Editing Abstract interpretation (section)

==Intuition==
This section illustrates abstract interpretation by means of real-world, non-computing examples.

Consider the people in a conference room.  Assume a unique identifier for each person in the room, like a [[social security number]] in the United States.  To prove that someone is not present, all one needs to do is see if their social security number is not on the list. Since two different people cannot have the same number, it is possible to prove or disprove the presence of a participant simply by looking up their number.

However it is possible that only the names of attendees were registered. If the name of a person is not found in the list, we may safely conclude that that person was not present; but if it is, we cannot conclude definitely without further inquiries, due to the possibility of [[homonym]]s (for example, two people named John Smith).  Note that this imprecise information will still be adequate for most purposes, because homonyms are rare in practice. However, in all rigor, we cannot say for sure that somebody was present in the room; all we can say is that they were ''possibly'' here. If the person we are looking up is a criminal, we will issue an ''alarm''; but there is of course the possibility of issuing a ''false alarm''. Similar phenomena will occur in the analysis of programs.

If we are only interested in some specific information, say, "was there a person of age <math>n</math> in the room?", keeping a list of all names and dates of births is unnecessary. We may safely and without loss of precision restrict ourselves to keeping a list of the participants' ages. If this is already too much to handle, we might keep only the age of the youngest, <math>m</math> and oldest person, <math>M</math>. If the question is about an age strictly lower than <math>m</math> or strictly higher than <math>M</math>, then we may safely respond that no such participant was present. Otherwise, we may only be able to say that we do not know.

In the case of computing, concrete, precise information is in general not computable within finite time and memory (see [[Rice's theorem]] and the [[halting problem]]). [[Abstraction]] is used to allow for generalized answers to questions (for example, answering "maybe" to a yes/no question, meaning "yes or no", when we (an algorithm of abstract interpretation) cannot compute the precise answer with certainty); this simplifies the problems, making them amenable to automatic solutions. One crucial requirement is to add enough vagueness so as to make problems manageable while still retaining enough precision for answering the important questions (such as "might the program crash?").