Library mcertikos.mcslock.MCSLockOpGenSpec

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 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.

Require Import AbstractDataType.
Require Import MMCSLockAbsIntro.

Definition of the refinement relation

Section MCSLOCKOP_DEFINE.

  Context `{real_params: RealParams}.
  Context `{mcs_oracle_prop: MCSOracleProp}.

  Context `{faireness: WaitTime}.

  Notation LDATAOps := (cdata RData).

  Inductive mcs_pass_lock_spec_low_step `{StencilOps} `{Mem.MemoryModelOps} `{UseMemWithData mem}:
    sextcall_sem (mem := mwd LDATAOps):=
  | mcs_pass_lock_spec_low_intro s (WB: _Prop) m´0 labd labd´ i ofs:
      mcs_pass_lock_spec (Int.unsigned i) (Int.unsigned ofs) labd = Some labd´
      kernel_mode labd
      high_level_invariant labd
      mcs_pass_lock_spec_low_step s WB (Vint i :: Vint ofs :: nil) (m´0, labd) Vundef (m´0, labd´).

  Inductive mcs_wait_lock_spec_low_step `{StencilOps} `{Mem.MemoryModelOps} `{UseMemWithData mem}:
    sextcall_sem (mem := mwd LDATAOps):=
  | wait_lock_spec_low_intro s (WB: _Prop) m´0 labd labd´ bound i ofs:
      mcs_wait_lock_spec (Int.unsigned bound) (Int.unsigned i) (Int.unsigned ofs) labd = Some labd´
      kernel_mode labd
      high_level_invariant labd
      mcs_wait_lock_spec_low_step s WB (Vint bound :: Vint i :: Vint ofs :: nil) (m´0, labd)
                                  Vundef (m´0, labd´).

  Section WITHMEM.

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

    Definition mcs_wait_lock_spec_low: compatsem LDATAOps :=
      csem mcs_wait_lock_spec_low_step (type_of_list_type (Tint32::Tint32::Tint32::nil)) Tvoid.

    Definition mcs_pass_lock_spec_low: compatsem LDATAOps :=
      csem mcs_pass_lock_spec_low_step (type_of_list_type (Tint32::Tint32::nil)) Tvoid.

  End WITHMEM.

End MCSLOCKOP_DEFINE.