Modular term rewriting systems and the termination

Kurihara, Masahito; Kaji, Ikuo

doi:10.1016/0020-0190(90)90221-i

Cited by 18 publications

(4 citation statements)

References 9 publications

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“…Middeldorp [10] showed that the property of having unique normal forms is modular for general tenn rewriting systems. An interesting alternative approach to modularity is explored in Kurihara and Kaji [7]. Middeldorp [12,13,14) extended the above results to conditional term rewriting systems.…”

Section: \1 = { F(o Lx)-7f(x X X)} { G(x Y) -7 Xmentioning

confidence: 99%

Completeness of combinations of constructor systems

Middeldorp¹,

Toyama

1991

Rewriting Techniques and Applications

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A term rewriting system is called complete if it is both confluent and strongly normalizing. Barendregt and Klop showed that the disjoint union of complete tenn rewriting systems does not need to be complete. In other words, completeness is not a modular property of term rewriting systems. Toyama, Klop and Barendregt showed that completeness is a modular property of left-linear TRS's. In 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 semi-completeness, i.e. the combination of confluence and weak normalization. IntroductionA property of tenn rewriting systems is modular if it is preserved under disjoint union.

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Section: \1 = { F(o Lx)-7f(x X X)} { G(x Y) -7 Xmentioning

confidence: 99%

Completeness of combinations of constructor systems

Middeldorp¹,

Toyama

1991

Rewriting Techniques and Applications

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“…Kurihara and Kaji [13] took an alternative approach to the modularity by defining the notion of modular reductions and established very interesting results (e.g. they proved that there is no infinite sequence of modular reductions even if some of the modules are non-terminating).…”

Section: Direct Summentioning

confidence: 99%

Modular proofs for completeness of hierarchical term rewriting systems

Rao

1995

Theoretical Computer Science

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“…Middeldorp (1989a) showed that the property of having unique normal forms is modular for general term rewriting systems. An interesting alternative approach to modularity is explored in Kurihara and Kaji (1990). Middeldorp (1991aMiddeldorp ( , 1991b extended the above results to conditional term rewriting systems.…”

Section: Introductionmentioning

confidence: 99%

Completeness of Combinations of Constructor Systems

Middeldorp¹,

Toyama²

1993

Journal of Symbolic Computation

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A term rewriting system is called complete if it is both confluent and strongly normalising. Barendregt and Klop showed that the disjoint union of complete term rewriting systems does not need to be complete. In other words, completeness is not a modular property of term rewriting systems. Toyama, Klop and Barendregt showed that completeness is a modular property of left-linear term rewriting systems. In 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 semi-completeness, i.e. the combination of confluence and weak normalisation.

show abstract

Modular term rewriting systems and the termination

Cited by 18 publications

References 9 publications

Completeness of combinations of constructor systems

Completeness of combinations of constructor systems

Modular proofs for completeness of hierarchical term rewriting systems

Completeness of Combinations of Constructor Systems

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