Data types as initial algebras: A unification of Scottery and ADJery

Abstract

This paper presents a formulation within the framework of data types as initial algebras, of parameterizations of data types. We will observe that Scott's data type constructors like +, ×, and circular definitions are parameterizations in our sense. Thence we will provide a uniform ground to compare ADJ-like data types with Lehmann-Smyth's data types, and will justify recent ADJ's claim that polynomial data types of Lehmann-Smyth could be simulated within ADJery.