LR parser

In computer science, LR parsers are a type of bottom-up parser that efficiently read deterministic context-free languages, in guaranteed linear time. There are several variants of LR parsers:SLR parsers, LALR parsers, Canonical LR(1) parsers, Minimal LR(1) parsers, GLR parsers. LR parsers can be generated by a parser generator from a formal grammar defining the syntax of the language to be parsed. They are widely used for the processing of computer languages.00 id9 0 Value70 Products40 Products4 *5 0 Products4 *5int8 0 Products4 *5Value60 Products4 0 Sums1 0 Sums1 +2 0 Sums1 +2 int80 Sums1 +2 Value7 0 Sums1 +2 Products30 Sums1 0 Products4 *5int8 In computer science, LR parsers are a type of bottom-up parser that efficiently read deterministic context-free languages, in guaranteed linear time. There are several variants of LR parsers:SLR parsers, LALR parsers, Canonical LR(1) parsers, Minimal LR(1) parsers, GLR parsers. LR parsers can be generated by a parser generator from a formal grammar defining the syntax of the language to be parsed. They are widely used for the processing of computer languages. An LR parser (Left-to-right, Rightmost derivation in reverse) reads input text from left to right without backing up (this is true for most parsers), and produces a rightmost derivation in reverse: it does a bottom-up parse - not a top-down LL parse or ad-hoc parse. The name LR is often followed by a numeric qualifier, as in LR(1) or sometimes LR(k). To avoid backtracking or guessing, the LR parser is allowed to peek ahead at k lookahead input symbols before deciding how to parse earlier symbols. Typically k is 1 and is not mentioned. The name LR is often preceded by other qualifiers, as in SLR and LALR. The LR(k) condition for a grammar was suggested by Knuth to stand for 'translatable from left to right with bound k.' LR parsers are deterministic; they produce a single correct parse without guesswork or backtracking, in linear time. This is ideal for computer languages, but LR parsers are not suited for human languages which need more flexible but inevitably slower methods. Some methods which can parse arbitrary context-free languages (e.g., Cocke-Younger-Kasami, Earley, GLR) have worst-case performance of O(n3) time. Other methods which backtrack or yield multiple parses may even take exponential time when they guess badly. The above properties of L, R, and k are actually shared by all shift-reduce parsers, including precedence parsers. 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).LR parsers can handle a larger range of languages and grammars than precedence parsers or top-down LL parsing. This is because the LR parser waits until it has seen an entire instance of some grammar pattern before committing to what it has found. An LL parser has to decide or guess what it is seeing much sooner, when it has only seen the leftmost input symbol of that pattern. An LR parser scans and parses the input text in one forward pass over the text. The parser builds up the parse tree incrementally, bottom up, and left to right, without guessing or backtracking. At every point in this pass, the parser has accumulated a list of subtrees or phrases of the input text that have been already parsed. Those subtrees are not yet joined together because the parser has not yet reached the right end of the syntax pattern that will combine them.