Sentential form

A sentential form of a formal grammar $G=(N,\Sigma ,P,S)$ is any word $\alpha \in (N\cup \Sigma {)}^{\ast }$ derivable from the start symbol: $S{\Rightarrow }^{\ast }\alpha$. It may contain both terminal symbols and nonterminal symbols. A terminal-only sentential form is a word of the generated formal language.

For productions $S\to aSb$ and $S\to \epsilon$, the derivation $S\Rightarrow aSb\Rightarrow aaSbb\Rightarrow aabb$ contains four sentential forms. The intermediate $aaSbb$ is not a sentence of the terminal language because $S$ remains. An arbitrary word over $N\cup \Sigma$ need not be a sentential form: it must actually be reachable by a grammar derivation.

Tracking sentential forms makes it possible to discuss intermediate parsing states and distinguish leftmost derivations from other orders of rewriting. The word need not be a complete output or a prefix of one in an arbitrary grammar.