1. Recursion - Secret sauce of Functional Programming

5. (foo bar)

6. (42 (foo bar))

8. ( foo bar baz )

9. (car lat)

10. foo

11. (cdr lat)

12. ( bar baz )

13. (car (cdr lat))

14. bar

16. ( baz )

17. (cons bar (baz))

18. ( bar baz )

19. (cons foo ( bar baz ) )

20. ( foo bar baz )

22. (null? foo ) is #f

24. (atom? ( foo bar )) is #f

26. (eq? foo bar ) is #f

28. (member? oops ( foo bar baz )) is #f

30. (member? baz (bar baz))

31. bar == baz is #f

32. (member? baz (baz))

33. baz == baz is #t member?

34. member? ( define member? ( lambda (a lat) ( cond (( null? lat) #f) (else (or ( eq? ( car lat) a) (member? a ( cdr lat)))) )))

36. (foo baz) ( define remove ( lambda (a lat) ( cond (( null? lat) (quote ())) (( eq? ( car lat) a) ( cdr lat)) (else ( cons ( car lat) (remove a ( cdr lat)))) )))

38. (foo bar baz) ( define insertR ( lambda (new old lat) ( cond (( null? lat) (quote ())) (( eq? ( car lat) old) ( cons old ( cons new ( cdr lat)))) (else ( cons ( car lat) (insertR new old ( cdr lat)))) )))

40. (foo baz bar) ( define insertL ( lambda (new old lat) ( cond (( null? lat) (quote ())) (( eq? ( car lat) old) ( cons new ( cons old ( cdr lat)))) (else ( cons ( car lat) (insertR new old ( cdr lat)))) )))

41. insert ( define insert ( lambda seq ( lambda (new old lat) ( cond (( null? lat) (quote ())) (( eq? ( car lat) old) ( seq new old lat)) (else ( cons ( car lat) (insertR new old ( cdr lat)))) ))))

42. insertR, insertL using HOF ( define seqR ( lambda new old lat ( cons old ( cons new ( cdr lat))) )) ( define seqL ( lambda new old lat ( cons new ( cons old ( cdr lat))) )) ( define insertR (insert seqR)) ( define insertL (insert seqR))

44. (add1 41) = 42

45. sub1

46. (sub1 43) = 42

47. zero?

48. (zero? 0) is #t

49. (zero? 42) is #f

50. Addition + 5 + 3 = 1 + (5 + 2) = 1 + 1 + (5 + 1) = 1 + 1 + 1 + (5 + 0) = 1 + 1 + 1 + 5 = 1 + 1 + 6 = 1 + 7 = 8

51. Addition + ( define + ( lambda (n m) ( cond (( zero? m) n) (else ( add1 (+ n (sub1 m)))) ))))

52. Multiplication X 5 * 3 = 5 + (5 * 2) = 5 + 5 + (5 * 1) = 5 + 5 + 5 + (5 * 0) = 5 + 5 + 5 + 0 = 5 + 5 + 5 = 5 + 10 = 15

53. Multiplication X ( define x ( lambda (n m) ( cond (( zero? m) 0) (else (+ n (x n (sub1 m)))) ))))

54. Exponent ^ 5 ^ 3 = 5 x (5 ^ 2) = 5 x 5 x (5 ^ 1) = 5 x 5 x 5 x (5 ^ 0) = 5 x 5 x 5 x 1 = 5 x 5 x 5 = 5 x 25 = 125

55. Exponent ^ ( define ^ ( lambda (n m) ( cond (( zero? m) 1) (else (x n (^ n (sub1 m)))) ))))

57. Tuple addition ( define addtup ( lambda (tup) ( cond (( null? tup) 0) (else (+ ( car tup) (addtup ( cdr tup)))) ))))

58. Questions? Further Reading