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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(** Extraction of [positive], [N] and [Z] into Ocaml's [big_int] *)
Require Import ZArith NArith.
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
simplifies the use of [Big_int] (it can be found in the sources
of Coq). *)
(** Disclaimer: trying to obtain efficient certified programs
by extracting [Z] into [big_int] isn't necessarily a good idea.
See the Disclaimer in [ExtrOcamlNatInt]. *)
(** Mapping of [positive], [Z], [N] into [big_int]. The last strings
emulate the matching, see documentation of [Extract Inductive]. *)
Extract Inductive positive => "Big.big_int"
[ "Big.doubleplusone" "Big.double" "Big.one" ] "Big.positive_case".
Extract Inductive Z => "Big.big_int"
[ "Big.zero" "" "Big.opp" ] "Big.z_case".
Extract Inductive N => "Big.big_int"
[ "Big.zero" "" ] "Big.n_case".
(** Nota: the "" above is used as an identity function "(fun p->p)" *)
(** Efficient (but uncertified) versions for usual functions *)
Extract Constant Pos.add => "Big.add".
Extract Constant Pos.succ => "Big.succ".
Extract Constant Pos.pred => "fun n -> Big.max Big.one (Big.pred n)".
Extract Constant Pos.sub => "fun n m -> Big.max Big.one (Big.sub n m)".
Extract Constant Pos.mul => "Big.mult".
Extract Constant Pos.min => "Big.min".
Extract Constant Pos.max => "Big.max".
Extract Constant Pos.compare =>
"fun x y -> Big.compare_case Eq Lt Gt x y".
Extract Constant Pos.compare_cont =>
"fun x y c -> Big.compare_case c Lt Gt x y".
Extract Constant N.add => "Big.add".
Extract Constant N.succ => "Big.succ".
Extract Constant N.pred => "fun n -> Big.max Big.zero (Big.pred n)".
Extract Constant N.sub => "fun n m -> Big.max Big.zero (Big.sub n m)".
Extract Constant N.mul => "Big.mult".
Extract Constant N.min => "Big.min".
Extract Constant N.max => "Big.max".
Extract Constant N.div =>
"fun a b -> if Big.eq b Big.zero then Big.zero else Big.div a b".
Extract Constant N.modulo =>
"fun a b -> if Big.eq b Big.zero then Big.zero else Big.modulo a b".
Extract Constant N.compare => "Big.compare_case Eq Lt Gt".
Extract Constant Z.add => "Big.add".
Extract Constant Z.succ => "Big.succ".
Extract Constant Z.pred => "Big.pred".
Extract Constant Z.sub => "Big.sub".
Extract Constant Z.mul => "Big.mult".
Extract Constant Z.opp => "Big.opp".
Extract Constant Z.abs => "Big.abs".
Extract Constant Z.min => "Big.min".
Extract Constant Z.max => "Big.max".
Extract Constant Z.compare => "Big.compare_case Eq Lt Gt".
Extract Constant Z.of_N => "fun p -> p".
Extract Constant Z.abs_N => "Big.abs".
(** Z.div and Z.modulo are quite complex to define in terms of (/) and (mod).
For the moment we don't even try *)
(** Test:
Require Import ZArith NArith.
Extraction "/tmp/test.ml"
Pos.add Pos.pred Pos.sub Pos.mul Pos.compare N.pred N.sub N.div N.modulo N.compare
Z.add Z.mul Z.compare Z.of_N Z.abs_N Z.div Z.modulo.
*)
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