(*  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;

       n = nat l;

       l' = n + n

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

proof -

  have "2 = nat 2" by simp

  show ?thesis

    apply (subst mult_2 [symmetric])

    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 "!sys.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 "Prelude.toInteger")

  (Scala "!_.as'_BigInt")

  (Eval "_")

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

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

end