-Assignment 4
-------------
-
#Reversing a list#
-How would you define an operation to reverse a list? (Don't peek at the
+1. How would you define an operation to reverse a list? (Don't peek at the
[[lambda_library]]! Try to figure it out on your own.) Choose whichever
implementation of list you like. Even then, there are various strategies you
can use.
+(See [[hints/Assignment 4 hint 1]] if you need some hints.)
+
#Comparing lists for equality#
; (might_for_all_i_know_still_be_equal?, tail_of_reversed_right)
; when left is empty, the lists are equal if right is empty
(make_pair
- (not (isempty right))
+ true ; for all we know so far, they might still be equal
(reverse right)
)
; when fold is finished, check sofar-pair
(\might_be_equal right_tail. and might_be_equal (isempty right_tail))
-->
+#Mutually-recursive functions#
+
+
+
#Enumerating the fringe of a leaf-labeled tree#
[[Implementing trees]]
--- /dev/null
+Hints for reverse.
+
+* If left and right are two v3 lists, what is the result of:
+
+ left make_list right
+
+* What is `reverse []`? What is `reverse [c]`? What is `reverse [b;c]`? How is it related to `reverse [c]`?
+
+* How is `reverse [a;b;c]` related to `reverse [b;c]`?
+
+* Getting any ideas?
+
+
+Another strategy.
+
+* Our version 3 lists are _right_-folds. That is, `[a;b;c]` is implemented as:
+
+ \f z. f a (f b (f c z))
+
+ which is the result of first combining the base value `z` with the rightmost element of the list, using `f`, then combining the result of that with the next element to the left, and so on.
+
+ A _left_-fold on the same list would be:
+
+ \f z. f (f (f z a) b) c
+
+ which is the result of first combining the base value `z` with the leftmost element of the list, then combining the result of that with the next element to the right, and so on.
+
+ It's conventional for `f` to take the accumulated value so far as its second argument when doing a right-fold, and for it to take it as its first argument when doing a left-fold. However, this convention could be ignored. We could also call this the left-fold of `[a;b;c]`:
+
+ \f z. f c (f b (f a z))
+
+* Getting any ideas?
+
+* Our `make_list` function for taking an existing, right-fold-based list, and a new element, and returning a new right-fold-based list, looks like this:
+
+ let make_list = \hd tl. \f z. f hd (tl f z)
+
+ How would you write a `make_left_list` function, that takes an existing, left-fold-based list, like `\f z. f c (f b z)`, and a new element, `a`, and returned the new, left-fold based list:
+
+ \f z. f c (f b (f a z))
+
+