add tests for stateful sum(f,x)

[CarloLucibello]

looks like we have a problem induced by JuliaDiff/ChainRules.jl#441.
On ChainRules 0.8.10 the test introduced in this PR passes, while on 0.8.15 the zygote gradient errors out with

sum(f, x): Error During Test at /home/carlo/.julia/dev/Zygote/test/lib/array.jl:11
  Got exception outside of a @test
  MethodError: no method matching +(::Base.RefValue{Any}, ::Base.RefValue{Any})
  Closest candidates are:
    +(::Any, ::Any, ::Any, ::Any...) at operators.jl:560
    +(::ChainRulesCore.AbstractThunk, ::Any) at /home/carlo/.julia/packages/ChainRulesCore/e5hAX/src/differential_arithmetic.jl:138
    +(::ChainRulesCore.Tangent{P, T} where T, ::P) where P at /home/carlo/.julia/packages/ChainRulesCore/e5hAX/src/differential_arithmetic.jl:162
    ...
  Stacktrace:
    [1] add_sum(x::Base.RefValue{Any}, y::Base.RefValue{Any})
      @ Base ./reduce.jl:24
    [2] _mapreduce(f::typeof(first), op::typeof(Base.add_sum), #unused#::IndexLinear, A::Vector{Tuple{Base.RefValue{Any}, Float64}})
      @ Base ./reduce.jl:408
    [3] _mapreduce_dim(f::Function, op::Function, #unused#::Base._InitialValue, A::Vector{Tuple{Base.RefValue{Any}, Float64}}, #unused#::Colon)
      @ Base ./reducedim.jl:318
    [4] #mapreduce#672
      @ ./reducedim.jl:310 [inlined]
    [5] mapreduce
      @ ./reducedim.jl:310 [inlined]
    [6] #_sum#682
      @ ./reducedim.jl:878 [inlined]
    [7] _sum
      @ ./reducedim.jl:878 [inlined]
    [8] #sum#680
      @ ./reducedim.jl:874 [inlined]
    [9] sum(f::Function, a::Vector{Tuple{Base.RefValue{Any}, Float64}})
      @ Base ./reducedim.jl:874
   [10] (::ChainRules.var"#sum_pullback#1262"{F, Vector{Zygote.var"#ad_pullback#41"{F, Tuple{Float64}, typeof(∂(λ))}}})(ȳ::Float64)
      @ ChainRules ~/.julia/packages/ChainRules/VDG9a/src/rulesets/Base/mapreduce.jl:58
   [11] ZBack
      @ ~/.julia/dev/Zygote/src/compiler/chainrules.jl:91 [inlined]
   [12] Pullback
      @ ~/.julia/dev/Zygote/test/lib/array.jl:29 [inlined]
   [13] (::typeof(∂(#6)))(Δ::Float64)
      @ Zygote ~/.julia/dev/Zygote/src/compiler/interface2.jl:0
   [14] (::Zygote.var"#46#47"{typeof(∂(#6))})(Δ::Float64)
      @ Zygote ~/.julia/dev/Zygote/src/compiler/interface.jl:41
   [15] gradient(f::Function, args::Vector{Float64})
      @ Zygote ~/.julia/dev/Zygote/src/compiler/interface.jl:59
   [16] macro expansion

Besides the problem in the ChainRules' rule, I wonder why we don't hit the Zygote adjoint instead

Zygote.jl/src/lib/array.jl

Line 299 in 8d5efcb

@adjoint function sum(f, xs::AbstractArray{<:AbstractArray}; kws...)

I thought zygote's adjoints had priority over ChainRules' rules

[mcabbott]

The adjoint you link looks to be only for arrays of arrays, hence not called by this example. Why it survived, I don't know. But it does explain why the sum(f,x) worked like broadcasting in my gist of examples here:
https://gist.github.com/mcabbott/c6cdc73d45ed3e35c3fd8966863993f8

Maybe an error is a good outcome, though. The docstring for sum says "as it is unspecified whether init is used for non-empty collections." which is a pretty strong hint that the order can't be relied on. So the forward pass with a stateful f is already, I think, producing garbage.