So far we have discussed the properties that a model of parallel computation ought to have and have claimed that models built from categorical data types have these properties. In this chapter we show how to build a simple but useful categorical data type, the type of join or concatenation lists, and illustrate its use as a model. We show how such a model satisfies the requirements, although some of the details are postponed to later chapters.

The language we construct for programming with lists is not different from other parallel list languages in major ways in the sense that most of the list operations are familiar maps, reductions, and prefixes. The differences are in the infrastructure that comes from the categorical data type construction: an equational transformation system, a deeper view of what operations on lists are, and a style of program development. When we develop more complex types, the construction suggests new operations that are not obvious from first principles.

For the next few chapters we concentrate on aspects of parallel computation on lists. We describe the categorical data type construction in more detail in Chapter 9 and move on to more complex types. The next few sections explain how to build lists in a categorical setting. They may be skipped by those who are not interested in the construction itself. The results of the construction and its implications are summarised in Section 5.5.