# Null and Array of T question

**URL:** <https://discourse.julialang.org/t/null-and-array-of-t-question/6230>\
**Category:** New to Julia\
**Tags:** question, array, type, parametric-types\
**Created:** [October 4, 2017, 4:06am UTC](https://discourse.julialang.org/t/null-and-array-of-t-question/6230 "2017-10-04T04:06:58Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![xiaodai](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/xiaodai/32/15937_2.png) [@xiaodai](https://discourse.julialang.org/u/xiaodai)\
**Post date:** [October 4, 2017, 4:06am UTC](https://discourse.julialang.org/t/null-and-array-of-t-question/6230/1 "2017-10-04T04:06:58Z")

</div>

I am trying to understanding how array operations work and how types work inside arrays. The system is Julia Pro 0.6.0.1 on 64bit Windows 7

The motivating example was

```julia
using Nulls
x = [1, null, 2]
typeof(x) # gives Vector{Union{Int64, Nulls.Null}}
y = x + 2
typeof(y) # gives Vector{Any}

```

So the type of vector changed which isn’t the behaviour I expected. I expected it to have remained at Vector{Union{Int64, Nulls.Null}}

The below is also puzzling. I thought all 3 definitions of the function ok should work. But it appears only the last one works. It seems that there is something going on with the interaction of arrays and types that I don’t fully understand. Please help to explain the behavior and if there are “rules” to let me work out how it works. Thanks

```julia
using Nulls
function ok(A::Array{Union{T,Nulls.Null} where T <: Number}, B::Number)
  return 1
end
@which ok([1, null, 2],2)

function ok(A::Array{Union{Integer,Nulls.Null}}, B::Number)
  return 1
end
@which ok([1, null, 2],2)

function ok(A::Array{Union{Int64,Nulls.Null}}, B::Number)
  return 1
end
@which ok([1, null, 2],2)

```

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<div class="post-metadata">

**Author:** ![mauro3](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mauro3/32/292_2.png) [@mauro3](https://discourse.julialang.org/u/mauro3)\
**Post date:** [October 4, 2017, 6:55am UTC](https://discourse.julialang.org/t/null-and-array-of-t-question/6230/2 "2017-10-04T06:55:48Z")

</div>

I suspect your `y = x + 2` example is a bug. The machinery to deal efficiently with `Union{T,Null}` types is very recent and still a bit of a work in progress. Maybe @quinnj can confirm.

The method definition should read:

```julia
function ok(A::Array{Union{T,Nulls.Null}}, B::Number) where T <: Number
  return 1
end

```

This is fairly subtle and I don’t think I can explain it. But essentially the reason it was not dispatched to your method is:

```julia
julia> [1, null, 2] isa Array{Union{T,Nulls.Null} where T <: Number}                                                                                  
false                                                                                                                                                 

```

---

<div class="post-metadata">

**Author:** ![mauro3](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mauro3/32/292_2.png) [@mauro3](https://discourse.julialang.org/u/mauro3)\
**Post date:** [October 4, 2017, 7:37am UTC](https://discourse.julialang.org/t/null-and-array-of-t-question/6230/3 "2017-10-04T07:37:59Z")

</div>

Ok, I got it. So this works too:

```julia
julia> function okkk(A::Array{Union{T,Nulls.Null}} where T<:Number, B::Number)
         return 1
       end                                                                                                                                            
okkk (generic function with 1 method)                                                                                                                 

julia> okkk([1,null],1)                                                                                                                               
1            

```

the reason is:

```julia
    julia> [1, null, 2] isa Array{Union{Nulls.Null,T} where T <: Number}                                                                                  
false                                                                                                                                                 

julia> [1, null, 2] isa Array{Union{Nulls.Null,T}} where T <: Number                                                                                  
true                                                                                                                                                  

```

The first is false because types in Julia are _invariant_ (except Tuples), i.e. `eltype([1, null, 2])<:Union{Nulls.Null,T} where T <: Number` does not imply `typeof([1, null, 2]) <: Array{Union{Nulls.Null,T} where T <: Number}`. See [https://docs.julialang.org/en/stable/manual/types/#Parametric-Composite-Types-1](https://docs.julialang.org/en/stable/manual/types/#Parametric-Composite-Types-1)