The imperative implementation of algebraic data types

Abstract

The synthesis of imperative programs for hierarchical, algebraically specified abstract data types is investigated. Two aspects of the synthesis are considered: the choice of data structures for efficient implementation, and the synthesis of linked implementations for the class of ADTs which insert and access data without explicit key. The methodology is based on an analysis of the algebraic semantics of the ADT. Operators are partitioned according to the behaviour of their corresponding operations in the initial algebra. A family of relations, the storage relations of an ADT, Is defined. They depend only on the operator partition and reflect an observational view of the ADT. The storage relations are extended to storage graphs: directed graphs with a subset of nodes designated for efficient access. The data structures in our imperative language are chosen according to properties of the storage relations and storage graphs. Linked implementations are synthesised in a stepwise manner by implementing the given ADT first by its storage graphs, and then by linked data structures in the imperative language. Some circumstances under which the resulting programs have constant time complexity are discussed.