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.