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A formal grammar that contains left recursion cannot be parsed by a LL(k)-parser or other naive recursive descent parser unless it is converted to a weakly equivalent right-recursive form. In contrast, left recursion is preferred for LALR parsers because it results in lower stack usage than right recursion.
For a general method, see removing left recursion. A simple example for left recursion removal: The following production rule has left recursion on E E -> E '+' T E -> T This rule is nothing but list of Ts separated by '+'. In a regular expression form T ('+' T)*. So the rule could be rewritten as E -> T Z Z -> '+' T Z Z -> ε Now there is no ...
An LALR parser is a software tool to process text into a very specific internal representation that other programs, such as compilers, can work with. This process happens according to a set of production rules specified by a formal grammar for a computer language. An LALR parser is a simplified version of a canonical LR parser.
An) then the grammar will grow exponentially. If the ordering is reversed (An, An-1, .. A1) the grammer is left untouched since every direct left corner already precedes it's definition. A good article on this and alternative algorithms for removing left recursion is Removing Left Recursion from Context-Free Grammars.
Any context-free grammar can be transformed into an equivalent grammar that has no left recursion, but removal of left recursion does not always yield an LL(k) grammar. A predictive parser runs in linear time. Recursive descent with backtracking is a technique that determines which production to use by trying
For example, a grammar for a context-free language is left recursive if there exists a non-terminal symbol A that can be put through the production rules to produce a string with A (as the leftmost symbol). [2] [3] All types of grammars in the Chomsky hierarchy can be recursive and it is recursion that allows the production of infinite sets of ...
In computer science, an operator-precedence parser is a bottom-up parser that interprets an operator-precedence grammar.For example, most calculators use operator-precedence parsers to convert from the human-readable infix notation relying on order of operations to a format that is optimized for evaluation such as Reverse Polish notation (RPN).
Nonetheless, if there is an indirect left recursion involved, the process of rewriting can be quite complex and challenging. If the time complexity requirements are loosened from linear to superlinear , it is possible to modify the memoization table of a Packrat parser to permit left recursion, without altering the input grammar.