Every GAP object has a type. The type of an object is the information which is used to decide whether an operation is admissible or possible with that object as an argument, and if so, how it is to be performed (see Chapter Method Selection in ``Programming in GAP'').
For example, the types determine whether two objects can be multiplied and what function is called to compute the product. Analogously, the type of an object determines whether and how the size of the object can be computed. It is sometimes useful in discussing the type system, to identify types with the set of objects that have this type. Partial types can then also be regarded as sets, such that any type is the intersection of its parts.
The type of an object consists of two main parts, which describe different aspects of the object.
The family determines the relation of the object to other objects. For example, all permutations form a family. Another family consists of all collections of permutations, this family contains the set of permutation groups as a subset. A third family consists of all rational functions with coefficients in a certain family.
The other part of a type is a collection of filters (actually stored as a bit-list indicating, from the complete set of possible filters, which are included in this particular type). These filters are all treated equally by the method selection, but, from the viewpoint of their creation and use, they can be divided (with a small number of unimportant exceptions) into categories, representations, attribute testers and properties. Each of these is described in more detail below.
This chapter does not describe how types and their constituent parts can be created. Information about this topic can be found in ``Programming in GAP'' in Section Creating New Objects.)
Note: Detailed understanding of the type system is not required to use GAP. It can be helpful, however, to understand how things work and why GAP behaves the way it does.
A discussion of the type system can be found in BreuerLinton98.
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GAP 4 manual