Grammars of this type can match anything that can be matched by a regular grammar, and furthermore, can handle the concept of recursive 'nesting' ('every A is eventually followed by a matching B'), such as the question of whether a given string contains correctly-nested parentheses. (This is typically handled by a Chomsky Type 2 grammar, also termed a context-free grammar.)ĭFA direct code, DFA table driven, and NFA regex librariesĭeterministic context-free languages Ĭontext-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. A classic example of a problem which a regular grammar cannot handle is the question of whether a given string contains correctly-nested parentheses. In particular, a regular language can match constructs like 'A follows B', 'Either A or B', 'A, followed by zero or more instances of B', but cannot match constructs which require consistency between non-adjacent elements, such as 'some instances of A followed by the same number of instances of B', and also cannot express the concept of recursive 'nesting' ('every A is eventually followed by a matching B'). Regular languages are a category of languages (sometimes termed Chomsky Type 3) which can be matched by a state machine (more specifically, by a deterministic finite automaton or a nondeterministic finite automaton) constructed from a regular expression.

4 General context-free, conjunctive, or boolean languages.

3 Parsing expression grammars, deterministic boolean grammars.

Install antlr4 under python3 for mac