Why Does Enumerable.All Return True for an Empty Sequence

Why does Enumerable.All return true for an empty sequence?

It's certainly not a bug. It's behaving exactly as documented:

true if every element of the source sequence passes the test in the specified predicate, or if the sequence is empty; otherwise, false.

Now you can argue about whether or not it should work that way (it seems fine to me; every element of the sequence conforms to the predicate) but the very first thing to check before you ask whether something is a bug, is the documentation. (It's the first thing to check as soon as a method behaves in a way other than what you expected.)

LINQ Enumerable.All always return True if collection is empty

That's what the Documentation says.

true if every element of the source sequence passes the test in the
specified predicate, or if the sequence is empty; otherwise, false.

Implementation:

public static bool All<TSource>(this IEnumerable<TSource> source, Func<TSource, bool> predicate) 
{
    if (source == null) throw Error.ArgumentNull("source");
    if (predicate == null) throw Error.ArgumentNull("predicate");
    foreach (TSource element in source) {
        if (!predicate(element)) return false;
    }
    return true;
}

So it's obvious, if there is no item in the IEnumerable the foreach loop will be skipped and it directly returns true.

Linq .All returning true for empty collection

According to MSDN:-

Enumerable.All

Return true if every element of the source sequence passes the
test in the specified predicate, or if the sequence is empty;
otherwise, false.

So in your case since items is an empty collection it is returning true.

C# Linq All & Any working differently on blank array

Seems logical to me.

• All: Are all numbers in arr greater than zero (meaning there is no number not greater than zero) => true
• Any: Is there any number in arr that is greater than zero => false

But more important, according to Boolean Algebra:

arr.All(n => n > 0); 

gives true, because it should be the logical opposite of

arr.Any(n => !(n > 0));

which gives false (actually this is what the above two points say).

Why does IQueryable.All() return true on an empty collection?

If my driveway is empty, I cannot assert that all cars parked there are red.

Consider the following statements.

S1: My driveway is empty.

S2: All the cars parked in my driveway are red.

I claim that S1 implies S2. That is, the statement S1 => S2 is true. I will do this by showing that its negation is false. In this case, the negation of S1 => S2 is S1 ^ ~S2; this is because S1 => S2 is false only when S1 is true and S2 is false. What is the negation of S2? It is

~S2: There exists a car parked in my driveway that is not red.

What is the truth value of S1 ^ ~S2? Let's write it out

S1 ^ ~S2: My driveway is empty and there exists a car parked in my driveway that is not red.

The only way that S1 ^ ~S2 can be true is if both S1 and ~S2 are true. But S1 says that my driveway is empty and S2 says that there exists a car in my driveway. My driveway can not be both empty and contain a car. Thus, it is impossible for S1 and ~S2 to both be true. Therefore, S1 ^ ~S2 is false so its negation S1 => S2 is true.

Therefore, if your driveway is empty you can assert that all cars parked there are red.

So now let's consider an IEnumerable<T> elements and a Predicate<T> p. Let us suppose that elements is empty. We wish to discover the value of

bool b = elements.All(x => p(x));

Let's consider its negation

bool notb = elements.Any(x => !p(x));

For notb to be true, there must be at least one x in elements for which !p(x) is true. But elements is empty so it is impossible to find an x for which !p(x) is true. Therefore notb can not be true so it must be false. Since notb is false, its negation is true. Therefore b is true and elements.All(x => p(x)) must be true if elements is empty.

Here's one more way to think of this. The predicate p is true if for all x in elements you can not find any for which it is false. But if there are no items in elements then it is impossible to find any for which it is false. Thus, for an empty collection elements, p is true for all x in elements

Now, what about elements.Any(x => p(x)) when elements is an empty IEnumerable<T> and p is a Predicate<T> as above? We already know the result will be false because we know its negation is true, but let's reason through it anyway; the intuition is valuable. For elements.Any(x => p(x)) to be true there must be at least one x in elements for which p(x) is true. But if there aren't any x in elements it is impossible to find any x for which p(x) is true. Therefore, elements.Any(x => p(x)) is false if elements is empty.

Finally, here's a related explanation on why s.StartsWith(String.Empty) is true when s is a non-null instance of string:

Why does IEnumerable.Any return True for a collection of False-booleans?

Any() doesn't do what you think it does. Without a lambda expression in Any(), it will just check if there is any element in the enumerable it is called on.

You either want:

types.Select((x, i) => values[i].GetType() != x).Any(x => x)

or maybe

types.Where((x, i) => values[i].GetType() != x).Any()

What the value of x within lambda in `Enumerable.All` when the List is empty?

The reason why you get true is provided by the documentation:

true if every element of the source sequence passes the test in the specified predicate, or if the sequence is empty; otherwise, false.

This makes sense logically, too, because All is supposed to mean the same thing as !Any(...). Since Any would evaluate to false for an empty collection, it follows that All should evaluate to true under the same circumstances.

why this condition returns true?

Enumerable.All

true if every element of the source sequence passes the test in the
specified predicate, or if the sequence is empty; otherwise, false.

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