@INPROCEEDINGS{HanusPrehofer96RTA,
author = "Hanus, M. and Prehofer, C.",
title = "Higher-Order Narrowing with Definitional Trees",
year = "1996",
pages = "138-152",
publisher = "Springer LNCS 1103",
booktitle = "Proc.\ Seventh International Conference on
Rewriting Techniques and Applications (RTA'96)",
abstract = {
Functional logic languages with a sound and complete operational
semantics are mainly based on narrowing. Due to the huge search
space of simple narrowing, steadily improved narrowing strategies have been
developed in the past. Needed narrowing is  currently the best
narrowing strategy for first-order functional logic programs
due to its optimality properties w.r.t.\ the length of derivations
and the number of computed solutions. In this paper, we extend
the needed narrowing strategy to higher-order functions
and $\lambda$-terms as data structures.
By the use of definitional trees, our strategy computes only
incomparable solutions. Thus, it is the first calculus
for higher-order functional logic programming which provides
for such an optimality result.
Since we allow higher-order logical variables denoting
$\lambda$-terms, applications go beyond current functional
and logic programming languages.
}
}