Derivations

A derivation is the process of deriving a sentence from the start symbol S according to a grammar, i.e., the replacement of nonterminal symbols by the right-hand sides of productions.

We use the symbol ⇒ to denote a derivation step. E ⇒ -E ⇒ -(E) ⇒ -(id) shows the steps in deriving the expression -(id) using an expression grammar.

⇒^* is used to denote derivation in zero or more steps, while ⇒⁺ is used to denote derivation in one or more steps.

In a leftmost derivation, the leftmost nonterminal is replaced in each step. If S ⇒^*_lm α , then α is called a left-sentential form of the grammar G . A leftmost derivation is traced by a predictive, top-down parser such as recursive descent.

In a rightmost (or canonical) derivation, the rightmost nonterminal is replaced in each step. A shift-reduce parser ( e.g. YACC) traces a rightmost derivation ``backwards''.