Algebraic Composition of Function Tables |
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Authors: | Martin von Mohrenschildt |
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Affiliation: | (1) Computing and Software, Faculty of Engineering, McMaster University, Hamilton, Ontario, Canada, CA |
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Abstract: | In general, a program is composed of smaller program segments using composition, conditional constructs or loop constructs.
We present a theory which enables us to algebraically define and compute the composition of conditional expressions. The conditional
expressions are represented using tabular notation. The formal definition of the composition allows us to compute the close
form representation of the composition of tabular expressions. The presented approach is based on a many sorted algebra containing
information preserving composition. This formal definition of composition is then “lifted” to an extended algebra containing
tabular expressions. The presented theory provides very compact algorithms and proofs.
Received July 1998 / Accepted in revised form January 2000 |
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Keywords: | : Tabular expressions Composition of algebraic functions Conditional expressions |
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