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Yes. At least one variant of C supports this. Its call stacks are bounded in size: you can't call functions within functions indefinitely. It is used for embedded devices.


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Can a programming language be designed to use a fixed amount of memory? Yes. Brainf*ck works on an array of $30,000$ memory cells. But, it's an esoteric language. Meaning, you're not supposed to use it for professional purposes.


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