  Wald's formula for black hole entropy, applied to extremal black holes, leads
to the entropy function formalism. We manipulate the entropy computed this way
to express it as the logarithm of the ground state degeneracy of a dual quantum
mechanical system. This provides a natural definition of the extremal black
hole entropy in the full quantum theory. Our analysis also clarifies the
relationship between the entropy function formalism and the Euclidean action
formalism.
