Definition:Parsing Sequence

Definition
Let $\mathcal F$ be a formal language.

Let $S$ be a word in $\mathcal F$.

A parsing sequence for $S$ in $\mathcal F$ is a sequence of well-formed words in $\mathcal F$ formed by application of rules of formation of $\mathcal F$ from previous well-formed words in this sequence, and ending in the string $S$.

If $S$ has no parsing sequence in $\mathcal F$, then it is not a well-formed word in $\mathcal F$.

A parsing sequence for a given well-formed word in any formal language is usually not unique.

Thus, we can determine whether $S$ is a well-formed word in any formal language by using a sequence of rules of formation of that language.

To parse a word in a formal language is to find a parsing sequence for that word, and thereby to determine whether or not it is a well-formed word.