Module Polynomial.ProofFormat

Proof format used by the proof-generating procedures. It is fairly close to Coq format but a bit more liberal.

It is used for proofs over Z, Q, R. However, certain constructions e.g. CutPrf are only relevant for Z.

type prf_rule =
| Annot of string * prf_rule
| Hyp of int
| Def of int
| Ref of int
| Cst of NumCompat.Q.t
| Zero
| Square of Vect.t
| MulC of Vect.t * prf_rule
| Gcd of NumCompat.Z.t * prf_rule
| MulPrf of prf_rule * prf_rule
| AddPrf of prf_rule * prf_rule
| CutPrf of prf_rule
| LetPrf of prf_rule * prf_rule
type proof =
| Done
| Step of int * prf_rule * proof
| Split of int * Vect.t * proof * proof
| Enum of int * prf_rule * Vect.t * prf_rule * proof list
| ExProof of int * int * int * var * var * var * proof
val pr_size : prf_rule -> NumCompat.Q.t
val pr_rule_max_def : prf_rule -> int
val pr_rule_max_hyp : prf_rule -> int
val proof_max_def : proof -> int
val normalise_proof : int -> proof -> int * proof
val output_prf_rule : Stdlib.out_channel -> prf_rule -> unit
val output_proof : Stdlib.out_channel -> proof -> unit
val add_proof : prf_rule -> prf_rule -> prf_rule
val mul_cst_proof : NumCompat.Q.t -> prf_rule -> prf_rule
val mul_proof : prf_rule -> prf_rule -> prf_rule
val compile_proof : int list -> proof -> Micromega.zArithProof
module Env : sig ... end
val cmpl_prf_rule : ( 'a Micromega.pExpr -> 'a Micromega.pol ) -> ( NumCompat.Q.t -> 'a ) -> Env.t -> prf_rule -> 'a Micromega.psatz
val proof_of_farkas : prf_rule Mutils.IMap.t -> Vect.t -> prf_rule
val eval_prf_rule : ( int -> LinPoly.t * op ) -> prf_rule -> LinPoly.t * op
val eval_proof : (LinPoly.t * op) Mutils.IMap.t -> proof -> bool
val simplify_proof : proof -> proof * Mutils.ISet.t
module PrfRuleMap : Stdlib.Map.S with type key = prf_rule