Structures considered

The kind of structures that I will be looking at will consist of the following elements.

• A set of nodes, all storing the same type of data
• A set of directions, grouped into levels, so that only directions in a lower level are accessible from a particular level.
• A collection of relations that hold between directions of a particular level. These include inverses and commutativity between directions.

It is important to emphasise that all nodes will contain the same type of data. This is not really a restriction, since the type of data will be user defined, and we could define an item of data that contains more than one type. For example, we could create a datatype that can store either an integer or real number.