The issue isn't whether it's possible to have parsers, but whether it's possible to have them be secure, and periodic CVEs "everywhere" suggest we don't
Aside from memory safety, which is solved by using a compiler that just doesn't allow unsafe memory operations (so not GCC or Clang upstream), which CVEs specifically would have been ameliorated by a parser written in Rust instead of C?
Aside from memory safety, which is solved by using a compiler that just doesn't allow unsafe memory operations (so not GCC or Clang upstream), which CVEs specifically would have been ameliorated by a parser written in Rust instead of C?