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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
(* \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 MinMax Euclid.
Require Import ExtrOcamlBasic.
(** NB: The extracted code should be linked with [nums.cm(x)a]
from ocaml's stdlib and with the wrapper [big.ml] that
simlifies the use of [Big_int] (it could be found in the sources
of Coq). *)
(** 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.big_int" [ "Big.zero" "Big.succ" ]
"Big.nat_case".
(** Efficient (but uncertified) versions for usual [nat] functions *)
Extract Constant plus => "Big.add".
Extract Constant mult => "Big.mult".
Extract Constant pred => "fun n -> Big.max Big.zero (Big.pred n)".
Extract Constant minus => "fun n m -> Big.max Big.zero (Big.sub n m)".
Extract Constant max => "Big.max".
Extract Constant min => "Big.min".
Extract Constant nat_beq => "Big.eq".
Extract Constant EqNat.beq_nat => "Big.eq".
Extract Constant EqNat.eq_nat_decide => "Big.eq".
Extract Constant Peano_dec.eq_nat_dec => "Big.eq".
Extract Constant Compare_dec.nat_compare =>
"Big.compare_case Eq Lt Gt".
Extract Constant Compare_dec.leb => "Big.le".
Extract Constant Compare_dec.le_lt_dec => "Big.le".
Extract Constant Compare_dec.lt_eq_lt_dec =>
"Big.compare_case (Some false) (Some true) None".
Extract Constant Even.even_odd_dec =>
"fun n -> Big.sign (Big.mod n Big.two) = 0".
Extract Constant Div2.div2 => "fun n -> Big.div n Big.two".
Extract Inductive Euclid.diveucl => "(Big.big_int * Big.big_int)" [""].
Extract Constant Euclid.eucl_dev => "fun n m -> Big.quomod m n".
Extract Constant Euclid.quotient => "fun n m -> Big.div m n".
Extract Constant Euclid.modulo => "fun n m -> Big.modulo m n".
(*
Require Import Euclid.
Definition test n m (H:m>0) :=
let (q,r,_,_) := eucl_dev m H n in
nat_compare n (q*m+r).
Extraction "/tmp/test.ml" test fact pred minus max min Div2.div2.
*)
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