A canonical cover for F (a set of functional dependencies on a relation scheme) is a set of dependencies such that F logically implies all dependencies in , and logically implies all dependencies in F.
The set has two important properties:
- No functional dependency in contains an extraneous attribute.
- Each left side of a functional dependency in is unique. That is, there are no two dependencies and in such that .
A canonical cover is not unique for a given set of functional dependencies, therefore one set F can have multiple covers .
Algorithm for computing a canonical cover
- Use the union rule to replace any dependencies in of the form and with ..
- Find a functional dependency in with an extraneous attribute and delete it from
- ... until does not change