(** * Phase 7f: Proof-Carrying Code Verifier Specification
     
    Formalizes the on-chip verification logic that validates
    program certificates before execution.
*)

From Coq Require Import PeanoNat.
From Coq Require Import List.
From Coq Require Import Bool.
From Coq Require Import ZArith.
Import ListNotations.

(** ** Hardware Capacity Constants (NASA P10) *)

Definition MAX_INSTRUCTIONS : nat := 1024.
Definition MAX_REGISTERS    : nat := 256.
Definition MAX_GUARDS       : nat := 32.

(** ** Certificate Structure *)

Record PropertyVerdict : Type := {
  pv_name : string;
  pv_verified : bool
}.

Record ProofCertificate : Type := {
  pc_program_hash     : list Z;
  pc_instr_count      : nat;
  pc_reg_count        : nat;
  pc_guard_count      : nat;
  pc_property_verdicts : list PropertyVerdict
}.

(** ** Verification Logic *)

Definition verify_bounds (cert : ProofCertificate) : bool :=
  (cert.(pc_instr_count) <=? MAX_INSTRUCTIONS) &&
  (cert.(pc_reg_count) <=? MAX_REGISTERS) &&
  (cert.(pc_guard_count) <=? MAX_GUARDS).

Definition all_properties_verified (pvs : list PropertyVerdict) : bool :=
  forallb (fun pv => pv.(pv_verified)) pvs.

Definition verify_certificate (cert : ProofCertificate) : bool :=
  (verify_bounds cert) && (all_properties_verified cert.(pc_property_verdicts)).

(** ** Correctness Invariants *)

Theorem verified_cert_obeys_instr_limit : forall cert,
  verify_certificate cert = true ->
  cert.(pc_instr_count) <= MAX_INSTRUCTIONS.
Proof.
  intros cert H.
  unfold verify_certificate in H.
  apply andb_true_iff in H. destruct H as [Hb Hp].
  unfold verify_bounds in Hb.
  apply andb_true_iff in Hb. destruct Hb as [Hi Hr].
  apply andb_true_iff in Hi. destruct Hi as [Hi Hg].
  apply leb_complete. assumption.
Qed.

Theorem verified_cert_obeys_reg_limit : forall cert,
  verify_certificate cert = true ->
  cert.(pc_reg_count) <= MAX_REGISTERS.
Proof.
  intros cert H.
  unfold verify_certificate in H.
  apply andb_true_iff in H. destruct H as [Hb Hp].
  unfold verify_bounds in Hb.
  apply andb_true_iff in Hb. destruct Hb as [Hi Hr].
  apply andb_true_iff in Hi. destruct Hi as [Hi Hg].
  apply leb_complete. assumption.
Qed.
