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Grammar
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1. \Gram"mar\, n. [OE. gramere, OF. gramaire, F. grammaire
   Prob. fr. L. gramatica Gr ?, fem. of ? skilled in grammar,
   fr. ? letter. See {Gramme}, {Graphic}, and cf. {Grammatical},
   {Gramarye}.]
   1. The science which treats of the principles of language;
      the study of forms of speech, and their relations to one
      another; the art concerned with the right use aud
      application of the rules of a language, in speaking or
      writing.
   Note: The whole fabric of grammar rests upon the classifying
         of words according to their function in the sentence.
         --Bain.
   2. The art of speaking or writing with correctness or
      according to established usage; speech considered with
      regard to the rules of a grammar.
            The original bad grammar and bad spelling.
                                                  --Macaulay.
   3. A treatise on the principles of language; a book
      containing the principles and rules for correctness in
      speaking or writing.
   4. treatise on the elements or principles of any science; as,
      a grammar of geography.
   {Comparative grammar}, the science which determines the
      relations of kindred languages by examining and comparing
      their grammatical forms.
   {Grammar school}.
      (a) A school, usually endowed, in which Latin and Greek
          grammar are taught, as also other studies preparatory
          to colleges or universities; as, the famous Rugby
          Grammar School. This use of the word is more common in
          England than in the United States.
                When any town shall increase to the number of a
                hundred families or householders, they shall set
                up a grammar school, the master thereof being
                able to instruct youth so far as they may be
                fitted for the University.        --Mass.
                                                  Records
                                                  (1647).
      (b) In the American system of graded common schools an
          intermediate grade between the primary school and the
          high school, in which the principles of English
          grammar are taught.
   

2. \Gram"mar\, v. i.
   To discourse according to the rules of grammar; to use
   grammar. [Obs.] --Beau. & Fl.
   

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.