We demonstrate that in the context of statically-typed
purely-functional lambda calculi without recursion, unchecked exceptions
(e.g., SML exceptions) can be strictly more powerful than call/cc.  More
precisely, we prove that a natural extension of the simply-typed lambda
calculus with unchecked exceptions is strictly more powerful than all
known sound extensions of Girard's F-omega (a superset of the
simply-typed lambda calculus) with call/cc.

    This result is established by showing that the first language is
Turing complete while the later languages permit only a subset of the
recursive functions to be written.  We show that our natural extension
of the simply-typed lambda calculus with unchecked exceptions is Turing
complete by reducing the untyped lambda calculus to it by means of a
novel method for simulating recursive types using
unchecked-exception-returning functions.  The result concerning
extensions of F-omega with call/cc stems from previous work of the
author and Robert Harper.