Henry - just a quick comment on the class description. I think it would
be better not to include the sentence "Since 1.8 ..." as it that will
quickly become a historical note. It would be much better (in my view)
to just highlight the methods with something like "Several of the
methods take a Supplier function ..." and make the potential performance
benefit of using these methods clear.

You should also add a note saying that the supplier can be specified as
a lambda and in that case, the lambda *must* not capture value of local
variable, otherwise a supplier object will be created each time you log
something.

No, don't do this.

First of all, just because the performance characteristics of capturing lambdas are one way today on HotSpot compared to non-capturing, does not mean we should burn this into spec. Also, there's no way to enforce it.

More importantly, a capturing lambda might still be way better than a String, as in this example:

  log(DEBUG, () -> "Children of " + name + ": " + getChildrenOf(name));

Collecting getChildren (and turning it into a String) commonly involves something thousands of times as expensive as an object creation.

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