Create an incremental object:

Return the first value from the incremental object:

The next value:

When no more values are available, a failure object is returned:

When an incremental object is used as the source for Table, it returns all remaining elements:

Create an incremental object and return a value:

Table returns only those remaining elements:

An incremental object can be used as the source for Do:

The values returned from incremental objects can be any Wolfram Language expression:

Incremental objects can be built from combinatorial sources such as permutations:

The first value in the permutation:

The remaining values:

Working incrementally generates results one at a time; which uses less memory:

A related operation with the Permutations function generates all the permutations at once and uses much more memory:

It would not be possible to create all the permutations for as many objects as this:

The next 100000 elements can be stepped over:

An incremental object that returns successive accumulations:

Return the remaining results:

An incremental object can be nested inside another incremental object. Using an incremental range like this allows successive integers to be tested:

Incremental objects are stateful and are not cloned when used as the source for other incremental objects:

Use an incremental object as the source for another:

The source incremental object has been modified:

Incremental functions can also be used as a source for an incremental object:

The first 10 Fibonacci numbers:

Create an incremental object that uses the incremental function as a source:

The first 40 even Fibonacci numbers: