项重写的图实现

图重写能够有效地实现项重写。文章从项重写的图实现的角度出发，研究了图重写模拟项重写的正确性和完备性：在无环出现的情况下，图重写对一切项重写下正确；在无环出现的条件下，图重写对左线性合流的项重写是完备的。     

归纳法推理中的项重写策略

本文介绍归纳法推理系统中的项重写策略，该策略根据不同的待重写项ｔｅｒｍ，分别运用公理、重写引理、函数定义、项重写规则等重写项ｔｅｒｍ，以期得到一个更接近推理目标的已重写项，这一策略已在微机上用编译ＬＩＳＰ语言实现。     

归纳法推理中的项重写策略*

本文介绍归纳法推理系统中的项重写策略．该策略根据不同的待重写项term，分别运用公理、重写引理、函数定义、项重写规则等重写项term，以期得到一个更接近推理目标的巳重写项．这一策略已在微机上用编译LlsP语言实现．     

半正则重写系统及其合流性

本文着重研究重写系统的合流性,通过引入符号测度的概念,本文定义了半正则重写系统,并证明了半正则重写系统的合流性。     

Knuth—Bendix过程的发散现象的研究

Ｋｎｕｔｈ－Ｂｅｎｄｉｘ完备过程不终止的起因研究得很少，本文研究引起不终止的重写规则的结构性质，提出了相容交叉规则对的概念，推广了文献６的结论，并提出了为构造系统检验该过程是否不终止的方法。     

项重写系统弱基终止性的归纳证明

1.引言项重写系统是一种受到广泛研究和应用的形式计算模型。一个项重写系统由一组称为重写规则的定向等式组成。例如,下面的R是一个由五个重写规则组成的、定义用({0,s})表示的自然数集N上的两倍函数d(x)=2×n:N→N的项重写系统:     

Knuth－Bendix过程的发散现象的研究

Ｋｎｕｔｈ－Ｂｅｎｄｉｘ完备过程不终止的起因研究得很少．本文研究引起不终止的重写规则的结构性质，提出了相容交叉规则对的概念，推广了文献［６］的结论，并提出了为构造系统检验该过程是否不终止的方法．     

动态项重写计算

1.引言项重写系统是一种受到广泛研究和应用的形式计算模型。一个项重写系统由一组称为重写规则的定向等式组成。它的计算基于代入、匹配和替换,除具有方向性外,与等式推导一致。虽然项重写系统形式简单、计算单纯,但它同时又具有与λ计算及图灵机相同的计算能力。正是它的简洁性及计算能力使它受到广泛的研究和应用:项重写系统为抽象数据类型提供类型、为函数型语言提供操作语义、为定理自动证明提供推理工具。对于项重写系统本身也有大量的研究:如合流性、终止性、等价性等。     

压缩路径序与重写系统的结构测度

结构测度对于判别重写系统的合流性是极为重要的,本文着重研究结构测度的有效定义方法。本文引入了压缩路径序概念,只要给出符号集上了拟序关系和相对该拟序关系协调的压缩结构,即可方便地生成良拟序的压缩路径序,同时可以有效地检查这一路径压缩序是否为给定重写系统的结构测度,本文提出的方法有力地支持了在非终止条件下对重写系统合流性的判别。     

一种基于ADT的函数语言及其操作语义模型

本文介绍一以ＡＤＴ为主要构件的函数语言，它是作者设计的函数式及面向对象式合成语言的函数部分，进而描述了其操作语义模型：多态λ演算十代数重写系统＝多态λ重写系统，并讨论该模型的Ｃｈｕｒｃｈ－Ｒｏｓｓｅｒ性质和强范式性质。     

Termination of term rewriting: interpretation and type elimination

We investigate proving termination of term rewriting systems by interpretation of terms in a well-founded monotone algebra. The well-known polynomial interpretations can be considered as a particular case in this framework. A classification of types of termination, including simple termination, is proposed based on properties in the semantic level. A transformation on term rewriting systems eliminating distributive rules is introduced. Using this distribution elimination a new termination proof of the system SUBST of Hardin and Laville (1986) is given. This system describes explicit substitution in λ-calculus.Another tool for proving termination is based on introduction and removal of type restrictions. A property of many-sorted term rewriting systems is called persistent if it is not affected by removing the corresponding typing restriction. Persistence turns out to be a generalization of direct sum modularity, but is more powerful for both proving confluence and termination. Termination is proved to be persistent for the class of term rewriting systems for which not both duplicating rules and collapsing rules occur, generalizing a similar result of Rusinowitch for modularity. This result has nice applications, in particular in undecidability proofs.     

A Deterministic Lazy Narrowing Calculus

In this paper we study the non-determinism between the inference rules of the lazy narrowing calculusLNC(Middeldorpet 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.     

Modular Properties of Composable Term Rewriting Systems

In this paper we prove several new modularity results for unconditional and conditional term rewriting systems. Most of the known modularity results for the former systems hold for disjoint or constructor-sharing combinations. Here we focus on a more general kind of combination: so-called composable systems. As far as conditional term rewriting systems are concerned, all known modularity result but one apply only to disjoint systems. Here we investigate conditional systems which may share constructors. Furthermore, we refute a conjecture of Middeldorp (1990, 1993).     

Counterexamples to termination for the direct sum of term rewriting systems

The direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols. It is shown that the direct sum of two term rewriting systems is not terminating, even if these systems are both terminating.     

Reducibility of operation symbols in term rewriting systems and its application to behavioral specifications

In this paper, we propose the notion of reducibility of symbols in term rewriting systems (TRSs). For a given algebraic specification, operation symbols can be classified on the basis of their denotations: the operation symbols for functions and those for constructors. In a model, each term constructed by using only constructors should denote an element, and functions are defined on sets formed by these elements. A term rewriting system provides operational semantics to an algebraic specification. Given a TRS, a term is called reducible if some rewrite rule can be applied to it. An irreducible term can be regarded as an answer in a sense. In this paper, we define the reducibility of operation symbols as follows: an operation symbol is reducible if any term containing the operation symbol is reducible. Non-trivial properties of context-sensitive rewriting, which is a simple restriction of rewriting, can be obtained by restricting the terms on the basis of variable occurrences, its sort, etc. We confirm the usefulness of the reducibility of operation symbols by applying them to behavioral specifications for proving the behavioral coherence property.     

Comparing Curried and Uncurried Rewriting

Currying is a transformation of term rewrite systems which may contain symbols of arbitrary arity into systems which contain only nullary symbols, together with a single binary symbol called application. We show that for all term rewrite systems (whether orthogonal or not) the following properties are preserved by this transformation: strong normalization, weak normalization, weak Church-Rosser, completeness, semi-completeness, and the non-convertibility of distinct normal forms. Under the condition of left-linearity we show preservation of the properties NF (if a term is reducible to a normal form,then its reducts are all reducible to the same normal form) and UN→ (a term is reducible to at most one normal form).We exhibit counterexamples to the preservation of NF and UN→ for non-left-linear systems.The results extend to partial currying(where some subset of the symbols are curried),and imply some modularity properties for unions of applicative systems.     

Transformation for Refining Unraveled Conditional Term Rewriting Systems

Unravelings, transformations from conditional term rewriting systems (CTRSs, for short) into unconditional term rewriting systems, are valuable for analyzing properties of CTRSs. In order to completely simulate rewrite sequences of CTRSs, the restriction by a particular context-sensitive and membership condition that is determined by extra function symbols introduced due to the unravelings, must be imposed on the rewrite relations of the unraveled CTRSs. In this paper, in order to weaken the context-sensitive and membership condition, we propose a transformation applied to the unraveled CTRSs, that reduces the number of the extra symbols. In the transformation, updating the context-sensitive condition properly, we remove the extra symbols that satisfy a certain condition. If the transformation succeeds in removing all of the extra symbols, we obtain the TRSs that are computationally equivalent with the original CTRSs.     

Modular Church-Rosser Modulo:The Complete Picture

In Ref.[19], Toyama proved that the union of two confluent term-rewriting systems that share absolutely no function symbols or constants is likewise confluent, a property called modularity. The proof of this beautiful modularity result, technically based on slicing terms into an homogeneous cap and a so called alien, possibly heterogeneous substitution,was later substantially simplified in Refs.[8,12]. In this paper, we present a further simplification of the proof of Toyama's result for confluence, which shows that the crux of the problem lies on two di?erent properties: a cleaning lemma, whose goal is to anticipate the application of collapsing reductions and a modularity property of ordered completion that allows to pairwise match the caps and alien substitutions of two equivalent terms obtained from the cleaning lemma. The approach allows for arbitrary kinds of rules, and scales up to rewriting modulo arbitrary sets of equations.     

A class of confluent term rewriting systems and unification

The narrowing mechanism and term rewriting systems are powerful tools for constructing complete and efficient unification algorithms for useful classes of equational theories. This has been shown for the case where term rewriting systems are confluent and noetherian (i.e., terminating). In this paper we show that the narrowing mechanism, combined with ordinary unification, yields a complete unification algorithm for equational theories that can be described by a closed linear term rewriting system with the non-repetition property; this class allows non-terminating rewrite systems. For some special forms of input terms, narrowing generates complete sets of E-unifiers without resorting to the non-repetition property. The key observation underlying the proof is that a reduction sequence in this class of term rewriting system can be transformed into one which possesses properties that enable a completeness proof.