for recursion.

A derivation starts with an initial tree, which is combined with further trees via either substitution or adjunction. Substitution replaces a frontier node with an initial tree whose root node has the same label as the leaf for which it is substituted. Adjunction inserts an auxiliary tree--at either a frontier or an internal node--whose root and foot labels both match the label of the node whereat it adjoins. Adjunction can thus have the effect of inserting an auxiliary tree into the center of another tree, which operation