The purpose of this thesis was to develop a program that would accept, as input, a finite set of algebraic equations and simple if-then conditional expressions that model a natural system, and then produce a continuous computer simulation with graphics and tabular output. The equations and conditionals can be in any order and key elements can be missing. The program can be used to run existing models or as a development tool to produce immediate prototypic computer simulations through synergistic man-machine interactions. The theoretical aspects of automatic program generation were discussed, as well as the architectural design of the system. The simulation system was used to develop a computer simulation of an exploited Northern Utah pheasant population and the results were compared to the results from an earlier FORTRAN computer simulation of the same model. It was concluded that the simulation system developed for this thesis produces verified computer simulations from mathematical models that are at least as accurate as the corresponding simulation written in FORTRAN. The system was easy to use and should be useful for unsophisticated users. Some "tuning'' of the input was needed to produce a verified simulation and it was concluded that further work was needed here.

Expert design knowledge is essential to develop a library of high-performance software. This includes how to implement and parallelize domain operations, how to optimize implementations, and estimates of which implementation choices are best. An expert repeatedly applies his knowledge, often in a rote and tedious way, to develop all of the related functionality expected from a domain-specific library. Expert knowledge is hard to gain and is easily lost over time when an expert forgets or when a new engineer starts developing code. The domain of dense linear algebra (DLA) is a prime example with software that is so well designed that much of experts' important work has become tediously rote in many ways. In this dissertation, we demonstrate how one can encode design knowledge for DLA so it can be automatically applied to generate code as an expert would or to generate better code. Further, the knowledge is encoded for perpetuity, so it can be reused to make implementing functionality on new hardware easier or it can be used to teach how software is designed to a non-expert. We call this approach to software engineering (encoding expert knowledge and automatically applying it) Design by Transformation (DxT). We present our vision, the methodology, a prototype code generation system, and possibilities when applying DxT to the domain of dense linear algebra. / text