Programming a state monad in Scala - scala

Question

The theory of how a state monad looks like I borrow from Philip Wadler's Monads for Functional Programming:
type M a = State → (a, State)
type State = Int
unit :: a → M a
unit a = λx. (a, x)
(*) :: M a → (a → M b) → M b
m * k = λx.
let (a, y) = m x in
let (b, z) = k a y in
(b, z)
The way I would like to use a state monad is as follows:
Given a list L I want different parts of my code to get this list and update this list by adding new elements at its end.
I guess the above would be modified as:
type M = State → (List[Data], State)
type State = List[Data]
def unit(a: List[Data]) = (x: State) => (a,x)
def star(m: M, k: List[Data] => M): M = {
(x: M) =>
val (a,y) = m(x)
val (b,z) = k(a)(y)
(b,z)
}
def get = ???
def update = ???
How do I fill in the details, i.e.?
How do I instantiate my hierarchy to work on a concrete list?
How do I implement get and update in terms of the above?
Finally, how would I do this using Scala's syntax with flatMap and unit?

Answer 1

Your M is defined incorrectly. It should take a/A as a parameter, like so:
type M[A] = State => (A, State)
You've also missed that type parameter elsewhere.
unit should have a signature like this:
def unit[A](a: A): M[A]
star should have a signature like this:
def star[A, B](m: M[A], k: A => M[B]): M[B]
Hopefully, that makes the functions more clear.
Your implementation of unit was pretty much the same:
def unit[A](a: A): M[A] = x => (a, x)
However, in star, the parameter of your lambda (x) is of type State, not M, because M[B] is basically State => (A, State). The rest you got right:
def star[A, B](m: M[A])(k: A => M[B]): M[B] =
(x: State) => {
val (a, y) = m(x)
val (b, z) = k(a)(y)
(b, z)
}
Edit: According to #Luis Miguel Mejia Suarez:
It would probably be easier to implement if you make your State a class and define flatMap inside it. And you can define unit in the companion object.
He suggested final class State[S, A](val run: S => (A, S)), which would also allow you to use infix functions like >>=.
Another way to do it would be to define State as a type alias for a function S => (A, S) and extend it using an implicit class.
type State[S, A] = S => (A, S)
object State {
//This is basically "return"
def unit[S, A](a: A): State[S, A] = s => (a, s)
}
implicit class StateOps[S, A](private runState: S => (A, S)) {
//You can rename this to ">>=" or "flatMap"
def *[B](k: A => State[S, B]): State[S, B] = s => {
val (a, s2) = runState(s)
k(a)(s2)
}
}
If your definition of get is
set the result value to the state and leave the state unchanged
(borrowed from Haskell Wiki), then you can implement it like this:
def get[S]: State[S, S] = s => (s, s)
If you mean that you want to extract the state (in this case a List[Data]), you can use execState (define it in StateOps):
def execState(s: S): S = runState(s)._2
Here's a terrible example of how you can add elements to a List.
def addToList(n: Int)(list: List[Int]): ((), List[Int]) = ((), n :: list)
def fillList(n: Int): State[List[Int], ()] =
n match {
case 0 => s => ((), s)
case n => fillList(n - 1) * (_ => addToList(n))
}
println(fillList(10)(List.empty)) gives us this (the second element can be extracted with execState):
((),List(10, 9, 8, 7, 6, 5, 4, 3, 2, 1))