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David Evans http://www.cs.virginia.edu/~evans

Lecture 8: Cons car cdr sdr wdr. David Evans http://www.cs.virginia.edu/~evans. CS200: Computer Science University of Virginia Computer Science. Menu. History of Scheme LISP Lists List Recursion. Confusion Is Good! It means you are learning new ways of thinking.

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David Evans http://www.cs.virginia.edu/~evans

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  1. Lecture 8: Cons car cdr sdr wdr David Evans http://www.cs.virginia.edu/~evans CS200: Computer Science University of Virginia Computer Science

  2. Menu • History of Scheme • LISP • Lists • List Recursion CS 200 Spring 2003

  3. Confusion Is Good!It means you are learning new ways of thinking. CS 200 Spring 2003

  4. History of Scheme • Scheme [1975] • Guy Steele and Gerry Sussman • Originally “Schemer” • “Conniver” [1973] and “Planner” [1967] • Based on LISP • John McCarthy (late 1950s) • Based on Lambda Calculus • Alonzo Church (1930s) • Last few lectures in course CS 200 Spring 2003

  5. LISP “Lots of Insipid Silly Parentheses” “LISt Processing language” Lists are pretty important – hard to write a useful Scheme program without them. CS 200 Spring 2003

  6. Making Lists CS 200 Spring 2003

  7. Making a Pair > (cons 1 2) (1 . 2) 1 2 consconstructs a pair CS 200 Spring 2003

  8. Splitting a Pair cons > (car (cons 1 2)) 1 > (cdr (cons 1 2)) 2 1 2 car cdr car extracts first part of a pair cdr extracts second part of a pair CS 200 Spring 2003

  9. Why “car” and “cdr”? • Original (1950s) LISP on IBM 704 • Stored cons pairs in memory registers • car = “Contents of the Address part of the Register” • cdr = “Contents of the Decrement part of the Register” (“could-er”) • Doesn’t matters unless you have an IBM 704 • Think of them as first and rest (define first car) (define rest cdr) CS 200 Spring 2003

  10. Implementing cons, car and cdr • Using PS2: (define cons make-point) (define car x-of-point) (define cdr y-of-point) • As we implemented make-point, etc.: (define (cons a b) (lambda (w) (if (w) a b))) (define (car pair) (pair #t) (define (cdr pair) (pair #f) CS 200 Spring 2003

  11. Pairs are fine, but how do we make threesomes? CS 200 Spring 2003

  12. Threesome? • (define (threesome a b c) • (lambda (w) • (if (= w 0) a (if (= w 1) b c)))) • (define (first t) (t 0)) • (define (second t) (t 1)) • (define (third t) (t 2)) Is there a better way of thinking about our triple? CS 200 Spring 2003

  13. Triple • A triple is just a pair where one of the parts is a pair! (define (triple a b c) (cons a (cons b c))) (define (t-first t) (car t)) (define (t-second t) (car (cdr t))) (define (t-third t) (cdr (cdr t))) CS 200 Spring 2003

  14. Quadruple • A quadruple is a pair where the second part is a triple (define (quadruple a b c d) (cons a (triple b c d))) (define (q-first q) (car q)) (define (q-second q) (t-first (cdr t))) (define (q-third t) (t-second (cdr t))) (define (q-fourth t) (t-third (cdr t))) CS 200 Spring 2003

  15. Multuples • A quintuple is a pair where the second part is a quadruple • A sextuple is a pair where the second part is a quintuple • A septuple is a pair where the second part is a sextuple • An octuple is group of octupi • A list (any length tuple) is a pair where the second part is a …? CS 200 Spring 2003

  16. Lists List ::= (consElementList) A list is a pair where the second part is a list. One little problem: how do we stop? This only allows infinitely long lists! CS 200 Spring 2003

  17. From Lecture 6 Recursive Transition Networks ORNATE NOUN end begin NOUN ARTICLE ADJECTIVE ORNATE NOUN ::= ARTICLE ADJECTIVE NOUN ORNATE NOUN ::= ARTICLE ADJECTIVE ADJECTIVE NOUN ORNATE NOUN ::= ARTICLE ADJECTIVE ADJECTIVE ADJECTIVE NOUN ORNATE NOUN ::= ARTICLE ADJECTIVE ADJECTIVE ADJECTIVE ADJECTIVE NOUN ORNATE NOUN ::= ARTICLE ADJECTIVE ADJECTIVE ADJECTIVE ADJECTIVE ADJECTIVE NOUN CS 200 Spring 2003

  18. Recursive Transition Networks ORNATE NOUN end begin NOUN ARTICLE ADJECTIVE ORNATE NOUN ::= ARTICLE ADJECTIVES NOUN ADJECTIVES ::= ADJECTIVE ADJECTIVES ADJECTIVES ::= CS 200 Spring 2003

  19. Lists List ::= (consElementList) List ::= It’s hard to write this! A list is either: a pair where the second part is a list or, empty CS 200 Spring 2003

  20. Null List ::= (consElementList) List ::= null A list is either: a pair where the second part is a list or, empty (null) CS 200 Spring 2003

  21. List Examples > null () > (cons 1 null) (1) > (list? null) #t > (list? (cons 1 2)) #f > (list? (cons 1 null)) #t CS 200 Spring 2003

  22. More List Examples > (list? (cons 1 (cons 2 null))) #t > (car (cons 1 (cons 2 null))) 1 > (cdr (cons 1 (cons 2 null))) (2) CS 200 Spring 2003

  23. List Recursion CS 200 Spring 2003

  24. Defining Recursive Procedures • Be optimistic. • Assume you can solve it. • If you could, how would you solve a bigger problem. • Think of the simplest version of the problem, something you can already solve. (This is the base case.) • Combine them to solve the problem. CS 200 Spring 2003

  25. Defining Recursive Procedures on Lists Be very optimistic • Be optimistic. • Assume you can solve it. • If you could, how would you solve a bigger problem. • Think of the simplest version of the problem, something you can already solve. • Combine them to solve the problem. For lists, assume we can solve it for the cdr For lists, the simplest version is usually null (the zero-length list) Combine something on the car of the list with the recursive evaluation on the cdr. Remember to test null? before using car or cdr. CS 200 Spring 2003

  26. Defining Sumlist > (sumlist (list 1 2 3 4)) 10 > (sumlist null) 0 (define sumlist (lambda (lst) (if (null? lst) ( (car lst) (sumlist (cdr lst)) 0 + CS 200 Spring 2003

  27. Defining Productlist > (productlist (list 1 2 3 4)) 24 > (productlist null) 1 (define productlist (lambda (lst) (if (null? lst) ( (car lst) (sumlist (cdr lst)) 1 * CS 200 Spring 2003

  28. Defining Length > (length (list 1 2 3 4)) 4 > (length null) 0 (define length (lambda (lst) (if (null? lst) ( (car lst) (length (cdr lst)) 0 + 1 CS 200 Spring 2003

  29. Defining insertl (define insertl (lambda (lst f stopval) (if (null? lst) stopval (f (car lst) (insertl (cdr lst) f stopval))))) CS 200 Spring 2003

  30. (define insertl (lambda (lst f stopval) (if (null? lst) stopval (f (car lst) (insertl (cdr lst) f stopval))))) Definitions (define (sumlist lst) (insertl lst + 0)) (define (productlist lst) (insertl lst * 1)) (define (length lst) (insertl lst (lambda (head rest) (+ 1 rest)) 0)) CS 200 Spring 2003

  31. Charge • Next Time: lots more things you can do with lists (including the peg board puzzle!) • PS3 Out Today • Use lists to make fractals • You have seen everything you need for it after today • Due next week Wednesday CS 200 Spring 2003

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