1. David Evans http://www.cs.virginia.edu/~evans
Lecture 9:
The Great Lambda Tree of Knowledge and Power
CS200: Computer Science
University of Virginia
Computer Science
David Evans

2. Programming with Lists PS3
Menu
insertl
Programming with Lists
PS3
6 February 2002
CS 200 Spring 2002

3. Review A list is either: a pair where the second part is a list
or null (note: book uses nil)
Pair primitives:
(cons a b) Construct a pair <a, b>
(car pair) First part of a pair
(cdr pair) Second part of a pair
6 February 2002
CS 200 Spring 2002

4. Sum (define (sum n) (insertl + (intsto n)))
;;; Evaluates to the list (1 2 3 … n) if n >= 1,
;;; null if n = 0.
(define (intsto n)
(if (= n 0) null
(append (intsto (- n 1)) (list n))))
6 February 2002
CS 200 Spring 2002

5. insertl ;;; (insertl f (list a b c d … ))
;;; evaluates to (f a (f b (f c (f d … (f)))))
(define (insertl f lst) … )
6 February 2002
CS 200 Spring 2002

6. insertl ;;; (insertl f (list a b c d … ))
;;; evaluates to (f a (f b (f c (f d … (f)))))
(define (insertl f lst)
(if (null? lst)
base case
… (insertl f (cdr lst)) … ))
6 February 2002
CS 200 Spring 2002

7. insertl ;;; (insertl f (list a b c d … ))
;;; evaluates to (f a (f b (f c (f d … (f)))))
(define (insertl f lst)
(if (null? lst)
(f)
(f (car lst) (insertl f (cdr lst)))))
6 February 2002
CS 200 Spring 2002

8. Examples > (sum 10) 55 > (insertl * (intsto 5)) 120
> (insertl cons (intsto 10))
cons: expects 2 arguments, given 0
6 February 2002
CS 200 Spring 2002

9. insertl2 (define (insertl2 f lst) (if (= (length lst) 2)
;;; (insertl2 f (list a b c d … y z))
;;; evaluates to (f a (f b (f c (f d … (f y z)))))
(define (insertl2 f lst)
(if (= (length lst) 2)
(f (car lst) (cadr lst))
(f (car lst) (insertl2 f (cdr lst)))))
6 February 2002
CS 200 Spring 2002

10. Examples > (insertl2 * (intsto 5)) 120
> (insertl2 cons (intsto 5))
( )
> (insertl2 (lambda (a b) (cons b a)) (intsto 5))
((((5 . 4) . 3) . 2) . 1)
6 February 2002
CS 200 Spring 2002

11. insertgen (define (insertlg f lst start) (if (= (length lst) 1)
;;; (insertlg f (list a b c d … y z) start)
;;; evaluates to (f a (f b (f c (f d
;;; … (f y (f z start)
(define (insertlg f lst start)
(if (= (length lst) 1)
(f (car lst) start)
(f (car lst) (insertlg f (cdr lst)
start))))
6 February 2002
CS 200 Spring 2002

12. Examples > (insertlg * (intsto 5) 1) 120 ;;; to copy a list:
(define (insertlg f lst start)
(if (= (length lst) 1)
(f (car lst) start)
(f (car lst)
(insertlg f (cdr lst) start))))
Examples
> (insertlg * (intsto 5) 1)
120
;;; to copy a list:
> (insertlg cons (intsto 5) null)
( )
How to define doubleall?
(doubleall (intsto 5))  ( )
6 February 2002
CS 200 Spring 2002

13. doubleall (define (doubleall lst) (insertlg (lambda (a b)
(cons (* 2 a) b))
lst
null))
6 February 2002
CS 200 Spring 2002

14. filter > (filter even? (intsto 9)) (2 4 6 8)
> (filter (lambda (x) (not (= x 3)))
(intsto 5))
( )
6 February 2002
CS 200 Spring 2002

15. Defining filter (define (filter f lst) (insertlg (lambda (a b)
(if (f a) (cons a b) b))
lst
null))
6 February 2002
CS 200 Spring 2002

16. map
(map f lst)
Evaluates to the list of values produced by applying f to each element of lst.
(define (doubleall lst)
(map (lambda (s) (* 2 s)) lst))
6 February 2002
CS 200 Spring 2002

17. map (define (map f lst) (insertlg (lambda (a b) (cons (f a) b)) lst
null))
6 February 2002
CS 200 Spring 2002

18. map (define (map f lst) (if (null? lst) null (cons (f (car lst))
(map f (cdr lst)))))
6 February 2002
CS 200 Spring 2002

19. map examples > (map (lambda (x) x) (intsto 5)) (1 2 3 4 5)
> (map (lambda (x) (* x x)) (intsto 5))
( )
> (map
(lambda (row)
(display-one-row output-file
row tile-width tile-height))
tiles)
Displays a photomosaic!
6 February 2002
CS 200 Spring 2002

20. PS3: Lindenmayer System Fractals
6 February 2002
CS 200 Spring 2002

21. L-Systems CommandSequence ::= ( CommandList )
CommandList ::= Command CommandList
CommandList ::=
Command ::= FDistance
Command ::= RAngle
Command ::= OCommandSequence
6 February 2002
CS 200 Spring 2002

22. L-System Rewriting Start: (F1) Rewrite Rule:
CommandSequence ::= ( CommandList )
CommandList ::= Command CommandList
CommandList ::=
Command ::= FDistance
Command ::= RAngle
Command ::= OCommandSequence
L-System Rewriting
Start: (F1)
Rewrite Rule:
F1  (F1 O(R30 F1) F1 O(R-60 F1) F1)
Work like BNF replacement rules, except replace all instances at once!
Why is this a better model for biological systems?
6 February 2002
CS 200 Spring 2002

23. Level 1 Level 0 (F1) Start: (F1) (F1 O(R30 F1) F1 O(R-60 F1) F1)

24. Level 2
Level 3
6 February 2002
CS 200 Spring 2002

25. 6 February 2002
CS 200 Spring 2002

26. Drawing Lambda Tree (define (draw-lambda-tree-of-knowledge)
(draw-region (make-color ))
(draw-region (make-color ))
(draw-curve-points (position-curve
(connect-curves-evenly
(convert-to-curve-list
(make-tree-fractal 4)
(lambda () (make-splotch-curve
(make-color (+ 128 (random 128))
(+ 128 (random 128)) (random 50))))
(lambda (dist) (make-vertical-line dist
(make-color )))))
) 50000))
6 February 2002
CS 200 Spring 2002

27. Charge PS3 Due Next Week Weds Make some interesting fractals
Once you have it working, its easy to produce lots of different pictures
Make “The Great Lambda Tree of Knowledge and Power” (for the CS200 course logo)
6 February 2002
CS 200 Spring 2002