Semantic routines and LR(k) parsers

Summary Most applications of parsing require that the parser call semantic action routines while processing the input. For LR(k) parsers it is well known that a semantic action routine can be called when the end of a production is recognized. Often, however, it is desirable to call routines at other times.This paper presents fast algorithms that determine, for an LR(k) (or SLR(k)) grammar, which positions are suitable for calling routines. The algorithms are practical for use with LR(1) (SLR(1)) parser building programs, because the worst case running time is dominated by the time required to build the LR(1) (SLR(1)) parser. Applications of the algorithms to attribute grammars and automatic indentation are discussed.     

The lane-tracing algorithm for constructing LR (k) parsers and ways of enhancing its efficiency

The paper presents, as far as the author is aware, the first practical general method for constructing LR (k) parsers. It has been used without computational difficulty to produce LR(1), LR(2), and LR(3) parsers for grammars of the size of ALGOL. The algorithm involved consists of two phases, where phase 2, the state-splitting phase, is applied if phase 1 fails. Only the most important case of phase 1 with k = 1 is presented in detail here. Ways of enhancing the efficiency of the algorithm are considered and, in particular, a method is provided whereby the work required for phase 1 when k = 1 is at most a linear function of the number of configurations.     

Upper bounds on the size of LR(k) parsers

It is shown that in many cases the trivial upper bound 2^{|G|k + 1} on the number of states of an LR(k) parser for a grammar G is too conservative. In particular, if G is not right-recursive, the canonical LR(k) parser for G has at most |G^k|G|·2^|G| states. Examples of grammars with large LR(k) parsers are given.     

An alternative approach to the improvement of LR(k) parsers

Summary The methods of improving LR(k) parsers proposed by DeRemer and Korenjak are shown to be based on a single concept — that of modifying the contextual information on which parsing decisions are made. This concept is then used to derive a straightforward algorithm for eliminating unit productions from an LR parser.     

Eliminating unit reductions from LR(k) parsers using minimum contexts

Summary This paper presents a new approach to the design and the proof of bypassed LR(k) parsers; a bypassed LR(k) parser is an LR(k) parser which does not perform any reductions caused by insignificant unit productions. We show that bypassed LR(k) parsers having minimum set of reduction contexts always exist for Knuth LR(k) parsers, but do not necessarily exist for SLR(k) and LALR(k) parsers. As byproducts of our approach, we naturally derive Anderson, Eve and Homing's algorithm [5] and a sufficient condition for the existence of bypassed SLR(1) parsers.     

On a method for optimizing LR parsers

It is shown that if the basic method for eliminating single productions from canonical LR parsers developed by Pager is applied to an SLR parser and the resulting parser is free of conflicts, then the resulting parser is a valid parser which accepts exactly the strings in the language. However, if the elimination process is performed during the construction of an SLR parser, then the resulting parser may be invalid even if it were free of conflicts.     

LR(0) grammars generated by LR(0) parsers

Summary Let be an LR(0) parser of a given LR(0) grammar G. Generally, does not only parse the words generated by G but also the words of some other LR(0) grammars different from G. In this paper we shall define a class of LR(0) parsers and shall present a characterization and a method for the construction of all LR(0) grammars which can be parsed by a given LR(0) parser.     

Truly prefix-correct chain-free LR(1) parsers

Summary A refinement of Pager's method for the elimination of chain productions from LR parsers is presented. A practical algorithm is given and it is shown that the resulting parsers are prefix-correct in a very strict sense.     

LR(k)任意文法位置的断点调试方法

LR(k)文法能描述所有确定型上下文无关语言,广泛应用于各类分析器生成器中.传统的LR(k)文法断点调试方法仅支持在产生式右部末尾设置断点(后文简称尾部断点),不支持在产生式右部中间位置设置断点(后文简称中间断点),这给分析器的开发和调试带来了不便.文中提出了一种新颖的LR(k)文法断点调试方法,不但支持传统的尾部断点,还支持中间断点.该方法可显著增加可利用的断点数量,可以跟踪到更细粒度的文法成分,从而帮助用户更好地进行文法调试,降低分析器的开发难度.     

Parsing extended LR(k) grammars

Summary An extended LR(k) (ELR(k)) grammar is a context free grammar in which the right sides of the productions are regular expressions and which can be parsed from left to right with k symbol look-ahead. We present a practical algorithm for producing small fast parsers directly from certain ELR(k) grammars, and an algorithm for converting the remaining ELR(k) grammars into a form that can be processed by the first algorithm. This method, when combined with previously developed methods for improving the efficiency of LR(k) parsers, usually produces parsers that are significantly smaller and faster than those produced by previous LR(k) and ELR(k) algorithms.     

Constructing LR parsers for regular right part grammars

Summary Regular right part (RRP) grammars differ from context free (CF) grammars by virtue of the fact that the production right parts are nondeterministic finite automatons (FAs). LR(k) parsers for RRP grammars are linear time parsers which can determine the right end of each handle by considering at most k terminal symbols to its right and the left end (after the right end has been found) by considering at most one parse stack state to its left. This paper is concerned with the construction of a class of LR(k) parsers for RRP grammars which makes use of FAs for determining both the right and left ends of the handle.This work has been supported by a Carleton University grant and National Research Council of Canada grant no. A3585     

On LR(k) grammars and languages

Many different definitions for LR(k) grammars exist in the literature. One of these definitions is chosen and many important implications are drawn from it. In particular, the LR(k) characterization theorem provides valuable information about chains of derivations. The LR(0) languages are then characterized by acceptance by deterministic pushdown automata with a special termination condition, by a condition on the strings in the language, and set theoretically. Important closure properties of the LR(0) languages and a related class of languages are then examined. These are used to examine some decidability questions relating to the class of LR languages. One of these questions is shown to be equivalent to the equality problem for deterministic pushdown automata.A survey of other LR(k) definitions is given and the exact differences are characterized. On the basis of this analysis, justification for the choice of definition used here is provided.     

On the relationship between the LL(k) and LR(k) grammars

In the literature various proofs of the inclusion of the class of LL(k) grammars into the class of LR(k) grammars can be found. Some of these proofs are not correct, others are informal, semi-formal or contain flaws. Some of them are correct but the proof is less straightforward than demonstrated here.     

A language independent error recovery method for LL(1) parsers

An efficient and systematic LL(1) error recovery method is presented that has been implemented for an LL(1) parser generator. Error messages which provide good diagnostic information are generated automatically. Error correction is done by discarding some input symbols and popping up some symbols from the parsing-stack in order to restore the parser to a valid configuration. Thus, symbol deletions and insertions are simulated. The choice between different possible corrections is made by comparing the cost of the inserted (popped) symbols with the reliability value of the recovery symbol (the first input symbol that is not discarded). Our concept of reliability is based on the observation that input symbols differ from each other in their ability to serve as recovery points. A high reliability value of a symbol asserts that it was probably not placed in the input by accident. So it is reasonable not to discard that symbol but to resume parsing. This is done even if a string with high insert-cost has to be inserted before that symbol in order to fit it to the part of the program that has already been analysed. The error recovery routine is invoked only when an error is detected. Thus, there is no additional time required for parsing correct programs. Error-correcting parsers for different languages, including Pascal, have been generated. Some experimental results are summarized.     

A scheme for LR(k) parsing with error recovery part II: error recovery

The paper is the second in a series of three papers devoted to a detailed study of LR(k) parsing with error recovery and correction. Error recovery in LR(k) parsing of a context-free grammar is formalized by extending an LR(k) parser of the grammar such that it accepts all strings over the terminal vocabulary. The parse produced by this extension for a terminal string is a right parse if the string is in the language. In the case of a string not in the language the parse produced by the extension contains so-called error productions which represent the error recovery actions performed by the extension. The treatment is based on the formalization of LR(k) parsing presented in the first paper in the series and it covers practically all error recovery methods designed for LR(k) parsing.     

A practical method for constructing the mixture model for a spectral class

Remotely sensed multispectral image data are found in grouped form with (say) s spectral components (bands). In this study, a practical method for constructing a mixture model or the probability density function of the mixture of k (3 =< k =< s) normal distributions for a spectral class is given. A new method for estimation of the mixing proportions of spectral components (bands) in the remotely sensed multispectral image data is proposed with the assumption that the spectral component (band) means are different from each other.     

Efficient parsing algorithms for general context-free parsers

A family of parsing algorithms for general context-free grammars is described. Its members have a top-down structure, while performing tests similar to those introduced in both LR and LL algorithms. A theoretical study shows that the algorithms have the same time and space bounds as Earley's algorithms, which are particular members of the family. Empirical comparisons show the effectiveness of the new members of the family, which appear to be definitely better than Earley's algorithms, except for a few pathological grammars.     

基于Z规格的LR(k)形式化分析及验证

在编译器的构造中,常由于语义的二义性等问题导致不正确的目标程序.为解决此问题,提出了一种新型的语法及语义正确性验证方案,即建立LR (k)文法和Z规格说明的联系,以此构造LR (k)文法的形式化描述及其形式化验证.实验结果表明,该方案能有效描述并检测LR (k)文法分析器中的语法错误及语义二义性,有助于提高分析器的有效性.     

A practical method of constructing surfaces in three-dimensional digitized space

We propose a new, practical algorithm for constructing the surface of a three-dimensional object from its planar cross-sections. This algorithm deals with a general case where each cross-section of the object is given as a two-dimensional digital image and no topological information about these two adjacent cross-sections is assumed. In particular, it can handle the case where there are several connected components with some holes in each cross-section. The algorithm's principle is derived from the region growing technique. which is well-known in two-dimensional image processing. By combining this algorithm with existing shading techniques, we can obtain a realistic image of a three-dimensional object.