(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

module Mc = Micromega


(** [use_simplex] is bound to the Coq option Simplex.
    If set, use the Simplex method, otherwise use Fourier *)
val use_simplex : bool ref

type ('prf,'model) res =
   | Prf of 'prf
   | Model of 'model
   | Unknown

type zres = (Mc.zArithProof , (int * Mc.z  list)) res

type qres = (Mc.q Mc.psatz , (int * Mc.q  list)) res

(** [dump_file] is bound to the Coq option Dump Arith.
    If set to some [file], arithmetic goals are dumped in filexxx.v *)
val dump_file : string option ref

(** [q_cert_of_pos prf] converts a Sos proof into a rational Coq proof *)
val q_cert_of_pos : Sos_types.positivstellensatz -> Mc.q Mc.psatz

(** [z_cert_of_pos prf] converts a Sos proof into an integer Coq proof *)
val z_cert_of_pos : Sos_types.positivstellensatz -> Mc.z Mc.psatz

(** [lia enum depth sys] generates an unsat proof for the linear constraints in [sys].
    If the Simplex option is set, any failure to find a proof should be considered as a bug. *)
val lia : bool -> int -> (Mc.z Mc.pExpr * Mc.op1) list -> zres

(** [nlia enum depth sys] generates an unsat proof for the non-linear constraints in [sys].
    The solver is incomplete -- the problem is undecidable *)
val nlia : bool -> int -> (Mc.z Mc.pExpr * Mc.op1) list -> zres

(** [linear_prover_with_cert depth sys] generates an unsat proof for the linear constraints in [sys].
    Over the rationals, the solver is complete. *)
val linear_prover_with_cert : int -> (Mc.q Mc.pExpr * Mc.op1) list -> qres

(** [nlinear depth sys] generates an unsat proof for the non-linear constraints in [sys].
    The solver is incompete -- the problem is decidable. *)
val nlinear_prover : int -> (Mc.q Mc.pExpr * Mc.op1) list -> qres