Library mcertikos.mm.ShareIntroGenDef
This file provide the contextual refinement proof between PKContextNew layer and PThreadIntro layer
Require Export Coqlib.
Require Export Errors.
Require Export AST.
Require Export Integers.
Require Export Floats.
Require Export Op.
Require Export Asm.
Require Export Events.
Require Export Globalenvs.
Require Export Smallstep.
Require Export Values.
Require Export Memory.
Require Export Maps.
Require Export CommonTactic.
Require Export AuxLemma.
Require Export FlatMemory.
Require Export AuxStateDataType.
Require Export Constant.
Require Export GlobIdent.
Require Export RealParams.
Require Export LoadStoreSem2.
Require Export AsmImplLemma.
Require Export GenSem.
Require Export RefinementTactic.
Require Export PrimSemantics.
Require Export XOmega.
Require Export liblayers.logic.PTreeModules.
Require Export liblayers.logic.LayerLogicImpl.
Require Export liblayers.compcertx.Stencil.
Require Export liblayers.compcertx.MakeProgram.
Require Export liblayers.compat.CompatLayers.
Require Export liblayers.compat.CompatGenSem.
Require Export compcert.cfrontend.Ctypes.
Require Export AbstractDataType.
Require Export LayerCalculusLemma.
Require Export MShareIntro.
Require Export MPTNew.
Open Scope string_scope.
Open Scope error_monad_scope.
Open Scope Z_scope.
Notation HDATA := RData.
Notation LDATA := RData.
Notation HDATAOps := (cdata (cdata_ops := mshareintro_data_ops) HDATA).
Notation LDATAOps := (cdata (cdata_ops := mptinit_data_ops) LDATA).
Require Export Errors.
Require Export AST.
Require Export Integers.
Require Export Floats.
Require Export Op.
Require Export Asm.
Require Export Events.
Require Export Globalenvs.
Require Export Smallstep.
Require Export Values.
Require Export Memory.
Require Export Maps.
Require Export CommonTactic.
Require Export AuxLemma.
Require Export FlatMemory.
Require Export AuxStateDataType.
Require Export Constant.
Require Export GlobIdent.
Require Export RealParams.
Require Export LoadStoreSem2.
Require Export AsmImplLemma.
Require Export GenSem.
Require Export RefinementTactic.
Require Export PrimSemantics.
Require Export XOmega.
Require Export liblayers.logic.PTreeModules.
Require Export liblayers.logic.LayerLogicImpl.
Require Export liblayers.compcertx.Stencil.
Require Export liblayers.compcertx.MakeProgram.
Require Export liblayers.compat.CompatLayers.
Require Export liblayers.compat.CompatGenSem.
Require Export compcert.cfrontend.Ctypes.
Require Export AbstractDataType.
Require Export LayerCalculusLemma.
Require Export MShareIntro.
Require Export MPTNew.
Open Scope string_scope.
Open Scope error_monad_scope.
Open Scope Z_scope.
Notation HDATA := RData.
Notation LDATA := RData.
Notation HDATAOps := (cdata (cdata_ops := mshareintro_data_ops) HDATA).
Notation LDATAOps := (cdata (cdata_ops := mptinit_data_ops) LDATA).
Section Refinement.
Section WITHMEM.
Context `{Hstencil: Stencil}.
Context `{Hmem: Mem.MemoryModelX}.
Context `{Hmwd: UseMemWithData mem}.
Context `{multi_oracle_prop: MultiOracleProp}.
Context `{real_params: RealParams}.
Section WITHMEM.
Context `{Hstencil: Stencil}.
Context `{Hmem: Mem.MemoryModelX}.
Context `{Hmwd: UseMemWithData mem}.
Context `{multi_oracle_prop: MultiOracleProp}.
Context `{real_params: RealParams}.
Section REFINEMENT_REL.
Inductive match_SharedMem: SharedMemState → val → val → val→ Prop :=
| MATCH_SharedMemUNDEF:
∀ v1 v2 v3, match_SharedMem SHRDUndef v1 v2 v3
| MATCH_SharedMemVALID:
∀ v1 v2 v3 si b,
Z2SharedMemInfo (Int.unsigned v1) = Some si →
ZtoBool (Int.unsigned v2) = Some b →
match_SharedMem (SHRDValid si b (Int.unsigned v3)) (Vint v3) (Vint v1) (Vint v2).
Inductive match_SharedMemSTPool: stencil → SharedMemSTPool → mem → meminj → Prop :=
| MATCH_SharedMemSTPool:
∀ sharedmemp m b f s,
(∀ pid1 pid2,
0 ≤ pid1 < num_proc →
0 ≤ pid2 < num_proc →
(∃ v1 v2 v3,
Mem.load Mint32 m b (pid1 × (num_proc × 12) + pid2 × 12) = Some v1 ∧
Mem.valid_access m Mint32 b (pid1 × (num_proc × 12) + pid2 × 12) Writable ∧
Mem.load Mint32 m b (pid1 × (num_proc × 12) + pid2 × 12 + 4) = Some v2 ∧
Mem.valid_access m Mint32 b (pid1 × (num_proc × 12) + pid2 × 12 + 4) Writable ∧
Mem.load Mint32 m b (pid1 × (num_proc × 12) + pid2 × 12 + 8) = Some v3 ∧
Mem.valid_access m Mint32 b (pid1 × (num_proc × 12) + pid2 × 12 + 8) Writable ∧
match_SharedMem (ZMap.get pid2 (ZMap.get pid1 sharedmemp)) v1 v2 v3))
→ find_symbol s SHRDMEMPOOL_LOC = Some b
→ match_SharedMemSTPool s sharedmemp m f.
Inductive match_SharedMem: SharedMemState → val → val → val→ Prop :=
| MATCH_SharedMemUNDEF:
∀ v1 v2 v3, match_SharedMem SHRDUndef v1 v2 v3
| MATCH_SharedMemVALID:
∀ v1 v2 v3 si b,
Z2SharedMemInfo (Int.unsigned v1) = Some si →
ZtoBool (Int.unsigned v2) = Some b →
match_SharedMem (SHRDValid si b (Int.unsigned v3)) (Vint v3) (Vint v1) (Vint v2).
Inductive match_SharedMemSTPool: stencil → SharedMemSTPool → mem → meminj → Prop :=
| MATCH_SharedMemSTPool:
∀ sharedmemp m b f s,
(∀ pid1 pid2,
0 ≤ pid1 < num_proc →
0 ≤ pid2 < num_proc →
(∃ v1 v2 v3,
Mem.load Mint32 m b (pid1 × (num_proc × 12) + pid2 × 12) = Some v1 ∧
Mem.valid_access m Mint32 b (pid1 × (num_proc × 12) + pid2 × 12) Writable ∧
Mem.load Mint32 m b (pid1 × (num_proc × 12) + pid2 × 12 + 4) = Some v2 ∧
Mem.valid_access m Mint32 b (pid1 × (num_proc × 12) + pid2 × 12 + 4) Writable ∧
Mem.load Mint32 m b (pid1 × (num_proc × 12) + pid2 × 12 + 8) = Some v3 ∧
Mem.valid_access m Mint32 b (pid1 × (num_proc × 12) + pid2 × 12 + 8) Writable ∧
match_SharedMem (ZMap.get pid2 (ZMap.get pid1 sharedmemp)) v1 v2 v3))
→ find_symbol s SHRDMEMPOOL_LOC = Some b
→ match_SharedMemSTPool s sharedmemp m f.
Relation between the new raw data at the higher layer with the mememory at lower layer
Inductive match_RData: stencil → HDATA → mem → meminj → Prop :=
| MATCH_RDATA:
∀ hadt m f s,
match_SharedMemSTPool s (smspool hadt) m f
→ match_RData s hadt m f.
| MATCH_RDATA:
∀ hadt m f s,
match_SharedMemSTPool s (smspool hadt) m f
→ match_RData s hadt m f.
Relation between raw data at two layers
Record relate_RData (f: meminj) (hadt: HDATA) (ladt: LDATA) :=
mkrelate_RData {
flatmem_re: FlatMem.flatmem_inj (HP hadt) (HP ladt);
vmxinfo_re: vmxinfo hadt = vmxinfo ladt;
ikern_re: ikern ladt = ikern hadt;
pg_re: pg ladt = pg hadt;
ihost_re: ihost ladt = ihost hadt;
AC_re: AC ladt = AC hadt;
ti_fst_re: (fst (ti ladt)) = (fst (ti hadt));
ti_snd_re: val_inject f (snd (ti hadt)) (snd (ti ladt));
LAT_re: LAT ladt = LAT hadt;
nps_re: nps ladt = nps hadt;
PT_re: PT ladt = PT hadt;
ptp_re: ptpool ladt = ptpool hadt;
ipt_re: ipt ladt = ipt hadt;
init_re: init ladt = init hadt;
pperm_re: pperm ladt = pperm hadt;
idpde_re: idpde ladt = idpde hadt;
CPU_ID_re: CPU_ID hadt = CPU_ID ladt;
cid_re: cid hadt = cid ladt;
multi_oracle_re: multi_oracle hadt = multi_oracle ladt;
multi_log_re: multi_log hadt = multi_log ladt;
lock_re: lock hadt = lock ladt;
com1_re: com1 hadt = com1 ladt;
console_re: console hadt = console ladt;
console_concrete_re: console_concrete hadt = console_concrete ladt;
ioapic_re: ioapic ladt = ioapic hadt;
lapic_re: lapic ladt = lapic hadt;
intr_flag_re: intr_flag ladt = intr_flag hadt;
curr_intr_num_re: curr_intr_num ladt = curr_intr_num hadt;
in_intr_re: in_intr ladt = in_intr hadt;
drv_serial_re: drv_serial hadt = drv_serial ladt
}.
Global Instance rel_ops: CompatRelOps HDATAOps LDATAOps :=
{
relate_AbData s f d1 d2 := relate_RData f d1 d2;
match_AbData s d1 m f := match_RData s d1 m f;
new_glbl := SHRDMEMPOOL_LOC :: nil
}.
End REFINEMENT_REL.
mkrelate_RData {
flatmem_re: FlatMem.flatmem_inj (HP hadt) (HP ladt);
vmxinfo_re: vmxinfo hadt = vmxinfo ladt;
ikern_re: ikern ladt = ikern hadt;
pg_re: pg ladt = pg hadt;
ihost_re: ihost ladt = ihost hadt;
AC_re: AC ladt = AC hadt;
ti_fst_re: (fst (ti ladt)) = (fst (ti hadt));
ti_snd_re: val_inject f (snd (ti hadt)) (snd (ti ladt));
LAT_re: LAT ladt = LAT hadt;
nps_re: nps ladt = nps hadt;
PT_re: PT ladt = PT hadt;
ptp_re: ptpool ladt = ptpool hadt;
ipt_re: ipt ladt = ipt hadt;
init_re: init ladt = init hadt;
pperm_re: pperm ladt = pperm hadt;
idpde_re: idpde ladt = idpde hadt;
CPU_ID_re: CPU_ID hadt = CPU_ID ladt;
cid_re: cid hadt = cid ladt;
multi_oracle_re: multi_oracle hadt = multi_oracle ladt;
multi_log_re: multi_log hadt = multi_log ladt;
lock_re: lock hadt = lock ladt;
com1_re: com1 hadt = com1 ladt;
console_re: console hadt = console ladt;
console_concrete_re: console_concrete hadt = console_concrete ladt;
ioapic_re: ioapic ladt = ioapic hadt;
lapic_re: lapic ladt = lapic hadt;
intr_flag_re: intr_flag ladt = intr_flag hadt;
curr_intr_num_re: curr_intr_num ladt = curr_intr_num hadt;
in_intr_re: in_intr ladt = in_intr hadt;
drv_serial_re: drv_serial hadt = drv_serial ladt
}.
Global Instance rel_ops: CompatRelOps HDATAOps LDATAOps :=
{
relate_AbData s f d1 d2 := relate_RData f d1 d2;
match_AbData s d1 m f := match_RData s d1 m f;
new_glbl := SHRDMEMPOOL_LOC :: nil
}.
End REFINEMENT_REL.
Section Rel_Property.
Lemma inject_match_correct:
∀ s d1 m2 f m2´ j,
match_RData s d1 m2 f →
Mem.inject j m2 m2´ →
inject_incr (Mem.flat_inj (genv_next s)) j →
match_RData s d1 m2´ (compose_meminj f j).
Proof.
inversion 1; subst; intros.
inv H0.
assert (HFB0: j b = Some (b, 0)).
{
eapply stencil_find_symbol_inject´; eauto.
}
econstructor; eauto; intros.
econstructor; eauto; intros.
specialize (H3 _ _ H0 H5).
destruct H3 as [v1[v2[v3[HL1[HV1[HL2[HV2[HL3[HV3 HM]]]]]]]]].
specialize (Mem.load_inject _ _ _ _ _ _ _ _ _ H1 HL1 HFB0).
specialize (Mem.load_inject _ _ _ _ _ _ _ _ _ H1 HL2 HFB0).
specialize (Mem.load_inject _ _ _ _ _ _ _ _ _ H1 HL3 HFB0).
repeat rewrite Z.add_0_r.
intros [v1´[HLD1´ HV1´]].
intros [v2´[HLD2´ HV2´]].
intros [v3´[HLD3´ HV3´]].
refine_split´; eauto.
specialize(Mem.valid_access_inject _ _ _ _ _ _ _ _ _ HFB0 H1 HV1).
rewrite Z.add_0_r; trivial.
specialize(Mem.valid_access_inject _ _ _ _ _ _ _ _ _ HFB0 H1 HV2).
rewrite Z.add_0_r; trivial.
specialize(Mem.valid_access_inject _ _ _ _ _ _ _ _ _ HFB0 H1 HV3).
rewrite Z.add_0_r; trivial.
inv HM. constructor.
inv HV1´. inv HV2´. inv HV3´. constructor; auto.
Qed.
Lemma store_match_correct:
∀ s abd m0 m0´ f b2 v v´ chunk,
match_RData s abd m0 f →
(∀ i b,
In i new_glbl →
find_symbol s i = Some b → b ≠ b2) →
Mem.store chunk m0 b2 v v´ = Some m0´ →
match_RData s abd m0´ f.
Proof.
intros. inv H. inv H2.
econstructor; eauto.
econstructor; eauto.
intros. specialize (H _ _ H2 H4).
destruct H as [v1[v2[v3[HL1[HV1[HL2[HV2[HL3[HV3 HM]]]]]]]]].
eapply H0 in H3; simpl; eauto.
repeat rewrite (Mem.load_store_other _ _ _ _ _ _ H1); auto.
refine_split´; eauto;
eapply Mem.store_valid_access_1; eauto.
Qed.
Lemma storebytes_match_correct:
∀ s abd m0 m0´ f b2 v v´,
match_RData s abd m0 f →
(∀ i b,
In i new_glbl →
find_symbol s i = Some b → b ≠ b2) →
Mem.storebytes m0 b2 v v´ = Some m0´ →
match_RData s abd m0´ f.
Proof.
intros. inv H. inv H2.
econstructor; eauto.
econstructor; eauto.
intros. specialize (H _ _ H2 H4).
destruct H as [v1[v2[v3[HL1[HV1[HL2[HV2[HL3[HV3 HM]]]]]]]]].
eapply H0 in H3; simpl; eauto.
repeat rewrite (Mem.load_storebytes_other _ _ _ _ _ H1); eauto.
refine_split´; eauto;
eapply Mem.storebytes_valid_access_1; eauto.
Qed.
Lemma free_match_correct:
∀ s abd m0 m0´ f ofs sz b2,
match_RData s abd m0 f→
(∀ i b,
In i new_glbl →
find_symbol s i = Some b → b ≠ b2) →
Mem.free m0 b2 ofs sz = Some m0´ →
match_RData s abd m0´ f.
Proof.
intros; inv H; inv H2.
econstructor; eauto.
econstructor; eauto.
intros. specialize (H _ _ H2 H4).
destruct H as [v1[v2[v3[HL1[HV1[HL2[HV2[HL3[HV3 HM]]]]]]]]].
eapply H0 in H3; simpl; eauto.
repeat rewrite (Mem.load_free _ _ _ _ _ H1); auto.
refine_split´; eauto;
eapply Mem.valid_access_free_1; eauto.
Qed.
Lemma alloc_match_correct:
∀ s abd m´0 m´1 f f´ ofs sz b0 b´1,
match_RData s abd m´0 f→
Mem.alloc m´0 ofs sz = (m´1, b´1) →
f´ b0 = Some (b´1, 0%Z) →
(∀ b : block, b ≠ b0 → f´ b = f b) →
inject_incr f f´ →
(∀ i b,
In i new_glbl →
find_symbol s i = Some b → b ≠ b0) →
match_RData s abd m´1 f´.
Proof.
intros. rename H1 into HF1, H2 into HB. inv H; inv H1.
econstructor; eauto.
econstructor; eauto.
intros. specialize (H _ _ H1 H5).
destruct H as [v1[v2[v3[HL1[HV1[HL2[HV2[HL3[HV3 HM]]]]]]]]].
refine_split´; eauto;
try (apply (Mem.load_alloc_other _ _ _ _ _ H0));
try (eapply Mem.valid_access_alloc_other); eauto.
Qed.
Lemma inject_match_correct:
∀ s d1 m2 f m2´ j,
match_RData s d1 m2 f →
Mem.inject j m2 m2´ →
inject_incr (Mem.flat_inj (genv_next s)) j →
match_RData s d1 m2´ (compose_meminj f j).
Proof.
inversion 1; subst; intros.
inv H0.
assert (HFB0: j b = Some (b, 0)).
{
eapply stencil_find_symbol_inject´; eauto.
}
econstructor; eauto; intros.
econstructor; eauto; intros.
specialize (H3 _ _ H0 H5).
destruct H3 as [v1[v2[v3[HL1[HV1[HL2[HV2[HL3[HV3 HM]]]]]]]]].
specialize (Mem.load_inject _ _ _ _ _ _ _ _ _ H1 HL1 HFB0).
specialize (Mem.load_inject _ _ _ _ _ _ _ _ _ H1 HL2 HFB0).
specialize (Mem.load_inject _ _ _ _ _ _ _ _ _ H1 HL3 HFB0).
repeat rewrite Z.add_0_r.
intros [v1´[HLD1´ HV1´]].
intros [v2´[HLD2´ HV2´]].
intros [v3´[HLD3´ HV3´]].
refine_split´; eauto.
specialize(Mem.valid_access_inject _ _ _ _ _ _ _ _ _ HFB0 H1 HV1).
rewrite Z.add_0_r; trivial.
specialize(Mem.valid_access_inject _ _ _ _ _ _ _ _ _ HFB0 H1 HV2).
rewrite Z.add_0_r; trivial.
specialize(Mem.valid_access_inject _ _ _ _ _ _ _ _ _ HFB0 H1 HV3).
rewrite Z.add_0_r; trivial.
inv HM. constructor.
inv HV1´. inv HV2´. inv HV3´. constructor; auto.
Qed.
Lemma store_match_correct:
∀ s abd m0 m0´ f b2 v v´ chunk,
match_RData s abd m0 f →
(∀ i b,
In i new_glbl →
find_symbol s i = Some b → b ≠ b2) →
Mem.store chunk m0 b2 v v´ = Some m0´ →
match_RData s abd m0´ f.
Proof.
intros. inv H. inv H2.
econstructor; eauto.
econstructor; eauto.
intros. specialize (H _ _ H2 H4).
destruct H as [v1[v2[v3[HL1[HV1[HL2[HV2[HL3[HV3 HM]]]]]]]]].
eapply H0 in H3; simpl; eauto.
repeat rewrite (Mem.load_store_other _ _ _ _ _ _ H1); auto.
refine_split´; eauto;
eapply Mem.store_valid_access_1; eauto.
Qed.
Lemma storebytes_match_correct:
∀ s abd m0 m0´ f b2 v v´,
match_RData s abd m0 f →
(∀ i b,
In i new_glbl →
find_symbol s i = Some b → b ≠ b2) →
Mem.storebytes m0 b2 v v´ = Some m0´ →
match_RData s abd m0´ f.
Proof.
intros. inv H. inv H2.
econstructor; eauto.
econstructor; eauto.
intros. specialize (H _ _ H2 H4).
destruct H as [v1[v2[v3[HL1[HV1[HL2[HV2[HL3[HV3 HM]]]]]]]]].
eapply H0 in H3; simpl; eauto.
repeat rewrite (Mem.load_storebytes_other _ _ _ _ _ H1); eauto.
refine_split´; eauto;
eapply Mem.storebytes_valid_access_1; eauto.
Qed.
Lemma free_match_correct:
∀ s abd m0 m0´ f ofs sz b2,
match_RData s abd m0 f→
(∀ i b,
In i new_glbl →
find_symbol s i = Some b → b ≠ b2) →
Mem.free m0 b2 ofs sz = Some m0´ →
match_RData s abd m0´ f.
Proof.
intros; inv H; inv H2.
econstructor; eauto.
econstructor; eauto.
intros. specialize (H _ _ H2 H4).
destruct H as [v1[v2[v3[HL1[HV1[HL2[HV2[HL3[HV3 HM]]]]]]]]].
eapply H0 in H3; simpl; eauto.
repeat rewrite (Mem.load_free _ _ _ _ _ H1); auto.
refine_split´; eauto;
eapply Mem.valid_access_free_1; eauto.
Qed.
Lemma alloc_match_correct:
∀ s abd m´0 m´1 f f´ ofs sz b0 b´1,
match_RData s abd m´0 f→
Mem.alloc m´0 ofs sz = (m´1, b´1) →
f´ b0 = Some (b´1, 0%Z) →
(∀ b : block, b ≠ b0 → f´ b = f b) →
inject_incr f f´ →
(∀ i b,
In i new_glbl →
find_symbol s i = Some b → b ≠ b0) →
match_RData s abd m´1 f´.
Proof.
intros. rename H1 into HF1, H2 into HB. inv H; inv H1.
econstructor; eauto.
econstructor; eauto.
intros. specialize (H _ _ H1 H5).
destruct H as [v1[v2[v3[HL1[HV1[HL2[HV2[HL3[HV3 HM]]]]]]]]].
refine_split´; eauto;
try (apply (Mem.load_alloc_other _ _ _ _ _ H0));
try (eapply Mem.valid_access_alloc_other); eauto.
Qed.
Prove that after taking one step, the refinement relation still holds
Lemma relate_incr:
∀ abd abd´ f f´,
relate_RData f abd abd´
→ inject_incr f f´
→ relate_RData f´ abd abd´.
Proof.
inversion 1; subst; intros; inv H; constructor; eauto.
Qed.
Global Instance rel_prf: CompatRel HDATAOps LDATAOps.
Proof.
constructor.
- apply inject_match_correct.
- apply store_match_correct.
- apply alloc_match_correct.
- apply free_match_correct.
- apply storebytes_match_correct.
- intros. eapply relate_incr; eauto.
Qed.
End Rel_Property.
End WITHMEM.
End Refinement.
∀ abd abd´ f f´,
relate_RData f abd abd´
→ inject_incr f f´
→ relate_RData f´ abd abd´.
Proof.
inversion 1; subst; intros; inv H; constructor; eauto.
Qed.
Global Instance rel_prf: CompatRel HDATAOps LDATAOps.
Proof.
constructor.
- apply inject_match_correct.
- apply store_match_correct.
- apply alloc_match_correct.
- apply free_match_correct.
- apply storebytes_match_correct.
- intros. eapply relate_incr; eauto.
Qed.
End Rel_Property.
End WITHMEM.
End Refinement.