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Beam is a register based VM that's probably used more than LUA.

SQLite implements a register based VM too.

I guess the most popular one is either the JVM or the .Net CLR ?

Those are both stack-based.

right. I was misreading this. So for a register based VM, I would have to refer to the Parrot virtual machine then.

ART is register based.

The JVM used an operand stack for local data flow, while the CLR uses registers.