  The notion of a real-valued function is central to mathematics, computer
science, and many other scientific fields. Despite this importance, there are
hardly any positive results on decision procedures for predicate logical
theories that reason about real-valued functions. This paper defines a
first-order predicate language for reasoning about multi-dimensional smooth
real-valued functions and their derivatives, and demonstrates that - despite
the obvious undecidability barriers - certain positive decidability results for
such a language are indeed possible.
