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(Speaking of which, Rust-GCC (or gcc-rs or gccrs or whichever other of their names they decide is the primary one) isn't even going to be a complete C++ implementation. Their plan is to implement enough to compile Polonius (the NLL 2.0 borrow checker being developed in Rust for rustc) and then share that since borrow-checking isn't necessary for codegen... only to identify and reject invalid programs... making the C++ portion of it not that different in scope from mrustc.)
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Work has, in fact, already started on a specification, too! Theres also Ferrocene, which seeks to certify a specific version of the compiler
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Additionally, there is gcc codegen for rustc (https://github.com/rust-lang/rustc_codegen_gcc), which is not a compiler per se, but an alternative code generator, with more architectures supported and other nice things. It's also coming along, but there's still a lot of work to do there too. There's also Cranelift codegen (https://github.com/bjorn3/rustc_codegen_cranelift), which is designed to make debug builds faster, but this is not as exciting/useful as the other 2.
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Additionally, there is gcc codegen for rustc (https://github.com/rust-lang/rustc_codegen_gcc), which is not a compiler per se, but an alternative code generator, with more architectures supported and other nice things. It's also coming along, but there's still a lot of work to do there too. There's also Cranelift codegen (https://github.com/bjorn3/rustc_codegen_cranelift), which is designed to make debug builds faster, but this is not as exciting/useful as the other 2.
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Also on the list of compilers making progress is https://github.com/LightningCreations/lccc. It is also pure rust from top to bottom, with a completely custom intermediate architecture, call xlang.
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And it's not the only significant language oriented project, where other approaches won over rust recently. Important research projects like LLHD had in fact to be rewritten from rust to C++, before the finally got accepted and found their way into the MLIR and CIRCT(https://circt.llvm.org/) mainline code base.