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13.11.3 Ways to compose advice

Here are the different possible values for the where argument of add-function and advice-add, specifying how the advice function and the original function should be composed.

:before
Call function before the old function. Both functions receive the same arguments, and the return value of the composition is the return value of the old function. More specifically, the composition of the two functions behaves like:
          (lambda (&rest r) (apply function r) (apply oldfun r))

(add-function :before funvar function) is comparable for single-function hooks to (add-hook 'hookvar function) for normal hooks.

:after
Call function after the old function. Both functions receive the same arguments, and the return value of the composition is the return value of the old function. More specifically, the composition of the two functions behaves like:
          (lambda (&rest r) (prog1 (apply oldfun r) (apply function r)))

(add-function :after funvar function) is comparable for single-function hooks to (add-hook 'hookvar function 'append) for normal hooks.

:override
This completely replaces the old function with the new one. The old function can of course be recovered if you later call remove-function.
:around
Call function instead of the old function, but provide the old function as an extra argument to function. This is the most flexible composition. For example, it lets you call the old function with different arguments, or many times, or within a let-binding, or you can sometimes delegate the work to the old function and sometimes override it completely. More specifically, the composition of the two functions behaves like:
          (lambda (&rest r) (apply function oldfun r))

:before-while
Call function before the old function and don't call the old function if function returns nil. Both functions receive the same arguments, and the return value of the composition is the return value of the old function. More specifically, the composition of the two functions behaves like:
          (lambda (&rest r) (and (apply function r) (apply oldfun r)))

(add-function :before-while funvar function) is comparable for single-function hooks to (add-hook 'hookvar function) when hookvar is run via run-hook-with-args-until-failure.

:before-until
Call function before the old function and only call the old function if function returns nil. More specifically, the composition of the two functions behaves like:
          (lambda (&rest r) (or (apply function r) (apply oldfun r)))

(add-function :before-until funvar function) is comparable for single-function hooks to (add-hook 'hookvar function) when hookvar is run via run-hook-with-args-until-success.

:after-while
Call function after the old function and only if the old function returned non-nil. Both functions receive the same arguments, and the return value of the composition is the return value of function. More specifically, the composition of the two functions behaves like:
          (lambda (&rest r) (and (apply oldfun r) (apply function r)))

(add-function :after-while funvar function) is comparable for single-function hooks to (add-hook 'hookvar function 'append) when hookvar is run via run-hook-with-args-until-failure.

:after-until
Call function after the old function and only if the old function returned nil. More specifically, the composition of the two functions behaves like:
          (lambda (&rest r) (or  (apply oldfun r) (apply function r)))

(add-function :after-until funvar function) is comparable for single-function hooks to (add-hook 'hookvar function 'append) when hookvar is run via run-hook-with-args-until-success.

:filter-args
Call function first and use the result (which should be a list) as the new arguments to pass to the old function. More specifically, the composition of the two functions behaves like:
          (lambda (&rest r) (apply oldfun (funcall function r)))

:filter-return
Call the old function first and pass the result to function. More specifically, the composition of the two functions behaves like:
          (lambda (&rest r) (funcall function (apply oldfun r)))