ELVM might be a related project, which takes C code and compiles to various languages, including VIM.
How does it work? Is it translating the C source code of the 8cc C compiler to lambda calculus?
So like C -> ELVM IR -> lambda calculus?
If so, it seems like 8cc is doing most of the heavy lifting
Interested parties should also check out awka (https://github.com/noyesno/awka) and ELVM (which can compile C into awk or sed, among various other things) (https://github.com/shinh/elvm)
Would be interesting to have some -small- (not necessarily small, but portable) C program such as info-zip compiled to bf via ELVM [1] and do a speed comparison.
ELVM (https://github.com/shinh/elvm) is a C compiler with a Turing machine backend.
ELVM [0] also has a C++14 constexpr target, also using 8cc as the frontend !
A C compiler that can output Malbolge (among many other esolangs) can be found at https://github.com/shinh/elvm - dunno if it has any relation to this work.
Note that the Malbolge (or rather LMAO/HeLL) backend was added back in July 2019, so I'm not so sure about their claim that "It's as of 2020 and 2021, the most advanced, usable Malbolge program ever created."
You are looking for ELVM: https://github.com/shinh/elvm/ (I have seen many others, but in terms of activity it seems the most maintained one.)
ELVM uses a modified version of 8cc to compile C into some utterly weird targets. Brainfuck, sed, TeX, whitespace...
And for the other direction (C->sed): https://github.com/shinh/elvm
& through https://github.com/shinh/elvm here's a lisp implementation: http://shinh.skr.jp/elvm/lisp.png
Good tut: http://homepages.vub.ac.be/~diddesen/piet/index.html
Would it be easier to write a HTTP server in C and compile to Brainfuck using ELVM (https://github.com/shinh/elvm)?