From 5b7eafd0f00a16d78f99a27f5c7d5a0de77dc7e6 Mon Sep 17 00:00:00 2001
From: Stephane Glondu <steph@glondu.net>
Date: Wed, 21 Jul 2010 09:46:51 +0200
Subject: Imported Upstream snapshot 8.3~beta0+13298

---
 plugins/extraction/ExtrOcamlNatInt.v | 75 ++++++++++++++++++++++++++++++++++++
 1 file changed, 75 insertions(+)
 create mode 100644 plugins/extraction/ExtrOcamlNatInt.v

(limited to 'plugins/extraction/ExtrOcamlNatInt.v')

diff --git a/plugins/extraction/ExtrOcamlNatInt.v b/plugins/extraction/ExtrOcamlNatInt.v
new file mode 100644
index 00000000..fe03bc60
--- /dev/null
+++ b/plugins/extraction/ExtrOcamlNatInt.v
@@ -0,0 +1,75 @@
+(************************************************************************)
+(*  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 [int] *)
+
+Require Import Arith Even Div2 EqNat MinMax Euclid.
+Require Import ExtrOcamlBasic.
+
+(** Disclaimer: trying to obtain efficient certified programs
+    by extracting [nat] into [int] is definitively *not* a good idea:
+
+    - Since [int] is bounded while [nat] is (theoretically) infinite,
+    you have to make sure by yourself that your program will not
+    manipulate numbers greater than [max_int]. Otherwise you should
+    consider the translation of [nat] into [big_int].
+
+    - Moreover, the mere translation of [nat] into [int] does not
+    change the complexity of functions. For instance, [mult] stays
+    quadratic. To mitigate this, we propose here a few efficient (but
+    uncertified) realizers for some common functions over [nat].
+
+    This file is hence provided mainly for testing / prototyping
+    purpose. For serious use of numbers in extracted programs,
+    you are advised to use either coq advanced representations
+    (positive, Z, N, BigN, BigZ) or modular/axiomatic representation.
+*)
+
+
+(** Mapping of [nat] into [int]. The last string corresponds to
+    a [nat_case], see documentation of [Extract Inductive]. *)
+
+Extract Inductive nat => int [ "0" "succ" ]
+ "(fun fO fS n -> if n=0 then fO () else fS (n-1))".
+
+(** Efficient (but uncertified) versions for usual [nat] functions *)
+
+Extract Constant plus => "(+)".
+Extract Constant pred => "fun n -> max 0 (n-1)".
+Extract Constant minus => "fun n m -> max 0 (n-m)".
+Extract Constant mult => "( * )".
+Extract Inlined Constant max => max.
+Extract Inlined Constant min => min.
+Extract Inlined Constant nat_beq => "(=)".
+Extract Inlined Constant EqNat.beq_nat => "(=)".
+Extract Inlined Constant EqNat.eq_nat_decide => "(=)".
+
+Extract Inlined Constant Peano_dec.eq_nat_dec => "(=)".
+
+Extract Constant Compare_dec.nat_compare =>
+ "fun n m -> if n=m then Eq else if n<m then Lt else Gt".
+Extract Inlined Constant Compare_dec.leb => "(<=)".
+Extract Inlined Constant Compare_dec.le_lt_dec => "(<=)".
+Extract Constant Compare_dec.lt_eq_lt_dec =>
+ "fun n m -> if n>m then None else Some (n<m)".
+
+Extract Constant Even.even_odd_dec => "fun n -> n mod 2 = 0".
+Extract Constant Div2.div2 => "fun n -> n/2".
+
+Extract Inductive Euclid.diveucl => "(int * int)" [ "" ].
+Extract Constant Euclid.eucl_dev => "fun n m -> (m/n, m mod n)".
+Extract Constant Euclid.quotient => "fun n m -> m/n".
+Extract Constant Euclid.modulo => "fun n m -> m mod 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.
+*)
\ No newline at end of file
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