possibly be simply-typeable? It turns out that this can't be done.
See the works cited by Oleg for details.
+Because lists are (in effect) a generalization of the Church numbers,
+computing the tail of a list is likewise beyond the reach of the
+simply-typed lambda calculus.
+
+This result is surprising. It illustrates how recursion is built into
+the structure of the Church numbers (and lists). Most importantly for
+the discussion of the simply-typed lambda calculus, it demonstrates
+that even fairly basic recursive computations are beyond the reach of
+a simply-typed system.