Let denote a constant interval number system, built from an underlying number system :
A general methodology for constructing constant interval models of real functions will be presented in this section. We will assume that an order-preserving mapping exists:
Throughout this section we may treat members of as constant functions, to ease the upcoming transition to linear interval arithmetic. Rather than describe the procedures and in a formal language, we will discuss evaluations of with examples. It is understood that much of the examination of g occurs while is being implemented, rather than during execution. Of course, such examination is possible during execution, and may be useful for complicated functions; interval arithmetic may be used to help perform such examinations. Complicated functions may be handled without direct analysis; the interval inclusion property allows such functions to be treated as compositions of simpler functions.
Knowledge of basic vector calculus is assumed; see  for reference. See, for example, [19, 27] for other approaches to the implementation of constant interval arithmetic.
|Jeff Tupper||March 1996|