A Study of Function Evaluation

Saadat, Sohrab (1973). A Study of Function Evaluation. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000f249


This thesis is concerned with an investigation into the techniques of function evaluation as used in symbol manipulation. The overall objective of this study is to investigate the possibility of constructing a programming system in which the performance of function evaluations improves in efficiency as a result of information provided by the user and gathered by the system as a result of previous evaluations. The approach to this problem is to construct a mechanism which allows the user and the system to work together to build up “useful properties of functions". The properties which are expressed in the form of relations between the function, its arguments and its corresponding function values, are used to improve the performance of function evaluations.

Various programming systems, each incorporating a particular set of facilities designed to improve the performance of function evaluation, are constructed and their performance relative to each other and relative to the underlying host system analysed. From the analysis of the experimental results, conclusions are drawn about those facilities which should be included in the design of a general purpose symbol manipulation system.

The present work is based on the assumption that by providing all the facilities within an interactive environment, the user can guide the course of an evaluation and thus improve the performance of the evaluation. This assumption, which is based on the assertion that no programming system can currently match the power of its human user to recognise “significant" and “useful" items of information, leads to an interactive symbol manipulation system being chosen as the host system for the investigation. A number of the results obtained are applicable to the design of other types of programming systems.

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