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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
grammar
A formal definition of the syntactic structure (the
syntax) of a language.
A grammar is normally represented as a set 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 parser (a kind of recogniser) uses a grammar to parse a
sentence, assigning 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. The
opposite, generation, starts from the top-level rule and
chooses one alternative production wherever there is a choice.
In computing, a formal grammar, e.g. in BNF, can be used to
parse a linear input stream, such as the source code of a
program, into a data structure that expresses the (or a)
meaning of the input in a form that is easier for the computer
to work with. A compiler compiler like yacc might be used
to convert a grammar into code for the parser of a compiler.
A grammar might also be used by a transducer, a translator
or a syntax directed editor.
See also attribute grammar.
(2009-02-06)