Why does Stream.allMatch() return true for an empty stream?

My colleague and I had a bug that was due to our assumption that an empty stream calling allMatch() would return false.

if (myItems.allMatch(i -> i.isValid()) { 
    //do something
}

Of course, it is kind of our fault for assuming and not reading documentation. But what I don’t understand is why the default allMatch() behavior for an empty stream returns true. What was the reasoning for this? Like the anyMatch() (which contrarily returns false), this operation is used in an imperative way that departs the monad and probably used in an if statement. Considering those facts, is there any reason why having allMatch() default to true on an empty stream be desirable for majority of uses?

Answer

This is known as vacuous truth. All members of an empty collection satisfy your condition; after all, can you point to one that doesn’t?

Similarly, anyMatch returns false, because you can’t find an element of your collection that does match the condition. This is confusing to a lot of people, but it turns out to be the most useful and consistent way to define “any” and “all” for empty sets.