However, once it is known that at some node, no further adjunctions are possible, then we might just as well unify the bottom- and top parts of that node immediately. This may be useful, in cases where this unification fails -- in that case we may abandon a search path without a solution much earlier. Thus, it is possible to implement the predicate in an incremental fashion.
The incremental unification of top and bottom features is easily implemented. Firstly, the predicate is defined in such a way that completed nodes are not penetrated: these nodes are already unified in a previous cycle. Furthermore, this predicate is now called when partial trees are completed; that is, after a substitution, and after an adjunction.
The predicate is defined as follows.
The predicate is changed as follows: