustini, R. Jagannatha, and W. Wadge. Multidimensional Programming. Oxford University Press, February 1995. ISBN 0-19-507597-8.

....further impetus for the development of the stream mechanism. 6] 7] The ability of a stream to provide a method for formally representing variables that change dynamically over time was used in several seminal declarative (or applicative) programming languages such as DFPL, VAL and Lucid. 8] 9] 10][11] The stream definition used was typically an ordered sequence of scalar values. Although streams of compound objects were sometimes supported (in particular, a stream of streams) these stream definitions were exclusively one dimensional. Specific details of more recent stream implementations will ....

....language was developed in an attempt to create a mathematically provable programming language, based on intensional logic. Although the original version allowed streams only to represent values changing in time, the current version of Lucid has been extended to support multidimensional streams. [11] The value (extension) of variables and expressions in an algorithm programmed in Lucid depends on an implicit index. Accesses to Lucid streams are not restricted to the current index, but must be addressed relative to the current index along a particular dimension. Intensional programming ....

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E. A. Ashcroft, A. A. Faustini, R. Jagannathan, and W. W. Wadge, Multidimensional Programming, Oxford Univ. Press, New York, 1995.

....highlevel programming language, Lucid. Q provides an implementation of Lucid which is reduced is some ways and extended in others. Examination of these differences may suggest possible areas for improvement. The multidimensional Lucid language proposed by Ashcroft, Faustini, Jaggannathan, and Wadge[2] is a intensional, stream based, multidimensional programming language, derived from Landin s ISWIM[3] It is an extension of earlier work with the original one dimensional version of Lucid[5] ferd Lucid, and an early attempt at multidimensionality [1] Hereafter, the Lucid refered to is the ....

.... multidimensional programming language, derived from Landin s ISWIM[3] It is an extension of earlier work with the original one dimensional version of Lucid[5] ferd Lucid, and an early attempt at multidimensionality [1] Hereafter, the Lucid refered to is the new multidimensional Lucid[2] unless otherwise noted. Lucid extends the simple applicative expressiveness of ISWIM with an intensional logic using a multidimensional space. The single variable of a simple algebra is extended into a stream which spans any dimensions over which the variable changes. The use of Lucid as a ....

Edward A. Ashcroft, Anthony A. Faustini, Rangaswamy Jagannathan, and William W. Wadge. Multidimensional Programming. Oxford Univ. Press, New York, 1995.

....Parallelism in GLU We illustrate here, the expressivity of GLU in different kinds of granular data parallelism. We then show how an existing imperative application can be transformed to a parallel GLU application with only nominal modification. 2. 1 Lucid The Intensional Core of GLU Lucid [4] is the multidimensional intensional language used by GLU to express the parallel structure of an application. The language Lucid is based on intensional logic, a form of mathematical logic commonly used in natural language semantics. In an intensional language, meanings of expressions do not just ....

....3 Parallel Program Generation We have shown how parallel applications can be described in GLU at a high level of abstraction where both expression and exploitation of parallelism are implicit. Abstractly, a GLU application can be evaluated using a parallel model of computation called eduction [3, 4]. For each high level application description, the GLU system generates a parallel program that when executed on the target system will eductively discover and harness programinherent parallelism. The generated parallel program, which reflects a particular embodiment of eduction, is referred to as ....

E.A. Ashcroft, A.A. Faustini, R. Jagannathan, and W.W. Wadge. Multidimensional Programming. Oxford University Press, New York, 1995.

....intensional language. For many applications such a language might be enough. However, there exist many natural problems which can be better thought of and solved if viewed from a multi dimensional perspective. Lucid has recently been extended to support more than one dimensional entities [AFJ91, AFJW95]. This new extended language was named GLU and its first implementation was developed in SRI. GLU allows the user to declare new dimensions and to define multidimensional entities that vary across these dimensions. So, a two dimensional entity can be thought as an infinite table, a ....

....ways. Its variants have been used to specify 3D spreadsheets [DW90] attribute grammars [Tao94] real time systems [FL89, JPL93] database systems [PP94] and so on. The most vital extension to the language was the addition of multiple dimensions which resulted in the language GLU (Granular Lucid) [AFJ91, AFJW95]. A GLU program consists of a declarative part (which is in fact a program in multidimensional Lucid) and an imperative part. The declarative part glues together sequential functions that are specified in an imperative language. GLU has been used for the development of real world applications ....

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E. A. Ashcroft, A. A. Faustini, R. Jagannathan, and W. W. Wadge. Multidimensional programming. Oxford University Press, 1995.

....of a set of imperatively specified sequential (e.g. C) functions and the composition part consists of an intensional program (using the lan To appear in Proceedings of the Second International Conference on High Performance Computing, Tata McGraw Hill, New Delhi, December 1995. guage Lucid[3]) that uses the C functions as building blocks to compose a parallel program. Parallelism is implicit in the specification given in Lucid which is sufficiently rich to express different kinds of parallelism including data, function, and stream parallelism[1] The granularity of parallelism depends ....

....shown in Figure 1. The hybrid philosophy of GLU where computation is separated from composition or coordination is similar to other parallel programming languages such as PCN[5] and Linda[6] It is unique in its use of intensionality[7, 8] to express the compositional aspects of parallel programs[3]. Being able to specify Multiprocessors MPPs Parallel Program Executables Generation Lucid Composition Sequential Functions GLU Program Compilation Parallel Program Sources NOWs Parallel Program Architectures Parallel Computer Operating Systems Figure 1: GLU System Architecture parallelism ....

E.A. Ashcroft, A.A. Faustini, R. Jagannathan, and W.W. Wadge. Multidimensional Programming. Oxford University Press, New York, 1995. ISBN 0-19-507597-8.

....with procedural programming, while the latter suits those who are familiar with nonprocedural programming. We appeal to both these views, as appropriate. 2. 1 Lucid The Graph Description Language The language used by GLU to implicitly describe the parallel structure of an application is Lucid [4]. While Lucid can be thought of as yet another textual language for describing a data dependency graph, it is much more than that. A Lucid program is equivalent to a data dependency graph whose edges denote multidimensional streams and whose nodes denote operations and functions on such streams. ....

E.A. Ashcroft, A.A. Faustini, R. Jagannathan, and W.W. Wadge. Multidimensional Programming. Oxford University Press, New York, 1995.

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E.A. Ashcroft, A.A. Faustini, R. Jagannathan, and W.W. Wadge. Multidimensional Programming. Oxford University Press, 1995.

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E. A. Ashcroft, A. A. Faustini, R. Jagannathan, and W. W. Wadge. Multidimensional programming. Oxford University Press, 1995.

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