Clean and type-safe state machine implementation in a statically typed language?

Question

I implemented a simple state machine in Python:

import time

def a():
    print \"a()\"
    return b

def b():
    print \"b()\"
    return c

def c():
    print         


        

Answer 1

Iit's not hard to make state machines in Haskell, once you realize that they are not monads! A state machine like the one you want is an arrow, an automaton arrow to be exact:

newtype State a b = State (a -> (b, State a b))

This is a function, which takes an input value and produces an output value along with a new version of itself. This is not a monad, because you cannot write join or (>>=) for it. Equivalently once you have turned this into an arrow you will realize that it's impossible to write an ArrowApply instance for it.

Here are the instances:

import Control.Arrow
import Control.Category
import Prelude hiding ((.), id)

instance Category State where
    id = State $ \x -> (x, id)

    State f . State g =
        State $ \x ->
            let (y, s2) = g x
                (z, s1) = f y
            in (z, s1 . s2)

instance Arrow State where
    arr f = let s = State $ \x -> (f x, s) in s
    first (State f) =
        State $ \(x1, x2) ->
            let (y1, s) = f x1
            in ((y1, x2), first s)

Have fun.