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Recursive descent with backtracking is a technique that determines which production to use by trying each production in turn. Recursive descent with backtracking is not limited to LL(k) grammars, but is not guaranteed to terminate unless the grammar is LL(k).
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 ≥ ...
For every LL(k) grammar, a structurally equivalent strong LL(k) grammar can be constructed. [6] 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.
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
The algorithm that is presented here does not need an explicit stack; instead, it uses recursive calls to implement the stack. The algorithm is not a pure operator-precedence parser like the Dijkstra shunting yard algorithm. It assumes that the primary nonterminal is parsed in a separate subroutine, like in a recursive descent parser.
Context-free languages are a category of languages (sometimes termed Chomsky Type 2) which can be matched by a sequence of replacement rules, each of which essentially maps each non-terminal element to a sequence of terminal elements and/or other nonterminal elements.
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Packrat parser: a linear time parsing algorithm supporting some context-free grammars and parsing expression grammars; Recursive descent parser: a top-down parser suitable for LL(k) grammars; Shunting-yard algorithm: converts an infix-notation math expression to postfix; Pratt parser; Lexical analysis