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Pluggable Functions

Pluggable functions in WordPress 1.5.1+ let you replace certain core functions with functions of your own using a plugin. A function can only be reassigned this way once, so you can’t install two plugins that plug the same function for different reasons. For safety, it is best to always wrap your functions with if(!function_exists()), otherwise you will produce fatal errors on plugin activation.

Reference

The default functions are defined in wp-includes/pluggable.php.

get_currentuserinfo() 
Grabs the information of the current logged in user, if there is one. Essentially a wrapper for get_userdata(), but it also stores information in global variables.
get_userdata($userid) 
Pulls user information for the specified user from the database.
get_userdatabylogin($user_login) 
Pulls user information for the specified user from the database.
wp_mail($to, $subject, $message, $headers = '') 
A convenient wrapper for PHP's mail function.
wp_login($username, $password, $already_md5 = false) 
Returns true if the specified username and password correspond to a registered user.
auth_redirect() 
If a user is not logged in, he or she will be redirected to WordPress' login page before being allowed to access content on the page from which this function was called. Upon successfully logging in, the user is sent back to the page in question.
wp_redirect($location) 
Redirects a browser to the absolute URI specified by the $location parameter.
wp_setcookie($username, $password, $already_md5 = false, $home = '', $siteurl = '') 
Sets the WordPress cookies for a logged in user. See WordPress Cookies.
wp_clearcookie() 
Clears the cookies for a logged in user. See WordPress Cookies.
wp_notify_postauthor($comment_id, $comment_type='')
Emails the author of the comment's post the content of the comment specified.
wp_notify_moderator($comment_id) 
Informs the administrative email account that the comment specified needs to be moderated. See Administration > Settings > General.

Example

An example of what you can do with a pluggable function is replace the default email handler. To do this, you'd need to write a plugin that defines a wp_mail() function. The default wp_mail() function looks like this: 

function wp_mail($to, $subject, $message, $headers = '') {
  if( $headers == '' ) {
    $headers = "MIME-Version: 1.0\n" .
      "From: " . get_settings('admin_email') . "\n" . 
      "Content-Type: text/plain; charset=\"" . get_settings('blog_charset') . "\"\n";
  }

  return @mail($to, $subject, $message, $headers);
}

But, for example, if you wanted to CC all your mail to another address, you could use this code in a plugin: 

if(!function_exists('wp_mail')) :
function wp_mail($to, $subject, $message, $headers = '') {
  if( $headers == '' ) {
    $headers = "MIME-Version: 1.0\n" .
      "From: " . get_settings('admin_email') . "\n" . 
      "Cc: dummy@example.com\n";
      "Content-Type: text/plain; charset=\"" . get_settings('blog_charset') . "\"\n";
  }

  return @mail($to, $subject, $message, $headers);
}
endif;

Notice that if you plug a core function like this the original is no longer available. I.e., the elegant solution here would have been to write a function that tacks our Cc header on the end of the exising $headers string then call the original wp_mail() with the extra header. However this would not work as the original wp_mail() does not exist if you plug it.

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