What does it mean to correct a formula?

Question

I apologize if this question is too imprecise. In logic textbooks, we are given certain rules for constructing well-formed formulas. For instance, $(x+y)$ is a term. Suppose the logic textbook gives us an exercise to "correct" the formula $x+y$. We would give the answer: $(x+y)$. It is the notion of correcting formulas that I want to make precise. More formally, we are given a certain string $S$, and we want to find a way to "correct" it to a certain well-formed formula $W$. This may not be possible for all strings $S$, and certain strings may have more than one correction. For an example of the latter, consider the string $x+y+z$ and its two corrections $((x+y)+z)$ and $(x+(y+z))$. So, what exactly does it mean to correct a formula? Also, has any book or paper discussed this topic?