Writes the buffer's `comint-input-ring' to a history file.
The name of the file is given by the variable `comint-input-ring-file-name'.
The original contents of the file are lost if `comint-input-ring' is not empty.
If `comint-input-ring-file-name' is nil this function does nothing.
Useful within process sentinels.
See also `comint-read-input-ring'.
(fn)