# Why is reduce with concatenation type unstable?

**URL:** <https://discourse.julialang.org/t/why-is-reduce-with-concatenation-type-unstable/45023>\
**Category:** General Usage\
**Tags:** question\
**Created:** [August 16, 2020, 5:41am UTC](https://discourse.julialang.org/t/why-is-reduce-with-concatenation-type-unstable/45023 "2020-08-16T05:41:32Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![jishnub](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jishnub/32/33620_2.png) [@jishnub](https://discourse.julialang.org/u/jishnub)\
**Post date:** [August 16, 2020, 5:41am UTC](https://discourse.julialang.org/t/why-is-reduce-with-concatenation-type-unstable/45023/1 "2020-08-16T05:41:32Z")

</div>

`reduce(vcat, arr)` returns a scalar or an array depending on the length of the array.

```julia
julia> reduce(vcat, [1])
1

julia> reduce(vcat, [1,2])
2-element Array{Int64,1}:
 1
 2

julia> @code_warntype reduce(vcat, [1,2])
Variables
  #self#::Core.Compiler.Const(reduce, false)
  op::Core.Compiler.Const(vcat, false)
  A::Array{Int64,1}

Body::Union{Int64, Array{Int64,1}}
1 ─ %1 = Core.NamedTuple()::Core.Compiler.Const(NamedTuple(), false)
│ %2 = Base.pairs(%1)::Core.Compiler.Const(Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}(), false)
│ %3 = Base.:(var"#reduce#622")(%2, #self#, op, A)::Union{Int64, Array{Int64,1}}
└── return %3

```

I find this surprising as `vcat` does not behave like this:

```julia
julia> vcat(1)
1-element Array{Int64,1}:
 1

julia> vcat(1,2)
2-element Array{Int64,1}:
 1
 2

```

The issue may be resolved by specifying an initial value, eg. as

```julia
julia> reduce(vcat, [1], init=Int[])
1-element Array{Int64,1}:
 1

```

Why is the type-unstable definition the default?

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<div class="post-metadata">

**Author:** ![yuyichao](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/yuyichao/32/20_2.png) [@yuyichao](https://discourse.julialang.org/u/yuyichao)\
**Post date:** [August 16, 2020, 6:13am UTC](https://discourse.julialang.org/t/why-is-reduce-with-concatenation-type-unstable/45023/2 "2020-08-16T06:13:05Z")

</div>

> [@jishnub](#):
>
> I find this surprising as `vcat` does not behave like this:

But reduce is not splatting. What you are doing is equivalent to

`1`, `vcat(1, 2)`, `vcat(vcat(1, 2), 3)` etc…

> [@jishnub](#):
>
> Why is the type-unstable definition the default?

And this has nothing to do with type stability. It’s just how it must behave by the definition.

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<div class="post-metadata">

**Author:** ![jishnub](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jishnub/32/33620_2.png) [@jishnub](https://discourse.julialang.org/u/jishnub)\
**Post date:** [August 19, 2020, 10:22am UTC](https://discourse.julialang.org/t/why-is-reduce-with-concatenation-type-unstable/45023/3 "2020-08-19T10:22:45Z")

</div>

Currently `reduce` with a single element calls `reduce_first`, and it is encouraged to define additional methods if it helps reduce become type-stable. I have found the following issues discussing this:

- [31169](https://github.com/JuliaLang/julia/issues/31169)

- [34380](https://github.com/JuliaLang/julia/issues/34380)

The docstring for `reduce_first` states

> The default is `x` for most types. The main purpose is to ensure type stability, so  
> additional methods should only be defined for cases where `op` gives a result with  
> different types than its inputs.

As discussed in the issues, concatenation is one such case where it makes sense to define `reduce_first` appropriately to obtain a type-stable method.

> And this has nothing to do with type stability. It’s just how it must behave by the definition.

I would argue that the use of `reduce_first` implies that it _does_ have to do with type-stability.