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Scientific Programming
Volume 5, Issue 4, Pages 279-300

A New Language Design for Prototyping Numerical Computation

Thomas Derby, Robert Schnabel, and Benjamin Zorn

Department of Computer Science, Campus Box 430, University of Colorado, Boulder, CO 80309, USA

Received 23 March 1995; Accepted 23 January 1996

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


To naturally and conveniently express numerical algorithms, considerable expressive power is needed in the languages in which they are implemented. The language Matlab is widely used by numerical analysts for this reason. Expressiveness or ease-of-use can also result in a loss of efficiency, as is the case with Matlab. In particular, because numerical analysts are highly interested in the performance of their algorithms, prototypes are still often implemented in languages such as Fortran. In this article we describe a language design that is intended to both provide expressiveness for numerical computation, and at the same time provide performance guarantees. In our language, EQ, we attempt to include both syntactic and semantic features that correspond closely to the programmer's model of the problem, including unordered equations, large-granularity state transitions, and matrix notation. The resulting language does not fit into standard language categories such as functional or imperative but has features of both paradigms. We also introduce the notion of language dependability, which is the idea that a language should guarantee that certain program transformations are performed by all implementations. We first describe the interesting features of EQ, and then present three examples of algorithms written using it. We also provide encouraging performance results from an initial implementation of our language.