Re: Proposal: 6NF

From: David Cressey <dcressey_at_verizon.net>
Date: Thu, 12 Oct 2006 11:05:26 GMT
Message-ID: <WjpXg.2659$lj2.1388_at_trndny01>


"Marshall" <marshall.spight_at_gmail.com> wrote in message news:1160537768.046280.133920_at_i42g2000cwa.googlegroups.com...
> On Oct 10, 5:28 pm, "David Cressey" <dcres..._at_verizon.net> wrote:
> >
> > It's not clear to me that the real number 2 is the
> > same thing as the integer 2.
>
> This is another one of those questions that can't be separated
> from its theory. Arithmetically, 2 and 2.0 are identical.
> Type-theoretically, they might not be. Depending on the particular
> type system, they might or might not be assignment compatible, or
> have some kind of subtype relationship.

Well, this is one of those areas where the computer is an imperfect model of the underlying mathematics. That's why I accept Brian's clarification that, in math, {2} and {2.0} are the same set. We still have the problem to solve, in the world of computing.

>
> And what kind of int 2 are we talking about? 8 bit, 16 bit, 32 bit,
> arbitrary? Signed or unsigned? What size float? It's true the
> integers are a subset of the reals, but we don't (and mostly
> can't) have a type that works the same as the reals in a computer.
> We could say that the 32 bit ints are a subset of double but
> not of float, etc. etc.
>
> As an aside, I'd love to see a system in which n-bit integer
> was a single generic definition, instantiated with different
> values of n. I think it might not actually be too hard to do.
>

As an aside, I have solved this problem, to my statisfaction, not only about n-bit integers, but about variable length datablocks of all types, such as text, compiled code, or what have you. Eventually, I'm going to build some kind of system around my solution.

> Floating point arithmetic isn't associative. I hate that.
>

That's because it doesn't have closure. If you came up with a floating point system with closure, you'd get associativity as a side benefit.

>
> Marshall
>
Received on Thu Oct 12 2006 - 13:05:26 CEST

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