Lazy Unification Algorithms for Canonical Rewrite Systems

Martelli, Alberto; Rossi, Gianfranco; Moiso, Corrado

doi:10.1016/b978-0-12-046371-8.50014-6

Cited by 9 publications

(10 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Section 3) has an infinite search space. The same is true for other lazy unification calculi [11,22] or lazy narrowing calculi [23,27]. Moreover, in a sequential implementation of lazy narrowing by backtracking [14] only an infinite set of specialized solutions would be computed without ever trying the second V-rule.…”

Section: Examplesmentioning

confidence: 84%

“…Lazy unification is very similar to lazy narrowing but manipulates sets of equations rather than terms. It has been proved to be complete for canonical term rewriting systems w.r.t, standard semantics [6,22].…”

Section: Computing In Equational Theoriesmentioning

confidence: 99%

“…In order to avoid this problem of eager variable eliminalion (see [11]), we perform only a partial binding which is also called "root imitation" in [11]. At first sight our lazy unification calculus has many similarities with the lazy unification rules presented in [6,11,22,25]. This is not accidental since these systems have inspired us.…”

Section: A Calculus For Lazy Unificationmentioning

confidence: 99%

“…This will lead to the following two derivations (the subterms manipulated in the next step are underlined): There are many proposals for such lazy unification strategies. For instanc% Martelli et al [22] have proposed a lazy unification algorithm for confluent and terminating equational axioms. Due to the confluence requirement, equations are only applied in one direction.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Lazy unification with simplification

Hanus

1994

Programming Languages and Systems — ESOP '94

View full text Add to dashboard Cite

Unification in the presence of an equational theory is an important problem in theorem-proving and in the integration of functional and logic programming languages. This paper presents an improvement of the proposed lazy unification methods by incorporating simplification into the unification process. Since simplification is a deterministic computation process, more efficient unification algorithms can be achieved. Moreover, simplification reduces the search space so that in some case infinite search spaces axe reduced to finite ones. We show soundness and completeness of our method for equational theories represented by ground confluent and terminating rewrite systems which is a reasonable class w.r.t, functional logic programming.

show abstract

Section: Examplesmentioning

confidence: 84%

Section: Computing In Equational Theoriesmentioning

confidence: 99%

Section: A Calculus For Lazy Unificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lazy unification with simplification

Hanus

1994

Programming Languages and Systems — ESOP '94

View full text Add to dashboard Cite

show abstract

“…"an algorithm which takes as its input a pair of terms (s,t) and a theory E E and generates a complete set of unifiers for <s=t> E " [22]), such as those based on narrowing or on some different rewriting technique (e.g. [17]). According to these approaches, the theory at hand should be represented as a canonical rewrite system.…”

Section: The Set Unification Problemmentioning

confidence: 99%

Embedding finite sets in a logic programming language

Dovier

Omodeo

Pontelli

et al. 1993

Extensions of Logic Programming

View full text Add to dashboard Cite

Abstract.A way of introducing simple (finite) set designations and operations as first-class objects of an (unrestricted) logic programming language is discussed from both the declarative and the operational semantics viewpoint. First, special set terms are added to definite Horn clause logic and an extended Herbrand Universe based on an axiomatic characterization of the kind of sets we are dealing with is defined accordingly. Moreover, distinguished predicates representing set membership and equality are added to the base language along with their negative counterparts (π and ). A new unification algorithm which can cope with set terms is developed and proved to terminate. Usual SLD resolution is modified so as to incorporate the new unification algorithm and to properly manage the distinguished predicates for set operations (in particular, conjunctions of atoms containing π and are dealt with as constraints, first reduced to a canonical form through a suitable canonization algorithm). Finally, the application of the resulting language to the definition of Restricted Universal Quantifiers is discussed.

show abstract

A Deterministic Lazy Narrowing Calculus

Middeldorp

Okui

1998

Journal of Symbolic Computation

View full text Add to dashboard Cite

In this paper we study the non-determinism between the inference rules of the lazy narrowing calculus lnc (Middeldorp et al., 1996, Theoret. Comput. Sci., 167, 95-130). We show that all non-determinism can be removed without losing the important completeness property by restricting the underlying term rewriting systems to left-linear confluent constructor systems and interpreting equality as strict equality. For the subclass of orthogonal constructor systems the resulting narrowing calculus is shown to have the nice property that solutions computed by different derivations starting from the same goal are incomparable. † A preliminary version of this paper appeared in the

show abstract

Lazy Unification Algorithms for Canonical Rewrite Systems

Cited by 9 publications

References 9 publications

Lazy unification with simplification

Lazy unification with simplification

Embedding finite sets in a logic programming language

A Deterministic Lazy Narrowing Calculus

Contact Info

Product

Resources

About