Scalaエンジニアのためのモナド入門

Scala
1
3 Scala 2016 7 10 erin

•
• Scalaz
•
• Haskell
2

•
→ Haskell
• Scala
→ List Option map flatMap for
•
→
4

val addTwo:Int=>Int = a => {
a+2
}
val addTwoThree = addTwo(3)
println(addTwoThree) // 5
↓ ↓
println(addTwo(3)) // 5
8

val acc=Array(0)
val addTwo:Int=>Int = a => {
acc(0) = acc(0)+a+2
acc(0)
}
val addTwoThree = addTwo(3)
↓ ↓
10

• List Option
IO State
•
→
17

•
→
•
→ A => M[B]
•
→ M[A] >>= (A => M[B])
→ x >>= f = ???
→ ??? >>=
→ flatMap
19
Int=>List[String]
List[String] >>= (String=>List[Int])

• Option
→ None None
Some(4).flatMap(a=>(Some(3).flatMap(b=>Some(a*b)))) // Some(12)
Some(4).flatMap(a=>((None:Option[Int]).flatMap(b=>Some(a*b)))) // None
• List
→
List(1,2,3).flatMap(a=>(List(4,5,6).flatMap(b=>List(a*b))))
// List(4, 5, 6, 8, 10, 12, 12, 15, 18)
• State
→
20
flatMap

val om = for {
a <- Some(4)
b <- None:Option[Int]
} yield (a*b) // None
val lm = for {
a <- List(1,2,3)
b <- List(4,5,6)
} yield (a*b) // List(4, 5, 6, 8, 10, 12, 12, 15, 18)
21
for

(A => M[B]) >>= (B => M[C]) >>= (C => M[D])
→ A => M[D]
→
val lm = (x:Int) => for {
a <- List(1,2,3).map(_*x)
b <- List(4,5,6).map(_*a)
} yield b
lm(2) // List(8, 10, 12, 16, 20, 24, 24, 30, 36)
22
List

•
• IO Reader Writer
•
25
State

•
A => S => (B,S)
B => S => (C,S)
C => S => (D,S)
•
A => M[B]
B => M[C]
C => M[D]
→ (A => M[B]) >>= (B => M[C]) >>= (C => M[D])
→ State[S,A] >>= (A => State[S,B])
→ flatMap
26

case class State[S,A](runState: S => (A,S)) {
def flatMap[B]:(A=>State[S,B])=>State[S,B] = f => State(s => {
val (a,s1) = this.runState(s)
f(a).runState(s1)
})
def map[B]:(A=>B)=>State[S,B] = f => flatMap(a=>State.unit(f(a)))
}
case object State {
def unit[S,A]:A=>State[S,A] = a => State(s => (a,s))
}
27
flatMap

val push:Int=>State[List[Int],Unit] = a => State(s => ((), a::s))
val pop:State[List[Int],Int] = State(s => (s.head, s.tail))
val calc:(Int=>Int=>Int)=>State[List[Int],Unit] = f => {
for {
a <- pop
b <- pop
_ <- push (f(a)(b))
} yield ()
}
val plus:Int=>Int=>Int = a => b => b+a
val minus:Int=>Int=>Int = a => b => b-a
val mult:Int=>Int=>Int = a => b => b*a
val div:Int=>Int=>Int = a => b => b%a
29

// 2 3 + 4 1 - * = (2+3)*(4-1)
val dc = for {
_ <- push (2)
_ <- push (3)
_ <- calc (plus)
_ <- push (4)
_ <- push (1)
_ <- calc (minus)
_ <- calc (mult)
} yield ()
dc.runState(List.empty)
30

case class Parser[S,A](runParser: S => Option[(A,S)]) {
def flatMap[B]:(A=>Parser[S,B])=>Parser[S,B] = f => Parser(s => {
val o = this.runParser(s)
o.flatMap{
case (a,s1) => f(a).runParser(s1)
}
})
def map[B]:(A=>B)=>Parser[S,B] = f => flatMap(a=>Parser.unit(f(a)))
}
case object Parser {
def unit[S,A]:A=>Parser[S,A] = a => Parser(s => Some((a,s)))
}
32
flatMap

val item:Parser[String,Char] = {
Parser(s => if (s.length > 0) {
Some((s.head, s.tail))
} else {
None
})
}
val satisfy:(Char=>Boolean)=>Parser[String,Char] = f => {
for {
c <- item
n <- Parser(s => if (f(c)) {
Some((c,s))
} else {
None
}):Parser[String,Char]
} yield n
}
val char:Char=>Parser[String,Char] = c => satisfy((x:Char)=>x==c)
val digit:Parser[String,Char] = satisfy((x:Char)=>x.isDigit)
val letter:Parser[String,Char] = satisfy((x:Char)=>x.isLetter)
34

val p = for {
a <- letter
b <- char(a)
c <- digit
d <- digit
e <- digit
f <- digit
} yield List(a,b,c,d,e,f).mkString
p.runParser(“AA0123") // Some(“AA0123”,)
p.runParser(“AB0123") // None
p.runParser("A90123") // None
p.runParser("990123") // None
35

• flatMap
•
→ for
•
→
•
→
37

Scalaエンジニアのためのモナド入門

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