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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.
An LL(1) grammar with symbols that have only the empty derivation may or may not be LALR(1). [9] LL grammars cannot have rules containing left recursion. [10] Each LL(k) grammar that is ε-free can be transformed into an equivalent LL(k) grammar in Greibach normal form (which by definition does not have rules with left recursion). [11]
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 ...
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 ...
A formal grammar that contains left recursion cannot be parsed by a naive recursive descent parser unless they are converted to a weakly equivalent right-recursive form. . However, recent research demonstrates that it is possible to accommodate left-recursive grammars (along with all other forms of general CFGs) in a more sophisticated top-down parser by use of curta
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. [5]
A simple tail recursive parser can be written much like a recursive descent parser. The typical algorithm for parsing a grammar like this using an abstract syntax tree is: Parse the next level of the grammar and get its output tree, designate it the first tree, F; While there is terminating token, T, that can be put as the parent of this node:
The multiple valid parse trees are computed simultaneously, without backtracking. GLR is sometimes helpful for computer languages that are not easily described by a conflict-free LALR(1) grammar. LC Left corner parsers use LR bottom-up techniques for recognizing the left end of alternative grammar rules. When the alternatives have been narrowed ...