Why do some languages index from 0 and not 1? Efficiency?

So in my lift in my flat the buttons aren't (being in the UK) labelled: G, 1, 2, 3 etc. Nor in the American fashion of: 1,2,3,4 etc.

They're labelled: 0, 1, 2, 3 i.e. they're index from 0

I though to myself: 'Clearly, if you were to write a goToFloor like function to represent moving between floors, you could do so by the index of the element. Easy!'

And then I realised not all languages start their arrays from 0, some start from 1.

How is this decision made? Is it one of efficiency (I doubt it!)? Ease on new programmers (arguably, anyone who makes the mistake once, won't again)?

I can't see any reason a programming language would deviate from a standard, whether it be 0, 1 or any other number. With that in mind, perhaps it would help to know the first language that had the ability to index and then the first language to break whatever convention was set?

I hope this isn't too 'wishy-washy' a question for SO, I'm very eager to hear the history behind indexing.

Answers


When the first programming languages were designed it used to start at 0 because an array maps to memory positions. The array mapped to a memory position and the number was used as an offset to retrieve the adjacent values. According to this, the number should be seen as the distance from the start, not as the order in the array.

From a mathematical point of view it makes sense, because it helps to implement algorithms more naturally.

However 0 is not appealing to humans, because we start counting at 1. It's counter intuitive and this is why some languages decided to "fake" the start arrays at 1. (Note that some of them like VB allows you to choose between 0 and 1 based arrays.)

Interesting information on this topic could be found in this famous Dijkstra article:


The first "language" would have been assembler. There an array is simply the memory address of the first element. To access one element in the array, an offset is added. So if the array is at position t0, then t0+0 is the first element, t0+1 is the second element etc. This leads to indexes starting at 0. Later, higher level languages added a better nicer syntax, but the indexes stayed the same way.

Sometimes however, exceptions were made. In Pascal for example, a String is an array of bytes. However the first byte of the array/string stores the length of the string, so that the first letter is stored at index 1. However index 0 still exists and can be used to get said length.


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