NARROWER: A New Algorithm for Unification and Its Application to Logic Programming

  title={NARROWER: A New Algorithm for Unification and Its Application to Logic Programming},
  author={Pierre R{\'e}ty and Claude Kirchner and H{\'e}l{\`e}ne Kirchner and Pierre Lescanne},

Narrowing with Built-In Theories

This paper shows how narrowing modulo equality theories may considerably increase the efficiency of the narrowing process.

A note on a canonical theory with undecidable unification and matching problem

  • A. Bockmayr
  • Mathematics
    Journal of Automated Reasoning
  • 2004
A natural example of a canonical theory with undecidable unification and matching problem is presented.

Compilation of Narrowing

In the following, a compilation technique for narrowing based on partial evaluation of the axioms of an algebraic program is shown.

Some Termination Criteria for Narrowing and E-Narrowing

Some restrictions on T are described which ensure that there are no infinite narrowing derivations using T when T is used to perform E-narrowing modulo a set of simple linear permutative equations E.

Narrowing Techniques Applied to Idempotent Unification

A complete unification algorithm for idempotent functions is presented and an improvement of the universal algorithm is shown that is derived from the universal unification algorithm, which is based on the narrowing process.

Nondeterministic algebraic specifications

This chapter will show precisely how to generalize the model classes and the specification language for algebraic specifications to the case of nondeterminism. Particular emphasis is laid on a

Unification in Conditional Equational Theories

  • H. Hussmann
  • Computer Science
    European Conference on Computer Algebra
  • 1985
A complete unification procedure for confluent conditional term rewriting systems is presented which is a generalization of the narrowing process described by Fay and Hullot, and has been built into the RAP system.

Improving Basic Narrowing Techniques

It is shown that the new and complete method based on narrowing for solving equations in equational theories is more efficient than the existing methods in many cases, and for that establish commutation properties on the narrowing.

An Interpreter with Lazy Evaluation for Prolog with Functions

If Horn clause logic is enriched with functions that are specified via (conditional) equations, the well-known SLD-resolution algorithm has to be extended by a semantic unification. An implementation

An Optimal Narrowing Strategy for General Canonical Systems

A new narrowing strategy is introduced, called LSE narrowing, which is complete for arbitrary canonical systems and optimal in the sense that two different L SE narrowing derivations cannot generate the same narrowing substitution.



A General Inductive Completion Algorithm and Application to Abstract Data Types

A general inductive completion algorithm is given, which turns out to be a well-suited tool to build up specifications by successive enrichments and allows verifying consistency of a specification or proving theorems in its initial algebra without using explicit induction.

Complete Sets of Unifiers and Matchers in Equational Theories

It is proved the nonexistence of complete sets of minimal unifiers (and matchers) in some equational theories, even regular, in order to present unification and matching problems.

Canonical Forms and Unification

The relations between narrowing and unification are studied and a new version of Fay's algorithm is given and it is shown how to eliminate many redundancies in this algorithm and give a sufficient condition for the termination of the algorithm.

An Introduction to OBJ 3

OBJ 3 is a new implementation of the OBJ language, with a new efficient operational semantics based on order-sorted term-rewriting, and is a wide-spectrum language that elegantly integrates coding, specification and design into a single framework.

Schematization of Infinite Sets of Rewrite Rules. Application to the Divergence of Completion Processes

A formalism to deal with the problem of divergence is proposed, namely the definition of melta-rules (rules with meta-variables), together with the derived notions of met-rewriting and meta-narrowing, to ensure that the set of meta-rules and the infinite set of rules can be used equivalently.

Computer experiments with the REVE term rewriting system generator

A term rewriting system generator called REVE is described which uses an incremental termination method based on recursive decomposition ordering which constructs the termination proof step by step from the presentation of the set of equations and which requires little knowledge of termination methods from the user.

Completion of a Set of Rules Modulo a Set of Equations

The Church–Rosser property is proved decidable for a very general reduction relation which may take into account the left-linearity of rules for efficiency reasons, under the only assumption of existence of a complete and finite unification algorithm for the underlying equational theory, whose congruence classes are assumed to be finite.

Equations and rewrite rules: a survey