I'll mention that the "Lean way" for constructivity is that you write `def`s for constructions. These can depend on classical reasoning for well-typedness if you want (like for being sure a number is in range when indexing an array), but there is a computability checker. In particular, the compiler sees if there is a way to lower the `def` into some simply typed IR, and this IR can be further compiled to C. If you trust the compiler, then you can trust whether it's real construction.

(Of course, you can also go and prove a definition evaluates to some value if you don't want to trust the evaluator.)