ABSTRACT
Our definition of a hypersubstitution, from Section 14.3, gave us a mapping which took operation symbols of one type or language to terms of that same type. Now we generalize this definition too, to include mappings from operation symbols of one language into terms of a second language. We also consider the corresponding tree transformations. We shall prove that the set of all tree transformations which are defined by hypersubstitutions of a given type forms a monoid with respect to the composition of binary relations, and that this monoid is isomorphic to the monoid of all hypersubstitutions of this type. We characterize transitivity, reflexivity and symmetry of tree transformations by properties of the corresponding hypersubstitutions. The results will be illustrated for type (2), with E = E2 = {f}.
