(*  Title:      HOL/Library/Code_Natural.thy

    Author:     Florian Haftmann, TU Muenchen

*)

theory Code_Natural

imports Main

begin

section {* Alternative representation of @{typ code_numeral} for @{text Haskell} and @{text Scala} *}

code_include Haskell "Natural"

{*import Data.Array.ST;

newtype Natural = Natural Integer deriving (Eq, Show, Read);

instance Num Natural where {

  fromInteger k = Natural (if k >= 0 then k else 0);

  Natural n + Natural m = Natural (n + m);

  Natural n - Natural m = fromInteger (n - m);

  Natural n * Natural m = Natural (n * m);

  abs n = n;

  signum _ = 1;

  negate n = error "negate Natural";

};

instance Ord Natural where {

  Natural n <= Natural m = n <= m;

  Natural n < Natural m = n < m;

};

instance Ix Natural where {

  range (Natural n, Natural m) = map Natural (range (n, m));

  index (Natural n, Natural m) (Natural q) = index (n, m) q;

  inRange (Natural n, Natural m) (Natural q) = inRange (n, m) q;

  rangeSize (Natural n, Natural m) = rangeSize (n, m);

};

instance Real Natural where {

  toRational (Natural n) = toRational n;

};

instance Enum Natural where {

  toEnum k = fromInteger (toEnum k);

  fromEnum (Natural n) = fromEnum n;

};

instance Integral Natural where {

  toInteger (Natural n) = n;

  divMod n m = quotRem n m;

  quotRem (Natural n) (Natural m)

    | (m == 0) = (0, Natural n)

    | otherwise = (Natural k, Natural l) where (k, l) = quotRem n m;

};*}

code_reserved Haskell Natural

code_include Scala "Natural"

{*import scala.Math

object Nat {

  def apply(numeral: BigInt): Nat = new Nat(numeral max 0)

  def apply(numeral: Int): Nat = Nat(BigInt(numeral))

  def apply(numeral: String): Nat = Nat(BigInt(numeral))

}

class Nat private(private val value: BigInt) {

  override def hashCode(): Int = this.value.hashCode()

  override def equals(that: Any): Boolean = that match {

    case that: Nat => this equals that

    case _ => false

  }

  override def toString(): String = this.value.toString

  def equals(that: Nat): Boolean = this.value == that.value

  def as_BigInt: BigInt = this.value

  def as_Int: Int = if (this.value >= Int.MinValue && this.value <= Int.MaxValue)

      this.value.intValue

    else error("Int value out of range: " + this.value.toString)

  def +(that: Nat): Nat = new Nat(this.value + that.value)

  def -(that: Nat): Nat = Nat(this.value - that.value)

  def *(that: Nat): Nat = new Nat(this.value * that.value)

  def /%(that: Nat): (Nat, Nat) = if (that.value == 0) (new Nat(0), this)

    else {

      val (k, l) = this.value /% that.value

      (new Nat(k), new Nat(l))

    }

  def <=(that: Nat): Boolean = this.value <= that.value

  def <(that: Nat): Boolean = this.value < that.value

}

*}

code_reserved Scala Natural

code_type code_numeral

  (Haskell "Natural.Natural")

  (Scala "Natural.Nat")

setup {*

  fold (Numeral.add_code @{const_name number_code_numeral_inst.number_of_code_numeral}

    false Code_Printer.literal_alternative_numeral) ["Haskell", "Scala"]

*}

code_instance code_numeral :: eq

  (Haskell -)

code_const "op + \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"

  (Haskell infixl 6 "+")

  (Scala infixl 7 "+")

code_const "op - \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"

  (Haskell infixl 6 "-")

  (Scala infixl 7 "-")

code_const "op * \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"

  (Haskell infixl 7 "*")

  (Scala infixl 8 "*")

code_const div_mod_code_numeral

  (Haskell "divMod")

  (Scala infixl 8 "/%")

code_const "eq_class.eq \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> bool"

  (Haskell infixl 4 "==")

  (Scala infixl 5 "==")

code_const "op \<le> \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> bool"

  (Haskell infix 4 "<=")

  (Scala infixl 4 "<=")

code_const "op < \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> bool"

  (Haskell infix 4 "<")

  (Scala infixl 4 "<")

end