Abstract
We examine type systems for support of subtypes and categories in computer algebra systems. By modelling representation of instances in terms of existential types instead of recursive types, we obtain not only a simplified model, but we build a basis for defining subtyping among algebraic domains. The introduction of metaclasses, facilitates the task, by allowing the inference of type classes. By means of type classes and existential types we construct subtype relations without involving coercions.
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