Re: Intended meaning

From: Bernd Brassel <bbr_at_informatik.uni-kiel.de>
Date: Fri, 02 Nov 2007 11:18:20 +0100

Thanks, Sergio, for the interesting discussion. I really do not think
that it is of such marginal importance.
And I think the "independence of the order of evaluation" is the key
problem to what you brought up. I also like Paco's example which seems
to me to be very direct to the point.

> Paco's example:
>
> f 0 = 0
> g 1 = 1
> f x ? g x where x free
>
> The results are 0 and 1 independently of the order of evaluation
> whether or not x is shared, since there is no residuation (easy
> to verify all the possibilities).

Why does the problem have to do with residuation? Why is 1 still a
result if you decide to reduce (f x) first? In order to be able to
really reduce this in most settings, you need x to be 0.
So, let us consider a setting, where there really is an arbitrary
choice of evaluation order for this example. To make things simpler, I
would like to look at a slightly different expression

e:=let x=0?1 in f x ? g x

Now there would be some possibilities (=> is a parallel step):

1) e -> (let x=0?1 in f x) ? (let x=0?1 in g x) => (f 0 ? f 1) ? (g 0 ?
g 1) => 0 ? _|_ ? _|_ ? 1 = 0 ? 1

2) e -> (f 0 ? g 0) ? (f 1 ? g 1) => 0 ? _|_ ? _|_ ? 1 = 0 ? 1

Is this maybe towards the "independence from evaluation order" you have
in mind for this example, Sergio?
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Received on Fri Nov 02 2007 - 12:05:05 CET

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