Transcript Lecture 9: Strange Loops and Sinister Repeaters Do be do be do CS200: Computer Science University of Virginia Computer Science David Evans http://www.cs.virginia.edu/evans.

Lecture 9:
Strange Loops
and Sinister
Repeaters
Do be do be do
CS200: Computer Science
University of Virginia
Computer Science
David Evans
http://www.cs.virginia.edu/evans
Menu
• Defining Control Structures
– repeat
– while
– for
• PS2
• PS3
4 February 2004
CS 200 Spring 2004
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Trick(y) Question
Define a procedure
(repeat expr n)
that evaluates the expression expr n times.
For example,
(repeat (display “Hello”) 3)
should produce
HelloHelloHello
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CS 200 Spring 2004
This is impossible!
Scheme rule for evaluating
applications evaluates all
the subexpressions first!
So, the repeat procedure
never even sees the
expression, just the value it
evaluates to.
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Trickery Question
Define a procedure
(repeat f n)
that evaluates (f) n times.
If we had repeat, how could we print
“Hello” n times?
(repeat (lambda () (display "Hello")) 5)
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Repetition
(define (repeat f n)
(if (= n 0)
(void)
(begin (f) (repeat f (- n 1)))))
(define (n-times f n)
(if (= n 0)
(lambda (x) x)
(compose f (n-times f (- n 1)))))
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Accumulation
• Repetition is more useful if we can collect
the results
(define (repeat f n)
(if (= n 0)
(void)
(begin (f) (repeat f (- n 1)))))
(define (crepeat f n)
(if (= n 0)
null
(cons (f) (crepeat f (- n 1)))))
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apply takes two parameters:
(define (crepeat f n)
a procedure
(if (= n 0)
a list
and applies the procedure to
null
the parameters in the list.
(cons
(apply * (list 1 2 3))
(f)
 (* 1 2 3)
(crepeat f (- n 1)))))
> (crepeat (lambda () 25) 4)
(25 25 25 25)
> (define (power n m)
(apply * (crepeat (lambda () n) m)))
> (power 2 10)
1024
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Variation
Repetition is more interesting if we can do
different things each time
Define a procedure
(define (dofor proc start end)
that produces a list of applying proc to all
integers between start and end.
(dofor square 0 4)  (0 1 4 9 16)
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dofor
(define (dofor proc start end)
(if (> start end)
null
(cons (proc start)
(dofor proc (+ start 1) end))))
Can you define intsto using dofor?
(define (intsto n) (dofor (lambda (x) x) 1 n))
Can you define map using dofor?
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CS 200 Spring 2004
No
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Generalizing dofor
• What if we sometimes want to count by 2?
• What if we sometimes want to count by
doubling?
• What if we sometimes want to count by -1
and stop when start <= end?
Make the stopping test and incrementing
function procedure parameters!
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dountil
(define (dountil proc stoptest next index)
(if (stoptest index)
null
(cons (proc index)
(dountil proc stoptest next
(next index)))))
> (dountil
(lambda (x) x)
(lambda (val) (< val 1))
(lambda (x) (- x 1)) 10)
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Challenge Problem
(from last time)
Define a procedure
(define (for index stoptest combiner
next accum)
…)
that can be used like this:
(define (gauss-sum n)
(for 1 (lambda (index) (> index n))
+ (lambda (x) (+ 1 x))
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0))
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(define (dountil proc stoptest next index)
(if (stoptest index)
null
(cons (proc index)
(dountil proc stoptest next
(next index)))))
(define (for index stoptest combine next
accum)
Instead of making a list of all the values, we want to
accumulate results in one value (accum).
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(define (dountil proc stoptest next index)
(if (stoptest index)
null
(cons (proc index)
(dountil proc stoptest next
(next index)))))
(define (for index stoptest combine next accum)
(if (stoptest index)
accum
(for (next index) stoptest combine next
(combine index accum))))
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Using for
(define (for index stoptest combine next accum)
(if (stoptest index)
accum
(for (next index) stoptest combine next
(combine index accum))))
(define (gauss-sum n)
(for 1
(lambda (index) (> index n))
+ (lambda (x) (+ 1 x))
0))
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(define (for index stoptest
combine next accum)
(if (stoptest index)
accum
(for (next index) stoptest
combine next
(combine index accum))))
(define (gauss-sum n)
(for 1
(lambda (index)
(> index n))
+
(lambda (x) (+ 1 x))
0))
4 February 2004
> (require (lib "trace.ss"))
> (trace +)
> (gauss-sum 3)
|(+ 1 1)
(next index)
|2
(combine index accum)
|(+ 1 0)
|1
|(+ 1 2)
|3
|(+ 2 1)
|3
|(+ 1 3)
|4
|(+ 3 3)
|6
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electorate-voters
(define (for index stoptest combine next accum)
(if (stoptest index)
accum
(for (next index) stoptest combine next
(combine index accum))))
(define (electorate-voters electorate start-position end-position)
(for start-position
(lambda (pos) (> pos end-position)) ;; stop when pos > end-position
(lambda (pos accum) (+ (electorate pos) accum))
(lambda (pos) (+ pos (/ 1 electorate-steps)))
0)) ;; initially, accumulator is 0
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PS3:
Lindenmayer System
Fractals
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CS 200 Spring 2004
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L-Systems
CommandSequence ::= ( CommandList )
CommandList ::= Command CommandList
CommandList ::=
Command ::= F
Command ::= RAngle
Command ::= OCommandSequence
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L-System
Rewriting
CommandSequence ::= ( CommandList )
CommandList ::= Command CommandList
CommandList ::=
Command ::= F
Command ::= RAngle
Command ::= OCommandSequence
Start: (F)
Rewrite Rule:
F  (F O(R30 F) F O(R-60 F) F)
Work like BNF replacement rules, except
replace all instances at once!
Why is this a better model for biological systems?
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Level 0
Level 1
Start: (F)
F  (F O(R30 F) F O(R-60 F) F)
(F)
(F O(R30 F) F O(R-60 F) F)
Level 2
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Level 3
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The Great
Lambda
Tree
of Ultimate
Knowledge
and Infinite
Power
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Charge
• No class Friday, no office
hours tomorrow
• Get started on PS3, it is
longer than PS2
• Make some interesting
fractals
– Once you have it working, its
easy to produce lots of
interesting pictures
– Make a better course logo
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