From mboxrd@z Thu Jan  1 00:00:00 1970
X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me
X-Spam-Level: 
X-Spam-Status: No, score=-0.9 required=5.0 tests=BAYES_00,FORGED_GMAIL_RCVD,
	FREEMAIL_FROM autolearn=no autolearn_force=no version=3.4.4
Path: 
 eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: Keith Thompson <Keith.S.Thompson+u@gmail.com>
Newsgroups: comp.lang.ada
Subject: Re: What is the history behind Natural'First = 0 ?
Date: Fri, 01 May 2020 12:03:14 -0700
Organization: None to speak of
Message-ID: <874ksz4gwd.fsf@nosuchdomain.example.com>
References: <9f0215ca-2760-47cf-a7cb-50184892e1d0@googlegroups.com>
	<r8gkf4$ul2$1@dont-email.me>
Mime-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 8bit
Injection-Info: reader02.eternal-september.org;
 posting-host="3a8562cb4f6a88758e42aeb600e70f1e";
	logging-data="792"; mail-complaints-to="abuse@eternal-september.org";
	posting-account="U2FsdGVkX18AtDDnwnLM34EeyMC3sZY0"
User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/26.3 (gnu/linux)
Cancel-Lock: sha1:tIh44Z99A0CL8Z2ARvnw9fPJPuU=
	sha1:aldZ4r7daNGZwRoaQjUyk/s2WxI=
Xref: reader01.eternal-september.org comp.lang.ada:58546
Date: 2020-05-01T12:03:14-07:00
List-Id: <comp.lang.ada>

"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 */