  We determine the computational complexity of the Hahn-Banach Extension
Theorem. To do so, we investigate some basic connections between reverse
mathematics and computable analysis. In particular, we use Weak Konig's Lemma
within the framework of computable analysis to classify incomputable functions
of low complexity. By defining the multi-valued function Sep and a natural
notion of reducibility for multi-valued functions, we obtain a computational
counterpart of the subsystem of second order arithmetic WKL_0. We study
analogies and differences between WKL_0 and the class of Sep-computable
multi-valued functions. Extending work of Brattka, we show that a natural
multi-valued function associated with the Hahn-Banach Extension Theorem is
Sep-complete.
