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Abstract: We introduce several approaches for solving higherorder equational problems by higher-order narrowing and give first completeness results. The results apply to higher-order functional-logic programming languages and to higher-order unification modulo a higher-order equational theory. We lift the general notion of first-order narrowing to so-called higher-order patterns and argue that the full higher-order case is problematic. Integrating narrowing into unification, called lazy narrowing, can... (Update)
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BibTeX entry: (Update)
Christian Prehofer. Higher-order narrowing. In Proc. Ninth Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, July 1994. http://citeseer.ist.psu.edu/article/prehofer94higherorder.html More
@inproceedings{ prehofer94higherorder,
author = "Christian Prehofer",
title = "Higher-order Narrowing",
booktitle = "Proceedings of the Ninth Annual {IEEE} Symposium on Logic in Computer Science",
publisher = "IEEE Computer Society Press",
address = "Paris, France",
pages = "507--516",
year = "1994",
url = "citeseer.ist.psu.edu/article/prehofer94higherorder.html" }
Citations (may not include all citations):788 Rewrite systems - Dershowitz, Jouannaud - 1990
251 A logic programming language with lambda-abstraction - Miller - 1991
210 Logic programming in the LF logical framework - Pfenning - 1991
166 An overview of -Prolog (context) - Nadathur, Miller - 1988
137 Introduction to Combinators and -Calculus (context) - Hindley, Seldin - 1986
126 Higher-order critical pairs (context) - Nipkow - 1991
112 The Art of Prolog Advanced Programming Techniques (context) - Sterling - 1986
87 Narrowing as the operational semantics of functional languag.. (context) - Reddy - 1985
56 Higher-order unification revisited: Complete sets of transfo.. (context) - Snyder, Gallier - 1989
46 Orthogonal higher-order rewrite systems are confluent (context) - Nipkow - 1993
41 HiLog: A First-Order Semantics for Higher-Order Logic Progra.. (context) - Chen, Kifer et al. - 1989
36 Unification of simply typed lambdaterms as logic programming (context) - Miller - 1991
30 Combinatory Reduction Systems (context) - Klop - 1980
27 Solving equations in abstract algebras: A rule-based survey .. (context) - Jouannaud, Kirchner - 1991
23 its Syntax and Semantics (context) - Barendregt, Calculus - 1984
22 Cambridge Tracts in Theoretical Computer Science (context) - Wolfram, Theory - 1993
19 Confluence and superdevelopments (context) - van Raamsdonk - 1993
19 Termination proofs for higher order rewrite systems - Pol - 1994
18 Canonical forms and unification (context) - Hullot - 1980
17 Decidable higher-order unification problems - Prehofer - 1994
17 Lazy unification with simplification - Hanus - 1994
14 A Theoretical Framework for Reasoning about Program Construc.. (context) - Lor'ia-S'aenz - 1993
14 The integration of functions into logic programming: A surve.. - Hanus - 1994
14 Higher-order logic programming as constraint logic programmi.. - Michaylov, Pfenning - 1993
12 Higher-order equational logic programming (context) - Qian - 1994
11 Lazy unification algorithms for canonical rewrite systems (context) - Martelli, Rossi et al. - 1989
11 Higher order E-unification (context) - Snyder - 1990
8 IDEAL: An ideal deductive applicative language (context) - Bosco, Giovannetti - 1986
6 The Implementation of Functional Logic Languages (context) - Lock - 1993
6 HIFUNLOG: Logic programming with higher-order relational fun.. (context) - Sheng - 1990
3 matching as a tool for automated theorem proving (context) - Curien - 1993
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