Quick Overview of Julia language [pdf]

Somehow I missed this comment. But as michaelcampbell wrote, in Ada you'd select the range that made sense for your application.

So if your application makes sense with 0-based (time series in your example) then you can do it:

  Cash_Flows : array (0..max_time) of Double;

It may even make sense to go negative for some things. For instance:

  Object_at_Altitude : array (-100..1000) of Object;

Or characters:

  Selected_Answers : array (range 'a'..'z') of Boolean;

Or a type that you've created:

  type Color is Red, Green, Blue, Yellow, Orange;
  Histogram_of_Colors : array (Color'Range) of Natural;

But a particularly nice thing is that arrays in Ada, unlike C, don't lose their size, so you can always do:

  for I in Cash_Flows'Range loop
    Some_Function(Cash_Flows(I));
  end loop;

So really the index never even has to be directly touched or known after creation.

    using OffsetArrays
    
    cash_flows = zeros(0:max_time)
    
    altitude = zeros(Bool, -100:100)
    
    for I in eachindex(cash_flows)
        some_function(cash_flows[I])
    end
    # or in this case avoiding indexing:
    for cf in cash_flows
        some_function(cf)
    end
    foreach(some_function, cash_flows)

> I haven't encountered a code base that uses non-default array indices,

If you're referring to <parent>'s mention of Ada with arbitrary ranges of indices, that's less about thinking of them as array indices and more of "a range of indices that make sense for your domain". Thinking about your problem in your problem's space rather than "how would my computer think of this"; making the map more like the territory, as it were.

Apparently you can [0]. However, it seems (in my first reading) to be something I'd avoid because it sounds like the "natural" way to code in Julia is to assume 1-based and you're likely to run into issues with libraries if you try and do anything else.

[0] https://docs.julialang.org/en/v1/devdocs/offset-arrays/

Lua's arrays/tables are more like hash tables, with an ability (still true? been a while since I've done anything with Lua) to optimize if you use a contiguous range starting at 1 for the key. But yes, you can use an arbitrary key.

(lets not let's)

I actually had that in my first draft of my comment. But I hadn't read it in a while and just did.

While he endorses 0-based in one of the remarks, he's actually endorsing the notational format of:

  a <= x < b or [a,b)

Where if b is renamed N, the length of a vector/array/list, in a 0-based notation, then you'd describe a 0-based vector's range as [0,N). The reasons he gives for preferring this notation for ranges (not, strictly, for 0-based ranges, but for all ranges):

1. Experience at Xerox where this notation (versus the other 3 he describes) leads to fewer errors. An informal study but a study none the less.

2. Using either [a,b) or (a,b], the size of the range is the difference between the provided bounds.

3. Using [a,b), adjacent ranges can be detected where b_1 = a_2. Given ranges [2,13) and [13,20) you can see that they're adjacent by just comparing two values. This certainly makes it quick to visually inspect as a code reader/writer. (the same argument can be made for (a,b])

4. An argument for either [a,b) or [a,b] is that the lower bound should be described by the minimum number in the range because it's more aesthetically pleasing.

So by process of elimination, he's left us with [a,b) as the better notation of the 4 options.

Based on an aesthetic argument, if you accept the above, then 0-based makes more sense because [0,N) is more aesthetically pleasing than [1,N+1). But if you use notation (c) from his report:

  a <= x <= b or [a,b]

Then 1-based can be described as the interval [1,N] where N is both the last element and the length of the vector/array/list. Which seems rather pleasant/natural to my eyes and fingers as well.

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If we accept the experience at Xerox, then his argument for 0-based indices is reasonable based on the assumption that ranges should be described as [a,b). If we don't accept it, then his argument is mostly based on aesthetics. That is, it's more pleasant to do a computation like:

  range size = b - a

than (for ranges described with [a,b]):

  range size = b - a + 1

And it's more pleasant to do a comparison like:

  adjacent? b_1 = a_2

than (for ranges described with [a,b]):

  adjacent? b_1 = a_2 - 1

But that first case doesn't matter in a 1-based array because the range size is just `b`, it's already stated in the range and there's no need for computation (just as it's present in 0-based ranges). Now, if your language permits arbitrary ranges then I think a case could be made for his suggested [a,b) notation. But if you're only choosing between 0-based or 1-based, I don't find it persuasive. It's still a tossup for me, neither is better than the other unless you also choose his notation for describing ranges, where [1,N+1) would be awkward but [1,N] is easier to use and understand.

It's really a strength, not a quirk. Negative indexing and array slicing in general are great in Python. Really easy to pick up and way more convenient than any other language that I've come across.

Corrections welcome, but I think Europeans don’t count floors, they count additional storeys, 1-based.

I think that’s influenced from French, which has parterre (“on the ground”) for the ground floor, and étage, derived from Latin stare, “to stand”, for higher (and lower) storeys (in the end, both may come from Latin)

If Europeans use 0-based counting for floors, I would expect at least some language to say “zeroth floor”. I’m not aware of any.

Indeed:

https://en.wikipedia.org/wiki/Storey#Numbering

Norway uses 1-based, which confused me once I was used to 0-based.