Normalization Results for Typeable Rewrite Systems

In this paper we introduce Curryfied term rewriting systems, and a notion of partial type assignment on terms and rewrite rules that uses intersection types with sorts andω. Three operations on types—substitution, expansion, and lifting—are used to define type assignment and are proved to be sound. With this result the system is proved closed for reduction. Using a more liberal approach to recursion, we define a general scheme for recursive definitions and prove that, for all systems that satisfy this scheme, every term typeable without using the type-constantωis strongly normalizable. We also show that, under certain restrictions, all typeable terms have a (weak) head-normal form, and that terms whose type does not containωare normalizable.     

Perpetuality and Uniform Normalization in Orthogonal Rewrite Systems

We study perpetuality of reduction steps, as well as perpetuality of redexes, in orthogonal rewrite systems. A perpetual step is a reduction step which retains the possibility of infinite reductions. A perpetual redex is a redex which, when put into an arbitrary context, yields a perpetual step. We generalize and refine existing criteria for the perpetuality of reduction steps and redexes in orthogonal term rewriting systems and the λ-calculus due to Bergstra and Klop and others. We first introduce context-sensitive conditional expression reduction systems (CCERSs) and define a concept of orthogonality (which implies confluence) for them. In particular, several important λ-calculi and their extensions and restrictions can naturally be embedded into orthogonal CCERSs. We then define a perpetual reduction strategy which enables one to construct minimal (w.r.t. Lévy's permutation ordering on reductions) infinite reductions in orthogonal fully-extended CCERSs. Using the properties of the minimal perpetual strategy, we prove   1. perpetuality of any reduction step that does not erase potentially infinite arguments, which are arguments that may become, via substitution, infinite after a number of outside steps, and   2. perpetuality (in every context) of any safe redex, which is a redex whose substitution instances may discard infinite arguments only when the corresponding contracta remain infinite.  We prove both these perpetuality criteria for orthogonal fully-extended CCERSs and then specialize and apply them to restricted λ-calculi, demonstrating their usefulness. In particular, we prove the equivalence of weak and strong normalization (whose equivalence is here called uniform normalization) for various restricted λ-calculi, most of which cannot be derived from previously known perpetuality criteria.     

Strong Normalization from Weak Normalization by Translation into the Lambda-I-Calculus

This paper offers a systematic account of techniques to infer strong normalization from weak normalization that make use of syntactic translations from -terms to I-terms. We present variants of such techniques due to Klop, Sørensen, Xi, Gandy, and Loader.We show that all the translations, in some cases via adjustments, are special cases of a generic scheme of translations, known as permutative inner interpretations. Having established this, which is easy, the fact that all the translations can be used to reduce strong normalization to weak normalization can be obtained from a single, general result concerning permutative inner interpretations.Furthermore, we show that each of the translations can be obtained as the composition of Klop's well-known -translation and some other translation of independent interest. For instance, in the case of Xi's translation, this other translation is a thunkification translation.Finally we compare the above techniques in some detail to the intimately related techniques by de Vrijer and Girard.A main contribution of the paper is to compare the techniques of Gandy, Klop, and Girard in detail. For instance, we prove the main property of Gandy's translation without reference to functionals using instead ideas from Klop's translation.     

微机BIOS的升级与修复方法

目前生产的大多数微机中,BIOS多采用可升级的FLASH芯片.用户使用专门的BIOS写入程序,就可以重写或升级自己机器的BIOS,以提高主板的适应能力.最新的BIOS程序,可以从同型号主板的BIOS中读取,或者从INTERNET上下载.本文简要论术了微机B1OS的写入和升级方法,并且给出了具体的操作步骤.     

Rewrite Systems with Constraints

We extend a widely used concept of rewrite systems with a unit holding a kind of global information which can influence and can be influenced by rewriting. The unit is similar to the store used in concurrent constraint programming, and can be also seen as a special (weak) state unit. We present how this extension changes the expressive power of rewrite systems classes which are included in Mayr's PRS hierarchy [8]. The new classes (fcBPA, fcBPP, fcPA, fcPAD, fcPAN, fcPRS) are described and inserted into the hierarchy.     

Scoped Dynamic Rewrite Rules

The applicability of term rewriting to program transformation is limited by the lack of control over rule application and by the context-free nature of rewrite rules. The first problem is addressed by languages supporting user-definable rewriting strategies. This paper addresses the second problem by extending rewriting strategies with scoped dynamic rewrite rules. Dynamic rules are generated at run-time and can access variables available from their definition context. Rules generated within a rule scope are automatically retracted at the end of that scope. The technique is illustrated by means of several program tranformations: bound variable renaming, function inlining, and dead function elimination.     

Infinite String Rewrite Systems and Complexity

We study the relation between time complexity and derivation work for the word problem of infinitely presented semigroups and groups. We introduce the notion of theworkof a derivation (defined as the sum of the lengths of all the rules used in the derivation, with multiplicity). The following results are proved:     

高效率重写型程序的设计

本文考虑如何设计高效率(即重写步数较少的)重写型程序。文中以计算Fibonacci数列的程序为例．比较具有相同功能的重写型程序,展示编写高效率重写型程序的可能性。介绍利用动态项重写计算编写高效率重写型程序的直观、简洁的方法。其中．动态项重写计算是项重写系统的元计算模型,其计算同样基于项重写。     

Cbase数据库查询重写模块的设计与实现

本文详细讨论了重写模块的设计思想与实现技术，并讨论了利用执行引擎特点引入的一组基于等价谓调的简单语句直写规则．测试结果表明，增加重写模块的查询优化器能显著提高系统的查询效率．     

Cbase查询优化的重写机制及其实现

Cbase是南京大学计算机系与南大谷元石油软件研究所有限公司研制的新一代商用关系数据库管理系统。为了提高查询效率,作者开发了Cbase数据库的查询优化器。文章详细论述了Cbase查询优化器中重写模块的设计思想与实现技术,并讨论了基于执行引擎特点引入的一组基于等价谓词的简单语句的重写规则。测试结果表明,所设计的重写器能够显著提高系统的查询效率。     

Rewrite systems on a lattice of types

Summary Re-writing systems for partial algebras are developed by modifying the Knuth-Bendix completion algorithm to permit the use of latticestructured domains. Some problems with the original algorithm, such as the treatment of division rings, are overcome conveniently by this means. The use of a type lattice also gives a natural framework for specifying data types in Computer Science without over-specifying error situations. The soundness and meaning of the major concepts involved in re-writing systems are reviewed when applied to such structures.     

一种自动的软件体系结构规约重写方法

在软件较高的抽象层次如软件体系结构,实施重构更有助于提高软件的易维护性,从而降低软件的维护成本。大量复杂的重构操作需要(半)自动化的支持。该文提出一种体系结构规约重写方法,将体系结构重构转换为接口重构和实现体重构2方面的规约重写,并给出规约重写基本操作规则。分析了实现体规约的重构操作,提出子构件提升操作、同级构件合并操作、跨级构件合并和构件分离合并操作4种基本操作。     

SPDR: 基于片段预测的多轮对话改写

对话系统对上文信息使用不充分是当前制约多轮对话效果的主要因素,基于上文信息对用户当前输入进行改写是该问题的一种重要解决方法。改写任务的核心在于指代消解(pronoun resolution)和省略补全(ellipsisrecovery)。该文提出了一种基于BERT的指针网络(Span Prediction for Dialogue Rewrite,SPDR),该模型会预测用户当前轮次输入语句中所有token前面需要填充的内容,在上文中对应的片段(span)起始和结束的位置,来实现多轮对话改写;该文还提出了一种新的衡量改写结果的评价指标sEMr。相较于基于指针生成网络的模型,该模型在不损失效果的前提下推理速度提升接近100%,基于RoBERTa-wwm的SPDR模型在5项指标上均有明显提升。     

Rewrite rule systems for modal propositional logic

This paper explains new results relating modal propositional logic and rewrite rule systems. More precisely, we give complete term rewriting systems for the modal propositional systems known as K, Q, T, and S5. These systems are presented as extensions of Hsiang's system for classical propositional calculus. We have checked local confluence with the rewrite rule system K.B. (cf. the Knuth-Bendix algorithm) developed by the Formel project at INRIA. We prove that these systems are noetherian, and then infer their confluence from Newman's lemma. Therefore each term rewriting system provides a new automated decision procedure and defines a canonical form for the corresponding logic. We also show how to characterize the canonical forms thus obtained.     

辨识非线性曲线的非线性极大似然—优化法

工程上经常碰到非线性曲线辨识问题。本文探讨一种非线性极大似然-优化法并结合三次样条函数拟配法,形成统一的逐次逼近的直接辨识非线性曲线的非线性辨识方法。该法兼有极大似然法的唯一性、很好的收敛性和优化法直接处理非线性系统的能力,辨识出的样条函数曲线能无限地光滑地逼近非线性曲线。     

Normalization and Deconfliction

In last month’s column we started the correlation process. This early work simply looked at individual pieces of evidence as they might relate to other pieces of evidence. However, there are some potential pitfalls if we stop here. First, digital evidence can be ambiguous. In other words, we can see the same event reported by various sources in various ways. Are we really looking at the same event, or are we looking at different ones? The second issue is that events may be reported in unusual ways leading the analyst to believe that the event occurred multiple times when, in fact, it did not. We need processes to analyze all the events that are reported and to help us to understand the actual data that we are seeing. Fortunately, we actually have two: normalization and deconfliction. Those two processes will be the topics of this month’s offering.     

Group Normalization

International Journal of Computer Vision - Batch Normalization (BN) is a milestone technique in the development of deep learning, enabling various networks to train. However, normalizing along the...     

Proving Modal Properties of Rewrite Theories Using Maude's Metalevel

Rewriting logic is a very expressive formalism for the specification of concurrent and distributed systems; more generally, it is a logic of change. In contrast, VLRL is a modal logic built on top of rewriting logic to reason precisely about that change. Here we present a technique to mechanically prove VLRL properties of rewrite theories using the reflective capability of rewriting logic through its Maude implementation.