Enriching the object-oriented paradigm via shadows in the context of mathematics

It is well-known that few object-oriented programming languages allow objects to change their nature at run-time. In this paper we discuss the need for object-oriented programming languages to reflect the dynamic nature of problems, particularly those arising in a mathematical context. It is from this context that we present a framework, together with a Java-like implementation of that framework, that realistically represents the dynamic and evolving characteristic of problems and algorithms.