Provide better error message for Vector+VariableRef

[odow]

https://discourse.julialang.org/t/methoderror-no-method-matching-zero-type-vector-affexpr/105639

julia> using JuMP

julia> model = Model()
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.

julia> @variable(model, x[1:2])
2-element Vector{VariableRef}:
 x[1]
 x[2]

julia> @variable(model, y)
y

julia> @constraint(model, x + y .>= 0)
ERROR: MethodError: no method matching zero(::Type{Vector{VariableRef}})

Closest candidates are:
  zero(::Union{Type{P}, P}) where P<:Dates.Period
   @ Dates ~/.julia/juliaup/julia-1.9.3+0.x64.apple.darwin14/share/julia/stdlib/v1.9/Dates/src/periods.jl:51
  zero(::GenericQuadExpr)
   @ JuMP ~/.julia/dev/JuMP/src/quad_expr.jl:126
  zero(::AbstractVariableRef)
   @ JuMP ~/.julia/dev/JuMP/src/variables.jl:348
  ...

Stacktrace:
  [1] _instantiate_zero(#unused#::Type{Vector{VariableRef}})
    @ MutableArithmetics ~/.julia/dev/MutableArithmetics/src/interface.jl:28
  [2] promote_operation_fallback(op::typeof(+), #unused#::Type{Vector{VariableRef}}, #unused#::Type{VariableRef})
    @ MutableArithmetics ~/.julia/dev/MutableArithmetics/src/interface.jl:51
  [3] promote_operation(::typeof(+), ::Type, ::Type)
    @ MutableArithmetics ~/.julia/dev/MutableArithmetics/src/interface.jl:113
  [4] promote_operation_fallback(op::typeof(MutableArithmetics.add_mul), T::Type, args::Type)
    @ MutableArithmetics ~/.julia/dev/MutableArithmetics/src/interface.jl:99
  [5] promote_operation(::typeof(MutableArithmetics.add_mul), ::Type, ::Type)
    @ MutableArithmetics ~/.julia/dev/MutableArithmetics/src/interface.jl:113
  [6] mutability(::Type, ::Function, ::Type, ::Type)
    @ MutableArithmetics ~/.julia/dev/MutableArithmetics/src/interface.jl:266
  [7] mutability(::Vector{VariableRef}, ::Function, ::Vector{VariableRef}, ::VariableRef)
    @ MutableArithmetics ~/.julia/dev/MutableArithmetics/src/interface.jl:274
  [8] operate!!(op::typeof(MutableArithmetics.add_mul), x::Vector{VariableRef}, args::VariableRef)
    @ MutableArithmetics ~/.julia/dev/MutableArithmetics/src/rewrite.jl:93
  [9] macro expansion
    @ ~/.julia/dev/MutableArithmetics/src/rewrite.jl:321 [inlined]
 [10] macro expansion
    @ ~/.julia/dev/JuMP/src/macros.jl:717 [inlined]
 [11] top-level scope
    @ REPL[5]:1

[odow]

I don't really know a good way of going about this. Perhaps we should just add a method to operate!!(op::typeof(MutableArithmetics.add_mul), x::Vector{VariableRef}, args::VariableRef)? We can't do it at the MA level, because there might be types that do support vector + scalar.

[blegat]

I think the issue is promote_operation. We could try using promote_op and only resort to the fallback in case promote_op does not return something concrete. I was discussing this with @vchuravy at the JuliaCon and it seems the takeaway was that promote_op is undecidable (like the HALT problem) and promote_op wants to always terminate so it has to give away something. So it guarantees to always return a supertype but it's not always the tightest possible supertype. For MA, we always want a concrete type so that's why we cannot completely rely on promote_op but in the case where promote_op does return a concrete type then we can just use it.
I also discussed this with @schlichtanders after the IsDef.jl talk as IsDef.Out is trying to achieve the same goal as promote_operation, see:
https://www.youtube.com/watch?v=2QLJOQNiZhI&t=1765s