Enable Mooncake in ADTypeCheckContext tests

[penelopeysm]

Turing.jl/test/test_utils/ad_utils.jl

Lines 240 to 249 in 24e6870

	# Check that the ADTypeCheckContext works as expected.
	Test.@testset "ADTypeCheckContext" begin
	Turing.@model test_model() = x ~ Turing.Normal(0, 1)
	tm = test_model()
	adtypes = (
	Turing.AutoForwardDiff(),
	Turing.AutoReverseDiff(),
	Turing.AutoZygote(),
	Turing.AutoTracker(),
	)

#2341 gets rid of AutoTracker from this list, but doesn't add back AutoMooncake. I tried to naively add it to the list, but the tests failed.

We should either add it in, or figure out why the tests don't pass and add a note explaining it.

[yebai]

@mhauru / @penelopeysm, can you give this another look so we can finish off #2411?

[mhauru]

I haven't thought about this carefully, but I'm unsure if ADTypeCheckContext can do anything meaningful for Mooncake since it doesn't use tracer types. I'm also not sure it needs to, because really ADTypeCheckContext just needs to check that our internal mechanisms for passing around ADTypes work, and we don't end up accidentally always using ForwardDiff or something like that (I think that was momentarily the case with MAP/MLE, which inspired these tests). But if it works for one non-default ADType, I don't see how it would fail for others.

[penelopeysm]

I'm unsure if ADTypeCheckContext can do anything meaningful for Mooncake since it doesn't use tracer types

This was my impression last time I tried to get it to work. Agreed on the other points --- I wouldn't be opposed to just closing this issue.

[mhauru]

With pleasure