  Dendric shift spaces simultaneously generalize codings of regular interval
exchanges and episturmian shift spaces, themselves both generalizations of
Sturmian words. One of the key properties enforced by dendricity is the Return
Theorem. In this paper, we prove its converse, providing the following natural
algebraic perspective on dendricity: A minimal shift space is dendric if and
only if every set of return words is a basis of the free group over the
alphabet.
