GAP is eager to maintain information that it has gathered about an object, possibly by lengthy calculations. The most important mechanism for information maintenance is the automatic storage and look-up that takes place for attributes; and this was already mentioned in section Attributes in the tutorial. In this chapter we will describe further mechanisms that allow storage of results that are not values of attributes.
The idea which is common to all sections is that certain operations, which are not themselves attributes, have an attribute associated with them. To automatically delegate tasks to the attribute, GAP knows, in addition to the operation and the attributes also an ordinary function, which is ``wrapped around'' the other two. This ``wrapper function'' is called by the user and decides whether to call the operation or the attribute or possibly both. The whole function-operation-attribute triple (or FOA triple) is set up by a single GAP command which writes the wrapper function and already installs some methods, e.g., for the attribute to fall back on the operation. The idea is then that subsequent methods, which perform the actual computation, are installed only for the operation, whereas the wrapper function remains unaltered, and in general no additional methods for the attribute are required either.
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GAP 4 manual