Continuous Data Types

Data types can be elegantly characterized as the algebraic quotient of the initial algebra in the appropriate class of algebras. In this paper, data types whose domain is continuous (continuous data types) are defined and studied. It is shown that an algebraic quotient of the appropriate initial continuous algebra can be used to characterize continuous data types when certain conditions are satisfied. Two well-known computer science examples are presented to illustrate the results. These types are lists, including infinite lists and control structures considered as operators of a data type.