Besides simple infinitives like (to) write, there are also progressive, perfect and passive infinitives.

Progressive Infinitive

Form: (to) + be + present participle
Examples are: (to) be writing, (to) be reading, (to) be walking etc.

The progressive infinitive is used to suggest that actions and events are/were/will be continuing around the time we are talking about.

• I happened to be waiting for the bus when the accident happened.
• You must be joking.

Perfect infinitive

Form: (to) have + past participle
Examples are: (to) have received, (to) have broken, (to) have seen etc.

Perfect infinitives can have the same kind of meaning as perfect tenses or past tenses.

• I am happy to have left school. (= I am happy that I have left school.)
• You seem to have annoyed him. (= It seems that you have annoyed him.)
• It is nice to have finished work. (= It is nice that I have finished work.)

We often use perfect infinitives to talk about ‘unreal’ past events.

• If you had run a bit faster, you would have won.
• You should have told me you were coming.

Passive infinitive

Form: (to) be + past participle
Examples are: (to) be given, (to) be seen, (to) be loved etc.

Passive infinitives have the same kind of meaning as other passive forms.

• Everybody needs to be loved.
• There is a lot of work to be done.
• She ought to be told about it.

Perfect progressive infinitive

Form: (to) have been + present participle
Examples are: (to) have been crying, (to) have been waiting etc.

• They seem to have been waiting for a long time

Perfect passive infinitive

Form: (to) + have been + past participle

Perfect passive infinitives are also common.

• They were lucky – they could have been killed.