Comment by Iwan-Zotow | Hacker News Reader

Comment by Iwan-Zotow | Hacker News Reader

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Suppose I have to compute sum for array of length N. In python it is something like

s = 0 for k in range(0, N): s += a[k]

Ok, I have more cores/CPUs, could I do it in parallel? Sure

v1 = Sum(0, N/2) v2 = Sum(N/2, N) s = v1 + v2

I even could do it on asymmetric cores (like most phone CPUs today)

v1 = Sum(0, K) v2 = Sum(K, N) s = v1 + v2

I could do a bit more complicated things, like calculating means. For that, I have to make a monoid

def mean(from, to, a): m = 0 for k in range(from, to): m += a[k] N = to - from return (m/N, N)

Here I'm returning tuple, and for that to be a monoid I have to state composition law:

def compose(M1, M2): A1, N1 = M1 A2, N2 = M2 N = N1+N2 return ((A1N1 + A2N2)/N, N)

If my identity is (0,0) tuple, it is quite easy to verify that indeed I have a monoid. Nice, simple, composable ranges.

For closed [1...N] ranges this is NOT nice, NOT simple, just plain fugly exercise. Sorry, looks like code samples are screwed up a bit, don't know how to fix it

But why should you have to care, why not just sum(range)? Or

    @threads for i in eachindex(object)

and let the details about how many cores be written once, correctly, elsewhere?

> But why should you have to care, why not just sum(range)?

Sure, if you have single infinitely fast CPU. In real life, we have to decompose problem, run it in parallel and compose it back.

> Or @threads for i in eachindex(object) & let the details about how many cores be written once, correctly, elsewhere?

Here I'm explicitly talking about details, how it should be done, importance of composition, monoids etc. I understand, that if someone did it for you, you might not care - well, more power to you then. But some basics rules about Pyton ranges are pretty good:

1. [0...K) + [K...N) = [0...N)

2. Given range [K...N), number of elements in the range is N-K, in case of [0...N) number of elements is N-0=N.

Simple, elegant, composable. I can't say the same about Julia

1-indexed ranges can still be composable if we define them as open on the right at N+1 (which is how I imagine one would want to define things in their implementation).

[1...N] = [1...N+1) = [1...K+1) + [K+1..N+1)

So the real loss is your point (2) - which, I agree, makes the implementation much less elegant and simple.

> 1-indexed ranges can still be composable

you could make them work, but improper abstraction leaks out in so many fugly ways. F.e. in Python you could compose functions, not only ranges. What do you pass in? Simple, [0, len(a)). What you get out? Simple, len(a). So you could operate on ranges composing function calls like in FP. Even works for unknown beforehand sequences/streams, just count along the sequence how many events you processed, and return it as length, and it could go into composition function. With Julia you have to think what is passed and what is returned. Shall I always return len(a)? Or maybe len(a)+1? What to return in case of streaming events? Sometimes len(a) and sometimes len(a)+1 with tons of comments and warnings? It is not a good way to deal with all that and not a good way to build API. Could be done and probably was already done, sure. BUt simplicity, elegance and composability is missing in the base design.

I don't buy it. Inclusive ranges are much more intuitive than left side inclusive and right side exclusive ranges. And they compose just fine; you just have to add a plus one at the right places. E.g.

    function mean(a, l, r)
        s = 0
        N = r-l+1
        for k in l:r
            s += a[k]
        end
        s/N, N
    end
    
    function mean2(a)
        N = length(a)
        lr1 = (1,div(N,2))
        lr2 = (div(N,2)+1,N)
        v1, N1 = mean(a, lr1...)
        v2, N2 = mean(a, lr2...)
        N = N1+N2
        (v1 * N1 + v2 * N2) / N, N
    end

    function compose(M1, M2)
        v1, N1 = M1
        v2, N2 = M2
        N = N1+N2
        (v1 * N1 + v2 * N2) / N
    end
    
    function mean3(a)
        N = length(a)
        lr1 = (1,div(N,2))
        lr2 = (div(N,2)+1,N)
        compose(mean(a, lr1...), mean(a, lr2...))
    end

You have to think about what is passed in and out anyway. Arguments of elegance etc. are most of the time personal preferences and very biased.

> Arguments of elegance etc. are most of the time personal preferences and very biased.

No, they are not. I'm talking about ability to build (and build upon) underlying algebraic structure.

ok, could you make a monoid out of your/Julia closed ranges? What would be a unit in this monoid? How would you make a null/empty range?

Empty range is 1:0 or a+1:a or a:a-1 for any integer a. Closed ranges (for integers) are equivalent to open ranges since [a,b] is the same as [a,b+1). You just put the plus ones in the right places.

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