Module `Micromega_plugin.Certificate`

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

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 : int -> (Mc.z Mc.pExpr * Mc.op1) list -> zres: lia depth sys generates an unsat proof for the linear constraints in sys.

val nlia : 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 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.