(*  Title:      HOL/Library/Code_Integer.thy

     Author:     Florian Haftmann, TU Muenchen

 *)

 header {* Pretty integer literals for code generation *}

 theory Code_Integer

 imports Main

 begin

 text {*

   HOL numeral expressions are mapped to integer literals

   in target languages, using predefined target language

   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")

   (Haskell "Integer")

   (Scala "BigInt")

 code_instance int :: eq

   (Haskell -)

 setup {*

   fold (Numeral.add_code @{const_name number_int_inst.number_of_int}

     true Code_Printer.literal_numeral) ["SML", "OCaml", "Haskell", "Scala"]

 *}

 code_const "Int.Pls" and "Int.Min" and "Int.Bit0" and "Int.Bit1"

   (SML "raise/ Fail/ \"Pls\""

      and "raise/ Fail/ \"Min\""

      and "!((_);/ raise/ Fail/ \"Bit0\")"

      and "!((_);/ raise/ Fail/ \"Bit1\")")

   (OCaml "failwith/ \"Pls\""

      and "failwith/ \"Min\""

      and "!((_);/ failwith/ \"Bit0\")"

      and "!((_);/ failwith/ \"Bit1\")")

   (Haskell "error/ \"Pls\""

      and "error/ \"Min\""

      and "error/ \"Bit0\""

      and "error/ \"Bit1\"")

   (Scala "!error(\"Pls\")"

      and "!error(\"Min\")"

      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 "!((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 "<")

   (Eval infixl 6 "<")

 code_const Code_Numeral.int_of

   (SML "IntInf.fromInt")

   (OCaml "_")

   (Haskell "toInteger")

   (Scala "!_.as'_BigInt")

   (Eval "_")

 text {* Evaluation *}

 code_const "Code_Evaluation.term_of \<Colon> int \<Rightarrow> term"

   (Eval "HOLogic.mk'_number/ HOLogic.intT")

 end