Past Participles – ‘Haven’t Eaten’ or ‘Haven’t Ate’?

past-participlesperfect-constructions

While chatting with somebody, I first used haven't eaten, then I thought that it was wrong, and switched to haven't ate.

Apparently, haven't ate is the one which is wrong.

Can someone explain the logic behind this? Verb tenses are still something I confuse a lot.

The principle parts of the verb eat are:

eat infinitive and present
ate past
eaten past participle
eating present participle

Accordingly, perfect constructions are formed with have + eaten:

I have eaten, you had eaten, he will have eaten, &c

Passive constructions are formed with be + eaten:

We are eaten, you were eaten, they will be eaten, &c

Progressive (continuous) constructions are formed with be + eating:

I am eating, you were eating, she will be eating, &c

You will occasionally hear et for the past, and even for the past participle but in US speech these are strictly non-standard dialect forms.