Why there is
file not found
and so on everywhere, when it should be (as far as I know)
the file was not found
the access is denied
I wonder which is actually correct? Both?
These are status messages similar to traffic signs like No Parking, One Way etc.
Even many news headlines in newspaper are very short and are not full sentences like "Man shot dead", "Man shot at", "Gold up" etc.
Statuses, titles etc need not be full sentences.
I think the main reason language such as this is used for error messages is simple: people don't want to read horrendously long error messages.
Case in point:
It's simple and yet it conveys all of the necessary information.
To answer your question, the shortened messages would not be appropriate anywhere formal language is used, however "the access is denied" is incorrect. You would not use "the" to refer to access, in this case. To be formal, you would say something like "Access to the resource was denied."
"The access" is not a proper construct. "Your access" is fine, but I don't think it's necessary. I'd say "Access was denied" if you want to spell it out more than tradition.
"The file was not found" is grammatically proper.
But "File not found" and "Access denied" get your point across just as well
That probably comes from limited memory in the early days of computing, where typing out a proper sentence would take up more memory and might cause problems. It would have made things simpler to use an improper sentence that still got it's point across. These days though it would hardly make any difference.
As a programmer, I suspect that the message is coming from an underlying error class. The application is merely reporting the name of the type of error that occurred; it's not trying to have an intelligent conversation with the user.
This answer applies to programming in general, but ere is an example of a list of status codes in the HTTP protocol. http://en.wikipedia.org/wiki/List_of_HTTP_status_codes#4xx_Client_Error
You will recognize some of them as messages you have received in your web browser at one time or another.