Past exam of the mathematics course of the University of Cambridge / 2006 / ia / Paper 5 / 5 / a / i / Solution

A FIFO queue provides an empty queue, an emptiness test, insertion at the rear, inspection of the front item, and removal of the front item. It preserves insertion order: after enqueuing $x$ and then $y$, removing an item returns $x$ first. Inspection and removal on an empty FIFO queue must have a specified outcome, such as an exception handling case or an option-valued result. In a functional interface, insertion and removal return the new FIFO queue rather than updating their argument.