The term "binding" is often used when talking about the process of unification. A set of entities are assigned values at once, but only if values for each entity can be found. The destination (left-hand side) entities cannot be assigned if an insufficient set of source (right-hand side) values are found.

If you understand databases, you can think of it like a transaction: if any of the portions of the database insertion fails, the whole transaction is rolled back as if it was never attempted.

You may want to look at my CPAN module Data::Binder which provides a similar, simplistic method of maintaining a set of entities, which can be bound against each other.