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。     

From Chemical Rules to Term Rewriting

In this paper, rule-based programming is explored in the field of automated generation of chemical reaction mechanisms. We explore a class of graphs and a graph rewriting relation where vertices are preserved and only edges are changed. We show how to represent cyclic labeled graphs by decorated labeled trees or forests, then how to transform trees into terms. A graph rewriting relation is defined, then simulated by a tree rewriting relation, which can be in turn simulated by a rewriting relation on equivalence classes of terms. As a consequence, this kind of graph rewriting can be implemented using term rewriting. This study is motivated by the design of the GasEl system for the generation of kinetics reactions mechanisms. In GasEl, chemical reactions correspond to graph rewrite rules and are implemented by conditional rewriting rules in ELAN. The control of their application is done through the ELAN strategy language.     

Operational termination of conditional term rewriting systems

We describe conditional rewriting by means of an inference system and capture termination as the absence of infinite inference: that is, all proof attempts must either successfully terminate, or they must fail in finite time. We call this notion operational termination. Our notion of operational termination is parametric on the inference system. We prove that operational termination of CTRSs is, in fact, equivalent to a very general notion proposed for 3-CTRSs, namely the notion of quasi-decreasingness, which is currently the most general one which is intended to be checked by comparing parts of the CTRS by means of term orderings. Therefore, existing methods for proving quasi-decreasingness of CTRSs immediately apply to prove operational termination of CTRSs.     

Formalizing and Analyzing the Needham-Schroeder Symmetric-Key Protocol by Rewriting

This paper reports on work in progress on using rewriting techniques for the specification and the verification of communication protocols. As in Genet and Klay's approach to formalizing protocols, a rewrite system describes the steps of the protocol and an intruder's ability of decomposing and decrypting messages, and a tree automaton encodes the initial set of communication requests and an intruder's initial knowledge. In a previous work we have defined a rewriting strategy that, given a term t that represents a property of the protocol to be proved, suitably expands and reduces t using the rules in and the transitions in to derive whether or not t is recognized by an intruder. In this paper we present a formalization of the Needham-Schroeder symmetric-key protocol and use the rewriting strategy for deriving two well-known authentication attacks.     

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.     

A calculus for and termination of rippling

Rippling is a type of rewriting developed for inductive theorem proving that uses annotations to direct search. Rippling has many desirable properties: for example, it is highly goal directed, usually involves little search, and always terminates. In this paper we give a new and more general formalization of rippling. We introduce a simple calculus for rewriting annotated terms, close in spirit to first-order rewriting, and prove that is has the formal properties desired of rippling. Next we develop criteria for proving the termination of such annotated rewriting, and introduce orders on annotated terms that lead to termination. In addition, we show how to make rippling more flexible by adapting the termination orders to the problem domain. Our work has practical as well as theoretical advantages: it has led to a very simple implementation of rippling that has been integrated in the Edinburgh CLAM system. Funded by the German Ministry for Research and Technology under grant ITS 9102. Supported by a Human Capital and Mobility Research Fellowship from the European Commission. Both authors thank members of the Edinburgh Mathematical Reasoning Group, as well as Alan Bundy, Leo Bachmair, Dieter Hutter, and Michael Rusinowitch, for their comments on previous drafts. Additional support was also received from the MInd grant EC-US 019-76094.     

含假结RNA二级结构类的图语法

用最小自由能法预测RNA二级结构是NP困难问题,其根本原因是假结的存在。近几年的预测算法都针具有一定结构特征的假结寻找多项式时间算法进行预测。论文针对RNA二级结构图提出一种图语法,该语法由初始结构图集和重写规则集构成,用重写规则在初始结构图上的不断重写得到的结构图都是该语法的语言。分析了5个主流RNA二级结构预测算法的目标集,给出它们的图语法,使得目标集的结构特征一目了然,目标集间的真包含关系也通过图语法直观地体现出来。     

Inequational Deduction as Term Graph Rewriting

Multi-algebras allow to model nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results.We propose a simple inequational deduction system, based on term graphs, for inferring inclusions of derived relations in a multi-algebra, and we show that term graph rewriting provides a sound and complete implementation of it.     

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.     

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.     

Implementing

This paper presents a term graph rewriting system as an implementation for the -calculus, a substitution-free language that can be used to describe the behaviour of functional programming languages at a very low level of granularity, and has first been defined in [Stéphane Lengrand. Call-by-value, call-by-name, and strong normalization for the classical sequent calculus. In Bernhard Gramlich and Salvador Lucas, editors, Electronic Notes in Theoretical Computer Science, volume 86. Elsevier, 2003; S. van Bakel, S. Lengrand, and P. Lescanne. The language : circuits, computations and classical logic. Submitted, 2004]. Since the calculus has a notion of binding, in the context of sharing a notion of rebinding is introduced that helps avoid double binding of names.     

Flatterms,discrimination nets,and fast term rewriting

We describe a new representation for first-order terms which is amenable to simple and fast traversal and matching operations. In addition, we describe some efficient discrimination net indexing algorithms which use the new term representation. We have implemented these ideas in a term rewriting system called HIPER, and have obtained substantial speedups.The work reported here was conducted at MCC and at the University of Texas at Austin.     

Graph-based query rewriting for knowledge sharing between peer ontologies

Peer knowledge management systems (PKMS) offer a flexible architecture for decentralized knowledge sharing. In PKMSs, the knowledge sharing and evolution processes are based on peer ontologies. Finding an effective and efficient query rewriting algorithm for regular expression queries is vital for knowledge sharing between peers in PKMSs; and for this our solution is characterized by graph-based query rewriting. Based on the graphs for both axioms and mappings, we design a novel algorithm, regular expression rewriting algorithm, to rewrite regular expression queries along semantic paths. The simulation results show that the performance of our algorithm is better than Mork’s reformulation algorithms [P. Mork, Peer architectures for knowledge sharing, PhD thesis, University of Washington, 2005. <http://www.mitre.org/staffpages/pmork/>], and our algorithm is more effective than the naive rewriting algorithm.     

Bisimilarity in Term Graph Rewriting

We present a survey of confluence properties of (acyclic) term graph rewriting. Results and counterexamples are given for different kinds of term graph rewriting; besides plain applications of rewrite rules, extensions with the operations of collapsing and copying, and both operations together are considered. Collapsing and copying together constitute bisimilarity of term graphs. We establish sufficient conditions for—and counterexamples to—confluence, confluence modulo bisimilarity, and the Church–Rosser property modulo bisimilarity. Moreover, we address rewriting modulo bisimilarity, that is, rewriting of bisimilarity classes of term graphs.     

Using graph rewriting methods for the semi-automatic generation of parametric infrastructure models

For the design of large infrastructure projects such as inner-city subway tracks, it proves necessary to consider differing model scales, ranging from the scale of several kilometers down to a few millimeters. This challenge can be addressed by using multi-scale product models comprising multiple levels of detail (LoD). Ensuring consistency across the different LoDs can be achieved by applying procedural and parametric modeling techniques while creating the model. This results in a flexible multi-scale model that can be easily modified on one scale while other scales are automatically updated. However, the correct application of parametric constraints and procedural dependencies has shown to be a very complex and time-consuming process. To address this issue, this papers presents a semi-automated detailing mechanism, which is based on formal procedures based on graphs and graph transformations. This paper discusses how procedural parametric models based on two-dimensional sketches can be represented by graphs and how detailing steps in the form of parametric modeling operations can be formalized by using rule-based graph rewriting.     

嵌入一致图语法的依赖图

图语法将字符串上的形式文法扩充为图上的形式文法,提供一种能够使用精确的数学方法来模拟图变换的机制.提出了几种新的基于一致图语法的方法来表示控制流图、数据流图、控制数据流图、二分图和超图,并说明如何通过图重写来自动生成依赖图并挖掘并行性,从而协助并行编译器和并行语言的设计和实现.     

Infinitary Combinatory Reduction Systems

We define infinitary Combinatory Reduction Systems (iCRSs), thus providing the first notion of infinitary higher-order rewriting. The systems defined are sufficiently general that ordinary infinitary term rewriting and infinitary λ-calculus are special cases.Furthermore, we generalise a number of known results from first-order infinitary rewriting and infinitary λ-calculus to iCRSs. In particular, for fully-extended, left-linear iCRSs we prove the well-known compression property, and for orthogonal iCRSs we prove that (1) if a set of redexes U has a complete development, then all complete developments of U end in the same term and that (2) any tiling diagram involving strongly convergent reductions S and T can be completed iff at least one of S/T and T/S is strongly convergent.We also prove an ancillary result of independent interest: a set of redexes in an orthogonal iCRS has a complete development iff the set has the so-called finite jumps property.     

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。     

Term Graphs for Computing Derivatives in Imperative Languages

Automatic differentiation is a technique for the rule-based transformation of a subprogram that computes some mathematical function into a subprogram that computes the derivatives of that function. Automatic differentiation algorithms are typically expressed as operating on a weighted term graph called a linearized computational graph. Constructing this weighted term graph for imperative programming languages such as C/C++ and Fortran introduces several challenges. Alias and definition-use information is needed to construct term graphs for individual statements and then combine them into one graph for a collection of statements. Furthermore, the resulting weighted term graph must be represented in a language-independent fashion to enable the use of AD algorithms in tools for various languages. We describe the construction and representation of weighted term graphs for C/C++ and Fortran, as implemented in the ADIC 2.0 and OpenAD/F tools for automatic differentiation.     

External Rewriting for Skeptical Proof Assistants

This paper presents the design, the implementation, and experiments of the integration of syntactic, conditional possibly associative-commutative term rewriting into proof assistants based on constructive type theory. Our approach is called external because it consists in performing term rewriting in a specific and efficient environment and checking the computations later in a proof assistant. Two typical systems are considered in this work: ELAN, based on the rewriting calculus, as the term rewriting-based environment, and Coq, based on the calculus of inductive constructions as the proof assistant. We first formalize the proof terms for deduction by rewriting and strategies in ELAN using the rewriting calculus with explicit substitutions. We then show how these proof terms can soundly be translated into Coq syntax where they can be directly type checked. For the method to be applicable for rewriting modulo associativity and commutativity, we provide an effective method to prove equalities modulo these axioms in Coq using ELAN. These results have been integrated into an ELAN-based rewriting tactic in Coq.