package object turing {

import scala.annotation.tailrec
import lib._

// tape cells
sealed abstract class Cell {
  def * (n: Int) : List[Cell] = n match {
    case 0 => Nil
    case n => this :: this * (n - 1)
  }
}
case object Bk extends Cell { override def toString = "0" }
case object Oc extends Cell { override def toString = "1" }

// actions
sealed abstract class Action
case object WBk extends Action
case object WOc extends Action
case object R extends Action
case object L extends Action
case object Nop extends Action

type State = Int
type Inst = (Action, State)
type Prog = List[Inst]

// tapes
case class Tape(l: List[Cell], r: List[Cell]) {
  
  def update(a: Action) = a match {
    case WBk => Tape(l, Bk::tl(r))
    case WOc => Tape(l, Oc::tl(r))
    case L => if (l == Nil) Tape(Nil, Bk::r) else Tape (tl(l), hd(l)::r)
    case R => if (r == Nil) Tape(Bk::l, Nil) else Tape(hd(r)::l, tl(r))
    case Nop => Tape(l, r)
  }

  def read = r match {
    case Nil => Bk
    case x::_ => x
  }

  override def toString = join(l.reverse) + ">" + join(r)
}

// standard tapes
object Tape {
  def apply(ns: List[Int]) : Tape = 
   Tape(Nil, ns.map(n => Oc * (n + 1)).reduceLeft(_ ::: List(Bk) ::: _))

  def apply(ns: Int*) : Tape = apply(ns.toList)
    
}

// configurations
case class Config(s: State, tp: Tape) {
  def is_final = s == 0

  override def toString = tp.toString
}

// Turing machines
case class TM(p: Prog) {

  // composition
  def ++ (that: TM) = TM(this.p ::: that.p)
  def :+ (that: TM) = this.adjust ++ that.shift(this.p.length / 2)

  def shift(n: Int) =
    TM(p.map{case (a, s) => (a, if (s == 0) 0 else s + n)})
  def adjust(n: Int) : TM =
    TM(p.map{case (a, s) => (a, if (s == 0) n else s)})
  def adjust : TM = adjust(p.length / 2 + 1)
  
  def fetch(s: State, a: Cell) = (s, a) match {
    case (0, _) => (Nop, 0)
    case (s, Bk) => nth_of(p, 2 * (s - 1)) match {
      case None => (Nop, 0)
      case Some(i) => i
    }
    case (s, Oc) => nth_of(p, 2 * (s - 1) + 1) match {
      case None => (Nop, 0)
      case Some(i) => i
    }
  } 

  def step(cf: Config) : Config = fetch (cf.s, cf.tp.read) match {
    case (a, s_next) => Config(s_next, cf.tp.update(a))
  }

  def steps(cf: Config, n: Int) : Config = n match {
    case 0 => cf
    case n => steps(step(cf), n - 1)
  } 

  @tailrec
  final def run(cf: Config) : Config = {
    if (cf.is_final) cf else run(step(cf))
  }
 
  def run(tp: Tape) : Tape = run(Config(1, tp)).tp
}

// some syntactical convenience
object TM {
  def apply(is: Inst*) : TM = TM(is.toList)
}

}