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8.1 Quick Visits
8.1.1 Folds vs Visitors

8 2/27: Quick Visits

Due: 2/27.

Language: class/2

8.1 Quick Visits

This problem builds on the quick lists problem.

Here was the interface you should have implemented for lists using the quick list data structure that supports a fast list-ref method:

;; A [List X] implements
;; - cons : X -> [List X]
;;   Cons given element on to this list.
;; - first : -> X
;;   Get the first element of this list
;;   (only defined on non-empty lists).
;; - rest : -> [List X]
;;   Get the rest of this
;;   (only defined on non-empty lists).
;; - list-ref : Natural -> X
;;   Get the ith element of this list
;;   (only defined for lists of i+1 or more elements).
;; - length : -> Natural
;;   Compute the number of elements in this list.
;; empty is a [List X] for any X.

Make sure your quick list implementation is working and place it into a file named "quick-lists.rkt". That file should provide one name, empty, by including the following at the top of the file:

(provide empty)

In a file named "slow-lists.rkt" re-develop an implementation of the list interface, but in the usual way as a recursive union of mt% and cons% classes. That file should also provide empty by including the same line above at the top.

Finally, start a third file called "use-lists.rkt" that will make use of both kinds of lists by including the following at the top of the file:

(require (prefix-in q: "quick-lists.rkt"))
(require (prefix-in s: "slow-lists.rkt"))

You now have two lists: q:empty and s:empty; both are represented in very different ways, but so long as you use them accoring to the list interface, they should be indistinguishable.

Let’s now revise the [List X] interface to include support for visitors:

;; A [List X] implements ...
;; - accept : [ListVisitor X Y] -> Y
;;   Accept given visitor and visit this list's data.
;; A [ListVisitor X Y] implements
;; - visit-mt : -> Y
;;   Visit an empty list.
;; - visit-cons : X [Listof X] -> Y
;;   Visit a cons lists.

Implement the revised [List X] interface in both "quick-lists.rkt" and "slow-lists.rkt".

In "use-lists.rkt" you should be able to define particular visitors and have it work on both representations of lists. As an example, here is a list visitor that computes the length of a list:

;; A (new length%) implements [ListVisitor X Natural].
;; List visitor for computing the length of a list.
(define-class length%
  (define (visit-mt) 0)
  (define (visit-cons x r)
    (add1 (r . accept this))))
(define len (new length%))
(check-expect (q:empty . accept len) 0)
(check-expect (s:empty . accept len) 0)
(check-expect (q:empty . cons 'c . cons 'b . cons 'a . accept len) 3)
(check-expect (s:empty . cons 'c . cons 'b . cons 'a . accept len) 3)

And here’s one for the sum of a list of numbers:

;; A (new sum%) implements [ListVisitor Number Number].
;; List visitor for computing the sum of a list of numbers.
(define-class sum%
  (define (visit-mt) 0)
  (define (visit-cons n r)
    (+ n (r . accept this))))
(define sum (new sum%))
(check-expect (q:empty . accept sum) 0)
(check-expect (s:empty . accept sum) 0)
(check-expect (q:empty . cons 3 . cons 4 . cons 7 . accept sum) 14)
(check-expect (s:empty . cons 3 . cons 4 . cons 7 . accept sum) 14)

Implement a [ListVisitor X X] named reverse% that reverses a list (note: you may need to implement a “helper” visitor that corresponds to the helper function you’d write for the reverse function). Note that this visitor will have to commit to produces either a quick list or a slow list, but it really doesn’t really matter which... well, except for testing. So for example, let’s say the reverse visitor produces slow lists. Then we would expect the following test to pass, assuming reverse% works as specified:

(define rev (new reverse%))
(check-expect (q:empty . accept rev) s:empty)
(check-expect (q:empty . cons 'c . cons 'b . cons 'a . accept rev)
              (s:empty . cons 'a . cons 'b . cons 'c))

Of course, this isn’t ideal since our test is testing more than is actually required of reverse%. In particular, it should be perfectly acceptable for reverse% to produce quick lists without tests failing.

What’s happening here is that check-expect is checking too much because it is not treating the objects it compares solely according to their interface. We will see how to fix this problem by defining an interface-respecting equality computation, but for now, just test as shown above.

Now to build some larger pieces with visitors. First, here’s an interface definition for functional objects that represent functions from Xs to Ys. Such an object has a single method called apply that consumes an X and produces a Y:

;; A [Fun X Y] implements
;; - apply : X -> Y
;;   Apply this function to given x.

Here’s an interface definition for functional objects that represent predicates:

;; A [Question X] implements
;; - ask : X -> Boolean
;;   Ask if this predicate holds on x.

Now implement the following two visitors:

;; A (new filter% [Question X]) implements [ListVisitor X [List X]].
;; Filters visited list to produce a list of elements satisfying predicate.
;; A (new map% [Fun X Y]) implements [ListVisitor X [List Y]].
;; Maps visited list to produce a list of results of applying the function.

Implement at least one [Fun Natural String] and one [Question String] to use for testing filter% and map%.

8.1.1 Folds vs Visitors

We can also implements folds over lists, in both for both kinds of lists. Extend your implementation of lists (both kinds) to support the fold method:
;; A [List X] implements ...
;; - fold : [ListFold X Y] -> Y
;;   Accept given fold and process this list's data.
;; A [ListFold X Y] implements
;; - fold-mt : -> Y
;;   Process an empty list.
;; - fold-cons : X Y -> Y
;;   Process a cons lists.

Now revise your implementations of the filter% and map% to implement folds as well as visitors. Be sure to specify what interfaces they implement.

Finally, implement the class list-ref%:
;; A (new list-ref% Number) implements [ListVisitor X X]
;; Retrieves the element at the specified index.

Could you implement this using the ListFold interface? Which was more elegant for map% and filter%?