[R] 'all' inconsistent?

[Peter Dalgaard]

Seth Falcon <sfalcon at fhcrc.org> writes:

> On 30 Jan 2006, ligges at statistik.uni-dortmund.de wrote:
> > Current behaviour is consistent in so far that identical(all(x),
> > !any(!x)) is TRUE and definition of any() is obvious.
> 
> That helps, thanks.  I'm not sure I've had enough coffee to continue,
> but, for the set analogy I think we are saying:
> 
> logical(0) is the empty set {}.
> Complement of {} is the universal set U.
> 
> Then !logical(0)  == !{} == U.  any(U) is TRUE, isn't it?  
> 
> I guess the real message is that you need to protect yourself by
> testing for positive length first.

This comes up repeatedly. Probably the most useful way of viewing
these empty sum/prod/any/all issues is that you want

sum(c(x,y)) == sum(x) + sum(y)
prod(c(x,y)) == prod(x) * prod(y)
any(c(x,y)) == any(x) | any(y)
all(c(x,y)) == all(x) & all(y)

even in the cases where x or y is empty, and of course the neutral
operations are 

adding 0
multiplying by 1
or'ing with FALSE
and'ing with TRUE

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