base Sublist_Order on Sublist (using a simplified form of embedding as sublist relation)
(* 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