From: Martin DeMello <martindemello@...>
Date: 2003-09-18T16:33:16+09:00
Subject: Re: Changing ==,>,<, etc

Marcin 'Qrczak' Kowalczyk <qrczak@knm.org.pl> wrote:
> Dnia ?ro 17. wrze?nia 2003 14:54, Martin DeMello napisa?:
> 
>> i.e., there is no reason the LHS should be in the outer loop, rather
>> than the RHS. My point was that the only reason there *was* an 'outer
>> loop' was that the language forces you to write loops nestedly, whereas
>> a cross product (essentially what this is) is flat.
> 
> I disagree. It's essential which is outer and which is inner unless 
> quantifiers happen to commute (both "any" or both "all"). The decision to 
> put LHS in the outer loop is arbitrary; if you wanted the other way you 
> must search for an operator with flipped arguments (which happens to be 
> easy among the six comparison operators).
> 
>> Also, any(1,2) != any(1,2) should be true.
> 
> I wrote any(1,2) != all(1,2). And what about all(1,2) != any(1,2)?
> If they are the same, then "any" and "all" must be treated with different 
> priority. If they are different, then != is no longer commutative.
> (I suspect the latter.) Both cases are unintuitive for me.

Good point. I see now that it's analogous to the fact that

(forall x)(there exists y)(x != y)

is different from

(there exists y)(forall x)(x != y)

So there is, indeed, as you pointed out, the notion of an inner and an
outer quantifier.

martin