Module `Micromega_plugin.Certificate`

module Mc = Micromega

val use_simplex : bool Stdlib.ref: use_simplex is bound to the Coq option Simplex. If set, use the Simplex method, otherwise use Fourier

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

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

val q_cert_of_pos : Sos_types.positivstellensatz -> Mc.q Mc.psatz: q_cert_of_pos prf converts a Sos proof into a rational Coq proof

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

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

val nlinear_prover : 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.