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Completeness of Combinations of Constructor Systems
 Journal of Symbolic Computation
, 1993
"... this paper we show that it is sufficient to impose the constructor discipline for obtaining the modularity of completeness. This result is a simple consequence of a quite powerful divide and conquer technique for establishing completeness of such constructor systems. Our approach is not limited to s ..."
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Cited by 31 (2 self)
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this paper we show that it is sufficient to impose the constructor discipline for obtaining the modularity of completeness. This result is a simple consequence of a quite powerful divide and conquer technique for establishing completeness of such constructor systems. Our approach is not limited to systems which are composed of disjoint parts. The importance of our method is that we may decompose a given constructor system into parts which possibly share function symbols and rewrite rules in order to infer completeness. We obtain a similar technique for semicompleteness, i.e. the combination of confluence and weak normalisation. 1. Introduction
Strongly Sequential and Inductively Sequential Term Rewriting Systems
, 1998
"... 1 Introduction Michael Hanus Salvador Lucas Aart Middeldorp Strongly sequential and inductively sequential term rewriting systems hanus@informatik.rwthaachen.de slucas@dsic.upv.es ami@score.is.tsukuba.ac.jp first(0,x) [] first(s(x),y::z) y::first(x,z) first x 1 0 s(x) x 2 first x 1 x 2 first 0 x ..."
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Cited by 28 (12 self)
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1 Introduction Michael Hanus Salvador Lucas Aart Middeldorp Strongly sequential and inductively sequential term rewriting systems hanus@informatik.rwthaachen.de slucas@dsic.upv.es ami@score.is.tsukuba.ac.jp first(0,x) [] first(s(x),y::z) y::first(x,z) first x 1 0 s(x) x 2 first x 1 x 2 first 0 x 2 first s x x 2 [] first s x y z y first x z first inductively sequential outermostneeded strategy needed rewriting needed Definitional trees inductively sequential inductively sequential index trees forwardbranching index trees matching dags outermostneeded strategy index reduction Informatik II, RWTH Aachen, D52056 Aachen, Germany, . Work partially supported by DFG (under grant Ha 2457/11) and Acci'on Integrada. DSIC, U.P. de Valencia, Camino de la Vera s/n, Apdo. 22012, E46071 Valencia, Spain, . Work partially supported by EECHCM grant ERBCHRXCT940624, Bancaixa (BancajaEuropa grant), Acci'on Integrada (HA19970073) and CICYT (under grant TIC 950433C0303). Institute of Informa...
Relating Innermost, Weak, Uniform and Modular Termination of Term Rewriting Systems
, 1993
"... We investigate restricted termination and confluence properties of term rewriting systems, in particular weak termination and innermost termination, and their interrelation. New criteria are provided which are sufficient for the equivalence of innermost / weak termination and uniform termination of ..."
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Cited by 28 (5 self)
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We investigate restricted termination and confluence properties of term rewriting systems, in particular weak termination and innermost termination, and their interrelation. New criteria are provided which are sufficient for the equivalence of innermost / weak termination and uniform termination of term rewriting systems. These criteria provide interesting possibilities to infer completeness, i.e. termination plus confluence, from restricted termination and confluence properties. Using these basic results we are also able to prove some new results about modular termination of rewriting. In particular, we show that termination is modular for some classes of innermost terminating and locally confluent term rewriting systems, namely for nonoverlapping and even for overlay systems. As an easy consequence this latter result also entails a simplified proof of the fact that completeness is a decomposable property of socalled constructor systems. Furthermore we show how to obtain similar re...
Lazy rewriting on eager machinery
 ACM Transactions on Programming Languages and Systems
, 2000
"... The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives a ..."
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Cited by 23 (1 self)
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The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives as an implementation of eager rewriting. 1
Adaptive Pattern Matching
, 1992
"... Pattern matching is an important operation used in many applications such as functional programming, rewriting and rulebased expert systems. By preprocessing the patterns into a DFAlike automaton, we can rapidly select the matching pattern(s) in a single scan of the relevant portions of the inp ..."
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Cited by 22 (5 self)
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Pattern matching is an important operation used in many applications such as functional programming, rewriting and rulebased expert systems. By preprocessing the patterns into a DFAlike automaton, we can rapidly select the matching pattern(s) in a single scan of the relevant portions of the input term. This automaton is typically based on lefttoright traversal of the patterns. By adapting the traversal order to suit the set of input patterns, it is possible to considerably reduce the space and matching time requirements of the automaton.
Open Problems in Rewriting
 Proceeding of the Fifth International Conference on Rewriting Techniques and Application (Montreal, Canada), LNCS 690
, 1991
"... Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27 ..."
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Cited by 19 (2 self)
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Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27, 28, 44, 56,57,76, 82, 81#; one edited collection of papers #1#; four monographs #3, 12,55,65#; and seven books #four of them still in progress# #8,9, 35, 54, 60,75, 84#. To encourage and stimulate continued progress in this area, wehave collected #with the help of colleagues# a number of problems that appear to us to be of interest and regarding whichwe do not know the answer. Questions on rewriting and other equational paradigms have been included; manyhave not aged su#ciently to be accorded the appellation #open problem". Wehave limited ourselves to theoretical questions, though there are certainly many additional interesting questions relating to applications and implementation
Programming with Equations, Subsets, and Relations
 Proceedings of NACLP89
, 1989
"... We discuss the declarative and computational issues in combining equational, subset, and relational assertions in a logic programming language. The novel feature in this work is the subset assertion, whose interactions with equational and relational assertions are discussed in this paper. The semant ..."
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Cited by 18 (6 self)
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We discuss the declarative and computational issues in combining equational, subset, and relational assertions in a logic programming language. The novel feature in this work is the subset assertion, whose interactions with equational and relational assertions are discussed in this paper. The semantics of subset assertions incorporate a collect all capability, which is expressed formally by the completion of the program. When used in conjunction with equational assertions, subset assertions serve to define setvalued functions, and the resulting paradigm is called subsetequational programming. We also present the class of stratified subsetequational programs for formalizing the class of closure functions, which are useful in defining various transitiveclosure sets. The declarative and operational semantics of simple and stratified subsetequational programs are the main focus of this paper. The operational semantics of closures is based on memotables (or extension tables). When sub...
Set Functions for Functional Logic Programming
, 2009
"... We propose a novel approach to encapsulate nondeterministic computations in functional logic programs. Our approach is based on set functions that return the set of all the results of a corresponding ordinary operation. A characteristic feature of our approach is the complete separation between a u ..."
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Cited by 13 (13 self)
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We propose a novel approach to encapsulate nondeterministic computations in functional logic programs. Our approach is based on set functions that return the set of all the results of a corresponding ordinary operation. A characteristic feature of our approach is the complete separation between a usuallynondeterministic operation and its possiblynondeterministic arguments. This separation leads to the first provably orderindependent approach to computing the set of values of nondeterministic expressions. The proof is provided within the framework of graph rewriting in constructorbased systems. We propose an abstract implementation of our approach and prove its independence of the order of evaluation. Our approach solves easily and naturally problems mishandled by current implementations of functional logic languages.
The ruleml family of web rule languages
 In 4th Int. Workshop on Principles and Practice of Semantic Web Reasoning
, 2006
"... harold.boley AT nrc DOT gc DOT ca Abstract. The RuleML family of Web rule languages contains derivation (deduction) rule languages, which themselves have a webized Datalog language as their inner core. Datalog RuleML’s atomic formulas can be (un)keyed and (un)ordered. Inheriting the Datalog features ..."
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Cited by 12 (5 self)
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harold.boley AT nrc DOT gc DOT ca Abstract. The RuleML family of Web rule languages contains derivation (deduction) rule languages, which themselves have a webized Datalog language as their inner core. Datalog RuleML’s atomic formulas can be (un)keyed and (un)ordered. Inheriting the Datalog features, Hornlog RuleML adds functional expressions as terms. In Hornlog with equality, such uninterpreted (constructorlike) functions are complemented by interpreted (equationdefined) functions. These are described by further orthogonal dimensions “single vs. setvalued ” and “first vs. higherorder”. Combined modal logics apply special relations as operators to atoms with an uninterpreted relation, complementing the usual interpreted ones. 1