Typed Higher-Order Narrowing without Higher-Order Strategies
نویسندگان
چکیده
We describe a new approach to higher-order narrowing computations in a class of systems suitable for functional logic programming. Our approach is based on a translation of these systems into ordinary (£rst-order) rewrite systems and the subsequent application of conventional narrowing strategies. Our translation is an adaptation to narrowing of Warren’s translation, but unlike similar previous work, we preserve static type information, which has a dramatic effect on the size of the narrowing space. Our approach supports sound, complete, and ef£cient higher-order narrowing computations in classes of systems larger than those previously proposed.
منابع مشابه
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 wh...
متن کاملHigher-Order Lazy Narrowing Calculus: A Solver for Higher-Order Equations
This paper introduces a higher-order lazy narrowing calculus (HOLN for short) that solves higher-order equations over the domain of simply typed λ-terms. HOLN is an extension and refinement of Prehofer’s higher-order narrowing calculus LN using the techniques developed in the refinement of a first-order lazy narrowing calculus LNC. HOLN is defined to deal with both unoriented and oriented equat...
متن کاملAlgebraic Semantics for Higher-order Functional-Logic Programming
In this paper we give a semantics of higher-order functional-logic programming in the framework of typed universal algebra. The functional-logic language concerned here is an applicative term rewriting system in which there is no lambda abstraction mechanism. Therefore ordinary rst-order narrowing can be used to solve higher-order query. The soundness and completeness of narrowing for both the ...
متن کاملA Combinatory Logic Approach to Higher-Order E-Unification
Let E be a rst-order equational theory. A translation of typed higher-order E-uniication problems into a typed combinatory logic framework is presented and justiied. The case in which E admits presentation as a convergent term rewriting system is treated in detail: in this situation, a modiication of ordinary narrowing is shown to be a complete method for enumerating higher-order E-uniiers. In ...
متن کاملA Logic Programming Approach to Implementing Higher-Order Term Rewriting
Term rewriting has proven to be an important technique in theorem proving. In this paper, we illustrate that rewrite systems and strategies for higher-order term rewriting, which includes the usual notion of rst-order rewriting, can be naturally speciied and implemented in a higher-order logic programming language. We adopt a notion of higher-order rewrite system which uses the simply typed-cal...
متن کامل