R devel - Jun 2007 - Expected behavior from: all(c(NA, NA, NA) < NA, na.rm = TRUE)?

Hi all,

Came across this curious behavior in:

  R version 2.5.0 Patched (2007-06-05 r41831)


A simplified example is:
> all(c(NA, NA, NA) > NA, na.rm = TRUE)
[1] TRUE


Is this expected by definition?

If one reduces this to individual comparisons, such as :
> NA > NA
[1] NA
> all(NA > NA)
[1] NA
> all(NA > NA, na.rm = TRUE)
[1] TRUE

the initial comparison on the 3 element vector would be consistent with
the last example. 

If one evaluates each side of the comparison within the parens in the
initial example, you get something along the lines of the following:

x <- c(NA, NA, NA)
x <- x[!is.na(x)]   # remove NA's (eg. mean.default(x, na.rm = TRUE))
> x
logical(0)
> logical(0) > NA
logical(0)
> all(logical(0))
[1] TRUE


If my train of thought is correct, it seems to me that the behavior
above distills down to the comparison between logical(0) and NA, which
rather than returning NA, returns logical(0). 

This would seem appropriate, given that there is no actual comparison
being made with NA, I think, since logical(0) is an 'empty' vector.

However, should all(logical(0)) return TRUE or logical(0)?  For example:
> logical(0) == logical(0)
logical(0)
> all(logical(0) == logical(0))
[1] TRUE


If the initial comparison of logical(0) returns logical(0), which is not
TRUE:
> logical(0) == TRUE
logical(0)

then why does all() return TRUE, if the individual comparison is not
TRUE?  By definition from ?all:

Given a sequence of logical arguments, a logical value indicating
whether or not all of the elements of x are TRUE. 
The value returned is TRUE if all of the values in x are TRUE, and FALSE
if any of the values in x are FALSE. 
If na.rm = FALSE and x consists of a mix of TRUE and NA values, the
value is NA.



Does this make any sense?

Thanks,

Marc Schwartz

Marc Schwartz wrote:
> Hi all,
>
> Came across this curious behavior in:
>
>   R version 2.5.0 Patched (2007-06-05 r41831)
>
>
> A simplified example is:
>
>   
>> all(c(NA, NA, NA) > NA, na.rm = TRUE)
>>     
> [1] TRUE
>
>
> Is this expected by definition?
>
> If one reduces this to individual comparisons, such as :
>
>   
>> NA > NA
>>     
> [1] NA
>
>   
>> all(NA > NA)
>>     
> [1] NA
>
>   
>> all(NA > NA, na.rm = TRUE)
>>     
> [1] TRUE
>
> the initial comparison on the 3 element vector would be consistent with
> the last example. 
>
> If one evaluates each side of the comparison within the parens in the
> initial example, you get something along the lines of the following:
>
> x <- c(NA, NA, NA)
> x <- x[!is.na(x)]   # remove NA's (eg. mean.default(x, na.rm =
TRUE))
>
>   
>> x
>>     
> logical(0)
>
>   
>> logical(0) > NA
>>     
> logical(0)
>
>   
>> all(logical(0))
>>     
> [1] TRUE
>
>
> If my train of thought is correct, it seems to me that the behavior
> above distills down to the comparison between logical(0) and NA, which
> rather than returning NA, returns logical(0). 
>
> This would seem appropriate, given that there is no actual comparison
> being made with NA, I think, since logical(0) is an 'empty' vector.
>
> However, should all(logical(0)) return TRUE or logical(0)?  For example:
>
>   
>> logical(0) == logical(0)
>>     
> logical(0)
>
>   
>> all(logical(0) == logical(0))
>>     
> [1] TRUE
>
>
> If the initial comparison of logical(0) returns logical(0), which is not
> TRUE:
>
>   
>> logical(0) == TRUE
>>     
> logical(0)
>
> then why does all() return TRUE, if the individual comparison is not
> TRUE?  By definition from ?all:
>
> Given a sequence of logical arguments, a logical value indicating
> whether or not all of the elements of x are TRUE. 
> The value returned is TRUE if all of the values in x are TRUE, and FALSE
> if any of the values in x are FALSE. 
> If na.rm = FALSE and x consists of a mix of TRUE and NA values, the
> value is NA.
>
>
>
> Does this make any sense?
>   
I don't see the problem. Isn't it just that all(logical(0))==TRUE by 
convention just like prod(numeric(0))==1 etc.?

On Wed, 20 Jun 2007, Marc Schwartz wrote:
>
> If my train of thought is correct, it seems to me that the behavior
> above distills down to the comparison between logical(0) and NA, which
> rather than returning NA, returns logical(0).
>
> This would seem appropriate, given that there is no actual comparison
> being made with NA, I think, since logical(0) is an 'empty' vector.
>
> However, should all(logical(0)) return TRUE or logical(0)?  For example:
>
>> logical(0) == logical(0)
> logical(0)
>
>> all(logical(0) == logical(0))
> [1] TRUE
Yes.
>
> If the initial comparison of logical(0) returns logical(0), which is not
> TRUE:
>
>> logical(0) == TRUE
> logical(0)
Yes, they have different lengths, so they aren't equal.
> then why does all() return TRUE, if the individual comparison is not
> TRUE?  By definition from ?all:
>
> Given a sequence of logical arguments, a logical value indicating
> whether or not all of the elements of x are TRUE.
This is the empty set question that should probably be a FAQ.

All elements of logical(0) are  TRUE, in the vacuous sense that it has no
elements.

The same sort of thing happens for any(logical(0)), which is FALSE;
sum(numeric(0)), which is 0; prod(numeric(0)), which is 1; max(numeric(0)),which
is -Inf; and min(numeric(0)), which is Inf.


This seems as though R is trying to be difficult, but there is a real benefit in
terms of associativity:
   all(all(x),all(y)) is always the same as all(x,y) under this definition.
   prod(prod(x), prod(y)) is prod(x,y)
   min(min(x),min(y)) is min(x,y)
and so on.

The general principle is that a function made by 'reducing' a vector
with an associative binary operator, when applied to an empty vector, gives the
identity element for the operator. The identity element for AND is TRUE.

>
> Does this make any sense?
>
Yes, although it is initially surprising.


      -thomas

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle