**Problem 2.1** The notion of constituent presupposes that sentences
have hierarchical structure. In a phrase structure representation of a
linguistic expression, a constituent is defined as a sub-expression
dominated by a single node. The substitution test works because the
pro-form substituted is itself a constituent and so must be dominated by a
single node in the tree where it appears. It follows that in a successful
substitution, the replaced expression will also be dominated by a single
node. The substitution operation defined in chapter one is precisely the
substitution of a tree rooted in some node labeled X for another node
labeled X with no children in a different tree. The substitution test will
be successful when it can be modeled as cutting out a subtree leaving
behind its root (labeled X) and then substituting the a tree rooted in X
with the pro-form as its leaf for that now daughterless root.