Class 16: Making Loops
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This document summarizes a class about making loops in Scheme. It recaps the Turing machine model and provides an example of a Turing machine that counts stars. It then introduces making loops in Scheme using a for procedure that takes an index, end value, and procedure as arguments. Examples are given to print numbers from 1 to 10 and to generate a multiplication table using nested for loops. The document also discusses tracing for to see how it works and introduces generalized while and accumulating loop procedures. It concludes by announcing assignments and due dates for Problem Set 4 and Exam 1.
Class 16: Making Loops
- 1. Class 16: Making Loops cs1120 Fall 2011 David Evans 28 September 2011
- 2. Plan Recap: Turing Machine Model Building 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 2
- 3. Recap: Turing Machine Model Input, Output, and Scratch Memory Infinite tape, divided into discrete squares Each square can contain a single symbol from a finite alphabet Model Processing Finite State Machine Keep track of a finite state (in your head) Follow transition rules: next state, write symbol, move = f(current state, input symbol) 3
- 4. Turing Machine Example read/write, move 1/0,R Input: 01101# 0/1,R State, Input, Next, Write, Move 1 1, 1, 1, 0, > 1, 0, 1, 1, > 1, #, H, #, > #/#,- HALT TM Simulator: http://ironphoenix.org/tril/tm/ 4
- 5. Turing Machine Example Input: 01101# 1/1,L 0/0,R State, Input, Next, Write, Move 1, 1, 1, 1, < Start 1, 0, 1, 0, > 1, #, H, #, > #/#,- HALT 5
- 6. Count the Stars Goal (example): # # #1111# 6
- 8. Turing Machine Design Painful and tedious: each step does very little But, 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 8
- 9. Making Loops 9
- 10. Loops in Other Languages Fortran (1956) Ada (1983) DO I = 1,9 for I in 1..9 loop PRINT I PutLine (I); END DO Java (1995) Algol (1960) for (int i = 1; i < 10; i++) { for i := 1 until 9 do System.out.println(i); print (i); } 10
- 11. 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)))) 11
- 12. Using for (for 1 10 (lambda (i) (display i))) Use for to print out a multiplication table: 1x1=1 1x2=2 … 1x9=9 2 x 1 =2 2 x 2 =4 … 2 x 9 =18 … 9 x 9 = 81 12
- 13. (define (times-table max) (for 1 max (lambda (i) (for 1 max (lambda (j) (printf "~a x ~a = ~a~n" i j (* i j))))))) 13
- 14. (define (for index end proc) > (require racket/trace) (if (>= index end) > (trace for) (void) ; this evaluates to no value > (times-table 3) (begin >(for 1 3 #<procedure:...class15.rkt:22:4>) (proc index) > (for 1 3 #<procedure:...class15.rkt:24:8>) (for (+ index 1) end proc)))) 1x1=1 > (for 2 3 #<procedure:...class15.rkt:24:8>) (define (times-table max) 1x2=2 (for 1 max > (for 3 3 #<procedure:...class15.rkt:24:8>) (lambda (i) < #<void> (for 1 max >(for 2 3 #<procedure:...class15.rkt:22:4>) (lambda (j) > (for 1 3 #<procedure:...class15.rkt:24:8>) (printf "~a x ~a = ~a~n" i j (* i j))))))) 2x1=2 > (for 2 3 #<procedure:...class15.rkt:24:8>) 2x2=4 > (for 3 3 #<procedure:...class15.rkt:24:8>) < #<void> >(for 3 3 #<procedure:...class15.rkt:22:4>) <#<void> 14
- 15. Generalized Loops (while p (lambda (p) (not (null? p))) cdr (lambda (p) (display (car p))))) 15
- 16. Generalized Loops (define (while index test update proc) (if (test index) (begin (proc index) (while (update index) test update proc)) index)) 16
- 17. Accumulating Results (define (loop index result test update proc) (if (test index) (loop (update index) (proc index result) test update proc) result)) 17
- 18. Charge PS4 due Monday 3 October Exam 1: out October 7, due October 12 Covers: Problem Sets 1-4 including PS Comments Course Book Chapters 1-6 Classes 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 18