Data Types as Term Algebras

Data types in programming have been mathematically studied from two different viewpoints, namely data types as (initial) algebras and data types as complete partial orders. In this paper, we explore a possibility of finitaristic approach. For finitarists, the only sets accepted are "recursively defined" sets. We observe that recursive definition not only defines a set of terms but also basic operations over them, thus it induces an algebra of terms. We compare this approach to the existing two approaches. Using our approach we present finer classification of data types.