(*  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"

 {*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