1. Recursion - Secret sauce of Functional Programming

2. Imperative to Functional

Immutability

Intermediate state?

No Looping constructs

Iteration?

3. Scheme (dialect of Lisp)

atom

42, foo

list

(foo bar)

4. (42 (foo bar)) s-expressions atom or list

42

5. (foo bar) 6. (42 (foo bar)) 7. car, cdr

lat

8. ( foo bar baz ) 9. (car lat) 10. foo 11. (cdr lat) 12. ( bar baz ) 13. (car (cdr lat)) 14. bar 15. cons

(consbaz())

16. ( baz ) 17. (cons bar (baz)) 18. ( bar baz ) 19. (consfoo ( bar baz ) ) 20. ( foo bar baz ) 21. Primitive functions

null?

(null? ( quote () ) is #t

22. (null?foo ) is #f 23. (null? ( foo bar )) is #f atom?

(atom?foo ) is #t

24. (atom? ( foo bar )) is #f 25. (atom? ( quote () ) is #f eq?

(eq?foo foo ) is #t

26. (eq?foo bar ) is #f 27.

(member?foo( quote () )) is #f

28. (member?oops( foo bar baz )) is #f 29. (member?baz( foo bar baz )) is #t

• foo == 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? ( definemember? ( lambda(a lat) ( cond (( null?lat) #f) (else (or ( eq?( carlat) a) (member? a ( cdrlat)))) ))) 35. remove

(remove bar (foo bar baz))

36. (foo baz) ( defineremove ( lambda(a lat) ( cond (( null?lat) (quote ())) (( eq?( carlat) a) ( cdrlat)) (else ( cons( carlat) (remove a ( cdrlat)))) ))) 37. insertR

(insertR baz bar (foo bar))

38. (foo bar baz) ( defineinsertR ( lambda(new old lat) ( cond (( null?lat) (quote ())) (( eq?( carlat) old)( consold ( consnew ( cdrlat)))) (else ( cons( carlat) (insertR new old ( cdrlat)))) ))) 39. insertL

(insertL baz bar (foo bar))

40. (foo baz bar) ( defineinsertL ( lambda(new old lat) ( cond (( null?lat) (quote ())) (( eq?( carlat) old)( consnew ( consold ( cdrlat)))) (else ( cons( carlat) (insertR new old ( cdrlat)))) ))) 41. insert ( defineinsert ( lambdaseq ( lambda(new old lat) ( cond (( null?lat) (quote ())) (( eq?( carlat) old)( seqnew old lat)) (else ( cons( carlat) (insertR new old ( cdrlat)))) )))) 42. insertR, insertL using HOF ( defineseqR ( lambdanew old lat ( consold ( consnew ( cdrlat))) )) ( defineseqL ( lambdanew old lat ( consnew ( consold ( cdrlat))) )) ( defineinsertR(insert seqR)) ( defineinsertL(insert seqR)) 43. Arithmetic

add1

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 ( definex ( 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)))) )))) 56. Tuple addition

(addtup (1 2 3 4 5)) = 1 + (addtup (2 3 4 5)) = 1 + (2 + (addtup (3 4 5))) = 1 + (2 + (3 + (addtup (4 5)))) = 1 + (2 + (3 + (4 + (addtup (5))))) = 1 + (2 + (3 + (4 + (5 + (addtup ()))))) = 1 + (2 + (3 + (4 + (5 + 0)))) = 1 + (2 + (3 + (4 + 5))) = 1 + (2 + (3 + 9)) = 1 + (2 + 12) = 1 + 14 = 15

57. Tuple addition ( defineaddtup ( lambda(tup) ( cond (( null?tup) 0) (else (+ ( cartup) (addtup ( cdrtup)))) )))) 58. Questions? Further Reading