getindex frule behavior

[samanklesaria]

I was hoping someone might be able to explain the current frule for getindex. Say I want to compute $\nabla_a \text{getindex}(a, i)$ with forward mode AD where $a$ is a 5-element vector. Intuitively, I would expect to get back a five element vector, where the only nonzero element is at index $i$. But when I try frule((NoTangent(), Ones(5), NoTangent()), getindex, ones(5), 1), I get a tangent of 1, not [1,0,0,0,0]. Why?

Specifically, I would have thought that the proper frule would be something like this:

function ChainRulesCore.frule((_, ẋ), ::typeof(getindex), x::AbstractArray, ix::Integer)
	return x[ix], sparsevec([ix], ẋ[ix], length(x))
end

[oxinabox]

the frule is returning the pushforward result, not the gradient (nor the pullback result).
It is the result of pertubing the input with by a small amount and measuring how much the output changes.
It is thus expected that it is the same "type" as the output, which in this case is a scalar.
(this is incontrast to rrules's pullback which is same "type" as the input)
More details can be found in the docs https://juliadiff.org/ChainRulesCore.jl/dev/maths/propagators.html