A formal definition of the syntactic structure of a language (see syntax), normally given in terms of production rules which specify the order of constituents and their sub-constituents in a sentence (a well-formed string in the language). Each rule has a left-hand side symbol naming a syntactic category (e.g. "noun-phrase" for a natural language grammar) and a right-hand side which is a sequence of zero or more symbols. Each symbol may be either a terminal symbol or a non-terminal symbol. A terminal symbol corresponds to one "lexeme" - a part of the sentence with no internal syntactic structure (e.g. an identifier or an operator in a computer language). A non-terminal symbol is the left-hand side of some rule.
One rule is normally designated as the top-level rule which gives the structure for a whole sentence.
A grammar can be used either to parse a sentence (see parser) or to generate one. Parsing assigns a terminal syntactic category to each input token and a non-terminal category to each appropriate group of tokens, up to the level of the whole sentence. Parsing is usually preceded by lexical analysis. Generation starts from the top-level rule and chooses one alternative production wherever there is a choice.
See also BNF, yacc, attribute grammar, grammar analysis.