Definition:Parsing Sequence

Let $$\mathcal{F}$$ be a formal language.

Let $$S$$ be a word in $$\mathcal{F}$$

A parsing sequence for $$S$$ in a $$\mathcal{F}$$ 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 $$S$$.

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.