In abstract mathematical terms, a language is a set of alphanumeric strings of finite length over some fixed, finite alphabet. A grammar is a set of production rules that specify how valid strings in the language may be got--every formal language has a formal grammar implicitly or explicitly associated with it, and vice versa.

Context-free grammars constitute members of a certain class that is described as containing generators of computer languages. Computer languages have rules about how strings must be generated in order to be syntactically correct and meaningful. Grammars are thus needed that generate precisely the correct strings and no others. Two major approaches are possible in respect of the specification of the relationship between grammars and languages--either the language must be specified formally and then a grammar constructed that generates it; or else, a grammar must be specified formally and the language that it...