I have a use case that hat needs to determine if a function supports with_logabsdet_jacobian in a type-stable fashion (try/catch won't do), so that fallback code (logabsdet(ForwardDiff.hessian(...)) in my case) can be run if not. I think such functionality would be useful in general.

We could do this via a has_logabsdet_jacobian function or via a default definition with_logabsdet_jacobian(f, x) = nothing (like the default of ChainRulesCore.rrule).

This is related to JuliaMath/InverseFunctions.jl#13.