From my talk at LCNUG. http://www.lcnug.org/News/14-12-16/LCNUG_January_8th_-_The_Marvelous_Land_of_Higher_Order_Functions.aspx Looking to be more pragmatic with LINQ? Want to see the connection between the C# you use every day and Functional Programming? Want to stop using for loops? Join me on a trip to the marvelous Land of Higher Order Functions. We’ll travel to the forest of Maps, Filters, and Folding—oh my! Then we’ll visit the towns of Zip and Mapcat. We’ll end our trip with a sight of the City of FP.

1. The Marvelous Land of
Higher Order Functions
Mike Harris

2. Travel Log
• Forest of Higher Order
• Reduce
• Map
• Filter
• City of Mapcat
• City of Zip
• The Emerald City of FP

4. Know thyself γνῶθι σεαυτόν

5. Croesus King of Lydia (560 - 547 BC)

6. –- Herodotus, The Histories
“[I]f Croesus attacked the Persians, he would
destroy a mighty empire”

7. Cyrus the Great founder of the Achaemenid Empire

8. Travel Log
• Forest of Higher Order
• Reduce
• Map
• Filter
• City of Mapcat
• City of Zip
• The Emerald City of FP

10. –- L. Frank Baum, The Marvelous Land of Oz
“Everything in life is unusual until you get
accustomed to it.”

11. f g
f(g)
Function

12. f
g
Function

13. Travel Log
• Forest of Higher Order
• Reduce
• Map
• Filter
• City of Mapcat
• City of Zip
• The Emerald City of FP

14. Reduce
• Reduce (Clojure, Underscore.js)
• Aggregate (C#)
• Fold (Haskell)
• Accumulate (C++)

15. Reducer
Collection
Result

16. 1 2 3 4
Add
10

17. var sum = 0;!
var arr =!
new[] {1, 2, 3, 4};!
foreach(var x in arr)!
{!
sum += x;!
}!
!
// 10

18. new[] {1, 2, 3, 4}!
.Aggregate(!
0,!
!(m, x) => m += x); !
!
// 10

19. (reduce!!!
#(+ %1 %2) !
!!![1 2 3 4])!
!
;; 10

20. Travel Log
• Forest of Higher Order
• Reduce
• Map
• Filter
• City of Mapcat
• City of Zip
• The Emerald City of FP

21. Map
• Map (Clojure, Haskell, Underscore.js)
• Select (C#)
• Transform (C++)

22. Mapper
Collection
Result

23. 1 2 3 4
Increment
2 3 4 5

24. new[] {1, 2, 3, 4}!
.Select(x => x+1); !
!
// { 2, 3, 4, 5 }

25. (map inc [1 2 3 4])!
!
;; [2 3 4 5]
(map inc [1 2 3 4])!
!
;; [2 3 4 5]

26. reduce
map
add to
collectionfunction

27. new[] {1, 2, 3, 4}!
.Aggregate(!
new List<int>(),!
(m, x) => {!
m.Add(x+1);!
return m;!
}).ToArray();!
!
// { 2, 3, 4, 5 }

28. new[] {1, 2, 3, 4}!
.Aggregate(!
new int[]{},!
(m, x) => m.Add(x+1));
!
// { 2, 3, 4, 5 }
FAKE C# CODE!!!
FAKE C# CODE!!!

29. new[] {1, 2, 3, 4}!
.Select(x => x+1); !
!
// { 2, 3, 4, 5 }

30. (reduce!!!
#(conj %1 (inc %2))!
[] !
!!![1 2 3 4])!
!
;; [2 3 4 5]

31. (map!
inc!
[1 2 3 4])!
!
;; [2 3 4 5]

32. Travel Log
• Forest of Higher Order
• Reduce
• Map
• Filter
• City of Mapcat
• City of Zip
• The Emerald City of FP

33. Filter
• Filter (Clojure, Haskell, Underscore.js)
• Where (C#)
• Remove (C++)

34. Filter
Collection
Result

35. 1 2 3 4
Odd?
1 3

36. new[] {1, 2, 3, 4}!
.Where(x => x%2 != 0);!
!
// { 1, 3 }

37. (filter odd? [1 2 3 4])!
!
;; [1 3]

38. reduce
filter
add to
collection
predicate

39. new[] {1, 2, 3, 4}!
.Aggregate(!
new List<int>(),!
(m, x) => {!
if (x%2 != 0)!
m.Add(x);!
return m;!
}).ToArray();!
// { 1, 3 }

40. new[] {1, 2, 3, 4}!
.Aggregate(!
new int[]{},!
(m, x) => !
(x%2 != 0)!
? m.Add(x+1) : m);
// { 1, 3 }
FAKE C# CODE!!!
FAKE C# CODE!!!

41. new[] {1, 2, 3, 4}!
.Where(x => x%2 != 0);!
!
// { 1, 3 }

42. (reduce !
#(if (odd? %2)!
(conj %1 %2)!
%1)!
[] !
[1 2 3 4])!
!
;; [1 3]

43. (filter!
odd?!
[1 2 3 4])!
!
;; [1 3]

44. FizzBuzz
Kata
1 2 Fizz 4 Buzz
Fizz 7 8 Fizz
Buzz 11 Fizz 13
14 FizzBuzz 16
17 Fizz 19 Buzz
Fizz 22 23 Fizz
Buzz 26 Fizz 28
29 FizzBuzz 31

45. Enumerable.Range(1, 35)!
.Select(x => {!
if (x%15 == 0) return “FizzBuzz”;!
if (x%3 == 0) return “Fizz”;!
if (x%5 == 0) return “Buzz”;!
return x.ToString();!
});!
!
// { “1”, “2”, “Fizz”, “4”, “Buzz”

46. Enumerable.Range(1, 35)!
.Aggregate(!
new List<string>(), !
(m, x) => {!
if (x%15==0) m.Add(“FizzBuzz”);!
else if (x%3==0) m.Add(“Fizz”);!
else if (x%5==0) m.Add(“Buzz”);!
else m.Add(x.ToString());!
return m;!
});!
!
// { “1”, “2”, “Fizz”, “4”, “Buzz”

47. Coin Changer
Kata

48. Func<int[], int, int[]> changer = !
(coins, amount) => coins.Select(!
coin => { !
var c = amount / coin; !
amount %= coin; !
return c;!
}).ToArray();!
!
changer(new[] {25,10,5,1}, 99);!
!
// { 3, 2, 0, 4 }

49. Func<int[], int, int[]> changer = !
(coins, amount) => coins.Aggregate(!
new List<int>(),!
(m, coin) => {!
m.Add(amount / coin); !
amount %= coin; !
return m;!
}).ToArray();!
!
changer(new[] {25,10,5,1}, 99);!
!
// { 3, 2, 0, 4 }

50. Travel Log
• Forest of Higher Order
• Reduce
• Map
• Filter
• City of Mapcat
• City of Zip
• The Emerald City of FP

52. –- L. Frank Baum, The Emerald City of Oz
“[I]t is folly for us to try to appear otherwise
than as nature has made us.”

53. Mapcat
• Mapcat (Clojure)
• SelectMany (C#*)
• >>= (Haskell*)
* not exactly the same as Clojure’s mapcat

54. Mapper
Catter
Collection
Result

55. 1 2 3 4
Identity
2 3 4 20
20 10
101

56. new[] {!
new[] {1, 2, 3, 4},!
new[] {20, 10}!
}.SelectMany(x => x);!
!
// { 1, 2, 3, 4, 20, 10 }

57. (mapcat identity !
[[1 2 3 4] [20 10]])!
!
;; [1 2 3 4 20 10]

58. 1 2 3 4
Increment
3 4 5 21
20 10
112

59. new[] {!
new[] {1, 2, 3, 4},!
new[] {20, 10}!
}.SelectMany(!
x => x.Select(!
y => y+1));!
!
// { 2, 3, 4, 5, 21, 11 }

60. new[] {!
new[] {1, 2, 3, 4},!
new[] {20, 10}!
}.SelectMany(x => x)!
.Select(x => x + 1);!
!
// { 2, 3, 4, 5, 21, 11 }

61. (mapcat!
#(map inc %) !
[[1 2 3 4] [20 10]])!
!
;; [2 3 4 5 21 11]

62. (map inc!
(mapcat identity!
[[1 2 3 4] [20 10]])!
)!
!
;; [2 3 4 5 21 11]

63. (->>!
[[1 2 3 4] [20 10]]!
(mapcat identity)!
(map inc))!
!
;; [2 3 4 5 21 11]

64. Travel Log
• Forest of Higher Order
• Reduce
• Map
• Filter
• City of Mapcat
• City of Zip
• The Emerald City of FP

66. –- L. Frank Baum, The Wonderful Wizard of Oz
“Even with eyes protected by the green
spectacles, Dorothy and her friends were at
first dazzled by the brilliancy of the wonderful
City.”

67. Zip
• Map (Clojure)
• Zip (C#)
• ZipWith (Haskell)

68. Zipper
Collection Collection
Result

69. 1 2 3
Add
10 20 30
11 22 33

70. new[] {1, 2, 3}!
.Zip(!
new[] {10, 20, 30},!
(x, y) => x + y);!
!
// { 11, 22, 33 }

71. (map + !
[1 2 3] [10 20 30])!
!
;; [11 22 33]

72. 1 2
Add
10 20 30
11 22 ???

73. new[] {1, 2}!
.Zip(!
new[] {10, 20, 30},!
(x, y) => x + y);!
!
// { 11, 22 }

74. (map + !
[1 2] [10 20 30])!
!
;; [11 22]

75. 1 2 3
Add
10 20
11 22 ???

76. new[] {1, 2, 3}!
.Zip(!
new[] {10, 20},!
(x, y) => x + y);!
!
// { 11, 22 }

77. (map + !
[1 2 3] [10 20])!
!
;; [11 22]

78. FizzBuzz
Kata
1 2 Fizz 4 Buzz
Fizz 7 8 Fizz
Buzz 11 Fizz 13
14 FizzBuzz 16
17 Fizz 19 Buzz
Fizz 22 23 Fizz
Buzz 26 Fizz 28
29 FizzBuzz 31

79. var inf = Enumerable.Range(0, int.MaxValue);!
var fizzes = inf.Select(x => x%3 == 0 ? “Fizz” : “”);!
var buzzes = inf.Select(x => x%5 == 0 ? “Buzz” : “”);!
var numbers = inf.Select(x => x.ToString());!
!
var fizzbuzzer = !
fizzes!
.Zip(buzzes, (f, b) => f + b)!
.Zip(numbers, (fb, n) => fb == “” ? n : fb);!
!
fizzbuzzer.Skip(33).First();!
// “Fizz”!
!
fizzbuzzer.Skip(55).First();!
// “Buzz”!
!
fizzbuzzer.Skip(150).First();!
// “FizzBuzz”!
!
fizzbuzzer.Skip(2).First();!
// “2”

80. var inf = Enumerable!
.Range(0, int.MaxValue);!
!
var fizzes = inf.Select(!
x => x%3 == 0 ? “Fizz” : “”);!
var buzzes = inf.Select(!
x => x%5 == 0 ? “Buzz” : “”);!
!
var numbers = inf.Select(!
x => x.ToString());

81. var fizzbuzzer = !
fizzes!
.Zip(buzzes,(f, b) => f + b)!
.Zip(numbers,!
(fb, n) => fb == “” ? n : fb);

82. fizzbuzzer.Skip(33).First();!
// “Fizz”!
!
fizzbuzzer.Skip(55).First();!
// “Buzz”!
!
fizzbuzzer.Skip(150).First();!
// “FizzBuzz”!
!
fizzbuzzer.Skip(2).First();!
// “2”

83. var inf = Enumerable.Range(0, int.MaxValue);!
var fizzes = inf.Select(x => x%3 == 0 ? “Fizz” : “”);!
var buzzes = inf.Select(x => x%5 == 0 ? “Buzz” : “”);!
var numbers = inf.Select(x => x.ToString());!
!
var fizzbuzzer = !
fizzes!
.Zip(buzzes, (f, b) => f + b)!
.Zip(numbers, (fb, n) => fb == “” ? n : fb);!
!
fizzbuzzer.Skip(33).First();!
// “Fizz”!
!
fizzbuzzer.Skip(55).First();!
// “Buzz”!
!
fizzbuzzer.Skip(150).First();!
// “FizzBuzz”!
!
fizzbuzzer.Skip(2).First();!
// “2”

84. Travel Log
• Forest of Higher Order
• Reduce
• Map
• Filter
• City of Mapcat
• City of Zip
• The Emerald City of FP

86. –- L. Frank Baum, The Marvelous Land of Oz
“To 'know Thyself' is considered quite an
accomplishment.”

87. What
!
How
Execute
Transduce

88. ;; transducer signature!
(whatever, input -> whatever) ->
(whatever, input -> whatever)
*from: http://clojure.org/transducers

89. reduce
map
add to
collectionfunction

90. new[] {1, 2, 3, 4}!
.Select(x => x+1); !
!
// { 2, 3, 4, 5 }

91. new[] {1, 2, 3, 4}!
.Aggregate(!
new List<int>(),!
(m, x) => {!
m.Add(x+1);!
return m;!
}).ToArray();!
!
// { 2, 3, 4, 5 }

92. new[] {1, 2, 3, 4}!
.Aggregate(!
new List<int>(),!
(m, x) => {!
m.Add(x+1);!
return m;!
}).ToArray();!
!
// { 2, 3, 4, 5 }

93. new[] {1, 2, 3, 4}!
.Aggregate(coll!
new typeof(coll),!
(m, x) => {!
m.Step(x+1);!
return m;!
});!
// { 2, 3, 4, 5 }
FAKE C# CODE!!!
FAKE C# CODE!!!

94. What
!
How
Execute
Transduce

95. ;; map
(defn map [f coll]
(reduce !
(fn [m x]!
(conj m (f x)))!
[] coll))
*from: http://youtu.be/6mTbuzafcII

96. ;; map
(defn map [f coll]
(reduce !
(fn [m x]!
(conj m (f x)))!
[] coll))
*from: http://youtu.be/6mTbuzafcII

97. ;; map
(defn mapping [f]!
(fn [step]!
(fn [m x]!
(step m (f x)))))!
!
(defn map [f coll]!
(reduce !
((mapping f) conj) !
[] coll))
*from: http://youtu.be/6mTbuzafcII

98. (defn mapping [f]!
(fn [step]!
(fn [m x]!
(step m (f x)))))
*from: http://youtu.be/6mTbuzafcII

99. (defn map [f coll]!
(reduce !
((mapping f) conj) !
[] coll))
*from: http://youtu.be/6mTbuzafcII

100. ;; map
(defn map [f coll]
(reduce !
(fn [m x]!
(conj m (f x)))!
[] coll))
*from: http://youtu.be/6mTbuzafcII

101. ;; map
(defn mapping [f]!
(fn [step]!
(fn [m x]!
(step m (f x)))))!
!
(defn map [f coll]!
(reduce !
((mapping f) conj) !
[] coll))
*from: http://youtu.be/6mTbuzafcII

102. –- L. Frank Baum, The Marvelous Land of Oz
“[A]lthough I feel that I know a tremendous lot, I
am not yet aware how much there is in the
world to find out about. It will take me a little
time to discover whether I am very wise or very
foolish.”

103. Thank you!
Mike Harris
@MikeMKH
http://comp-phil.blogspot.com/

104. –- L. Frank Baum, The Marvelous Land of Oz
“Everything has to come to an end, sometime.”

105. Bibliography (conference sessions)
• Rich Hickey - Transducers
Strange Loop 2014
https://www.youtube.com/watch?v=6mTbuzafcII
• Rich Hickey - Inside Transducers + more.async
Clojure Conj 2014
https://www.youtube.com/watch?v=4KqUvG8HPYo

106. Bibliography (blog posts)
• Martin Fowler - Collection Pipelines
http://martinfowler.com/articles/collection-pipeline/
• Justin Etheredge - A Visual Look at the LINQ SelectMany
Operator
http://www.codethinked.com/a-visual-look-at-the-linq-
selectmany-operator

107. Bibliography (white papers)
• Graham Hutton - A Tutorial on the Universality and
Expressiveness of fold
http://www.cs.nott.ac.uk/~gmh/fold.pdf

108. Bibliography (websites)
• Sam Allen - Dot Net Perls
http://www.dotnetperls.com/
• lots of smart people - ClojureDocs
https://clojuredocs.org/
• Rich Hickey - Transducers
http://clojure.org/transducers

109. Bibliography (Pluralsight classes)
• Scott Allen - LINQ Architecture
http://www.pluralsight.com/courses/linq-architecture
• Deborah Kurata - Practical LINQ
http://www.pluralsight.com/courses/practical-linq

110. Bibliography (books)
• Michael Fogus and Chris Houser - The Joy of Clojure
http://www.manning.com/fogus2/

111. Images
• [1] The International Wizard of Oz Club, http://ozclub.org/
• [3-5, 7] Wikipedia, public domain
• [9] W.W. Denslow - The Wonderful Wizard of Oz
• [47] Flicker - Jeremy Schultz, https://www.flickr.com/photos/
tao_zhyn/442965594/
• [51] W.W. Denslow - The Marvelous Land of Oz
• [65, 85] W.W. Denslow - The Wonderful Wizard of Oz
• [103] Me taken at dinner by my wife while at Strange Loop 2014