An example of a non-settable function would be labels. You can only set factor labels when they are created with the factor() function. There is no labels<- function. Not that 'labels' and 'levels' in factors make any sense....
> fac <- factor(1:3, labels=c("one", "two", "three"))
> fac
[1] one two three
Levels: one two three
> labels(fac)
[1] "1" "2" "3"
OK, I asked for labels, which one might assume were as set by the factor call, but I get something quite ... what's the word, unintuitive?
> levels(fac)
[1] "one" "two" "three"
So it appears that setting labels is really setting levels.
> fac <- factor(1:3, levels=c("one", "two", "three"))
> levels(fac)
[1] "one" "two" "three"
OK that is as expected. So what are labels when one sets levels?
> fac <- factor(1:3, levels=c("one", "two", "three"), labels=c("x","y", "z") )
> labels(fac)
[1] "1" "2" "3"
> levels(fac)
[1] "x" "y" "z"
It would seem that 'labels' arguments for factor() trump any 'levels' arguments for the specification of levels. Why should this be? And why does labels() return what I would have imagined to be retrieved with as.character(as.numeric(fac))?
(This was a tangential comment [labelled as such] in an earlier answer about assignment functions to which I was asked to move to a question. So here's your opportunity to enlighten me.)
I think the way to think about the difference between labels and levels (ignoring the labels() function that Tommy describes in his answer) is that levels is intended to tell R which values to look for in the input (x) and what order to use in the levels of the resulting factor object, and labels is to change the values of the levels after the input has been coded as a factor ... as suggested by Tommy's answer, there is no part of the factor object returned by factor() that is called labels ... just the levels, which have been adjusted by the labels argument ... (clear as mud).
For example:
> f <- factor(x=c("a","b","c"),levels=c("c","d","e"))
> f
[1] <NA> <NA> c
Levels: c d e
> str(f)
Factor w/ 3 levels "c","d","e": NA NA 1
Because the first two elements of x were not found in levels, the first two elements of f are NA. Because "d" and "e" were included in levels, they show up in the levels of f even though they did not occur in x.
Now with labels:
> f <- factor(c("a","b","c"),levels=c("c","d","e"),labels=c("C","D","E"))
> f
[1] <NA> <NA> C
Levels: C D E
After R figures out what should be in the factor, it re-codes the levels. One can of course use this to do brain-frying things such as:
> f <- factor(c("a","b","c"),levels=c("c","d","e"),labels=c("a","b","c"))
> f
[1] <NA> <NA> a
Levels: a b c
Another way to think about levels is that factor(x,levels=L1,labels=L2) is equivalent to
f <- factor(x,levels=L1)
levels(f) <- L2
I think an appropriately phrased version of this example might be nice for Pat Burns's R inferno -- there are plenty of factor puzzles in section 8.2, but not this particular one ...