Library mcertikos.mm.ContainerGenSpec


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.

Require Import AbstractDataType.
Require Import MContainerIntro.

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

Definition of the refinement relation

Section CONTAINERGEN_DEFINE.

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

  Notation LDATAOps := (cdata RData).

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

  Function container_split_low_spec (id: Z) (q: Z) (adt: RData) : option (RData×Z) :=
    if zle_lt 0 id num_proc then
      if zle (cquota (ZMap.get id (AC adt))) Int.max_unsigned then
        if zle_le 0 (cusage (ZMap.get id (AC adt))) (cquota (ZMap.get id (AC adt))) then
          let c := ZMap.get id (AC adt) in
          let i := id × max_children + 1 + Z_of_nat (length (cchildren c)) in
          match (init adt, ikern adt, ihost adt, cused c, cused (ZMap.get i (AC adt)), zle_lt 0 i num_proc,
                 zlt (Z_of_nat (length (cchildren c))) max_children,
                 zle_le 0 q (cquota c - cusage c)) with
          | (true, true, true, true, false, left _, left _, left _)
            let child := mkContainer q 0 id nil true in
            let cur := mkContainer (cquota c) (cusage c + q) (cparent c)
                                   (i :: cchildren c) (cused c) in
            Some (adt {AC: ZMap.set i child (ZMap.set id cur (AC adt))}, i)
          | _None
          end
        else None
      else None
    else None.

  Inductive container_split_low_step `{StencilOps} `{Mem.MemoryModelOps} `{UseMemWithData mem}:
    sextcall_sem (mem := mwd LDATAOps) :=
  | container_split_low_intro s (WB: _Prop) m´0 labd labd´ i n c:
      container_split_low_spec (Int.unsigned i) (Int.unsigned n) labd = Some (labd´, c)
      kernel_mode labd
      high_level_invariant labd
      container_split_low_step s WB (Vint i :: Vint n :: nil) (m´0, labd) (Vint (Int.repr c)) (m´0, labd´).


  Section WITHMEM.

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

    Definition container_init_spec_low: compatsem LDATAOps :=
      csem container_init_low_step (type_of_list_type (Tint32::nil)) Tvoid.
    Definition container_split_spec_low: compatsem LDATAOps :=
      csem container_split_low_step (type_of_list_type (Tint32::Tint32::nil)) Tint32.

  End WITHMEM.


End CONTAINERGEN_DEFINE.