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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(** Extraction of [nat] into Ocaml's [big_int] *)
+
+Require Import Arith Even Div2 EqNat Euclid.
+Require Import ExtrOcamlBasic.
+
+(** NB: The extracted code should be linked with [nums.(cma|cmxa)]. *)
+
+(** Disclaimer: trying to obtain efficient certified programs
+    by extracting [nat] into [big_int] isn't necessarily a good idea.
+    See comments in [ExtrOcamlNatInt.v].
+*)
+
+
+(** Mapping of [nat] into [big_int]. The last string corresponds to
+    a [nat_case], see documentation of [Extract Inductive]. *)
+
+Extract Inductive nat => "Big_int.big_int"
+ [ "Big_int.zero_big_int" "Big_int.succ_big_int" ]
+ "(fun fO fS n -> if Big_int.sign_big_int n = 0 then fO () else fS (Big_int.pred_big_int n))".
+
+(** Efficient (but uncertified) versions for usual [nat] functions *)
+
+Extract Constant plus => "Big_int.add_big_int".
+Extract Constant mult => "Big_int.mult_big_int".
+Extract Constant pred =>
+ "fun n -> Big_int.max_big_int Big_int.zero_big_int (Big_int.pred_big_int n)".
+Extract Constant minus =>
+ "fun n m -> Big_int.max_big_int Big_int.zero_big_int (Big_int.sub_big_int n m)".
+Extract Constant max => "Big_int.max_big_int".
+Extract Constant min => "Big_int.min_big_int".
+Extract Constant nat_beq => "Big_int.eq_big_int".
+Extract Constant EqNat.beq_nat => "Big_int.eq_big_int".
+Extract Constant EqNat.eq_nat_decide => "Big_int.eq_big_int".
+
+Extract Inlined Constant Peano_dec.eq_nat_dec => "Big_int.eq_big_int".
+
+Extract Constant Compare_dec.nat_compare =>
+"fun n m ->
+ let s = Big_int.compare_big_int n m in
+ if s=0 then Eq else if s<0 then Lt else Gt".
+
+Extract Inlined Constant Compare_dec.leb => "Big_int.le_big_int".
+Extract Inlined Constant Compare_dec.le_lt_dec => "Big_int.le_big_int".
+Extract Constant Compare_dec.lt_eq_lt_dec =>
+"fun n m ->
+ let s = Big_int.sign_big_int n m in
+ if s>0 then None else Some (s<0)".
+
+Extract Constant Even.even_odd_dec =>
+ "fun n -> Big_int.sign_big_int (Big_int.mod_big_int n (Big_int.big_int_of_int 2)) = 0".
+Extract Constant Div2.div2 =>
+ "fun n -> Big_int.div_big_int n (Big_int.big_int_of_int 2)".
+
+Extract Inductive Euclid.diveucl => "(Big_int.big_int * Big_int.big_int)" [""].
+Extract Constant Euclid.eucl_dev => "fun n m -> Big_int.quomod_big_int m n".
+Extract Constant Euclid.quotient => "fun n m -> Big_int.div_big_int m n".
+Extract Constant Euclid.modulo => "fun n m -> Big_int.mod_big_int m n".
+
+(*
+Definition test n m (H:m>0) :=
+ let (q,r,_,_) := eucl_dev m H n in
+ nat_compare n (q*m+r).
+
+Recursive Extraction test fact.
+*)