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It's not impossible, it is just highly unlikely that you'll never write a single safety-related bug - especially in nontrivial applications and in mixed C-plus-Rust codebases. For every single bug-free codebase there will be thousands containing undiscovered subtle-but-usually-harmless bugs.

After all, if humans were able to routinely write bug-free code, why even worry about unsoundness and UB in C? Surely having developers write safe C code would be easier than trying to get a massive ecosystem to adopt a completely new and not exactly trivial programming language?

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Rust is not really "completely new" for a good C/C++ coder, it just cleans up the syntax a bit (for easier machine-parsing) and focuses on enforcing the guidelines you need to write safe code. This actually explains much of its success. The fact that this also makes it a nice enough high-level language for the Python/Ruby/JavaScript etc. crowd is a bit of a happy accident, not something that's inherent to it.
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