What exactly is copy-on-modify semantics in R, and where is the canonical source?

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Call-by-value

The R Language Definition says this (in section 4.3.3 Argument Evaluation)

The semantics of invoking a function in R argument are call-by-value. In general, supplied arguments behave as if they are local variables initialized with the value supplied and the name of the corresponding formal argument. Changing the value of a supplied argument within a function will not affect the value of the variable in the calling frame. [Emphasis added]

Whilst this does not describe the mechanism by which copy-on-modify works, it does mention that changing an object passed to a function doesn’t affect the original in the calling frame.

Additional information, particularly on the copy-on-modify aspect are given in the description of SEXPs in the R Internals manual, section 1.1.2 Rest of Header. Specifically it states [Emphasis added]

The named field is set and accessed by the SET_NAMED and NAMED
macros, and take values 0, 1 and 2. R has a ‘call by value’
illusion, so an assignment like

b <- a

appears to make a copy of a and refer to it as b. However, if
neither a nor b are subsequently altered there is no need to copy.
What really happens is that a new symbol b is bound to the same
value as a and the named field on the value object is set (in this
case to 2). When an object is about to be altered, the named field
is consulted. A value of 2 means that the object must be duplicated
before being changed. (Note that this does not say that it is
necessary to duplicate, only that it should be duplicated whether
necessary or not.) A value of 0 means that it is known that no other
SEXP shares data with this object, and so it may safely be altered.
A value of 1 is used for situations like

dim(a) <- c(7, 2)

where in principle two copies of a exist for the duration of the
computation as (in principle)

a <- `dim<-`(a, c(7, 2))

but for no longer, and so some primitive functions can be optimized to
avoid a copy in this case.

Whilst this doesn’t describe the situation whereby objects are passed to functions as arguments, we might deduce that the same process operates, especially given the information from the R Language definition quoted earlier.

Promises in function evaluation

I don’t think it is quite correct to say that a promise is passed to the function. The arguments are passed to the function and the actual expressions used are stored as promises (plus a pointer to the calling environment). Only when an argument gets evaluated is the expression stored in the promise retrieved and evaluated within the environment indicated by the pointer, a process known as forcing.

As such, I don’t believe it is correct to talk about pass-by-reference in this regard. R has call-by-value semantics but tries to avoid copying unless a value passed to an argument is evaluated and modified.

The NAMED mechanism is an optimisation (as noted by @hadley in the comments) which allows R to track whether a copy needs to be made upon modification. There are some subtleties involved with exactly how the NAMED mechanism operates, as discussed by Peter Dalgaard (in the R Devel thread @mnel cites in their comment to the question)

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