Let's say I have Java or C or C++ or foo language on a computer with a connection to the world wide web and I want to programmatically check if a domain foo.com, or bar.net has been registered, how could I do it without relying on an outside service?
I'm looking for the principle here, code to make a connection is not needed.
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If you need all information, you'll need to implement the whois protocol. I found this wiki for a list of whois servers (dutch wiki, might be less informative than the english)
Your best bet is to ask WHOIS. AFAIK a DNS lookup might not always return a result even though the domain might still be registered.