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An LL parser is called an LL(k) parser if it uses k tokens of lookahead when parsing a sentence. A grammar is called an LL grammar if an LL(k) parser can be constructed from it. A formal language is called an LL(k) language if it has an LL(k) grammar. The set of LL(k) languages is properly contained in that of LL(k+1) languages, for each k ≥ ...
The class of LL(k) languages forms a strictly increasing sequence of sets: LL(0) ⊊ LL(1) ⊊ LL(2) ⊊ …. [7] It is decidable whether a given grammar G is LL(k), but it is not decidable whether an arbitrary grammar is LL(k) for some k. It is also decidable if a given LR(k) grammar is also an LL(m) grammar for some m. [8]
Yacc (Yet Another Compiler-Compiler) is a computer program for the Unix operating system developed by Stephen C. Johnson.It is a lookahead left-to-right rightmost derivation (LALR) parser generator, generating a LALR parser (the part of a compiler that tries to make syntactic sense of the source code) based on a formal grammar, written in a notation similar to Backus–Naur form (BNF). [1]
The parsing problem, checking whether a given word belongs to the language given by a context-free grammar, is decidable, using one of the general-purpose parsing algorithms: CYK algorithm (for grammars in Chomsky normal form) Earley parser; GLR parser; LL parser (only for the proper subclass of LL(k) grammars)
An LL parser is a type of parser that does top-down parsing by applying each production rule to the incoming symbols, working from the left-most symbol yielded on a production rule and then proceeding to the next production rule for each non-terminal symbol encountered. In this way the parsing starts on the Left of the result side (right side ...
But by convention, the LR name stands for the form of parsing invented by Donald Knuth, and excludes the earlier, less powerful precedence methods (for example Operator-precedence parser). [1] LR parsers can handle a larger range of languages and grammars than precedence parsers or top-down LL parsing. [3]
The LALR(1) parser is less powerful than the LR(1) parser, and more powerful than the SLR(1) parser, though they all use the same production rules. The simplification that the LALR parser introduces consists in merging rules that have identical kernel item sets , because during the LR(0) state-construction process the lookaheads are not known.
The LALR parser and its alternatives, the SLR parser and the Canonical LR parser, have similar methods and parsing tables; their main difference is in the mathematical grammar analysis algorithm used by the parser generation tool. LALR generators accept more grammars than do SLR generators, but fewer grammars than full LR(1).