By E. A. Ashcroft, A. A. Faustini, R. Jagannathan, W. W. Wadge

This publication describes a strong language for multidimensional declarative programming referred to as Lucid. Lucid has advanced significantly long ago ten years. the most catalyst for this metamorphosis used to be the invention that Lucid is predicated on intensional common sense, one common in learning traditional languages. Intensionality, and extra in particular indexicality, has enabled Lucid to implicitly convey multidimensional items that fluctuate, a basic potential with numerous results that are explored during this publication. the writer covers a wide variety of themes, from foundations to purposes, and from implementations to implications. The function of intensional common sense in Lucid in addition to its results for programming quite often is mentioned. The syntax and mathematical semantics of the language are given and its skill for use as a proper method for transformation and verification is gifted. using Lucid in either multidimensional purposes programming and software program structures development (such as a parallel programming process and a visible programming method) is defined. a unique version of multidimensional computation--education--is defined in addition to its serendipitous sensible advantages for harnessing parallelism and tolerating faults. because the basically quantity that displays the advances during the last decade, this paintings can be of significant curiosity to researchers and complex scholars concerned with declarative language structures and programming.

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4 Sorting The idea behind the above tournament for summing numbers can be used for sorting numbers. The point is that any operation can be used in a tournament as long as it is associative, and the operation of merging sorted lists is clearly associative and it returns sorted lists. ) Thus, all we have to do is start with trivial sorted lists of one element each and merge them all, using a tournament, to get all the elements in order. We start, as suggested, with a u-sequence of trivial, one-element w-sequences, and use the function merge instead of addition.

2 Denotational Semantics The language Lucid has many novel and unusual features, such as intensionality, the use of arbitrary, even temporary, new dimensions, dimensionally abstracted definitions of variables and functions, and a serendipity principle that makes everything mean more than it appears at first sight. So what does this all really mean? What is its semantics? The semantics of Lucid is denotational rather than operational. Rather than specify a conventional denotational semantics, we will indicate how the semantics has grown from the semantics of Lucid's predecessors, the earlier versions of Lucid described in Chapter 2 and the earlier functional languages.

The values we want correspond to the nonzero values of sawtooth. This second definition of wanted is more efficient, in that it performs less computation for a given number of results, but the first definition may be preferable in some circumstances because the results can all be computed in parallel. The values of sawtooth, on the other hand, have to be computed sequentially. Whichever definition of wanted we decide to use, we must now compress seq, using only the elements for which wanted is true.