Abstract
new geometric framework for program representation has recently been proposed by d'Auriol (1999) to address the difficulties of (parallel) programming. The essential focus of this framework is the expression of collections of computations and the inter-, intra-relationships thereof. Collections of computations are encapsulated by geometric objects, termed polytopes, wherein particular computations are mapped to selected integer points inside of the polytopes. Spatial relationships can be quantified by the dimension of the geometric object and by the spatial orientation of the contained computations. Temporal, hierarchal or other relationships can also be represented by superimposing dependency graphs over the geometric object(s). The notion of such collections of program fragments is central to human perception of program design, for example, the separation of program fragments into modules, objects, tasks, packages, functions, procedures and subroutines, etc. The software development process is thus completed by (a) specifying one or more groupings by describing polytopes and (b) constructing relationships between particular computations and between polytopes. A complete program may be represented by hierarchies of polytopes.

Even a small-size program represented geometrically may include numerous complex properties, for example, higher dimensional space, sub-space existence, multiple relationship types, etc. In addition, we are often interested in program analysis, in particular, complexity analysis. Due to the complexities of the geometric representation, it is essential that scientific visualization techniques be applied to assist the programmer in `visualizing' such a geometrically represented program. The AVS/Express product, marketed by Advanced Visual Systems Inc., is a state-of-the-art high-quality scientific visualization tool that is used in this research to assist in the visualization of programs.

This talk will introduce the concept of geometric representation of programs, present some of the underlying mathematical framework used in such representations, introduce the AVS/Express product and provide a `live' demonstration of some of the visualization techniques currently being investigated in this research. Throughout this talk, the Shell Sort algorithm will be used as the example.