A Higher-Order Demand-Driven Narrowing Calculus with Definitional Trees

We generalize the Constructor-based ReWriting Logic CRWL to the setting of the simply typed λ-calculus, where theories are presented by conditional overlapping fully extended pattern rewrite systems. We claim that this logic is useful for higher-order functional-logic programming, and propose a Higher-Order Lazy Narrowing calculus HOLNDT for answering joinability and reducibility queries, in which a variant of Definitional Trees is used to efficiently control the demand-driven narrowing strategy. The calculus HOLNDT is shown to be sound and strongly complete with respect to this higher-order conditional rewriting logic.