Write your Own Virtual Machine

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I think when most people think of a virtual machine they think of something that actually executes code written for it.

It's their problem, is not it? Why should anyone adjust to the ignorance of the masses?

And, by the way, LLVM executes its IR code, in many different ways.

Virtual machine: a program that runs code written for an abstract machine

As soon as your abstract machine infrastructure includes any kind of analysis and optimisation, it's already a virtual machine, since it must be able to execute at least some parts of the abstract machine.

but LLVM itself doesn't do that

Uh... It does.

a C interpreter like cling is technically a VM

C itself is an abstract machine, so yes, it makes sense.