Chapter 9
Algebraic types

Aims

• To present the Miranda algebraic type mechanism, by means of a graduated series of examples.
• To compare algebraic types with other Miranda types, including tuples and synonym declarations.
• To explain recursive definitions over algebraic types, both by structural recursion and by more general forms of recursion.
• To present case studies of polymorphic algebraic types, which are strong candidates for re-use.
• To examine how data type definitions can be designed step-by-step; the examples introduced here are taken up in subsequent chapters.
• To show how to reason about definitions over algebraic types.

Issues

Running examples

The simulation and calculator examples are taken up in subsequent chapters; it would be quite possible to cover the examples in one session, but only later in the course.

Exercises

A number of exercises in the chapter are open-ended, calling as they do for the design of data types to model various situations. These can form a focus for a small-group discussion, in which students are encouraged to compare their designs with others, and to evaluate their suitabilty for purpose. The implicit message of such exercises is important: there is more to the programming process than sitting in front of a terminal, coding.

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