(*  Title:      HOL/Library/Code_Integer.thy

     Author:     Florian Haftmann, TU Muenchen

 *)

 header {* Pretty integer literals for code generation *}

 theory Code_Integer

 imports Main Code_Natural

 begin

 text {*

   Representation-ignorant code equations for conversions.

 *}

 lemma nat_code [code]:

   "nat k = (if k \<le> 0 then 0 else

      let

        (l, j) = divmod_int k 2;

        l' = 2 * nat l

      in if j = 0 then l' else Suc l')"

 proof -

   have "2 = nat 2" by simp

   show ?thesis

     apply (auto simp add: Let_def divmod_int_mod_div not_le

      nat_div_distrib nat_mult_distrib mult_div_cancel mod_2_not_eq_zero_eq_one_int)

     apply (unfold `2 = nat 2`)

     apply (subst nat_mod_distrib [symmetric])

     apply simp_all

   done

 qed

 lemma (in ring_1) of_int_code:

   "of_int k = (if k = 0 then 0

      else if k < 0 then - of_int (- k)

      else let

        (l, j) = divmod_int k 2;

        l' = 2 * of_int l

      in if j = 0 then l' else l' + 1)"

 proof -

   from mod_div_equality have *: "of_int k = of_int (k div 2 * 2 + k mod 2)" by simp

   show ?thesis

     by (simp add: Let_def divmod_int_mod_div mod_2_not_eq_zero_eq_one_int

       of_int_add [symmetric]) (simp add: * mult_commute)

 qed

 declare of_int_code [code]

 text {*

   HOL numeral expressions are mapped to integer literals

   in target languages, using predefined target language

   operations for abstract integer operations.

 *}

 code_type int

   (SML "IntInf.int")

   (OCaml "Big'_int.big'_int")

   (Haskell "Integer")

   (Scala "BigInt")

   (Eval "int")

 code_instance int :: equal

   (Haskell -)

 code_const "0::int"

   (SML "0")

   (OCaml "Big'_int.zero'_big'_int")

   (Haskell "0")

   (Scala "BigInt(0)")

 setup {*

   fold (Numeral.add_code @{const_name Int.Pos}

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

 *}

 setup {*

   fold (Numeral.add_code @{const_name Int.Neg}

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

 *}

 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 Int.dup

   (SML "IntInf.*/ (2,/ (_))")

   (OCaml "Big'_int.mult'_big'_int/ 2")

   (Haskell "!(2 * _)")

   (Scala "!(2 * _)")

   (Eval "!(2 * _)")

 code_const Int.sub

   (SML "!(raise/ Fail/ \"sub\")")

   (OCaml "failwith/ \"sub\"")

   (Haskell "error/ \"sub\"")

   (Scala "!error(\"sub\")")

 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 "HOL.equal \<Colon> int \<Rightarrow> int \<Rightarrow> bool"

   (SML "!((_ : IntInf.int) = _)")

   (OCaml "Big'_int.eq'_big'_int")

   (Haskell infix 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 "_")

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

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

 end