package object comp2 {

//  Recusive function to Abacus translation

import lib._
import abacus._
import recs._

def AbacusAdd(m: Int, n: Int, p: Int) = 
  Abacus(Dec(m, 4), Inc(n), Inc(p), Goto(0), Dec(p, 7), Inc(m), Goto(4))

def MVReg(m: Int, n: Int) = Abacus(Dec(m, 3), Inc(n), Goto(0))

//move the registers ranging from i to i + n to range j to j + n
def MVRegs(i: Int, j: Int, n: Int) : Abacus = n match { 
  case 0 => Abacus() 
  case n => MVRegs(i, j, n - 1) :+ MVReg(i + n - 1, j + n - 1)
}

// clears the first n registers
def ClearRegs(n: Int) : Abacus = n match {
  case 0 => Abacus()
  case n => ClearRegs(n - 1) :+ Abacus(Dec(n - 1, 2), Goto(0))
}

def cn_merge_gs(x: List[(Abacus, Int)], n: Int, p: Int) : Abacus = x match {
  case Nil => Abacus(Nil)
  case (gprog, gn)::gs => gprog :+ MVReg(n, p) :+ cn_merge_gs(gs, n, p + 1)
}

// translation: 
// second component is the arity of the recursive function, 
// third componen is the maximum of registers used
def compile_rec(f: Rec) : (Abacus, Int) = f match {
  case Z => (Abacus(Goto(1)), 2)
  case S => (AbacusAdd(0, 1, 2) :+ Abacus(Inc(1)), 3)
  case Id(i, j) => (AbacusAdd(j, i, i + 1), i + 2) 
  case Cn(n, f, gs) => {
    val cied_gs = gs.map(compile_rec)
    val (fprog, fn) = compile_rec(f) 
    val qstr = (fn :: (cied_gs.map(_._2))).max
    (cn_merge_gs(cied_gs, n, qstr) :+ 
     MVRegs(0, qstr + gs.length, n) :+
     MVRegs(qstr, 0, gs.length) :+
     fprog :+ 
     MVReg(f.arity, qstr + gs.length + 1) :+ 
     ClearRegs(gs.length) :+
     MVRegs(qstr + gs.length , 0, n + 1), qstr + gs.length + n + 1)
  }
  case Pr(n, f, g) => { 
    val (fprog, fn) = compile_rec(f) 
    val (gprog, gn) = compile_rec(g) 
    val qstr = List(fn, gn).max 
    val e = gprog.p.length + 7 
    (MVReg(0, qstr) :+
     MVRegs(1, 0, n) :+ 
     fprog :+ 
     MVReg(n, n + 1) :+ 
     MVRegs(0, 2, n) :+ 
     ((Abacus(Dec(qstr, e)) :+ gprog :+ Abacus(Inc(0), Dec(n + 1, 3), Goto(1))) ++
       Abacus(Dec(n + 2, 0), Inc (1), Goto (gprog.p.length + 4))), qstr + 1)
  }
  case Mn(n, f) => {
    val (fprog, fn) = compile_rec(f)
    val len = fprog.p.length
    (MVRegs(0, 1, n) :+
     (fprog ++ Abacus(Dec(n + 1, len + 5), Dec(n + 1, len + 3), Goto(len + 1), Inc(0), Goto(0))), 
     fn)
  }
}

}