True for some approaches, but numerical analysis does account for machine epsilon and truncation errors.
I am aware that Inria works with Coq as your link shows. However, the link itself does not answer my question. As a concrete example, how would you prove an implementation of a Kalman filter is correct?
See ACL2's support for floating point arithmetic.
https://www.cs.utexas.edu/~moore/publications/double-float.p...
SMT solvers also support real number theories:
https://shemesh.larc.nasa.gov/fm/papers/nfm2019-draft.pdf
Z3 also supports real theories:
https://youtu.be/_LjN3UclYzU has a different attempt to formalize Kalman filters which I think we can all agree was not a successful formalization.
https://arxiv.org/pdf/2304.10558