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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 [positive], [N] and [Z] into Ocaml's [big_int] *)
Require Import ZArith NArith ZOdiv_def.
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 [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 Pplus => "Big.add".
Extract Constant Psucc => "Big.succ".
Extract Constant Ppred => "fun n -> Big.max Big.one (Big.pred n)".
Extract Constant Pminus => "fun n m -> Big.max Big.one (Big.sub n m)".
Extract Constant Pmult => "Big.mult".
Extract Constant Pmin => "Big.min".
Extract Constant Pmax => "Big.max".
Extract Constant Pcompare =>
"fun x y c -> Big.compare_case c Lt Gt x y".
Extract Constant Nplus => "Big.add".
Extract Constant Nsucc => "Big.succ".
Extract Constant Npred => "fun n -> Big.max Big.zero (Big.pred n)".
Extract Constant Nminus => "fun n m -> Big.max Big.zero (Big.sub n m)".
Extract Constant Nmult => "Big.mult".
Extract Constant Nmin => "Big.min".
Extract Constant Nmax => "Big.max".
Extract Constant Ndiv =>
"fun a b -> if Big.eq b Big.zero then Big.zero else Big.div a b".
Extract Constant Nmod =>
"fun a b -> if Big.eq b Big.zero then Big.zero else Big.modulo a b".
Extract Constant Ncompare => "Big.compare_case Eq Lt Gt".
Extract Constant Zplus => "Big.add".
Extract Constant Zsucc => "Big.succ".
Extract Constant Zpred => "Big.pred".
Extract Constant Zminus => "Big.sub".
Extract Constant Zmult => "Big.mult".
Extract Constant Zopp => "Big.opp".
Extract Constant Zabs => "Big.abs".
Extract Constant Zmin => "Big.min".
Extract Constant Zmax => "Big.max".
Extract Constant Zcompare => "Big.compare_case Eq Lt Gt".
Extract Constant Z_of_N => "fun p -> p".
Extract Constant Zabs_N => "Big.abs".
(** Zdiv and Zmod 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"
Pplus Ppred Pminus Pmult Pcompare Npred Nminus Ndiv Nmod Ncompare
Zplus Zmult BinInt.Zcompare Z_of_N Zabs_N Zdiv.Zdiv Zmod.
*)
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