Re: What is the history behind Natural'First = 0 ?

[Keith Thompson <Keith.S.Thompson+u@gmail.com>]

"J-P. Rosen" <rosen@adalog.fr> writes:
> Le 01/05/2020 à 06:51, reinert a écrit :
>> Why Natural'First = 0 ?
>> 
> Because that's the way it is  ;-)
>
> Anyway, type Integer is not the mathematical notion of (infinite)
> integers, and more generaly computer types are only reduced abstractions
> of mathematical notions.
>
> There is a need for a subtype of type Integer with lower bound 0, and
> another one for lower bound 1. The names have been chosen by Ichbiah
> following usual practice, they could have been anything else.

When I was learning about sets of numbers in elementary school, we
were told that the natural numbers are positive integers and the
whole numbers are non-negative integers (including 0).  Based on
that, if I had been designing the language I probably would have used
the name Natural for 1..Integer'Last and Whole for 0..Integer'Last.

On the other hand, the word "Whole" sounds like "Hole" (at least
in my version of non-accented American English), so I can see that
being awkward in some contexts.

Wikipedia says that some definitions have "natural numbers" starting
with 0, and others have them starting with 1 -- and the term "whole
numbers" is sometimes used to refer to the set of all integers.

It's ultimately arbitrary.  I found the use of Natural in Ada
slightly jarring the first time I encountered it, but I have no
complaints.  And the name Positive seems entirely reasonable.

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Philips Healthcare
void Void(void) { Void(); } /* The recursive call of the void */