Every quantifier

This checks whether all elements in a collection satisfy a given condition.

Note that this quantifier always returns true for empty collections. This is known in logic as vacuous truth, meaning that the quantifier is satisfied because there are no elements in the collection that do not satisfy the condition.

Is every unicorn in the room shining?

This might sound funny, but since there are no unicorns in the room, there's no unicorn that isn't shining. So, technically, they all are!

Syntax

This quantifier has the following syntax:

every /*<item>*/ in /*<collection>*/ satisfies /*<condition>*/

Either satisfy or satisfies can be used interchangeably:

every /*<item>*/ in /*<collection>*/ satisfy /*<condition>*/

You can also specify a name to refer to the index of the element in the collection:

every /*<item>*/ in /*<collection>*/ indexed by /*<index>*/ satisfies /*<condition>*/

You must replace the /*<item>*/ and /*<index>*/ placeholders with a valid identifier. These variables will refer to the element and its index in the collection, as exemplified in the following section.

Examples

Here is a basic example that checks if all numbers in a collection are even:

every number in [2, 4, 6] satisfies number mod 2 is 0 // true

The following example shows how to use the index of the element in the condition:

every item in cart indexed by index satisfies item's brand is "Apple" and index >= 1

In the above example, it checks whether the user only added Apple products as the second or subsequent item in the cart.