And no, a constitutional republic is not government ruled by a constitution. That would be a constitutional anything. Communist China is ruled by a constitution. Iran has a constitution. Interestingly, the Kingdom of Saudi Arabia, while a monarchy, says its constitution is the Koran...and I have heard some Christians say such should be the case with the USA and the Holy Bible, which is as good an argument for separation of church and state as any.
Constitutional Republic definition by the Oxford Dictionary is given as, A form of government which is a republican government which is governed on the basis of the Law of constitution.
We are NOT a democracy.