B - Historical Background

Summary

Chapter 2 covers desirable model properties and shows how categorical data types satisfy these properties. I developed this view of model properties during 1992 (an early survey of models using them appeared as [179]) and extended and refined it over the next two years. A preliminary version of Chapter 4 was given as a talk at the Workshop on Programming Tools for Parallel Machines at Alimini, Italy, in the summer of 1993.

Chapter 3 is based on Valiant's work which can be found in a series of papers [197,199, 200]. The results on emulation on SIMD architectures appears in [178], although they seem to have been widely understood before that.

The construction of lists as a categorical data type in Chapter 5 follows the general presentation in Grant Malcolm's thesis [138]. An alternative presentation that emphasises the role of adjunctions in the CDT construction is due to Mike Spivey [189]. Much of the category theory on which this work depends was done in the Sixties [25]. The demonstration that lists can be efficiently implemented comes from [178].

The material on software development in Chapter 6 is a selection from a much larger range of material developed in what has become known as the Bird-Meertens formalism [17,31–35]. The material on almost-homomorphisms (and the name) come from work by Murray Cole [55].

The development of operations to compute recurrences (Chapter 7) and the cost calculus for lists (Chapter 8) is joint work by myself and Wentong Cai during 1992, when he was a postdoctoral fellow.