A Smalltalk system for algebraic manipulation

Abstract

This paper describes the design of an algebra system Views implemented in Smalltalk. Views contains facilities for dynamic creation and manipulation of computational domains , for viewing these domains as various categories such as groups, rings, or fields, and for expressing algorithms generically at the level of categories. The design of Views has resulted in the addition of some new abstractions to Smalltalk that are quite useful in their own right. Parameterized classes provide a means for run-time creation of new classes that exhibit generally very similar behavior, differing only in minor ways that can be described by different instantiations of certain parameters. Categories allow the abstraction of the common behavior of classes that derives from the class objects and operations satisfying certain laws independently of the implementation of those objects and operations. Views allow the run-time association of classes with categories (and of categories with other categories), facilitating the use of code written for categories with quite different interpretations of operations. Together, categories and views provide an additional mechanism for code sharing that is richer than both single and multiple inheritance. The paper gives algebraic as well as non-algebraic examples of the above-mentioned features.