Top-Down Parsing Language (TDPL) is a type of analytic formal grammar developed by Alexander Birman in the early 1970s in order to study formally the behavior of a common class of practical top-down parsers that support a limited form of backtracking. Birman originally named his formalism the TMG Schema (TS), after TMG, an early parser generator, but it was later given the name TDPL by Aho and Ullman in their classic anthology The Theory of Parsing, Translation and Compiling. Definition of a TDPL grammar Formally, a TDPL grammar G is a tuple consisting of the following components: A finite set N of nonterminal symbols. A finite set Σ of terminal symbols that is disjoint from N. A finite set P of production rules, where a rule has one of the following forms: A ← ε, where A is a nonterminal and ε is the empty string. A ← f, where f is a distinguished symbol representing unconditional failure. A ← a, where a is any terminal symbol. A ← BC/D, where B, C, and D are nonterminals. Interpretation of a grammar A TDPL grammar can be viewed as an extremely minimalistic formal representation of a recursive descent parser, in which each of the nonterminals schematically represents a parsing function. Each of these nonterminal-functions takes as its input argument a string to be recognized, and yields one of two possible outcomes: success, in which case the function may optionally move forward or consume one or more characters of the input string supplied to it, or failure, in which case no input is consumed. Note that a nonterminal-function may succeed without actually consuming any input, and this is considered an outcome distinct from failure. A nonterminal A defined by a rule of the form A ← ε always succeeds without consuming any input, regardless of the input string provided. Conversely, a rule of the form A ← f always fails regardless of input. A rule of the form A ← a succeeds if the next character in the input string is the terminal a, in which case the nonterminal succeeds and consumes that one terminal; if the next input character does not match (or there is no next character), then the nonterminal fails. A nonterminal A defined by a rule of the form A ← BC/D first recursively invokes nonterminal B, and if B succeeds, invokes C on the remainder of the