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From: Reid Sweatman (borderland_at_[hidden])
Date: 20000731 10:43:35
Coming from a math background, I personally think that trying to use exact
mathematical definitions of mathematical terms with very different semiotic
intentions behind them constitutes false analogy. What's important is
whether or not a programmer using the *programming* construct knows what the
sonamed construct promises and does. Now, if the mathematical meaning is
so obvious that everyone would be mislead by, say, AXIOM or POSTULATE, then
I'd say they're not good choices. Likewise, if they're so alien to anyone
not a mathematician that they don't carry *any* meaning, then they're
inappropriate, as well. Personally I don't have a problem with AXIOM,
because unless you're trying to derive theorems, or prove metatheorems about
axiomatic systems a la Goedel, even most mathematicians treat the word as
simply meaning "the stuff you assume is true, no matter what" (real
technical definition, I know <g>).
Having said all that, I'd have to agree that something like
COMPILE_TIME_ASSERT is about the best I've seen so far, without going to
some ridiculously literal name like COMPILER_BREAKS_IF_THIS_ISNT_TRUE <g>.
Sorry; listening to Lagrange (nothing to do with the mathematician) right
now, so I feel a bit flip.
Reid Sweatman, returning to that home out on the range_error <g>
> Original Message
> From: Borgerding, Mark A. [mailto:MarkAB_at_[hidden]]
> Sent: Friday, July 28, 2000 8:19 AM
> To: boost_at_[hidden]
> Subject: RE: [boost] metactrl header [compile time asserts]
>
>
> A postulate is the basic foundation upon which a mathematical proof is
> built. If the postulate is incorrect then a proof that assumes it may not
> be correct. I think this is a close analogy to a computer
> program. If the
> basic assumptions of the program's author are not met, then the
> program may
> not operate correctly.
>
> I agree with the need of simplicity in the assumptions. It is
> very easy for
> a code's author to comment that a function will only work on big endian
> machines. This is a basic assumption and is so simple it is not
> questioned
> for a given domain. The concept of domain being key here.
>
> The target platform of the program makes up the domain for the
> compiletime
> postulate.
> For a given platform, the postulate will always be strictly true,
> or false.
>
> A mathematical example:
> postulate: "Any number must be greater than, equal to, or less than zero."
> This postulate is quite reasonable and is in fact used as the basis for
> mathematical, but the domain is limited to real numbers. A couple of
> attempts to prove Fermat's last conjecture were foiled because they
> attempted to use this postulate in the domain of complex numbers.
>
> I am not suggesting that a programmer would be able to apply the same
> scrutiny and rigor to a piece of code as a mathematician does to a proof.
> If the code is laid out thoughtfully, then the successful
> compilation of the
> program could be considered analogous to a mathematical proof, with most
> assumptions checked at compile time. However, there are generally very
> basic concepts that we assume when programming: the computer will not lose
> power, memory will not have bit errors, filesystems will not be corrupted.
> We make these assumptions, not because they are obviously true,
> but because
> without assuming *something*, we cannot make functional programs.
> Even if I
> were to write a program that checked a filesystem's integrity, I would
> probably need to assume the memory in the computer was reliable.
>
>
>
> > Original Message
> > From: David Abrahams [mailto:abrahams_at_[hidden]]
> > Sent: Friday, July 28, 2000 9:38 AM
> > To: boost_at_[hidden]
> > Subject: Re: [boost] metactrl header [compile time asserts]
> >
> >
> >
> >  Original Message 
> > From: "Borgerding, Mark A." <MarkAB_at_[hidden]>
> >
> >
> > > According to Webster:
> > > postulate:
> > > Function: transitive verb
> > > 1 : DEMAND, CLAIM
> > > 2 a : to assume or claim as true, existent, or necessary :
> > > depend upon or start from the postulate of b : to assume as
> > a postulate or
> > > axiom (as in logic or mathematics)
> > > Function: noun
> > > 1 : a hypothesis advanced as an essential presupposition,
> > > condition, or premise of a train of reasoning
> > > 2 : AXIOM 3
> > >
> > >
> > > Along those lines, I also like any of these forms:
> > >
> > > AXIOM( sizeof(int == 4 );
> > > DEMAND( sizeof(int) == 4 );
> > > PREMISE( sizeof(int) == 4 );
> >
> > Ah, but that's exactly why postulate is the wrong word. To postulate
> > something means to offer it as a premise without proof. Any
> > logical system
> > depends on some truths which cannot be proven (read:
> > "checked") inside the system (Godel, said that, I think). I
> > think the point
> > of an axiom is to make your assumptions so simple on the face
> > of it that
> > even skeptics are willing to concede them. But our
> > compiletime assert is
> > inherently provable, or there would be no point in writing it!
> >
> > Dave
> >
> > P.S. I like COMPILE_TIME_ASSERT
> >
> >
> >
> >
> > 
> > <e
> > Download iPlanet Web Server, FastTrack Edition 4.1 for FREE,
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> > http://click.egroups.com/1/7540/4/_/9351/_/964791174/
> > 
> > e>
> >
> >
> >
>
>
>
>
>
>
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