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The \Boom hierarchy" is a hierarchy of types that begins at the level of trees and includes lists, bags and sets. This hierarchy forms the basis for the calculus of total functions developed by Bird and Meertens, and which has become known as the \Bird-Meertens formalism". This paper describes a hierarchy of types that logically precedes the Boom hierarchy.… (More)

Polytypic programs are programs that are parameterised by type constructors (like List), unlike polymorphic programs which are parameterised by types (like Int). In this paper we formulate precisely the polytypic programming problem of \commut-ing" two datatypes. The precise formulation involves a novel notion of higher order polymorphism. We demonstrate… (More)

In this paper we demonstrate that the basic rules and calcu-lational techniques used in two extensively documented program derivation methods can be expressed, and, indeed, can be generalised within a relational theory of datatypes. The two methods to which we refer are the so-called \Bird-Meertens formalism" (see 22]) and the \Dijkstra-Feijen calculus"… (More)

In this paper we demonstrate that the basic rules and calculational techniques used in two extensively documented program derivation methods can be expressed, and, indeed, can be generalised within a relational theory of datatypes. The two methods to which we refer are the so-called " Bird-Meertens formalism " for the construction of functional programs and… (More)

The study of inductive and coinductive types (like nite lists and streams, respectively) is usually conducted within the framework of category theory, which to all intents and purposes is a theory of sets and functions between sets. Allegory theory, an extension of category theory due to Freyd, is better suited to modelling relations between sets as opposed… (More)