Reland "add more methods and tests for reductions over empty arrays"

[vtjnash]

Relands #29919

[vtjnash]

Looks like this still runs into this SparseArray problem:

SparseArrays/sparsematrix_ops                    (10) |         failed at 2024-04-16T20:47:52.441
Test Failed at /home/vtjnash/julia/usr/share/julia/stdlib/v1.12/SparseArrays/test/sparsematrix_ops.jl:248
  Expression: minimum(sparse(Int[]))
    Expected: errchecker
  No exception thrown

Test Failed at /home/vtjnash/julia/usr/share/julia/stdlib/v1.12/SparseArrays/test/sparsematrix_ops.jl:249
  Expression: maximum(sparse(Int[]))
    Expected: errchecker
  No exception thrown

[mbauman]

OK, I have two good examples of why I don't like these behaviors. With this patch:

julia> minimum(Union{Missing,Int}[])
ERROR: MethodError: no method matching typemax(::Type{Union{Missing, Int64}})

julia> minimum(abs, Union{Missing,Int}[])
9223372036854775807

julia> maximum(Union{Missing,Int}[])
ERROR: MethodError: no method matching typemin(::Type{Union{Missing, Int64}})

julia> maximum(abs, Union{Missing,Int}[])
0

While I think it makes some sense that zero(Union{Missing, Int}) would be 0, I don't find it near as defensible that typemin or typemax should work — with or without an abs thrown into the mix. It seems like maximum(abs, Union{Missing,Int}[]) could be either missing or 0.

It also just doesn't seem like this is necessarily true in the abstract — for example:

julia> maximum(abs, Int8[])
0

julia> maximum(abs, Int8[-128]) # But there _does exist_ a lesser least element!
-128

That last example doesn't even require this patch — that's the current behavior of Julia. Still bad, though, and representative of what this patch wants to do more of.

[adienes]

julia> maximum(identity, [])
ERROR: MethodError: reducing over an empty collection is not allowed; consider supplying `init` to the reducer

julia> maximum(abs, [])
ERROR: MethodError: no method matching zero(::Type{Any})

julia> maximum(abs, Int8[])
0

😬 that's unfortunate.

maybe that can be fixed in your PR which is already slightly breaking? after all (slightly breaking ---> slightly more breaking) is a much smaller jump than (not breaking ---> slightly breaking)