Class 16: Making Loops

cs1120 Fall 2011David Evans28 September 2011

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Plan

Recap: Turing Machine ModelBuilding a Turing Machine to count stars

(Hint: useful for PS4, Question 3)Making Loops

(Questions 2 and 3 from Monday, useful for PS4, Question 12)

PS3 Comments Posted on Web: everyone is expected to understand these before Exam 1

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Recap: Turing Machine

Model Input, Output, and Scratch MemoryInfinite tape, divided into discrete squaresEach square can contain a single symbol from a finite alphabet

Model ProcessingFinite State Machine

Keep track of a finite state (in your head)Follow transition rules:

next state, write symbol, move = f(current state, input symbol)

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Turing Machine Example

1

#/#,-

HALT

0/1,R1/0,R

read/write, move

State, Input, Next, Write, Move1, 1, 1, 0, >1, 0, 1, 1, >1, #, H, #, >

TM Simulator: http://ironphoenix.org/tril/tm/

Input: 01101#

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Turing Machine Example

Start

#/#,-

HALT

0/0,R1/1,L

State, Input, Next, Write, Move1, 1, 1, 1, <1, 0, 1, 0, >1, #, H, #, >

Input: 01101#

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Count the StarsGoal (example): ## #1111#

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http://www.youtube.com/watch?v=cYw2ewoO6c4

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Turing Machine DesignPainful and tedious: each step

does very littleBut, important to do a few times

to help convince yourself a TM really can do any computation

Thinking about what the machine needs to keep track of: states (finite) and tape (infinite)

Every computer scientist should do it at least once!You will have to do it at least twice:

Question 3 on PS4, Problem on Exam 1

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Making Loops

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Loops in Other Languages

Fortran (1956)DO I = 1,9 PRINT IEND DO

Java (1995)for (int i = 1; i < 10; i++) { System.out.println(i);}

Algol (1960)for i := 1 until 9 do print (i);

Ada (1983)for I in 1..9 loop PutLine (I);

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Making Loops in Scheme

(define (for index end proc) (if (>= index end) (void) ; this evaluates to no value (begin (proc index) (for (+ index 1) end proc))))

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Using for(for 1 10 (lambda (i) (display i)))

Use for to print out a multiplication table:1 x 1 = 11 x 2 = 2

…1 x 9 = 9

2 x 1 =22 x 2 =4

…2 x 9 =18

… 9 x 9 = 81

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(define (times-table max) (for 1 max (lambda (i) (for 1 max (lambda (j) (printf "~a x ~a = ~a~n" i j (* i j)))))))

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> (require racket/trace)> (trace for)> (times-table 3)>(for 1 3 #<procedure:...class15.rkt:22:4>)> (for 1 3 #<procedure:...class15.rkt:24:8>)1 x 1 = 1> (for 2 3 #<procedure:...class15.rkt:24:8>)1 x 2 = 2> (for 3 3 #<procedure:...class15.rkt:24:8>)< #<void>>(for 2 3 #<procedure:...class15.rkt:22:4>)> (for 1 3 #<procedure:...class15.rkt:24:8>)2 x 1 = 2> (for 2 3 #<procedure:...class15.rkt:24:8>)2 x 2 = 4> (for 3 3 #<procedure:...class15.rkt:24:8>)< #<void>>(for 3 3 #<procedure:...class15.rkt:22:4>)<#<void>

(define (for index end proc) (if (>= index end) (void) ; this evaluates to no value (begin (proc index) (for (+ index 1) end proc))))

(define (times-table max) (for 1 max (lambda (i) (for 1 max (lambda (j) (printf "~a x ~a = ~a~n" i j (* i j)))))))

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Generalized Loops(while p (lambda (p) (not (null? p))) cdr (lambda (p) (display (car p)))))

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Generalized Loops

(define (while index test update proc) (if (test index) (begin (proc index) (while (update index) test update proc)) index))

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Accumulating Results

(define (loop index result test update proc) (if (test index) (loop (update index) (proc index result) test update proc) result))

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Charge

PS4 due Monday 3 OctoberExam 1: out October 7, due October 12

Covers: Problem Sets 1-4 including PS CommentsCourse Book Chapters 1-6Classes 1-18

Reading: no reading assignment until after Exam 1, but I will start covering things in Chapter 7-8 soon and encourage you to read The Information, Chapters 5-7