On the implementation of abstract data types by programming language constructs

AbstractImplementations of abstract data types are defined via enrichments of a target type. We propose to use an extended typed λ-calculus for enrichments in order to meet the conceptual requirement that an implementation has to bring us closer to a (functional) program. Composability of implementations is investigated, the main result being that composition of correct implementations is correct if terminating programs are implemented by terminating programs. Moreover, we provide syntactical criteria to guarantee correctness of composition. The proof is based on strong normalization and Church-Rosser results of the extended λ-calculus which seem to be of interest in their own right

A systematic study of models of abstract data types

AbstractThe term-generated models of an abstract data type can be represented by congruence relations on the term algebra. Total and partial heterogeneous algebras are considered as models of hierarchical abstract data types.Particular classes of models are studied and it is investigated under which conditions they form a complete lattice. This theory allows also to describe programming languages (and their semantic models) by abstract types. As example we present a simple deterministic stream processing language