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

q_cert_of_pos prf converts a Sos proof into a rational Coq proof

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.