On Programming Scientific Applications in Sac -
a Functional Language Extended by a Subsystem for High-Level Array Operations
Sven-Bodo Scholz

Dept of Computer Science, University of Kiel, 24105 Kiel, Germany
e-mail: sbs@informatik.uni-kiel.de

Abstract. This paper discusses some of the pros and cons of extending
a simple functional language called Sac (for Single Assignment C) by
array operations similar to those that are available in Apl. The array
operations in Sac are based on the /-calculus, an algebra of arrays which
provides a formalism for specifying and simplifying array operations in
terms of index set manipulations.
The programming techniques made possible by Sac are demonstrated
by means of a functional program for the approximation of numerical
solutions of partial differential equations by multigrid relaxation. This
application is not only of practical relevance but also fully exposes the
flavors of using high-level array operations. In contrast to specifications
in other languages, e.g. in Fortran or Sisal, the Sac program is well
structured, reasonably concise, and - what is most important - invariant
against dimensionalities and shapes. However, sophisticated compilation
techniques are necessary to avoid, whenever possible, the creation of
temporary arrays and to eliminate redundant operations.
The paper also includes performance figures for a Sac implementation of
the NAS-mgrid-benchmark which are competetive with those of a Sisal
implementation.