Support Sum operations

[bartvanerp]

Following ReactiveBayes/RxInfer.jl#60:

Currently GraphPPL.jl allows for nesting linear operations, i.e. y ~ x1 + x2 + x3 * x4 , something which in my opinion is very cool and partly solves a remark in the above issue. Next up would be to also implement the sum() operation. I think we can get away with using it as an alias depending on its inputs:

# defaults to a + b + c + d (if independent)
y ~ sum(a, b, c, d)
y ~ sum([a, b, c, d])

# defaults to dot(a_array, ones(..)) (if dependent)
y ~ sum(a_array)
y ~ sum(a_array[1], a_array[2], ...)
y ~ sum([a_array[1], a_array[2], ...])

# more complicated structures can be unrolled
y ~ sum(a_array[1], a_array[2], b) # here y ~ sum(a_array[1], a_array[2]) + b

[wouterwln]

I'll mark this as closed now, for two reasons. In the following code snippet:

@model function sum_test(out, x, y)
    τ := sum([1,2,3,4])
    σ := sum(ones(4))
    out := sum(x, y)
end

τ and σ will both be variables with value 10 and 4 respectively, and for out a sum node will be created if either (or both) x or y is a random variable. This is, as far as I know, everything we can do in this regard. Your last example will sadly not work. We know that sum is a commutative operation, however we do not have this guarantee in general, therefore we will always materialize this sum node if either a_array[1], a_array_2 or b is a random variable. I don't feel like having a trait based system that labels commutative operations is in the scope of GraphPPL.