Should `to_vec(::Integer)` return an empty vector

[mzgubic]

Integers can't be perturbed, so their to_vec should be empty. Originally suggested in #187

function to_vec(x::Integer)
     Integer_from_vec(v) = x
     return Bool[], Integer_from_vec
end

Would also fix (a part of) chrisbrahms/Hankel.jl#27

Did not test yet whether it messes up any existing ChainRules tests.

[willtebbutt]

This would make sense to me.

[oxinabox]

The practical problem with this, is that sometimes people want to test special case methods that take integers.
Which is just all round hard, since when finite diferencing they don't get integers.

But they might still want to test it against custom rules that do.
So I wonder if we really need to handle this better in CRTU or somewhere in FiniteDifferences.

Right now we often (always?) error for it

[willtebbutt]

Could you provide an example @oxinabox ? I'm not really clear what sort of thing you're imagining.

[oxinabox]

For example

function rrule(::typeof(sinpi), x)
    sinpi_pullback(dy) = -pi*cospi(x)
    foo(x), sinpi_pullback
end

function rrule(::typeof(sinpi), x::Integer)
    sinpi_pullback(dy) = Zero()
    foo(x), sinpi_pullback
end

[willtebbutt]

And what we're proposing to do here would solve this problem, yes?

[oxinabox]

Would it? Cool!

[mcabbott]

Isn't this example the thing which already works? Integer taken to mean non-differentiable:

julia> mysinpi(x) = sinpi(x)
mysinpi (generic function with 1 method)

julia> function ChainRulesCore.rrule(::typeof(mysinpi), x)
           sinpi_pullback(dy) = NoTangent(), pi*cospi(x)*dy
           sinpi(x), sinpi_pullback
       end

julia> function ChainRulesCore.rrule(::typeof(mysinpi), x::Integer)
           sinpi_pullback(dy) = NoTangent(), NoTangent()
           sinpi(x), sinpi_pullback
       end

julia> test_rrule(mysinpi, 1.23)
Test Summary:                  | Pass  Total
test_rrule: mysinpi on Float64 |    7      7
Test.DefaultTestSet("test_rrule: mysinpi on Float64", Any[], 7, false, false)

julia> test_rrule(mysinpi, 1)
Test Summary:                | Pass  Total
test_rrule: mysinpi on Int64 |    6      6
Test.DefaultTestSet("test_rrule: mysinpi on Int64", Any[], 6, false, false)

[willtebbutt]

Oh, yeah, this particular example is. I think stuff would need to be nested in order to break it.