(A bit of a long post because error messages)

i’m trying to generate a binary heap (from DataStructures) where the data item is a pair consisting of an integer and a function.

The following works

```
julia> function f1() println("hello") end
f1 (generic function with 1 method)
julia> function f2() println("goodbye") end
f2 (generic function with 1 method)
julia> using DataStructures
julia> x = BinaryHeap(Base.By(first), [ ])
BinaryHeap{Any,Base.Order.By{typeof(first),Base.Order.ForwardOrdering}}(Base.Order.By{typeof(first),Base.Order.ForwardOrdering}(first, Base.Order.ForwardOrdering()), Any[])
julia> push!(x, 1=>f1)
BinaryHeap{Any,Base.Order.By{typeof(first),Base.Order.ForwardOrdering}}(Base.Order.By{typeof(first),Base.Order.ForwardOrdering}(first, Base.Order.ForwardOrdering()), Any[1 => f1])
julia> push!(x, 2=>f2)
BinaryHeap{Any,Base.Order.By{typeof(first),Base.Order.ForwardOrdering}}(Base.Order.By{typeof(first),Base.Order.ForwardOrdering}(first, Base.Order.ForwardOrdering()), Any[1 => f1, 2 => f2])
```

but this doesn’t.

```
julia> x = BinaryHeap(Base.By(first), [ 1=>f1 ])
BinaryHeap{Pair{Int64,typeof(f1)},Base.Order.By{typeof(first),Base.Order.ForwardOrdering}}(Base.Order.By{typeof(first),Base.Order.ForwardOrdering}(first, Base.Order.ForwardOrdering()), [1 => f1])
julia> push!(x, 2=>f2)
ERROR: MethodError: Cannot `convert` an object of type typeof(f2) to an object of type typeof(f1)
Closest candidates are:
convert(::Type{T}, ::T) where T at essentials.jl:171
Stacktrace:
[1] convert(::Type{Pair{Int64,typeof(f1)}}, ::Pair{Int64,typeof(f2)}) at ./pair.jl:71
[2] push!(::Array{Pair{Int64,typeof(f1)},1}, ::Pair{Int64,typeof(f2)}) at ./array.jl:934
[3] heappush!(::Array{Pair{Int64,typeof(f1)},1}, ::Pair{Int64,typeof(f2)}, ::Base.Order.By{typeof(first),Base.Order.ForwardOrdering}) at /home/briand/.julia/packages/DataStructures/ixwFs/src/heaps/arrays_as_heaps.jl:72
[4] push!(::BinaryHeap{Pair{Int64,typeof(f1)},Base.Order.By{typeof(first),Base.Order.ForwardOrdering}}, ::Pair{Int64,typeof(f2)}) at /home/briand/.julia/packages/DataStructures/ixwFs/src/heaps/binary_heap.jl:91
[5] top-level scope at REPL[8]:1
```

I’m unclear on why the functions are “typeof(f1)” and “typeof(f2)”. I looked through the documentation because I know the subject of function type annotation has come up before, but I couldn’t find anything which talked about it.

More importantly, if I wanted to explicitly type the array when creating the BinaryHeap structure how would I do that ?

Here’s my attempt.

```
julia> x = BinaryHeap(Base.By(first), Array{Pair{Int,Function},1}[ ])
BinaryHeap{Array{Pair{Int64,Function},1},Base.Order.By{typeof(first),Base.Order.ForwardOrdering}}(Base.Order.By{typeof(first),Base.Order.ForwardOrdering}(first, Base.Order.ForwardOrdering()), Array{Pair{Int64,Function},1}[])
julia> push!(x, 1=>f1)
ERROR: MethodError: Cannot `convert` an object of type Pair{Int64,typeof(f1)} to an object of type Array{Pair{Int64,Function},1}
Closest candidates are:
convert(::Type{T}, ::AbstractArray) where T<:Array at array.jl:554
convert(::Type{T}, ::T) where T<:AbstractArray at abstractarray.jl:14
convert(::Type{T}, ::LinearAlgebra.Factorization) where T<:AbstractArray at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.5/LinearAlgebra/src/factorization.jl:55
...
Stacktrace:
[1] push!(::Array{Array{Pair{Int64,Function},1},1}, ::Pair{Int64,typeof(f1)}) at ./array.jl:934
[2] heappush!(::Array{Array{Pair{Int64,Function},1},1}, ::Pair{Int64,typeof(f1)}, ::Base.Order.By{typeof(first),Base.Order.ForwardOrdering}) at /home/briand/.julia/packages/DataStructures/ixwFs/src/heaps/arrays_as_heaps.jl:72
[3] push!(::BinaryHeap{Array{Pair{Int64,Function},1},Base.Order.By{typeof(first),Base.Order.ForwardOrdering}}, ::Pair{Int64,typeof(f1)}) at /home/briand/.julia/packages/DataStructures/ixwFs/src/heaps/binary_heap.jl:91
[4] top-level scope at REPL[10]:1
```

I’ve been trying various things, aka guessing, and reading through the docs, can’t seem to locate anything that will help.

Thank you.