Framework design is a multifaceted endeavor undertaken to promote reuse of software within a family of related applications. Traditional approaches involve either the evolution or the systematic design of the needed generic structure. This paper explores a systematic design approach called function generalization. In this approach, framework design begins with an executable specification expressed as a set of functions in a functional programming language. This set is analyzed to identify the common and variable aspects of the family of related applications. The set of functions is then transformed in a series of steps to produce a generalized application corresponding to the family. Each step generalizes one variable aspect of the family by introducing higher-order (function) parameters or polymorphic parameters into the functions in the set. The resulting set of generalized functions can be converted to Java code using design patterns to guide the framework construction.