Chapter 6
Generalization

Aims

To show how functions are used as arguments of other functions.
To show how code may be polymorphic, so that a single definition can be applicable to a collection of types.
To show that the styles of definition pointed to in Chapter 4 can be realised by higher-order polymorphic functions.
To discuss from the design and software engineering point of view the consequences of functions being higher-order and polymorphic.

Issues

Re-visiting earlier examples

The approach of the book is bottom-up, so on introducing more powerful techniques we re-visit earlier examples to see how their definitions might use the new techniques. This is worth emphasising both for the examples in the text and for any exercises or examples introduced earlier by the teacher.

Properties

It is worth spending some time exploring the idea that a function of type

    * -> bool

represents a property of objects of the type *; it is something that it is harder to get across than might first be thought. This makes filter somewhat less straightforward than map.

Generalising

The example of generalisation, given in Section 6.5, can be applied in many other circumstances. Again, it is useful to apply it to functions which the students have seen previously.

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