Parametric Polymorphism Optimization for Deeply Nested Types in Computer Algebra

Computer algebra systems, such as Axiom, and programming languages designed for computer algebra, such as Aldor, have very flexible mechanisms for generic code, with type parameterization. Modern versions of Maple can support this style of programming through the use of Maple's module system, and by using module-producing functions to give parametric type constructors. From the software design point of view, generic programming allows better code re-usability so main-stream programming languages, such as C++ and Java, have evolved to support it. Computer algebra programs that use parametric polymorphism tend to do so very heavily, leading to deeply nested type constructions. Optimization of deeply nested type constructions thus becomes an important problem for system efficiency. The goal of the current work is to present optimizations for this situation. Our approach is to specialize generic types at compiletime, based on global program analysis. We anticipate that the problem of optimizing deeply nested type construction will also find application outside computer algebra.