Dimensional Analysis of Dataflow Programming

Abstract

In this paper, we present an algorithm for the Dimensional Analysis (DA) of a two-dimensional dialect of the dataflow language Lucid, one in which the dimensions are ‘space’ as well as ‘time’. DA is indispensable for an efficient implementation of multidimensional Lucid. A Lucid program is a set of equations defining a family of multidimensional datasets; each data set being a collection of data points indexed by coordinates in a number of dimensions. Every variable in a Lucid program denotes one such dataset, and they are defined in terms of input and transformations applied to other variables. In general, not every dimension is relevant in every data set. It is very important not to include irrelevant dimensions because otherwise you have the same data duplicated with different values of the irrelevant dimension. In most multidimensional systems it is the administrator’s responsibility to exclude irrelevant dimensions and to keep track of changes in dimensionality that result from transformations. In other words, DA is performed manually. In Lucid, however, we have an alternative, namely, automated DA. Static program analysis allows us to calculate or estimate the dimensionality of program variables. This is the goal of our research. The problem is far from straightforward because Lucid programs can allow many potential dimensions, the programmer can declare local temporary dimensions, and the transformations can have complicated and even recursive definitions. Our software will be tested and incorporated in the PyLucid (Python-Based) interpreter.

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