Function privileges

By default, when a function is created, the right to execute it is is not restricted by role, but this probably isn't consistent with best practices for an API design. If you want functions to be executable exclusively by a given role upon their creation, issue psql instructions similar to this:

-- To stop functions from being universally executable upon creation (note the IN SCHEMA part).
ALTER DEFAULT PRIVILEGES IN SCHEMA api REVOKE EXECUTE ON FUNCTIONS FROM PUBLIC;
-- To grant execution rights for functions to a specific role upon function creation.
ALTER DEFAULT PRIVILEGES IN SCHEMA api GRANT EXECUTE ON FUNCTIONS TO my_role;

See PostgreSQL alter default privileges for more details.

The foregoing example may not be appropriate in all situations. For instance you may have a situation where different functions are intended to be called by different roles. In that case you will not want to grant EXECUTE to one specific role by default. Instead you will want to manually grant executability on a case by case basis.

By default, a function is executed with the privileges of the user who calls it. This means that the user has to have all permissions to do the operations the procedure performs.

Another option is to define the function with the SECURITY DEFINER option. Then only one permission check will take place, the permission to call the function, and the operations in the function will have the authority of the user who owns the function itself. See PostgreSQL documentation for more details.