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From: Chris.Holt@newcastle.ac.uk (Chris Holt)
Newsgroups: comp.software-eng
Subject: Re: Tolerance (was Re: Reusability considered harmful??(!!))
Message-ID: <1991Feb5.153917.20752@newcastle.ac.uk>
Date: 5 Feb 91 15:39:17 GMT
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dave@cs.arizona.edu (Dave P. Schaumann) writes:

[about "close is good enough" programming]
>Ok, so I stand corrected.  There are a lot of applications out there that
>don't need exact answers.  But my question was in the context of code re-use.
>How could you say something like, "well, I really need a stack, but I'll
>settle for something sort of stacky"?  Will we see code like this in the
>future:
>  assert( stackyness(re_used_type) > 0.9 ) ; /* stackyness(a real stack)=1.0 */

>I can't see how the "tolerence paradigm" could possibly lead to a reasonable
>means of code re-use.

Imagine you've got two objects/modules that you want to stick together;
e.g. A calls B, which returns something to A.  Suppose both of their
specifications are defined in terms of tolerances, so that
        A sends a value with tolerance t to B;
        A requires a result with tolerance u from B.
Then B's specification has to be such that given a tolerance t', it
returns a result with tolerance u'; and we have to show that t<=t',
u'<=u.  Given this, the combination is proved okay.

Applications?  Who's to know?  Perhaps, for example:
        Find the least element of a nearly sorted sequence.
If the sequence has tolerance
        Each element is no more than 3 positions from where it
        would be in the ordered sequence,
then only the first 4 elements need be examined.  This might mean
that the result could be returned within some given time constraint,
e.g. delta_t; and the proof would require knowing the time constraint
of a single comparison, and how many processors were available.
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 Chris.Holt@newcastle.ac.uk      Computing Lab, U of Newcastle upon Tyne, UK
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 "[War's] glory is all moonshine... War is hell." - General Sherman, 1879