A Type System for Computer Algebra

This paper presents a type system for support of subtypes, parameterized types with sharing and categories in a computer algebra environment. By modeling representation of instances in terms of existential types, we obtain a simplified model, and build a basis for defining subtyping among algebraic domains. The inheritance at category level has been formalized; this allows the automatic inference of type classes. By means of type classes and existential types we construct subtype relations without involving coercions. A type sharing mechanism works in parallel and allows the consistent extension and combination of domains. The expressiveness of the system is further increased by viewing domain types as special case of package types, forming weak and strong sums respectively. The introduced system, although awkward at first sight, is simpler than other proposed systems for computer algebra without including some of their problems. The system can be further extended in order to support more constructs and increase its flexibility.