Simple LR(k) grammars

Abstract

A class of context-free grammars, called the "Simple LR(k)" or SLR(k) grammars is defined. This class has been shown to include weak precedence and simple precedence grammars as proper subsets. How to construct parsers for the SLR(k) grammars is also shown. These parser-construction techniques are extendible to cover all of the LR(k) grammars of Knuth; they have been implemented and by direct comparison proved to be superior to precedence techniques, not only in the range of grammars covered, but also in the speed of parser construction and in the size and speed of the resulting parsers.

Validating LR(1) Parsers

“…We claim that this property holds: the automata produced by Menhir use default actions for this purpose (see Remark 1 in §2. 4). However, at present, we cannot even state this property, because it is an intensional property of the function parse: "if parse(ω, n) = parsed v ω , then ω has not been forced".…”

“…(We discuss this issue in §7. ) Barthwal and Norrish [2] and Barthwal [3] use the HOL4 proof assistant to formalize SLR [4] parsing. For a context-free grammar, they construct an SLR parser, and are able to prove it sound and complete: the guarantees that they obtain are analogous to our Theorems 1 and 3.…”

“…It is relatively simple, and, to the best of our knowledge, original. It applies indifferently to many flavors of LR(1) automata, including LR(0) (a degenerate case), SLR [4], LALR [5], Pager's method [6], and canonical LR(1) [7]. The second contribution is a soundness proof for this algorithm, mechanized using the Coq proof assistant, guaranteeing with the highest confidence that if the validation of an automaton A against a grammar G succeeds, then the automaton A and the interpreter that executes it form a correct parser for G. The last contribution is an experimental assessment of our approach over the ISO C99 grammar, demonstrating applicability to realistic parsers of respectable size.…”

A general scheme for some deterministically parsable grammars and their strong equivalents

“…As typical examples strong LL(k) grammars and simple LR(k) grammars [2] deserve to be mentioned. This fact has lead to the investigation of transformations converting grammars into their "strong" counterparts (cf.…”

“…This fact has lead to the investigation of transformations converting grammars into their "strong" counterparts (cf. [2,17]). We next show all these classes of grammars to possess a certain "common denominator".…”