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(************************************************************************)
(* * The Rocq Prover / The Rocq Development Team *)
(* v * Copyright INRIA, CNRS and contributors *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(* \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
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
(** [q_cert_of_pos prf] converts a Sos proof into a rational Rocq 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 Rocq proof *)
val z_cert_of_pos : Sos_types.positivstellensatz -> Mc.z Mc.psatz
(** [lia depth sys] generates an unsat proof for the linear constraints in [sys]. *)
val lia : int -> (Mc.z Mc.pExpr * Mc.op1) list -> zres
(** [nlia depth sys] generates an unsat proof for the non-linear constraints in [sys].
The solver is incomplete -- the problem is undecidable *)
val nlia : 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
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