Higher-Order Narrowing with De nitional Trees

Functional logic languages with a sound and complete opera tional 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 nar rowing strategy for rst order functional logic programs due to its opti mality properties w r t the length of derivations and the number of com puted solutions In this paper we extend the needed narrowing strategy to higher order functions and terms as data structures By the use of def initional trees our strategy computes only incomparable solutions Thus it is the rst calculus for higher order functional logic programming which provides for such an optimality result Since we allow higher order logical variables denoting terms applications go beyond current functional and logic programming languages