
haftmann@37968: (*  Title:      HOL/Library/Code_Natural.thy
haftmann@24999:     Author:     Florian Haftmann, TU Muenchen
haftmann@24999: *)
haftmann@24999: 
haftmann@37968: theory Code_Natural
haftmann@31203: imports Main
haftmann@24999: begin
haftmann@24999: 
haftmann@37968: section {* Alternative representation of @{typ code_numeral} for @{text Haskell} and @{text Scala} *}
haftmann@24999: 
haftmann@37968: code_include Haskell "Natural"
haftmann@38810: {*import Data.Array.ST;
haftmann@38810: 
haftmann@38810: newtype Natural = Natural Integer deriving (Eq, Show, Read);
haftmann@37958: 
haftmann@37958: instance Num Natural where {
haftmann@37958:   fromInteger k = Natural (if k >= 0 then k else 0);
haftmann@37958:   Natural n + Natural m = Natural (n + m);
haftmann@37958:   Natural n - Natural m = fromInteger (n - m);
haftmann@37958:   Natural n * Natural m = Natural (n * m);
haftmann@37958:   abs n = n;
haftmann@37958:   signum _ = 1;
haftmann@37958:   negate n = error "negate Natural";
haftmann@37958: };
haftmann@37958: 
haftmann@37958: instance Ord Natural where {
haftmann@37958:   Natural n <= Natural m = n <= m;
haftmann@37958:   Natural n < Natural m = n < m;
haftmann@37958: };
haftmann@37958: 
haftmann@37968: instance Ix Natural where {
haftmann@37968:   range (Natural n, Natural m) = map Natural (range (n, m));
haftmann@37968:   index (Natural n, Natural m) (Natural q) = index (n, m) q;
haftmann@37968:   inRange (Natural n, Natural m) (Natural q) = inRange (n, m) q;
haftmann@37968:   rangeSize (Natural n, Natural m) = rangeSize (n, m);
haftmann@37968: };
haftmann@37968: 
haftmann@37958: instance Real Natural where {
haftmann@37958:   toRational (Natural n) = toRational n;
haftmann@37958: };
haftmann@37958: 
haftmann@37958: instance Enum Natural where {
haftmann@37958:   toEnum k = fromInteger (toEnum k);
haftmann@37958:   fromEnum (Natural n) = fromEnum n;
haftmann@37958: };
haftmann@37958: 
haftmann@37958: instance Integral Natural where {
haftmann@37958:   toInteger (Natural n) = n;
haftmann@37958:   divMod n m = quotRem n m;
haftmann@37958:   quotRem (Natural n) (Natural m)
haftmann@37958:     | (m == 0) = (0, Natural n)
haftmann@37958:     | otherwise = (Natural k, Natural l) where (k, l) = quotRem n m;
haftmann@37968: };*}
haftmann@37958: 
haftmann@38810: 
haftmann@37958: code_reserved Haskell Natural
haftmann@37958: 
haftmann@38774: code_include Scala "Natural"
haftmann@38968: {*object Natural {
haftmann@37958: 
haftmann@38968:   def apply(numeral: BigInt): Natural = new Natural(numeral max 0)
haftmann@38968:   def apply(numeral: Int): Natural = Natural(BigInt(numeral))
haftmann@38968:   def apply(numeral: String): Natural = Natural(BigInt(numeral))
haftmann@37958: 
haftmann@37958: }
haftmann@37958: 
haftmann@38968: class Natural private(private val value: BigInt) {
haftmann@37958: 
haftmann@37958:   override def hashCode(): Int = this.value.hashCode()
haftmann@37958: 
haftmann@37958:   override def equals(that: Any): Boolean = that match {
haftmann@38968:     case that: Natural => this equals that
haftmann@37958:     case _ => false
haftmann@37958:   }
haftmann@37958: 
haftmann@37958:   override def toString(): String = this.value.toString
haftmann@37958: 
haftmann@38968:   def equals(that: Natural): Boolean = this.value == that.value
haftmann@37958: 
haftmann@37958:   def as_BigInt: BigInt = this.value
haftmann@37958:   def as_Int: Int = if (this.value >= Int.MinValue && this.value <= Int.MaxValue)
haftmann@37958:       this.value.intValue
haftmann@37968:     else error("Int value out of range: " + this.value.toString)
haftmann@37958: 
haftmann@38968:   def +(that: Natural): Natural = new Natural(this.value + that.value)
haftmann@38968:   def -(that: Natural): Natural = Natural(this.value - that.value)
haftmann@38968:   def *(that: Natural): Natural = new Natural(this.value * that.value)
haftmann@37958: 
haftmann@38968:   def /%(that: Natural): (Natural, Natural) = if (that.value == 0) (new Natural(0), this)
haftmann@37958:     else {
haftmann@37958:       val (k, l) = this.value /% that.value
haftmann@38968:       (new Natural(k), new Natural(l))
haftmann@37958:     }
haftmann@37958: 
haftmann@38968:   def <=(that: Natural): Boolean = this.value <= that.value
haftmann@37958: 
haftmann@38968:   def <(that: Natural): Boolean = this.value < that.value
haftmann@37958: 
haftmann@37958: }
haftmann@37958: *}
haftmann@37958: 
haftmann@37958: code_reserved Scala Natural
haftmann@37958: 
haftmann@37958: code_type code_numeral
haftmann@37958:   (Haskell "Natural.Natural")
haftmann@38968:   (Scala "Natural")
haftmann@37958: 
haftmann@37958: setup {*
haftmann@37958:   fold (Numeral.add_code @{const_name number_code_numeral_inst.number_of_code_numeral}
haftmann@37958:     false Code_Printer.literal_alternative_numeral) ["Haskell", "Scala"]
haftmann@37958: *}
haftmann@37958: 
haftmann@38857: code_instance code_numeral :: equal
haftmann@37958:   (Haskell -)
haftmann@37958: 
haftmann@37958: code_const "op + \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"
haftmann@37958:   (Haskell infixl 6 "+")
haftmann@37958:   (Scala infixl 7 "+")
haftmann@37958: 
haftmann@37958: code_const "op - \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"
haftmann@37958:   (Haskell infixl 6 "-")
haftmann@37958:   (Scala infixl 7 "-")
haftmann@37958: 
haftmann@37958: code_const "op * \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"
haftmann@37958:   (Haskell infixl 7 "*")
haftmann@37958:   (Scala infixl 8 "*")
haftmann@37958: 
haftmann@37958: code_const div_mod_code_numeral
haftmann@37958:   (Haskell "divMod")
haftmann@37958:   (Scala infixl 8 "/%")
haftmann@37958: 
haftmann@38857: code_const "HOL.equal \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> bool"
haftmann@37958:   (Haskell infixl 4 "==")
haftmann@37958:   (Scala infixl 5 "==")
haftmann@37958: 
haftmann@37958: code_const "op \<le> \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> bool"
haftmann@37958:   (Haskell infix 4 "<=")
haftmann@37958:   (Scala infixl 4 "<=")
haftmann@37958: 
haftmann@37958: code_const "op < \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> bool"
haftmann@37958:   (Haskell infix 4 "<")
haftmann@37958:   (Scala infixl 4 "<")
haftmann@37958: 
haftmann@37968: end




