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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 to Ocaml: conversion from/to [int]
+
+ Nota: no check that [int] values aren't generating overflows *)
+
+Require Import Arith ZArith.
+
+Parameter int : Type.
+Parameter int_zero : int.
+Parameter int_succ : int -> int.
+Parameter int_opp : int -> int.
+Parameter int_twice : int -> int.
+
+Extract Inlined Constant int => int.
+Extract Inlined Constant int_zero => "0".
+Extract Inlined Constant int_succ => "succ".
+Extract Inlined Constant int_opp => "-".
+Extract Inlined Constant int_twice => "2 *".
+
+Definition int_of_nat : nat -> int :=
+ (fix loop acc n :=
+ match n with
+ | O => acc
+ | S n => loop (int_succ acc) n
+ end) int_zero.
+
+Fixpoint int_of_pos p :=
+ match p with
+ | xH => int_succ int_zero
+ | xO p => int_twice (int_of_pos p)
+ | xI p => int_succ (int_twice (int_of_pos p))
+ end.
+
+Fixpoint int_of_z z :=
+ match z with
+ | Z0 => int_zero
+ | Zpos p => int_of_pos p
+ | Zneg p => int_opp (int_of_pos p)
+ end.
+
+Fixpoint int_of_n n :=
+ match n with
+ | N0 => int_zero
+ | Npos p => int_of_pos p
+ end.
+
+(** NB: as for [pred] or [minus], [nat_of_int], [n_of_int] and
+ [pos_of_int] are total and return zero (resp. one) for
+ non-positive inputs. *)
+
+Parameter int_natlike_rec : forall A, A -> (A->A) -> int -> A.
+Extract Constant int_natlike_rec =>
+"fun fO fS ->
+ let rec loop acc i = if i <= 0 then acc else loop (fS acc) (i-1)
+ in loop fO".
+
+Definition nat_of_int : int -> nat := int_natlike_rec _ O S.
+
+Parameter int_poslike_rec : forall A, A -> (A->A) -> (A->A) -> int -> A.
+Extract Constant int_poslike_rec =>
+"fun f1 f2x f2x1 ->
+ let rec loop i = if i <= 1 then f1 else
+ if i land 1 = 0 then f2x (loop (i lsr 1)) else f2x1 (loop (i lsr 1))
+ in loop".
+
+Definition pos_of_int : int -> positive := int_poslike_rec _ xH xO xI.
+
+Parameter int_zlike_case : forall A, A -> (int->A) -> (int->A) -> int -> A.
+Extract Constant int_zlike_case =>
+"fun f0 fpos fneg i ->
+ if i = 0 then f0 else if i>0 then fpos i else fneg (-i)".
+
+Definition z_of_int : int -> Z :=
+ int_zlike_case _ Z0 (fun i => Zpos (pos_of_int i))
+ (fun i => Zneg (pos_of_int i)).
+
+Definition n_of_int : int -> N :=
+ int_zlike_case _ N0 (fun i => Npos (pos_of_int i)) (fun _ => N0).
+
+(** Warning: [z_of_int] is currently wrong for Ocaml's [min_int],
+ since [min_int] has no positive opposite ([-min_int = min_int]).
+*)
+
+(*
+Extraction "/tmp/test.ml"
+ nat_of_int int_of_nat
+ pos_of_int int_of_pos
+ z_of_int int_of_z
+ n_of_int int_of_n.
+*) \ No newline at end of file