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2013-10-28

Zero based indexing

Habit is habit, and not to be flung out of the window by
any man, but coaxed downstairs a step at a time.
Pudd'nhead Wilson's Calendar

Откуда вообще началось использование 0-based индексации?
Есть мнение, что начало было положено создателем языка BCPL, который делал язык, приближенный к машинному коду. Где регистры и машинные слова содержат числа, представляющие что угодно. Где адресная арифметика логично начинается с 0:

The fact of it is this: before pointers, structs, C and Unix existed, at a time when other languages with a lot of resources and (by the standard of the day) user populations behind them were one- or arbitrarily-indexed, somebody decided that the right thing was for arrays to start at zero.
As for BCPL and C subscripts starting at zero. BCPL was essentially designed as typeless language close to machine code. Just as in machine code registers are typically all the same size and contain values that represent almost anything, such as integers, machine addresses, truth values, characters, etc. BCPL has typeless variables just like machine registers capable of representing anything. If a BCPL variable represents a pointer, it points to one or more consecutive words of memory. These words are the same size as BCPL variables. Just as machine code allows address arithmetic so does BCPL, so if p is a pointer p+1 is a pointer to the next word after the one p points to. Naturally p+0 has the same value as p.


Что интереснее, автор находит у этого решения социальный контекст, не очень лестный для руководства IBM. А в конце статьи сокрушается о том, что люди всегда выбирают краткосрочную перспективу в ущерб долгосрочной, после чего отказываются от ответственности за свои решения, говоря «это было неизбежно».

Познавательно.

А знаете, почему в Python индексация zero-based? Гвидо решил, что в таком случае слайсы выглядят изящнее:

Using 0-based indexing, half-open intervals, and suitable defaults (as Python ended up having), they are beautiful: a[:n] and a[i:i+n]; the former is long for a[0:n].
Using 1-based indexing, if you want a[:n] to mean the first n elements, you either have to use closed intervals or you can use a slice notation that uses start and length as the slice parameters. Using half-open intervals just isn't very elegant when combined with 1-based indexing. Using closed intervals, you'd have to write a[i:i+n-1] for the n items starting at i. So perhaps using the slice length would be more elegant with 1-based indexing? Then you could write a[i:n]. And this is in fact what ABC did -- it used a different notation so you could write a@i|n.(See http://homepages.cwi.nl/~steven/abc/qr.html#EXPRESSIONS.)
But how does the index:length convention work out for other use cases? TBH this is where my memory gets fuzzy, but I think I was swayed by the elegance of half-open intervals. Especially the invariant that when two slices are adjacent, the first slice's end index is the second slice's start index is just too beautiful to ignore. For example, suppose you split a string into three parts at indices i and j -- the parts would be a[:i], a[i:j], and a[j:].
So that's why Python uses 0-based indexing.


Такие дела.



original post http://vasnake.blogspot.com/2013/10/zero-based-indexing.html

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