LIFO stack algorithm design

Question

I'm implementing a stack-based VM and I've been trying to read up on literature that explains or outlines algorithms for dealing with stacks no no avail. Here's an example:

int i = 3
int j = 4
int k = 5

Lets assume i, j, and k are local variables so they would be traditionally stored on the stack. The assembly/bytecode translation would look something like:

pushi 3
pushi 4
pushi 5

And the stack would be: 5 4 3

I have an integer stack and a string stack, hence the pushi, however my question is without storing these on the heap (with some ptr* or literal identifier), how would a compiler or interpreter know that if I want to do something like int x = i + j after the definition, I have to pop two and three times, respectively, as well as do my best not to lose k (save it in a register or something, then push it back)?

I hope my question made some sense and there's probably a much smarter approach :P Thank you for any insight!

Answer 1

This is usually done with something called a stack frame. You allocate space for all local variables at once (modulo variables allocated/optimized into registers), store base address of that block, and operate on offsets from there. Then pop everything off the stack on scope exit.