It is often useful to think of a derivation as a tree . BNF and EBNF BNF was invented ca. 1960 and used in the formal description of Algol-60. Descriptions are usually structured around the language's grammar, e.g., they describe what each nonterminal does. Natural-language descriptions tend to be imprecise , incomplete , and inconsistent . If is omitted, it is assumed to be 1.
Implementation becomes standard of correctness.
Rigorous and unambiguous definition in terms of a well-understood formalism, e.g., logic, naive set theory, etc. Independence from implementation . Definition should describe how the language behaves as abstractly as possible. Basis for language comparison. Basis for language design.