notations_operators.jl

# I'd live to use the usual mathematical notations to do summatories and productories
# turns out, in Julia it's pretty easy as long as we keep things simple
# as we can just embellish the already defined sum() and prod() function
# only tweak is choosing a negative step if we want to sum from i = N to M with N>M

# for the summatory:
function ∑(f::T;from::Int, to::Int) where T <: Function
    step_sum = from > to ? 1 : -1
    sum(safer(f), range(from, stop = to, step = step_sum))
end

# for the productory
function ∏(f::T;from::Int, to::Int) where T <: Function
    step_sum = from > to ? 1 : -1
    prod(safer(f), range(from, stop = to, step = step_sum))
end

# where we use the safer wrapper (something along the lines of R's purrr::safely()
function safer(my_function)
    try
        my_function
    catch e
        missing
    end
end

# I was also playing with the idea of summatories where the Nth therm is defined as a function of the (N-1)th term

## this can clearly be done better:
function ∑ₛ(start::N, f::T;from::Int, to::Int) where N<:Number where T <: Function
    step_sum = from < to ? 1 : -1
    result = start
    step_value = start
    for i in from:step_sum:to
        step_value = f(step_value)
        result += step_value
    end
    return result
end