CSC151.01 2006S, Class 28: Deep Recursion

Admin:
* Wednesday EC:
  * Transgendered UU Minister at 4:15
* Thursday EC:
  * Convo: Molly's friend (Interpretation of Race in American Museums)
    [may be cancelled - NOOOOOOO]
  * 4:15: "Women in Computer Science at Grinnell"
* Are there questions on the project report?
  * One report per group.
* Reading for Friday: Vectors

Overview:
* Lists, revisited.
* Trees, introduced.
* Deep recursion, considered.
* Lab.

/What is a list?/

* Lists are defined recursively.
* Recursive definitions have
  * A base case: null
  * A recursive case: 
    * A good, but incorrect, guess: pair of lists
        null, (cons null null), (cons null (cons null null))
    * Another good, but insufficient, guess: A pair
        (cons 'a 'b)
    * A good, but non-recursive defintion: A sequence of pairs ending
      with null.
    * A pair in which the first element is /anything you want/ and the
      second is a list.

/Observation: Process vs. Data/

* We typically use recursion for /process/ (how we do something)
* Here, we use recrusion to describe /structure/ (how something is organized)
* The natural numbers are either
  base case: 0
  recursive case: the successor of a natural number (you get a successor by adding 1)

* Note: Our recursive processes reflect these recursive structures

/New Recursive Structure: The Tree/

* A tree is either
  base case: any non-pair value
  recursive case: a pair whose car is a tree and whose cdr is a tree

* To recurse over trees, we must acknowledge their doubly-recursive nature
(define recursive-proc
  (lambda (tree)
    (if (pair? tree)
        (COMBINE (recursive-proc (car tree)) 
                 (recursive-proc (cdr tree)))
        (BASE-CASE tree))))

* Two related issues:
  * Helpers with so-far less likely to be helpful
  * Husk and kernel still useful for checking preconditions

/LAB!/

Some number trees

5   *      *      *
   / \    / \    / \
  5   7  *   3  3   *
        / \        / \
       1   8      6   12

That is
    5
    (cons 5 7)
    (cons (cons 1 8) 3)
    (cons 3 (cons 6 12))

Some non-number trees

null   *      *      *
      / \    / \    / \
 "soren" 7  *   3  3   *
           / \        / \
        "is"  8      6  'doomed

That is
    null
    (cons "soren" 7)
    (cons (cons "is" 8) 3)
    (cons 3 (cons 6 'doomed))