src/HOL/Library/Code_Natural.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/Code_Natural.thy	Mon Jul 26 11:10:35 2010 +0200
@@ -0,0 +1,145 @@
+(*  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 Natural {
+
+  def apply(numeral: BigInt): Natural = new Natural(numeral max 0)
+  def apply(numeral: Int): Natural = Natural(BigInt(numeral))
+  def apply(numeral: String): Natural = Natural(BigInt(numeral))
+
+}
+
+class Natural private(private val value: BigInt) {
+
+  override def hashCode(): Int = this.value.hashCode()
+
+  override def equals(that: Any): Boolean = that match {
+    case that: Natural => this equals that
+    case _ => false
+  }
+
+  override def toString(): String = this.value.toString
+
+  def equals(that: Natural): 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: Natural): Natural = new Natural(this.value + that.value)
+  def -(that: Natural): Natural = Natural(this.value - that.value)
+  def *(that: Natural): Natural = new Natural(this.value * that.value)
+
+  def /%(that: Natural): (Natural, Natural) = if (that.value == 0) (new Natural(0), this)
+    else {
+      val (k, l) = this.value /% that.value
+      (new Natural(k), new Natural(l))
+    }
+
+  def <=(that: Natural): Boolean = this.value <= that.value
+
+  def <(that: Natural): Boolean = this.value < that.value
+
+}
+*}
+
+code_reserved Scala Natural
+
+code_type code_numeral
+  (Haskell "Natural.Natural")
+  (Scala "Natural")
+
+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