Re: Proposal: 6NF

From: vc <boston103_at_hotmail.com>
Date: 20 Oct 2006 16:43:16 -0700
Message-ID: <1161387796.158559.98490@h48g2000cwc.googlegroups.com>

vc wrote:
[...]

>...  The LSP will not be violated with covariance,  but the artificial '+' will

> be nonsensical. The LSP won't be violated in the first case either
> at least superficially, although the interpretation depends on whether
> you consider converting an operation to a function acceptable behavior.

I am afraid I was too hasty. After some thinking, I think that it's fairly obvious that the LSP *will* be violated with just about any math structure. I was tricked by a specific inheritance model syntactical substitution acceptance into thinkinkg that won't.

Courtesy of Wikipedia:

"
Let q(x) be a property provable about objects x of type T. Then q(y) should be true for objects y of type S where S is a subtype of T. "

Let q(x) be a property that each integer has the additive inverse. Clearly, the property is violated in N as a subset of Z. That's equivalent to not 'inheriting' subtraction.

Let q(x) be a property that each element of N has a successor. Clearly, the property fails both for odd as well as even subsets of N.

etc. Received on Fri Oct 20 2006 - 18:43:16 CDT