The AbstractArray is the abstract type for all Julia array containers. Many Julia packages implement the array interface and are made to be subtypes of AbstractArray. It would be a shame if we go so far to make the sumprod function versatile enough, and yet we cannot support sparse matrices or other types of array-type containers. To make it more general, let's turn our function definition from Array to AbstractArray as follows:

sumprod_6(A::AbstractArray{S,N}, B::AbstractArray{T,N}) where 
    {N, S <: Number, T <: Number} = sum(A .* B)

The signature is the same as the previous option, except that the function can be dispatched with any AbstractArray container types. Let's make sure that the function works as expected:

The function is working properly for our existing cases. Let's just try it once again using the sparse matrix type:

Bravo! It is working great now, even with a non-dense array type. We are almost done. Let's look at our last option—duck typing.