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From: Shark8 <onewingedshark@gmail.com>
Newsgroups: comp.lang.ada
Subject: Re: How do I write directly to a memory address?
Date: Wed, 9 Feb 2011 13:40:41 -0800 (PST)
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Date: 2011-02-09T13:40:41-08:00
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On Feb 9, 2:26=A0pm, Hyman Rosen <hyro...@mail.com> wrote:
> On 2/9/2011 3:29 PM, Shark8 wrote:
>
> > On Feb 9, 12:43 pm, Hyman Rosen<hyro...@mail.com> =A0wrote:
> >> On 2/9/2011 2:20 PM, Shark8 wrote:
>
> >>> Sure I can; but to do that I need to be given a value of N, obviously=
.
>
> >> OK, how about N =3D 90?
>
> >> =A0 > =A0We can also show its correctness via mathematical induction.
>
> >> Go ahead, do that.
>
> > The Fibonacci Sequence is defined as...
>
> OK, let's see if I understand:
>
> =A0 =A0 =A0Function SumTo( N : Positive ) Return Positive is
> =A0 =A0 =A0begin
> =A0 =A0 =A0 =A0 Case N is
> =A0 =A0 =A0 =A0 =A0 When 1 =3D> Return 1;
> =A0 =A0 =A0 =A0 =A0 When Others =3D> Return 1 + SumTo(N-1);
> =A0 =A0 =A0 =A0 end case;
> =A0 =A0 =A0end SumTo;
>
> The induction should be similar, correct? So the induction
> will tell me what result I will get for SumTo(100_000_000)?

Er, no.
Induction just proves that for some statement P, and some
parameter n {where n may or may not be constrained}, that
P(n) being true necessarily means that P(N+Step) is also
true. {I have to wax quite general here because* the
statement, P, and the step are not fixed in any way.}

What induction *CAN* do is tell you whether or not SumTo
is correctly constructed and that, barring exceptions, is
what guarantees the return-value to be correct.

IE It is a proof of correctness; not per se a returner of values.

* it is perfectly valid to run induction on, say, prime numbers
as steps (1,2,3,5,7,11,...)... though I can't readily think of
a case requiring it.