Some Observations Concerning Formal Differentiation of Set Theoretic Expressions

Abstract

A variety of matters related to formal differentiation are considered.First, an algebraic approach to formal differentiation of a class of set theoretic expressions is suggested.Then the application of formal .differentiationto loop fusion is discussed.Finally, formal differentiation is applied to optimization of incremental construction of composite objects satisfying a given Predicate.The techniques developed are illustrated by transformational construction of a variety of algorithms.