In MongoDB, the $allElementsTrue aggregation pipeline operator evaluates an array as a set and returns true if no element in the array is false.

If the array contains an element that is false, then $allElementsTrue returns false.

An array’s element is true if it’s not false, null, 0, or undefined.

Example

Suppose we have a collection with the following document:

{ "_id" : 1, "data" : [ 1, 2, 3 ] }

This document contains an array.

We can run the following query with $allElementsTrue to find out whether or not the array contains an element that is false:

db.test.aggregate(
   [
     { $project: { 
        _id: 0,
        allElementsTrue: { $allElementsTrue: [ "$data" ] } } 
         }
   ]
)

Result:

{ "allElementsTrue" : true }

In this case, none of the array elements are false, and so we get a result of true.

When the Array Contains False

Let’s add the following document to the collection:

{ "_id" : 2, "data" : [ true, false ] }

And let’s run $allElementsTrue against that document:

db.test.aggregate(
  [
    { $match: { _id: 2 } },
    { $project: { 
      _id: 0,
      allElementsTrue: { $allElementsTrue: [ "$data" ] } } 
        }
  ]
)

Result:

{ "allElementsTrue" : false }

This time we get false, even though there’s another element that is true. This is to be expected, because $allElementsTrue returns false whenever there is at least one element that is false, regardless of how many other elements are true.

Empty Arrays

Empty arrays return true.

Suppose we add the following document to our collection:

{ "_id" : 3, "data" : [ ] }

This document contains an empty array.

Now let’s run $allElementsTrue again:

db.test.aggregate(
  [
    { $match: { _id: 3 } },
    { $project: { 
      _id: 0,
      allElementsTrue: { $allElementsTrue: [ "$data" ] } } 
        }
  ]
)

Result:

{ "allElementsTrue" : true }

As expected, it returns true.

Null, 0, and Undefined Values

It’s not entirely true that $allElementsTrue evaluates to false only when the array contains false.

The $allElementsTrue operator also evaluates to false whenever an array contains null, 0, or undefined values.

Suppose we add the following documents to our collection:

{ "_id" : 4, "data" : [ 1, null, 3 ] }
{ "_id" : 5, "data" : [ 1, undefined, 3 ] }
{ "_id" : 6, "data" : [ 0, 1, 2 ] }

Each document’s array contains an element of either null, 0, or undefined.

Now let’s run $allElementsTrue against those documents:

db.test.aggregate(
  [
    { $match: {_id: { $in: [4,5,6] }} },
    { $project: { 
      allElementsTrue: { $allElementsTrue: [ "$data" ] } } 
        }
  ]
)

Result:

{ "_id" : 4, "allElementsTrue" : false }
{ "_id" : 5, "allElementsTrue" : false }
{ "_id" : 6, "allElementsTrue" : false }

All documents return false as expected.

Nested Arrays

If the array contains a nested array that contains an element that is false, then that is not enough for $allElementsTrue to return false. As far as $allElementsTrue is concerned, the nested array is the element, and therefore not false.

To demonstrate what I mean, suppose we insert the following documents:

{ "_id" : 7, "data" : [ 1, [ false ], 3 ] }
{ "_id" : 8, "data" : [ 1, [ false ], false ] }

Now let’s run $allElementsTrue against those two documents:

db.test.aggregate(
  [
    { $match: {_id: { $in: [7,8] }} },
    { $project: { 
      allElementsTrue: { $allElementsTrue: [ "$data" ] } } 
        }
  ]
)

Result:

{ "_id" : 7, "allElementsTrue" : true }
{ "_id" : 8, "allElementsTrue" : false }

We can see that the first document returned true and the second returned false.

This is because, in the first document, the false value is nested inside another array, and therefore doesn’t count as a false value (i.e. the array itself is the value).

The second document however, also contains false as one of the array elements, and therefore, that value is what causes $allElementsTrue to evaluate to false.