Library mcertikos.mm.PTNewGenSpec


This file provide the contextual refinement proof between MBoot layer and MALInit layer
Require Import Coqlib.
Require Import Errors.
Require Import AST.
Require Import Integers.
Require Import Floats.
Require Import Op.
Require Import Asm.
Require Import Events.
Require Import Globalenvs.
Require Import Smallstep.
Require Import Values.
Require Import Memory.
Require Import Maps.
Require Import AuxLemma.
Require Import FlatMemory.
Require Import AuxStateDataType.
Require Import Constant.
Require Import GlobIdent.
Require Import RealParams.
Require Import AsmImplLemma.
Require Import GenSem.
Require Import PrimSemantics.

Require Import MPTInit.
Require Import AbstractDataType.

Require Import liblayers.logic.PTreeModules.
Require Import liblayers.logic.LayerLogicImpl.
Require Import liblayers.compcertx.Stencil.
Require Import liblayers.compcertx.MakeProgram.
Require Import liblayers.compat.CompatLayers.
Require Import liblayers.compat.CompatGenSem.
Require Import compcert.cfrontend.Ctypes.

Local Open Scope string_scope.
Local Open Scope error_monad_scope.
Local Open Scope Z_scope.

Definition of the refinement relation

Section PTBITGEN_DEFINE.

  Context `{real_params: RealParams}.
  Context `{oracle_prop: MultiOracleProp}.

  Notation LDATA := RData.

  Notation LDATAOps := (cdata LDATA).

  Inductive pmap_init_spec_low_step `{StencilOps} `{Mem.MemoryModelOps} `{UseMemWithData mem}:
    sextcall_sem (mem := mwd LDATAOps):=
  | pmap_init_spec_low_intro s (WB: _Prop) m´0 labd labd´ mbi_adr:
      pmap_init_spec (Int.unsigned mbi_adr) labd = Some labd´
      kernel_mode labd
      high_level_invariant labd
      pmap_init_spec_low_step s WB (Vint mbi_adr :: nil) (m´0, labd) Vundef (m´0, labd´).


  Inductive ptResv_spec_low_step `{StencilOps} `{Mem.MemoryModelOps} `{UseMemWithData mem}:
    sextcall_sem (mem := mwd LDATAOps):=
  | ptResv_spec_low_intro s (WB: _Prop) m´0 labd labd´ n vadr p r:
      ptResv_spec (Int.unsigned n) (Int.unsigned vadr) (Int.unsigned p) labd =
      Some (labd´, Int.unsigned r)
      kernel_mode labd
      high_level_invariant labd
      ptResv_spec_low_step s WB (Vint n :: Vint vadr :: Vint p :: nil) (m´0, labd) (Vint r) (m´0, labd´).

  Inductive ptResv2_spec_low_step `{StencilOps} `{Mem.MemoryModelOps} `{UseMemWithData mem}:
    sextcall_sem (mem := mwd LDATAOps):=
  | ptResv2_spec_low_intro s (WB: _Prop) m´0 labd labd´ n vadr p vadr´ r:
      ptResv2_spec (Int.unsigned n) (Int.unsigned vadr) (Int.unsigned p)
                          (Int.unsigned ) (Int.unsigned vadr´) (Int.unsigned ) labd =
      Some (labd´, Int.unsigned r)
      kernel_mode labd
      high_level_invariant labd
      ptResv2_spec_low_step s WB (Vint n :: Vint vadr :: Vint p :: Vint :: Vint vadr´ :: Vint :: nil)
                            (m´0, labd) (Vint r) (m´0, labd´).

  Inductive pt_new_spec_low_step `{StencilOps} `{Mem.MemoryModelOps} `{UseMemWithData mem}:
    sextcall_sem (mem := mwd LDATAOps):=
  | pt_new_spec_low_intro s (WB: _Prop) m´0 labd labd´ id q n:
      pt_new_spec (Int.unsigned id) (Int.unsigned q) labd = Some (labd´, Int.unsigned n)

      kernel_mode labd
      high_level_invariant labd
      pt_new_spec_low_step s WB (Vint id :: Vint q :: nil) (m´0, labd) (Vint n) (m´0, labd´).

  Section WITHMEM.

    Context `{Hstencil: Stencil}.
    Context `{Hmem: Mem.MemoryModel}.
    Context `{Hmwd: UseMemWithData mem}.

    Definition pmap_init_spec_low: compatsem LDATAOps :=
      csem pmap_init_spec_low_step (type_of_list_type (Tint32::nil)) Tvoid.


    Definition ptResv_spec_low: compatsem LDATAOps :=
      csem ptResv_spec_low_step (type_of_list_type (Tint32::Tint32::Tint32::nil)) Tint32.

    Definition ptResv2_spec_low: compatsem LDATAOps :=
      csem ptResv2_spec_low_step
           (type_of_list_type (Tint32::Tint32::Tint32::Tint32::Tint32::Tint32::nil))
           Tint32.

    Definition pt_new_spec_low: compatsem LDATAOps :=
      csem pt_new_spec_low_step (type_of_list_type (Tint32::Tint32::nil)) Tint32.

  End WITHMEM.

End PTBITGEN_DEFINE.