src/HOL/Library/Code_Integer.thy
changeset 37958 9728342bcd56
parent 37947 844977c7abeb
child 37968 52fdcb76c0af
--- a/src/HOL/Library/Code_Integer.thy	Fri Jul 23 18:42:46 2010 +0200
+++ b/src/HOL/Library/Code_Integer.thy	Sat Jul 24 18:08:41 2010 +0200
@@ -14,6 +14,142 @@
   operations for abstract integer operations.
 *}
 
+text {*
+  Preliminary: 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 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 this.value.intValue
+
+  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 "<")
+
+text {*
+  Setup for @{typ int} proper.
+*}
+
+
 code_type int
   (SML "IntInf.int")
   (OCaml "Big'_int.big'_int")
@@ -26,8 +162,6 @@
 setup {*
   fold (Numeral.add_code @{const_name number_int_inst.number_of_int}
     true Code_Printer.literal_numeral) ["SML", "OCaml", "Haskell", "Scala"]
-  #> Numeral.add_code @{const_name number_int_inst.number_of_int}
-    true Code_Printer.literal_numeral "Scala"
 *}
 
 code_const "Int.Pls" and "Int.Min" and "Int.Bit0" and "Int.Bit1"
@@ -48,72 +182,82 @@
      and "!error(\"Bit0\")"
      and "!error(\"Bit1\")")
 
-
 code_const Int.pred
   (SML "IntInf.- ((_), 1)")
   (OCaml "Big'_int.pred'_big'_int")
   (Haskell "!(_/ -/ 1)")
   (Scala "!(_/ -/ 1)")
+  (Eval "!(_/ -/ 1)")
 
 code_const Int.succ
   (SML "IntInf.+ ((_), 1)")
   (OCaml "Big'_int.succ'_big'_int")
   (Haskell "!(_/ +/ 1)")
   (Scala "!(_/ +/ 1)")
+  (Eval "!(_/ +/ 1)")
 
 code_const "op + \<Colon> int \<Rightarrow> int \<Rightarrow> int"
   (SML "IntInf.+ ((_), (_))")
   (OCaml "Big'_int.add'_big'_int")
   (Haskell infixl 6 "+")
   (Scala infixl 7 "+")
+  (Eval infixl 8 "+")
 
 code_const "uminus \<Colon> int \<Rightarrow> int"
   (SML "IntInf.~")
   (OCaml "Big'_int.minus'_big'_int")
   (Haskell "negate")
   (Scala "!(- _)")
+  (Eval "~/ _")
 
 code_const "op - \<Colon> int \<Rightarrow> int \<Rightarrow> int"
   (SML "IntInf.- ((_), (_))")
   (OCaml "Big'_int.sub'_big'_int")
   (Haskell infixl 6 "-")
   (Scala infixl 7 "-")
+  (Eval infixl 8 "-")
 
 code_const "op * \<Colon> int \<Rightarrow> int \<Rightarrow> int"
   (SML "IntInf.* ((_), (_))")
   (OCaml "Big'_int.mult'_big'_int")
   (Haskell infixl 7 "*")
   (Scala infixl 8 "*")
+  (Eval infixl 9 "*")
 
 code_const pdivmod
   (SML "IntInf.divMod/ (IntInf.abs _,/ IntInf.abs _)")
   (OCaml "Big'_int.quomod'_big'_int/ (Big'_int.abs'_big'_int _)/ (Big'_int.abs'_big'_int _)")
   (Haskell "divMod/ (abs _)/ (abs _)")
-  (Scala "!(_.abs '/% _.abs)")
+  (Scala "!((k: BigInt) => (l: BigInt) =>/ if (l == 0)/ (BigInt(0), k) else/ (k.abs '/% l.abs))")
+  (Eval "Integer.div'_mod/ (abs _)/ (abs _)")
 
 code_const "eq_class.eq \<Colon> int \<Rightarrow> int \<Rightarrow> bool"
   (SML "!((_ : IntInf.int) = _)")
   (OCaml "Big'_int.eq'_big'_int")
   (Haskell infixl 4 "==")
   (Scala infixl 5 "==")
+  (Eval infixl 6 "=")
 
 code_const "op \<le> \<Colon> int \<Rightarrow> int \<Rightarrow> bool"
   (SML "IntInf.<= ((_), (_))")
   (OCaml "Big'_int.le'_big'_int")
   (Haskell infix 4 "<=")
   (Scala infixl 4 "<=")
+  (Eval infixl 6 "<=")
 
 code_const "op < \<Colon> int \<Rightarrow> int \<Rightarrow> bool"
   (SML "IntInf.< ((_), (_))")
   (OCaml "Big'_int.lt'_big'_int")
   (Haskell infix 4 "<")
-  (Scala infixl 4 "<=")
+  (Scala infixl 4 "<")
+  (Eval infixl 6 "<")
 
 code_const Code_Numeral.int_of
   (SML "IntInf.fromInt")
   (OCaml "_")
-  (Haskell "_")
-  (Scala "!BigInt((_))")
+  (Haskell "toInteger")
+  (Scala "!_.as'_BigInt")
+  (Eval "_")
 
 text {* Evaluation *}