La negación en el present perfect sigue la regla general. Si hay un verbo modal o verbo auxiliar, es este verbo auxiliar o modal que realiza la negación. Como los tiempos compuestos siempre tienen un verbo auxiliar (to have), se forma la negación en este caso negando el verbo auxiliar to have.

ejemplos
I have already baked the cake. I have not (haven't) baked the cake.*
Have you ever been to London? Haven't you ever been to London?
= Have you not ever (= never) been to London?
She has worked here for 20 years. She has not (hasn't) worked here for 20 years.
We have just opened a bottle of wine. We have not (haven't) just opened a bottle of wine.
Have you seen Alex lately? Have you not seen Alex lately?
= Haven't you seen Alex lately?
He has worked a lot recently. He has not (hasn't) worked a lot recently.
She has lived here since 1980. She has not (hasn't) lived here since 1980.

* Already no es posible en este caso. En español tampoco se puede decir La tarta ya no la he hecho.
Lo que sería posible es not yet, todavía no.

En el caso de que haya un verbo modal y un verbo auxiliar, se realiza la negación con el verbo modal.

ejemplos
I have already baked the cake. I cannot (can't) have baked the cake.
She has worked here for 20 years. She may not have worked here for 20 years.
We have just opened a bottle of wine. We must not (mustn't) have just opened a bottle of wine.
He has worked a lot recently. He didn't need to have worked a lot recently.
She has lived here since 1980. She has not (hasn't) to have lived here since 1980.