In English, we often use the ‘must + have + p.p’ to draw a conclusion about a particular situation we are witnessing. For instance, arriving at the gate of an house which has been on sale for a while, I tell my wife, after seeing some trucks being unloaded and words of felicitations being exchanged between some people: “O love! We are late! The house must have already been bought/sold.” The must-pattern is used when there is high probability for the veracity of the speaker’s conclusion. Should we be less certain about the circumstances, we tend to dilute the certainty by using ‘might + have + p.p.’
Here is a summary of what I have learnt about the passive form in German, yet none seems to fit the example I have given above.
Present: „Das Haus wird gekauft.“ corresponding to “The house is being bought.”
It must be noted that using werden+p.p emphasises the action rather than the result, i.e. to say “the house is bought” we should either say „Das Haus ist gekauft.“ or use the perfect form below.
Perfect: „Das Haus ist gekauft worden.“ corresponding to “The house has been bought.”
I have also come to realise that this pattern is used when the speaker intends to break something new to his hearer the same way as in English.
Past: „Das Haus
warwurde gekauft.“ corresponding to “The house was bought.”
Past Perfect: „Das Haus war gekauft worden.“ corresponding to “The house had been bought.”
Future: „Das Haus wird gekauft werden.“ corresponding to “The house will be bought.”
Future Perfect: „Das Haus wird gekauft
werdenworden sein.“ corresponding to “The house will have been bought.”
This usage requires modification by time-adverbs of some sort: „Bis Freitag wird das Haus gekauft werden sein.“ “The house will have been bought by Friday.”
The last form in particular is interesting in as much as it differs, at least in the English form, from ‘must+have+p.p’ structure in only one element, i.e. will vs. must. So, considering all this, can we possibly translate the sentence in the question as follows?
„Das Haus muss bereits gekauft worden sein. Wir hätten früher kommen sollen.“