Parametrized Data Types Do Not Need Highly Constrained Parameters

Data types may be considered as objects in any suitable category, and need not necessarily be ordered structures or many-sorted algebras. Arrays may be specified having as parameter any object from a category J.f with finite products and eoproducts, if products distribute over coproducts. The Lehmann-Smith least fixpoint approach to recursively-defined data types is extended by introducing the dual notion of greatest fixpoint, which allows the definition of infinite lists and trees without recourse to domains bearing a partial order structure. Finally, the least fixpoint approach is shown allowing the definition of queues directly in terms of stacks, rather than through a separate equational specification.