All safe methods are also idempotent, but not all idempotent methods are safe. For example, PUT and DELETE are both idempotent but unsafe.

So every program starts in the IO monad. From here you can get any input you need, call into relatively "pure" code with the inputs, and then output the result in some way. The reverse does not work. You cannot call into IO code from pure code like you can call into a Maybe function from pure code.

Magnetic materials are always made of metal, but not all metals are magnetic