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$\begingroup$ Great answer! But, strictly, the prover we run on top of CakeML (which we call Candle) is based on HOL Light. And that version of the kernel is verified to the extent that Gödel's theorem permits. The tower is thus: SML (poly/ml) / HOL4 / CakeML / Candle (HOL Light-ish) $\endgroup$
– Michael Norrish
Commented Feb 19 at 23:00
1

$\begingroup$ Re the right tool for the job: it is not just parsers and interpreters, a lot of what happens in proof assistant implementation is manipulation of very structured data, aka algebraic datatypes, such as ASTs. These constructs were historically only available in functional languages (along with good pattern-matching, which is necessary to manipulate these structures easily). $\endgroup$
– Meven Lennon-Bertrand ♦
Commented Feb 20 at 10:21

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