Top-down parser that parses input from left to right
In computer science, an LL parser (Left-to-right, leftmost derivation) is a top-down parser for a restricted context-free language. It parses the input from Left to right, performing Leftmost derivation of the sentence.
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(k) 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 ≥ 0.[1] A corollary of this is that not all context-free languages can be recognized by an LL(k) parser.
An LL parser is called LL-regular (LLR) if it parses an LL-regular language.[clarification needed][2][3][4] The class of LLR grammars contains every LL(k) grammar for every k. For every LLR grammar there exists an LLR parser that parses the grammar in linear time.[citation needed]
Two nomenclative outlier parser types are LL(*) and LL(finite). A parser is called LL(*)/LL(finite) if it uses the LL(*)/LL(finite) parsing strategy.[5][6] LL(*) and LL(finite) parsers are functionally closer to PEG parsers. An LL(finite) parser can parse an arbitrary LL(k) grammar optimally in the amount of lookahead and lookahead comparisons. The class of grammars parsable by the LL(*) strategy encompasses some context-sensitive languages due to the use of syntactic and semantic predicates and has not been identified. It has been suggested that LL(*) parsers are better thought of as TDPL parsers.[7]
Against the popular misconception, LL(*) parsers are not LLR in general, and are guaranteed by construction to perform worse on average (super-linear against linear time) and far worse in the worst-case (exponential against linear time).
LL grammars, particularly LL(1) grammars, are of great practical interest, as parsers for these grammars are easy to construct, and many computer languages are designed to be LL(1) for this reason.[8] LL parsers may be table-based,[citation needed] i.e. similar to LR parsers, but LL grammars can also be parsed by recursive descent parsers. According to Waite and Goos (1984),[9] LL(k) grammars were introduced by Stearns and Lewis (1969).[10]
^Rosenkrantz, D. J.; Stearns, R. E. (1970). "Properties of Deterministic Top Down Grammars". Information and Control. 17 (3): 226–256. doi:10.1016/s0019-9958(70)90446-8.
^Jarzabek, Stanislav; Krawczyk, Tomasz (1974). "LL-Regular Grammars". Instytutu Maszyn Matematycznych: 107–119.
^Jarzabek, Stanislav; Krawczyk, Tomasz (Nov 1975). "LL-Regular Grammars". Information Processing Letters. 4 (2): 31–37. doi:10.1016/0020-0190(75)90009-5.
^David A. Poplawski (Aug 1977). Properties of LL-Regular Languages (Technical Report). Purdue University, Department of Computer Science.
^Parr, Terence and Fisher, Kathleen (2011). "LL (*) the foundation of the ANTLR parser generator". ACM SIGPLAN Notices. 46 (6): 425–436. doi:10.1145/1993316.1993548.{{cite journal}}: CS1 maint: multiple names: authors list (link)
^Belcak, Peter (2020). "The LL(finite) parsing strategy for optimal LL(k) parsing". arXiv:2010.07874 [cs.PL].
^Pat Terry (2005). Compiling with C# and Java. Pearson Education. pp. 159–164. ISBN 9780321263605.
^William M. Waite and Gerhard Goos (1984). Compiler Construction. Texts and Monographs in Computer Science. Heidelberg: Springer. ISBN 978-3-540-90821-0. Here: Sect. 5.3.2, p. 121-127; in particular, p. 123.
^Richard E. Stearns and P.M. Lewis (1969). "Property Grammars and Table Machines". Information and Control. 14 (6): 524–549. doi:10.1016/S0019-9958(69)90312-X.
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