Why are there no types as natural and real numbers?

It is for a long time now known how to implement arbitrary precision numbers.
Why is there not some way that I can choose types for my variables as natural number or rational number (a division between arbitrary precision natural numbers) or real number?

What I want to have is this mathematical hierarchy of numbers.

It's impossible to implement the true set of real numbers in a computer, because some real numbers are not computable.

As for your other question, you can use a library such as GMP.
https://gmplib.org/
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