Eliminating unit productions from LR parsers

Summary In this paper we show how one can improve upon an algorithm by Aho and Ullman [3] for eliminating unit productions from an LR(k) parser so that the elimination concerned can be made in all cases, instead of only in the special case required by [3] where no two unit productions have the same left-hand side. In most practical grammars this special case does not in fact arise. Since the elimination of unit productions both reduces the size of the parser and increases its speed, it is of value to have a general method for achieving this objective.The algorithm provided eliminates from the parser all nonterminals that occur as left-hand sides of unit productions. This substantially contributes to the reduction in size obtained, and also provides a solution to an open problem by Aho and Ullman [3]. An application of the Algorithm to the parser construction method of Pager [19] is considered, and a method is provided for the use of default reductions and the elimination of final states in conjunction with the elimination of unit reductions. The sizes of the parsers obtained using the parser's algorithm are compared with those of Anderson, Eve, and Horning [4].This work was supported by the National Science Foundation under Grant GJ-43362. A shortened version of the paper was presented at the 2nd colloquium on Automata, Languages and Programming, University of Saarbrücken, July 1974     

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.     

A practical general method for constructing LR(k) parsers

Summary The paper presents in detail the case for k=1 of a practical general method for constructing LR(k) parsers. For k=1 this method is of rival efficiency to the previous general algorithm described by the author in [21]. The method involves combining the states of an LR(k) parser as they are generated, reducing to a fraction, in the process, the number of configurations that need actually be evaluated, or for which space must be assigned — compared to such general methods as those of [1, 11, 12, 17]. The criteria of compatibility introduced for this purpose are such that the parser obtained is in practice identical in size to, or negligibly larger than, that obtained by resolving the inadequacies of an LR(o) parser (as is done for various subsets of the LR(k) grammars in [5, 8, 14, 20]).This paper is a development of one of the ideas proposed in Pager [16]. The work was supported by the National Science Foundation under Grant GJ-43362.     

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.     

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.     

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.     

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.     

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.     

On the space optimizing effect of eliminating single productions from LR parsers

Summary Single productions in the syntax of a programming language usually have no semantic significance, and thus parsers can be modified so that they do not perform reductions by single productions. In this paper we show that the basic method developed by Pager for eliminating all undesired single productions from LR parsers can cause a quadratic increase in the number of states of the parser. We then define an improvement of Pager's basic method such that generally smaller parsers are produced; in fact, even a quadratic decrease in the number of states is possible. This improvement is further evaluated by giving a sequence of practically motivated grammars for which substantial savings in space are obtained. We also characterize this improvement by a grammatical condition under which it is guaranteed that no increase in the number of states can occur. This condition is compared with a similar condition derivable in the case of Pager's original method.Part of this work was carried out when the author was visiting the University of California, Department of Mathematics, at Santa Barbara as an ASLA Fulbright Scholar     

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.     

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 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.     

On comparingLL(k) andLR(k) grammars

A new and rigorous proof of the well-known fact thatLL(k) grammars areLR(k) grammars is provided. The proof is elementary in the sense that it is directly based on relations defining leftmost and rightmost derivations and no additional formalism is needed.     

Very fast YACC-compatible parsers (for very little effort)

We have developed a yacc-compatible parser generator that creates parsers that are 2.0 to 6.0 times faster than those generated by yacc or bison. Our tool, mule, creates directly-executable, hard-coded parsers in ANSI; yacc produces interpreted, table-driven parsers. Two attributes distinguish mule from other parser generators that create hard-coded LR parsers; mule is compatible wtih yacc (including yacc's peculiar error recovery mechanisms), and mule does absolutely none of the complex automata analysis of previous hard-coded-parser generators. Mule creates simple, fast parsers after very little analysis. © 1998 John Wiley & Sons, Ltd.