Supertotal Function Definition in Mathematics and Software Engineering
IEEE Transactions on Software Engineering
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Bottom is used in functional programming languages to denote abnormal situations. We propose the incorporation of this value in any existing imperative language. We show how this can be done and finally what are the benefits of the bottom incorporation in any imperative language.Covariant deep subtyping has always been viewed as a way to narrow the range of a component in subtypes. In this paper, however, we will see covariant deep subtyping in a new light---a way to clarify a vague but fixed range of a component in subclasses. We will also examine such concepts as class substitution, generic calss by BETA/Cluster, and a number of theoretic approaches in relation to covariant deep subtyping.