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I definitely cannot get behind the “no recursion” rule. There are plenty of algorithms where the iterative equivalent is significantly harder and less natural. For example, post-order DFS.
I guess maybe when lives depend on it. But they should be testing and fuzzing their code anyway, right?
EDIT: I can’t even find in the NASA PDF where it mentions recursion.
I would take a look at LEAN4.
https://lean-lang.org/functional_programming_in_lean/