# Introduction

In today's tutorial you will use Boxes to implement circular data structures.

Start with the following `plait`

code. The `MList`

type represents a
mutable list type, where the value representing the tail of a list can
be replaced with `set-box!`

. `mlist`

transforms a regular `plait`

list of numbers into this form, while `take`

returns a `plait`

list
with up to `k`

elements in it.

```
(define-type MList
[MPair (n : Number) (tail : (Boxof MList))]
[Empty])
(define (mlist lst)
(cond
[(empty? lst) (Empty)]
[else (MPair (first lst) (box (mlist (rest lst))))]))
(test (mlist empty) (Empty))
(test (mlist '(1)) (MPair 1 (box (Empty))))
(test (mlist '(1 2)) (MPair 1 (box (MPair 2 (box (Empty))))))
(define (take k mlst)
(cond
[(<= k 0) empty]
[else
(type-case MList mlst
[(Empty) empty]
[(MPair n tail-box)
(cons n (take (sub1 k) (unbox tail-box)))])]))
(define big-mlist
(mlist (build-list 50 identity)))
(test (take 10 big-mlist) '(0 1 2 3 4 5 6 7 8 9))
```

Write a function `set-last!`

to update the `tail`

field of the last
pair in an MList. Your function should pass the following tests.

```
(define test-lst1 (mlist '(1 2 3)))
(define test-lst2 (mlist '(4 5 6)))
(set-last! test-lst1 test-lst2)
(test (take 6 test-lst1) '(1 2 3 4 5 6))
(test (take 3 test-lst2) '(4 5 6))
(test (take 1000 test-lst1) '(1 2 3 4 5 6))
(test/exn (set-last! (Empty) test-lst1) "cannot set tail")
```

# Cyclic lists

Write a wrapper `cycle`

around `set-last!`

to make a cyclic list.
Your function should pass the following tests.

```
(define small-cycle (cycle (mlist '(0 1 2))))
(define big-cycle (cycle big-mlist))
(test (cycle (Empty)) (Empty))
(test (take 0 big-cycle) empty)
(test (take 0 small-cycle) empty)
(test (take 5 big-cycle) '(0 1 2 3 4))
(test (take 5 small-cycle) '(0 1 2 0 1))
(test (take 107 big-cycle) (build-list 107 (lambda (n) (modulo n 50))))
```