For comparison, crypt function is used in a slightly different way. It accepts 2 arguments.
if ( (crypt(str $user_input, $password_hash) == $password_hash)
You can go to this link for a better understanding! (Or refer to login.php in public directory of pset7)
Before you can add a feature to allow users to reset a forgotten password, you will need to add a simpler feature: create a Controller and View that will allow an authenticated user (already logged in) to change their password to a new one -- perhaps only after entering their current, valid password.
Once you have done that, you can use a similar mechanism ...
From php manual
password_hash() creates a new password hash using a strong one-way hashing algorithm.
one-way being the operative.
More info on cryptographic hashing here. Or check out any of the other 2 million+ hits from Google for "one way hash".
As a user I wouldn't be happy to see a password sent via email in plaintext!