The conditional perfect is a grammatical construction that combines the conditional mood with perfect aspect. A typical example is the English would have written. The conditional perfect is used to refer to a hypothetical, usually counterfactual, event or circumstance placed in the past, contingent on some other circumstance (again normally counterfactual, and also usually placed in the past). Like the present conditional (a form like would write), the conditional perfect typically appears in the apodosis (the main clause, expressing the consequent) in a conditional sentence.
In English, the conditional perfect is formed using would have together with the past participle of the main verb. The auxiliary would marks the conditional mood (it is occasionally replaced by should in the first person; see shall and will), while the auxiliary have (used in combination with the past participle) marks the perfect aspect (prior occurrence of the event in question). The conditional perfect is used chiefly in the main clause (apodosis) of "third conditional" (or sometimes "mixed conditional") sentences, as described under English conditional sentences. Examples:
It is also possible for the auxiliary would to be replaced by the modals should, could or might to express appropriate modality in addition to conditionality.
Sometimes, in (chiefly American English) informal speech, the would have construction appears in the if-clause as well ("If we would have run faster, we would have arrived earlier"), but this is considered incorrect in formal speech and writing (see English conditional sentences § Use of will and would in condition clauses).