Conversion to tail recursion in term rewriting

Tail recursive functions are a special kind of recursive functions where the last action in their body is the recursive call. Tail recursion is important for a number of reasons (e.g., they are usually more efficient). In this article, we introduce an automatic transformation of first-order functions into tail recursive form. Functions are defined using a (first-order) term rewrite system. We prove the correctness of the transformation for constructor-based reduction over constructor systems (i.e., typical first-order functional programs).     

Graph grammars with string-regulated rewriting

Multicellular organisms undergo a complex developmental process, orchestrated by the genetic information in their cells, in order to form a newborn individual from a fertilized egg. This complex process, not completely understood yet, is believed to have a key role in generating the impressive biotic diversity of organisms found on earth. Inspired by mechanisms of Eukaryotic genetic expression, we propose and analyse graph grammars with string-regulated rewriting. In these grammatical systems a genome sequence is represented by a regulatory string, a graph corresponds to an organism, and a set of graph grammar rules represents different forms of implementing cell division. Accordingly, a graph derivation by the graph grammar resembles the developmental process of an organism. We give examples of the concept and compare its generative power to the power of the traditional context-free graph grammars. We demonstrate that the power of expression increases when genetic regulation is included in the model, as compared to non-regulated grammars. Additionally, we propose a hierarchy of string-regulated graph grammars, arranged by expressive power. These results highlight the key role that the transmission of regulatory information during development has in the emergence of biological diversity.     

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.     

Monolithic and modular termination analyses for higher-order attribute grammars

In this paper we describe a sound, but not complete, analysis to prove the termination of higher-order attribute grammar evaluation caused by the creation of an unbounded number of (finite) trees as local tree-valued attributes, which are then themselves decorated with attributes. The analysis extracts a set of term-rewriting rules from the grammar that model creation of new syntax trees during the evaluation of higher-order attributes. If this term rewriting system terminates, then only a finite number of trees will be created during attribute grammar evaluation. The analysis places an ordering on nonterminals to handle the cases in which higher-order inherited attributes are used to ensure that a finite number of trees are created using such attributes. When paired with the traditional completeness and circularity analyses for attribute grammars and the assumption that each attribute equation defines a terminating computation, this analysis can be used to show that attribute grammar evaluation will terminate normally. This analysis can be applied to a wide range of common attribute grammar idioms and has been used to show that evaluation of our specification of Java 1.4 terminates. We also describe a modular version of the analysis that is performed on independently developed language extension grammars and the host language being extended. If the extensions individually pass the modular analysis then their composition is also guaranteed to terminate.     

Reachability and confluence are undecidable for flat term rewriting systems

Ground reachability, ground joinability and confluence are shown undecidable for flat term rewriting systems, i.e., systems in which all left and right members of rule have depth at most one.     

Decidable call-by-need computations in term rewriting

The theorem of Huet and Lévy stating that for orthogonal rewrite systems (i) every reducible term contains a needed redex and (ii) repeated contraction of needed redexes results in a normal form if the term under consideration has a normal form, forms the basis of all results on optimal normalizing strategies for orthogonal rewrite systems. However, needed redexes are not computable in general. In the paper we show how the use of approximations and elementary tree automata techniques allows one to obtain decidable conditions in a simple and elegant way. Surprisingly, by avoiding complicated concepts like index and sequentiality we are able to cover much larger classes of rewrite systems. We also study modularity aspects of the classes in our hierarchy. It turns out that none of the classes is preserved under signature extension. By imposing various conditions we recover the preservation under signature extension. By imposing some more conditions we are able to strengthen the signature extension results to modularity for disjoint and constructor-sharing combinations.     

The undecidability of self-embedding for term rewriting systems

The self-embedding property of term rewriting systems is closely related to the uniform termination property, since a nonself-embedding term rewriting system is uniform terminating. The self-embedding property is shown to be undecidable and partially decidable. It follows that the nonself-embedding property is not partially decidable. This is true even for globally finite term rewriting systems. The same construction gives an easy alternate proof that uniform termination is undecidable in general and also for globally finite term rewriting systems. Also, the looping property is shown to be undecidable in the same way.     

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.     

Circular attribute grammars with remote attribute references and their evaluators

Attribute grammars (AGs) are a suitable formalism for the development of language processing systems. However, for languages including unrestricted labeled jumps, such as “goto” in C, the optimizers in compilers are difficult to write in AGs. This is due to two problems that few previous researchers could deal with simultaneously, i.e., references of attribute values on distant nodes and circularity in attribute dependency. This paper proposescircular remote attribute grammars (CRAGs), an extension of AGs that allows (1) direct relations between two distant attribute instances through pointers referring to other nodes in the derivation tree, and (2) circular dependencies, under certain conditions including those that arise from remote references. This extension gives AG programmers a natural means of describing language processors and programming environments for languages that include any type of jump structure. We also show a method of constructing an efficient evaluator for CRAGs called amostly static evaluator. The performance of the proposed evaluator has been measured and compared with dynamic and static evaluators. Akira Sasaki: He is a research fellow of the Advanced Clinical Research Center in the Institute of Medical Science at the University of Tokyo. He received his BSc and MSc from Tokyo Institute of Technology, Japan, in 1994 and 1996, respectively. His research interests include programming languages, programming language processors and programming environments, especially compiler compilers, attribute grammars and systematic debugging. He is a member of the Japan Society for Software Science and Technology. Masataka Sassa, D.Sc.: He is Professor of Computer Science at Tokyo Institute of Technology. He received his BSc, MSc and DSc from the University of Tokyo, Japan, in 1970, 1972 and 1978, respectively. His research interests include programming languages, programming language processors and programming environments, currently he is focusing on compiler optimization, compiler infrastructure, attribute grammars and systematic debugging. He is a member of the ACM, IEEE Computer Society, Japan Society for Software Science and Technology, and Information Processing Society of Japan.     

An initial algebra approach to term rewriting systems with variable binders

We present an extension of first-order term rewriting systems. It involves variable binding in the term language. We develop systems called binding term rewriting systems (BTRSs) in a stepwise manner. First we present the term language, then formulate equational logic. Finally, we define rewriting systems. This development is novel because we follow the initial algebra approach in an extended notion of Σ-algebras in various functor categories. These are based on Fiore-Plotkin-Turi’s presheaf semantics of variable binding and Lüth-Ghani’s monadic semantics of term rewriting systems. We characterise the terms, equational logic and rewrite systems for BTRSs as initial algebras in suitable categories. Then, we show an important rewriting property of BTRSs: orthogonal BTRSs are confluent. Moreover, by using the initial algebra semantics, we give a complete characterisation of termination of BTRSs. Finally, we discuss our design choice of BTRSs from a semantic perspective. An erlier version appeared in Proc. Fifth ACM-SIGPLAN International Conference on Principles and Practice of Declarative Programming (PPDP2003).     

Term rewriting and its application to recognizing handwritten Hindu numerals

In this paper the theoretical basis is presented and the implementation of a term rewriting system based on algebraic specifications is described. The input to this system is represented by an algebraic specification language, which forms not only the set of axioms but also the sorts, variables, operators and terms of a specific simulated theory or application. Rewriting and matching mechanisms provide the formal methodology for evaluating terms and proving assertions in an algebraic theory. Specifications are evaluated by interpreting terms by means of rewrite rules. The rules are described by the axioms of the specifications where the finite termination and congruence properties are assumed. A term rewriting system to recognize handwritten Hindu numerals is introduced as a case study. Besides rewriting, a robust algorithm is proposed to segment the numeral's image into strokes based on feature points and to identify cavity features. A syntactic representation (term) of the input image is matched and rewritten against a set of rules. Experimental results proved that the proposed system is tolerant to recognize a variety of numeral shapes with 96% successful recognition rate.     

Term rewriting and beyond — theorem proving in Isabelle

The subject of this paper is theorem proving based on rewriting and induction. Both principles are implemented as tactics within the generic theorem prover Isabelle. Isabelle's higher-order features enable us to go beyond first-order rewriting and express rewriting with conditionals, induction schemata, higher-order functions and program transformers. Applications include the verification and transformation of functional versions of insertion sort and quicksort.     

Using induction and rewriting to verify and complete parameterized specifications

In software engineering there is a growing demand for formal methods for the specification and validation of software systems. The formal development of a system might give rise to many proof obligations. We must prove the completeness of the specification and the validity of some inductive properties. In this framework, many provers have been developed. However they require much user interaction even for simple proof tasks. In this paper, we present new procedures to test sufficient completeness and to prove or disprove inductive properties automatically in para-meterized conditional specifications. The method has been implemented in the prover SPIKE. Computer experiments illustrate the improvements in length and structure of proofs, due to parameterization. Moreover, SPIKE offers facilities to check and complete specifications.     

A unifying theory of control dependence and its application to arbitrary program structures

There are several similar, but not identical, definitions of control dependence in the literature. These definitions are given in terms of control flow graphs which have had extra restrictions imposed (for example, end-reachability).We define two new generalisations of non-termination insensitive and non-termination sensitive control dependence called weak and strong control-closure. These are defined for all finite directed graphs, not just control flow graphs and are hence allow control dependence to be applied to a wider class of program structures than before.We investigate all previous forms of control dependence in the literature and prove that, for the restricted graphs for which each is defined, vertex sets are closed under each if and only if they are either weakly or strongly control-closed. Low polynomial-time algorithms for producing minimal weakly and strongly control-closed sets over generalised control flow graphs are given.This paper is the first to define an underlying semantics for control dependence: we define two relations between graphs called weak and strong projections, and prove that the graph induced by a set of vertices is a weak/strong projection of the original if and only if the set is weakly/strongly control-closed. Thus, all previous forms of control dependence also satisfy our semantics. Weak and strong projections, therefore, precisely capture the essence of control dependence in our generalisations and all the previous, more restricted forms. More fundamentally, these semantics can be thought of as correctness criteria for future definitions of control dependence.     

FIOWHM operator and its application to multiple attribute group decision making

To study the problem of multiple attribute decision making in which the decision making information values are triangular fuzzy number, a new group decision making method is proposed. Then the calculation steps to solve it are given. As the key step, a new operator called fuzzy induced ordered weighted harmonic mean (FIOWHM) operator is proposed and a method based on the fuzzy weighted harmonic mean (FWHM) operator and FIOWHM operators for fuzzy MAGDM is presented. The priority based on possibility degree for the fuzzy multiple attribute decision making problem is proposed. At last, a numerical example is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.     

基于免疫的粗糙集属性约简算法及应用

地下施工中影响施工的风险影响因素十分繁杂,为了从中剔除不必要或不重要的因素,提出一种新的基于免疫的粗糙集属性约简算法--IRSAR.该算法在求出决策表的相对核core的基础上初始化抗体群,并定义了新的亲和度计算函数和克隆增殖函数,有效地提高了亲和度的收敛速度.利用记忆数组存放每一代中满足条件的抗体,制定了记忆数组更新策略,从而得到最优抗体.实验结果表明,IRSAR算法能够较快地得出合理有效的约简结果.     

A new approach to code motion and its application to hoisting

An approach to code motion and hoisting, a program optimization technique, is discussed. The safety and profitability of optimization in general and hoisting in particular are analyzed. By restricting the analysis to a spanning tree imposed on the program graph, a linear algorithm is developed that provides sufficient but not necessary conditions for hoisting.     

粒的位表示及其在属性约简中的应用

粒计算是一种新的软计算思想,它涵盖了所有和粒度相关的理论、方法和技术.提出了一种信息粒的位表示方法,从而将繁琐的集合运算转化为更适于计算机运算的二进制数的逻辑运算,并基于此提出了一种新的属性约简算法.实验结果表明,该算法在时间上较当前的其它同类算法具有更高的效率.     

An integrated crosscutting concern migration strategy and its semi-automated application to JHotDraw

In this paper we propose a systematic strategy for migrating crosscutting concerns in existing object-oriented systems to aspect-oriented programming solutions. The proposed strategy consists of four steps: mining, exploration, documentation and refactoring of crosscutting concerns. We discuss in detail a new approach to refactoring to aspect-oriented programming that is fully integrated with our strategy, and apply the whole strategy to an object-oriented system, namely the JHotDraw framework. Moreover, we present a method to semi-automatically perform the aspect-introducing refactorings based on identified crosscutting concern sorts which is supported by a prototype tool called sair. We perform an exploratory case study in which we apply this tool on the same object-oriented system and compare its results with the results of manual migration in order to assess the feasibility of automated aspect refactoring. Both the refactoring tool sair and the results of the manual migration are made available as open-source, the latter providing the largest aspect-introducing refactoring available to date. We report on our experiences with conducting both case studies and reflect on the success and challenges of the migration process. M. Marin is a guest at Delft University of Technology.     

Hybrid similarity measure for case retrieval in CBR and its application to emergency response towards gas explosion

Case retrieval is a primary step in case-based reasoning (CBR). It is important to measure the similarity between each historical case and the target case during the case retrieval process. In recent years, some methods for similarity measure with multiple formats of attribute values can be found in the practical CBR applications, but the in-depth study is still lacking. The objective of this paper is to develop a new method for hybrid similarity measure with five formats of attribute values: crisp symbols, crisp numbers, interval numbers, fuzzy linguistic variables and random variables. First, for each format of the attribute values, the calculation formula to measure the attribute similarity is presented. Then, the method for measuring hybrid similarity between each historical case and the target case is given by aggregating attribute similarities using the simple additive weighting method, and the proper historical case(s) can be retrieved according to the obtained hybrid similarities afterwards. Finally, a case study in the field of emergency response towards gas explosion is introduced to illustrate the use of the proposed method.