This document discusses functional programming concepts in Scala including recursion, higher-order functions, and working with lists. It provides examples of recursively defining functions to calculate the sum, product, maximum value, and length of a list. It also discusses representing lists as nested pairs and using pattern matching to deconstruct lists. Finally, it recommends resources for learning more about functional programming in Scala and OCaml.

1. revival
Scala Summit 2017
https://goo.gl/iKyEKs

2. •

3. Scala

4. Scala ?

5. ?

6. •Scala
•
•
Scala ?

7. •
•
•
•

8. •
•
•
•

10. f(x) = x + 1
Scala
• = ( )
•
Which
is
better?
def f(x: Int) {x + 1}
def f(x: Int) = x + 1
def f(x: Int) = return x + 1
※ : 2

11. ( )
• (mutable)
•
•

13. ?
int sum = 0;
for (int i = 0; i < array.length; i++) {
sum += array[i];
}
return sum;

16. https://goo.gl/iKyEKs

18. • 1 n
•
int f(int n) {
int total = 0;
for (int i = 1; i <= n; i++) {
total += i;
}
return total;
}

19. f(1) = 1
f(2) = 1 + 2
f(3) = 1 + 2 + 3
...
f(n) = 1 + 2 + 3 + ... + n

20. f(1) = 1
f(2) = f(1) + 2
f(3) = f(2) + 3
...
f(n) = f(n - 1) + n
f(1) = 1
f(n) = f(n - 1) + n

21. def f(n: Int): Int =
if (n == 1) 1
else f(n - 1) + n
f(1) = 1
f(n) = f(n - 1) + n

23. f(0) = 1
f(1) = 1
f(2) = 2 * 1
f(3) = 3 * 2 * 1
...
f(n) = n * ... * 3 * 2 * 1

24. f(0) = 1
f(1) = 1 * f(0)
f(2) = 2 * f(1)
f(3) = 3 * f(2)
...
f(n) = n * f(n - 1)

25. f(0) = 1
f(n) = n * f(n - 1)
def f(n: Int): Int =
if (n == 0) 1
else n * f(n - 1)

26. n
?
1, 1, 2, 3, 5, 8, 13, …

27. f(0) = 0
f(1) = 1
f(2) = 0 + 1
f(3) = 1 + 1
f(4) = 1 + 2
f(5) = 2 + 3
...

28. f(0) = 0
f(1) = 1
f(2) = f(0) + f(1)
f(3) = f(1) + f(2)
f(4) = f(2) + f(3)
f(5) = f(3) + f(4)
...
f(n) = f(n - 2) + f(n - 1)

29. f(0) = 0
f(1) = 1
f(n) = f(n - 2) + f(n - 1)
def f(n: Int): Int =
if (n == 0) 0
else if (n == 1) 1
else f(n - 2) + f(n - 1)

30. sum
def sum(ints: List[Int]): Int

31. • Nil
•head tail
head :: tail
3
Nil
Nil::
3 :: Nil2 ::
2 :: 3 :: Nil1 ::
•
•

33. Nil
Nil::8
8 :: Nil::2
2 :: 8 :: Nil::1
1 :: 2 :: 8 :: Nil::5
5 :: 1 :: 2 :: 8 :: Nil

34. sum(5 :: 1 :: 2 :: 8 :: Nil)
sum( )
= + sum( )
sum( ) = + sum( )
sum( ) = + sum( )
sum( ) = + sum( )
sum( ) = 0Nil
8 :: Nil
2 :: 8 :: Nil
5 :: 1 :: 2 :: 8 :: Nil
Nil8
8 :: Nil2
2 :: 8 :: Nil1
5 1 :: 2 :: 8 :: Nil
1 :: 2 :: 8 :: Nil

35. sum( ) = + sum( )
sum( ) = + sum( )
sum( ) = + sum( )
sum( ) = 0Nil
8 :: Nil
2 :: 8 :: Nil
Nil8
8 :: Nil22 :: 8 :: Nil
1
head
head tail
head tail
head tail head :: tail
1 :: 2 :: 8 :: Nil
tail

36. sum(Nil) = 0
sum(head :: tail) = head + sum(tail)
def sum(list: List[Int]): Int =
if (list.isEmpty) 0
else list.head + sum(list.tail)
def sum(list: List[Int]): Int = list match {
case Nil => 0
case head :: tail => head + sum(tail)
}

37. product
def product(ints: List[Int]): Int

38. max
def max(ints: List[Int]): Int

39. reverse
def reverse(ints: List[Int]): List[Int]

40. length
def length(ints: List[Int]): Int

41. def sum(list: List[Int]): Int = list match {
case Nil => 0
case head :: tail => head + sum(tail)
}
def sum(list: List[Int]): Int = {
def loop(acc: Int, l: List[Int]): Int = l match {
case Nil => acc
case head :: tail => loop(acc + head, tail)
}
loop(0, list)
}

43. • Functional Programming Principles in Scala
Scala Martin Odersky
https://www.coursera.org/course/progfun
•
OCaml
http://www.amazon.co.jp/dp/4781911609

44. • Scala & ―
Scalaz
2
http://www.amazon.co.jp/dp/4844337769