依赖项重写系统及其在程序设计语言中的应用

面重写系统是一种简洁通用的计算模型，在许多领域中有着重要的应用。     

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。     

重写系统的模块分解

Ｍｉｄｄｅｌｄｏｒｐ和Ｔｏｙａｍａ证明，强加构造原则到项重写系统可获得完备概念的模块性，并且系统分解成的各部分间可共亨函数符号和重量写规则。本文推广他们的结论，当构造性的项重写系统引用定义在其它系统中的函数符号时，完备概念的模块性仍保持。该结论对代数规范和基于项重写的编程语言等方面是很有意义的。     

项重写系统的并行实现方案

项重写系统的并行归约可以提高归约的效率，在无共享内存的Ｔｒａｎｓｐｕｔｅｒ网络上实现时要考虑任务的分配，项的拼装，归约任务的控制等问题，其中怎么样减少机间的机内进程的通信慢提高系统效果的关键。本文从控制方式角度讨论在不同拓扑结构的Ｔｒａｎｓｐｕｔｅｒ网络上实现项重写系统的方案，重点介绍基于树形结构下的控制方法，进程安排和通讯形式。     

基于重写方法的程序开发系统的设计和实现

本文介绍了一个基于重写方法的程序开发系统的设计和实现。该系统使用代数规范说明语言和扩展的函数式语言合成而形成的混合语言进行程序设计。系统将代数规范转换为合流的重写系统，并以平行最外方法辅以必要归约进行计算。该文详细介绍了系统的原理和实现技术，并以一些实例说明了系统的特点。     

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。     

项重写系统等价性的归纳证明

尽管学者们在计算机软件理论及相关数学理论方面做出了不懈的努力,但伴随着计算机硬件的高速发展而来的软件危机却日益严峻,其原因复杂多样。其中,主要原因之一是缺乏程序验证的方法和工具。程序设计的主要步骤有:描述问题、设计程序、实现程序及测试程序。需要注意的是,这里是测试程序的正确性而非证明程序的正确性,这样程序的正确性就不能从根     

基于项重写的动态可重构系统建模与仿真框架

可重构系统建模与仿真是一项复杂的任务.本文从可重构计算模式的基本特征出发,建立计算与通讯并重的生产者-消费者系统架构,并提取其数据、计算、通讯基本元素,解决运行时的调度和加载问题,形成基于项重写理论的动态可重构计算系统建模框架.最后指出基于本框架进行系统规范描述、系统设计和仿真验证的方法与步骤.并以实例说明了不同的调度策略产生满足不同规范的应用系统,显示了本框架的通用性.     

基于重写技术的程序开发与验证

完整地介绍了一个基于重写技术的程序开发和验证系统,重点展示验证子系统的理论、方法 和技术.验证子系统使得系统能自动证明程序和规范中的优化规则及测试等式,从而进一步保 证程序开发过程的正确性.验证子系统所采用的主要技术是以成批证明方法和证据测试集为 特色的重写归纳方法.     

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:     

Autowrite: A Tool for Term Rewrite Systems and Tree Automata

Autowrite is an experimental software tool written in Common Lisp Oriented System (CLOS) which handles term rewrite systems and bottom-up tree automata. A graphical interface written using McCLIM, (the free implementation of the CLIM specification) frees the user of any Lisp knowledge. Software and documentation can be found at http://dept-info.labri.u-bordeaux.fr/~idurand/autowrite. Autowrite was initially designed to check call-by-need properties of term rewrite systems. For this purpose, it implements the tree automata constructions used in [F. Jacquemard. Decidable approximations of term rewriting systems. In Proc. 7th RTA, volume 1103 of LNCS, pages 362–376, 1996; I. Durand and A. Middeldorp. Decidable call by need computations in term rewriting (extended abstract). In Proc. 14th CADE, volume 1249 of LNAI, pages 4–18, 1997; Irène Durand and Aart Middeldorp. On the complexity of deciding call-by-need. Technical Report 1196–98, LaBRI, 1998; T. Nagaya and Y. Toyama. Decidability for left-linear growing term rewriting systems. Information and Computation, 178(2):499–514, 2002] and many useful operations on terms, term rewrite systems and tree automata.     

Lifting Infinite Normal Form Definitions From Term Rewriting to Term Graph Rewriting

nfinite normal forms are a way of giving semantics to non-terminating rewrite systems. The notion is a generalization of the Böhm tree in the lambda calculus. It was first introduced in [Ariola, Z. M. and S. Blom, Cyclic lambda calculi, in: Abadi and Ito [Abadi, M. and T. Ito, editors, “Theoretical Aspects of Computer Software,” Lecture Notes in Computer Science 1281, Springer Verlag, 1997], pp. 77–106] to provide semantics for a lambda calculus on terms with letrec. In that paper infinite normal forms were defined directly on the graph rewrite system. In [Blom, S., “Term Graph Rewriting - syntax and semantics,” Ph.D. thesis, Vrije Universiteit Amsterdam (2001)] the framework was improved by defining the infinite normal form of a term graph using the infinite normal form on terms. This approach of lifting the definition makes the non-confluence problems introduced into term graph rewriting by substitution rules much easier to deal with. In this paper, we give a simplified presentation of the latter approach.     

From Functional Programs to Interaction Nets via the Rewriting Calculus

We use the ρ-calculus as an intermediate language to compile functional languages with pattern-matching features, and give an interaction net encoding of the ρ-terms arising from the compilation. This encoding gives rise to new strategies of evaluation, where pattern-matching and 'traditional' β-reduction can proceed in parallel without overheads.     

Nonterminating Rewritings with Head Boundedness

We define here the concept of head boundedness,head normal form and head confluence of term rewriting systems that allow infinite derivation.Head confluence iw weaker than confluence,but sufficient to guarantee the correctness of lazy implementations of equational logic programming languages.Then we prove several results.First,if a left-linear system is locally confluent and head-bounded.then it is head-confluent.Second,head-confluent and head-bounded systems have the heau Church-Rosser property.Last,if an orthogonal system is head-terminating,then it is head-bounded.These results can be applied to generalize equational logic programming languages.     

Translation of Algebraic Programs into Executable Codes

An approach to the problem of translation of algebraic programs into executable codes is presented. In particular, an algorithm for translation of algebraic programs represented in the language Aplan into C codes is proposed. An algorithm of reconstruction of types in Aplan is considered that also checks the absence of features used for dynamic specification of procedures in a code. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 168–176, September–October 2005.     

Chain properties of rule closures

This article introduces a generalisation of the crossed rule approach to the detection of Knuth-Bendix completion procedure divergence. It introduces closure chains, which are special rule closures constructed by means of particular substitution operations and operators, as a suitable formalism for progress in this direction. Supporting substitution algebra is developed first, followed by considerations concerning rule closures in general, concluding with an investigation of closure chain properties. Issues concerning the narrowing process are not discussed here.     

Mechanizing Weakly Ground Termination Proving of Term Rewriting Systems by Structural and Cover-Set Inductions

The paper presents three formal proving methods for generalized weakly ground terminating property, i.e., weakly terminating property in a restricted domain of a term rewriting system, one with structural induction, one with cover-set induction, and the third without induction, and describes their mechanization based on a meta-computation model for term rewriting systems-dynamic term rewriting calculus. The methods can be applied to non-terminating, non-confluent and/or non-left-linear term rewriting systems. They can do "forward proving" by applying propositions in the proof, as well as "backward proving" by discovering lemmas during the proof.     

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.     

A Rewriting Calculus for Cyclic Higher-order Term Graphs

Introduced at the end of the nineties, the Rewriting Calculus (ρ-calculus, for short) is a simple calculus that fully integrates term-rewriting and λ-calculus. The rewrite rules, acting as elaborated abstractions, their application and the obtained structured results are first class objects of the calculus. The evaluation mechanism, generalizing beta-reduction, strongly relies on term matching in various theories.In this paper we propose an extension of the ρ-calculus, handling graph like structures rather than simple terms. The transformations are performed by explicit application of rewrite rules as first class entities. The possibility of expressing sharing and cycles allows one to represent and compute over regular infinite entities.The calculus over terms is naturally generalized by using unification constraints in addition to the standard ρ-calculus matching constraints. This therefore provides us with the basics for a natural extension of an explicit substitution calculus to term graphs. Several examples illustrating the introduced concepts are given.