How does copy-on-write work with read-only virtual pages in mmap function?

When calling mmap, the caller must choose between a shared (MAP_SHARED) or private (MAP_PRIVATE) mapping. The use of copy-on-write is an implementation detail; compare with the POSIX definition of mmap.

The type of mapping (shared or private) only determines what happens to writes. Thus with PROT_READ, it doesn’t matter, and the use of copy-on-write doesn’t either. Any change made to the backing file will ultimately be visible in the process’ mapping, even with a private mapping. In theory, this behaviour could change:

Updates to the mapping are not visible to other processes mapping the same file, and are not carried through to the underlying file. It is unspecified whether changes made to the file after the mmap() call are visible in the mapped region.

(from the MAP_PRIVATE description in man 2 mmap).

Note too that a process can change the memory protection with mprotect, assuming it is able to write to the underlying file. The type of mapping can’t be changed, but the protection can, so a process can map a file read-only, then change to read-write (if the file itself was opened read-write); copy-on-write becomes relevant then.

(Thanks to user414777 for correcting a number of errors in previous versions of this answer. Any remaining errors are my own.)