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(*       ___                                                              *)
(*      ||M||                                                             *)
(*      ||A||       A project by Andrea Asperti                           *)
(*      ||T||                                                             *)
(*      ||I||       Developers:                                           *)
(*      ||T||         The HELM team.                                      *)
(*      ||A||         http://helm.cs.unibo.it                             *)
(*      \   /                                                             *)
(*       \ /        This file is distributed under the terms of the       *)
(*        v         GNU General Public License Version 2                  *)
(*                                                                        *)
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include "RTLabs/RTLabsToRTL.ma".
include "common/StatusSimulation.ma".
include "joint/Traces.ma".
include "RTLabs/RTLabs_abstract.ma".
include "RTL/RTL_semantics.ma".
include "RTLabs/MeasurableToStructured.ma". (* for make_ext_initial_state *)

definition RTLabsToRTLstacksizes_ok : (ident → option ℕ) → RTLabs_program → Prop ≝
λstack_sizes,p.
All …
  (λi_f.let 〈i, f〉 ≝ i_f in
    match f with
    [ External _ ⇒ True
    | Internal def ⇒
      ∃sz.stack_sizes i = Some ? sz ∧ f_stacksize … def ≤ sz
    ]) (prog_funct … p).

axiom RTLabsToRTL_ok :
∀stacksizes : ident → option ℕ.
∀cost.
∀p_in : RTLabs_program.
RTLabsToRTLstacksizes_ok stacksizes p_in →
let p_out ≝ rtlabs_to_rtl cost p_in in
∀init_in.make_ext_initial_state p_in = OK … init_in →
∃init_out : state_pc RTL_semantics_separate.
  make_initial_state
   (mk_prog_params RTL_semantics_separate p_out stacksizes) =
    OK ? init_out ∧
∃[1] R.
  status_simulation_with_init
    (RTLabs_status (make_global … p_in))
    (joint_status RTL_semantics_separate p_out stacksizes) R
    init_in init_out.