"Post kiam mi laboris, mi dormis."

This question was asked three years ago, and obviously a lot of people, including myself, wondered much the same thing. My question would have been "what is the purpose of kiam in this sentence?". As nobody has answered it, I'll try to do so for myself, and hope that somebody more knowledgeable will either confirm or correct my reply.

In English, after can be either a preposition (followed by a noun), as in after dinner or a conjunction (followed by a subordinate clause) as in after I had dinner.

In Esperanto, post is a preposition meaning after or behind, and as such would be followed by a noun, e.g. post la manĝo (after the meal), post la pordo (behind the door). Post kiam is a shorted form of post la tempo, kiam (after the time when), and effectively serves as a subordinating conjunction, so is followed by a subordinate clause, as in post kiam mi vespermanĝis (after I had dinner) or, as in this sentence, post kiam mi laboris (after I worked).

The "-is" verb ending indicates the past tense; "have worked" is the present perfect tense, and "sleep" is the simple present tense.

If nothing else, learning Esperanto will help us all improve our grammar.

I'm not sure, but I think that "mi estas skribinta", for example, means "I have written". But, anyway, nobody says that. Everyone just says "mi skribis".

It's an english grammar error. This statement is not about to compare the durations of two actions either about they happened in a specific moment or one of them lasted long. These actions followed eachother so simple past "I slept" or due to the word "after" I might say "After I had worked, I slept" would be the correct translation.