It seems to me that all democratic countries, e.g. republics and representative monarchies, also have a constitution of sorts.
On the other hand, what defines a democratic country is the "power to the people" ergo the ability to decide, directly or indirectly, what laws are passed.
So, it's not so obvious to me that a constitution, in other words a primary set of rules, is necessary. Countries could do with tradition or simply with a set of laws, none of which are more fundamental than others.
Is this correct? If yes, are there examples of democratic countries with no constitution or equivalent?