abstract = "Recursive functions are a compact and expressive way
to solve challenging problems in terms of local
processing. These properties have made recursive
functions a popular target for genetic programming.
Unfortunately, the evolution of substantial recursive
programs has proved difficult. One cause of this
problem is the difficulty in evolving both correct base
and recursive cases using just information derived from
running test cases. In this work we describe a
framework that exploits additional information in the
form of partial call-trees. Such trees - a by-product
of deriving input-output cases by hand - guides the
search process by allowing the separate evolution of
the recursive case. We show that the speed of evolution
of recursive functions is significantly enhanced by the
use of partial call-trees and demonstrate application
of the technique in the derivation of functions for a
suite of numerical functions.",