Re: Issues with the logical consistency of The Third Manifesto
Date: Tue, 16 Nov 2004 07:07:30 GMT
Message-ID: <SGhmd.102152$R05.26010_at_attbi_s53>
"Laconic2" <laconic2_at_comcast.net> wrote in message news:zdqdneWfr8Q8xwrcRVn-vg_at_comcast.com...
>
> All we have inside of computers is representations. That's all there is in
> there, fellas. There is not a single "value" actually inside the machine.
> I don't care whether you follow Codd or Date or Dawn or Neo, it's all
> representation. I don't care whether you follow Babbage or Ada Lovelace or
> John Von Neumann or Knuth, it's all representation.
Yes; this is an important point.
> So the point is that, if two representations represent the same value, we
> have to work things out so that the equality tester can detect that fact,
> and return the right result. If we indeed find that two distinct
> representations of the "state of a relvar" can represent the same relation,
> then we are going to have to find an algorithm for reducing equivalent
> representations to a common representation, one that can be used for
> comparison.
Okay, so you're right; if we find ourselves is this situation, then we have to, as it were, normalize the representation. This is hard. If we only have one possible representation for a type and it's always normalized, then this isn't an issue. For example, we can have a rational type, and normalize the fraction after every operation. In this case, comparing the representation and comparing the values is the same.
So let's try to figure out what we buy with all this complexity. If we're going to allow multiple representations for a type, then it ought to be for a reason, eh?
So what's the reason? I sure can't think of any. As I've pointed out before, the canonical TTM example of polar vs. cartesian point isn't even mathematically sound (horrors!) and immediately introduces all kinds of complexity around either representing values algebraically, or else having to deal with approximate values, a dilemma that TTM doesn't even acknowledge, let alone solve.
Marshall Received on Tue Nov 16 2004 - 08:07:30 CET