Library mcertikos.proc.KContextNewGen
This file provide the contextual refinement proof between PKContext layer and PKCtxtNew 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 CommonTactic.
Require Import AuxLemma.
Require Import FlatMemory.
Require Import AuxStateDataType.
Require Import Constant.
Require Import GlobIdent.
Require Import RealParams.
Require Import LoadStoreSem2.
Require Import AsmImplLemma.
Require Import GenSem.
Require Import RefinementTactic.
Require Import PrimSemantics.
Require Import XOmega.
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 LayerCalculusLemma.
Require Import PKContextNew.
Require Import KContextNewGenSpec.
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 CommonTactic.
Require Import AuxLemma.
Require Import FlatMemory.
Require Import AuxStateDataType.
Require Import Constant.
Require Import GlobIdent.
Require Import RealParams.
Require Import LoadStoreSem2.
Require Import AsmImplLemma.
Require Import GenSem.
Require Import RefinementTactic.
Require Import PrimSemantics.
Require Import XOmega.
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 LayerCalculusLemma.
Require Import PKContextNew.
Require Import KContextNewGenSpec.
Section Refinement.
Local Open Scope string_scope.
Local Open Scope error_monad_scope.
Local Open Scope Z_scope.
Context `{real_params: RealParams}.
Notation HDATA := RData.
Notation LDATA := RData.
Notation HDATAOps := (cdata HDATA).
Notation LDATAOps := (cdata LDATA).
Section WITHMEM.
Context `{Hstencil: Stencil}.
Context `{Hmem: Mem.MemoryModel}.
Context `{Hmwd: UseMemWithData mem}.
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;
devout_re: devout hadt = devout ladt;
CR3_re: CR3 hadt = CR3 ladt;
ikern_re: ikern hadt = ikern ladt;
pg_re: pg hadt = pg ladt;
ihost_re: ihost hadt = ihost ladt;
AC_re: AC hadt = AC ladt;
ti_fst_re: (fst (ti hadt)) = (fst (ti ladt));
ti_snd_re: val_inject f (snd (ti hadt)) (snd (ti ladt));
LAT_re: LAT hadt = LAT ladt;
nps_re: nps hadt = nps ladt;
init_re: init hadt = init ladt;
pperm_re: pperm hadt = pperm ladt;
PT_re: PT hadt = PT ladt;
ptp_re: ptpool hadt = ptpool ladt;
idpde_re: idpde hadt = idpde ladt;
ipt_re: ipt hadt = ipt ladt;
smspool_re: smspool hadt = smspool ladt;
kctxt_re: kctxt_inj f num_proc (kctxt hadt) (kctxt ladt)
}.
Inductive match_RData: stencil → HDATA → mem → meminj → Prop :=
| MATCH_RDATA: ∀ habd m f s, match_RData s habd m f.
Local Hint Resolve MATCH_RDATA.
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 := nil
}.
Local Open Scope string_scope.
Local Open Scope error_monad_scope.
Local Open Scope Z_scope.
Context `{real_params: RealParams}.
Notation HDATA := RData.
Notation LDATA := RData.
Notation HDATAOps := (cdata HDATA).
Notation LDATAOps := (cdata LDATA).
Section WITHMEM.
Context `{Hstencil: Stencil}.
Context `{Hmem: Mem.MemoryModel}.
Context `{Hmwd: UseMemWithData mem}.
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;
devout_re: devout hadt = devout ladt;
CR3_re: CR3 hadt = CR3 ladt;
ikern_re: ikern hadt = ikern ladt;
pg_re: pg hadt = pg ladt;
ihost_re: ihost hadt = ihost ladt;
AC_re: AC hadt = AC ladt;
ti_fst_re: (fst (ti hadt)) = (fst (ti ladt));
ti_snd_re: val_inject f (snd (ti hadt)) (snd (ti ladt));
LAT_re: LAT hadt = LAT ladt;
nps_re: nps hadt = nps ladt;
init_re: init hadt = init ladt;
pperm_re: pperm hadt = pperm ladt;
PT_re: PT hadt = PT ladt;
ptp_re: ptpool hadt = ptpool ladt;
idpde_re: idpde hadt = idpde ladt;
ipt_re: ipt hadt = ipt ladt;
smspool_re: smspool hadt = smspool ladt;
kctxt_re: kctxt_inj f num_proc (kctxt hadt) (kctxt ladt)
}.
Inductive match_RData: stencil → HDATA → mem → meminj → Prop :=
| MATCH_RDATA: ∀ habd m f s, match_RData s habd m f.
Local Hint Resolve MATCH_RDATA.
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 := nil
}.
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.
- eapply kctxt_inj_incr; eauto.
Qed.
Lemma relate_kernel_mode:
∀ abd abd' f,
relate_RData f abd abd'
→ (kernel_mode abd ↔ kernel_mode abd').
Proof.
inversion 1; simpl; split; congruence.
Qed.
Lemma relate_observe:
∀ p abd abd' f,
relate_RData f abd abd' →
observe p abd = observe p abd'.
Proof.
inversion 1; simpl; unfold ObservationImpl.observe; congruence.
Qed.
Global Instance rel_prf: CompatRel HDATAOps LDATAOps.
Proof.
constructor; intros; simpl; trivial.
eapply relate_incr; eauto.
eapply relate_kernel_mode; eauto.
eapply relate_observe; eauto.
Qed.
End Rel_Property.
∀ 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.
- eapply kctxt_inj_incr; eauto.
Qed.
Lemma relate_kernel_mode:
∀ abd abd' f,
relate_RData f abd abd'
→ (kernel_mode abd ↔ kernel_mode abd').
Proof.
inversion 1; simpl; split; congruence.
Qed.
Lemma relate_observe:
∀ p abd abd' f,
relate_RData f abd abd' →
observe p abd = observe p abd'.
Proof.
inversion 1; simpl; unfold ObservationImpl.observe; congruence.
Qed.
Global Instance rel_prf: CompatRel HDATAOps LDATAOps.
Proof.
constructor; intros; simpl; trivial.
eapply relate_incr; eauto.
eapply relate_kernel_mode; eauto.
eapply relate_observe; eauto.
Qed.
End Rel_Property.
Section Exists.
Lemma kctxt_new_exist:
∀ s habd habd' labd b b' ofs' id q n f,
ObjThread.kctxt_new_spec habd b b' ofs' id q = Some (habd', n)
→ relate_RData f habd labd
→ high_level_invariant habd
→ find_symbol s STACK_LOC = Some b
→ (∃ id, find_symbol s id = Some b')
→ inject_incr (Mem.flat_inj (genv_next s)) f
→ ∃ labd', kctxt_new_spec labd b b' ofs' id q = Some (labd', n)
∧ relate_RData f habd' labd'
∧ kernel_mode labd.
Proof.
unfold ObjThread.kctxt_new_spec, kctxt_new_spec,
kctxt_ra_spec, kctxt_sp_spec, pt_new_spec.
intros until f; intros HP HR; inv HR. simpl.
intros HH Hsys Hsys' Hincr.
revert HP. subrewrite'. intros HQ.
subdestruct; simpl.
destruct HH; rewrite <- AC_re0 in Hdestruct3.
assert (Hpos:= cvalid_child_id_pos _ valid_container _ Hdestruct3
(Z.of_nat (length (cchildren (ZMap.get id (AC labd)))))).
rewrite zeq_false.
subrewrite'. rewrite zlt_lt_true; simpl.
subrewrite'. rewrite zlt_lt_true; simpl.
- inv HQ. refine_split'; eauto 2.
econstructor; eauto 2; simpl.
rewrite ZMap.gss; rewrite ZMap.set2.
unfold kctxt_inj in *; kctxt_inj_simpl.
+ destruct Hsys' as [id' Hsys'].
eapply stencil_find_symbol_inject'; eauto.
+ rewrite Int.add_zero; trivial.
+ eapply stencil_find_symbol_inject'; eauto.
+ rewrite Int.add_zero; trivial.
- omega.
- omega.
- omega.
Qed.
End Exists.
Section FRESH_PRIM.
Lemma kctxt_new_spec_ref:
compatsim (crel HDATA LDATA) (dnew_compatsem ObjThread.kctxt_new_spec)
kctxt_new_spec_low.
Proof.
compatsim_simpl (@match_AbData).
exploit kctxt_new_exist; eauto 1.
intros (labd' & HP & HM & Hkern).
destruct H8 as [fun_id Hsymbol].
exploit (stencil_find_symbol_inject' s ι fun_id b'); eauto.
intros HFB.
refine_split; try econstructor; eauto. constructor.
Qed.
End FRESH_PRIM.
Section PASSTHROUGH_PRIM.
Global Instance: (LoadStoreProp (hflatmem_store:= flatmem_store) (lflatmem_store:= flatmem_store)).
Proof.
accessor_prop_tac.
- eapply flatmem_store_exists; eauto.
Qed.
Lemma passthrough_correct:
sim (crel HDATA LDATA) pkcontextnew_passthrough pkcontext.
Proof.
sim_oplus.
- apply fload_sim.
- apply fstore_sim.
- apply flatmem_copy_sim.
- apply vmxinfo_get_sim.
- apply device_output_sim.
- apply pfree_sim.
- apply setPT_sim.
- apply ptRead_sim.
- apply ptResv_sim.
- apply sharedmem_init_sim.
- apply shared_mem_status_sim.
- apply offer_shared_mem_sim.
- apply ptin_sim.
- apply ptout_sim.
- apply clearCR2_sim.
- apply container_get_nchildren_sim.
- apply container_get_quota_sim.
- apply container_get_usage_sim.
- apply container_can_consume_sim.
- apply alloc_sim.
- apply trapin_sim.
- apply trapout_sim.
- apply hostin_sim.
- apply hostout_sim.
- apply trap_info_get_sim.
- apply trap_info_ret_sim.
- apply kctxt_switch_sim.
- layer_sim_simpl.
+ eapply load_correct2.
+ eapply store_correct2.
Qed.
End PASSTHROUGH_PRIM.
End OneStep_Forward_Relation.
End WITHMEM.
End Refinement.
Lemma kctxt_new_exist:
∀ s habd habd' labd b b' ofs' id q n f,
ObjThread.kctxt_new_spec habd b b' ofs' id q = Some (habd', n)
→ relate_RData f habd labd
→ high_level_invariant habd
→ find_symbol s STACK_LOC = Some b
→ (∃ id, find_symbol s id = Some b')
→ inject_incr (Mem.flat_inj (genv_next s)) f
→ ∃ labd', kctxt_new_spec labd b b' ofs' id q = Some (labd', n)
∧ relate_RData f habd' labd'
∧ kernel_mode labd.
Proof.
unfold ObjThread.kctxt_new_spec, kctxt_new_spec,
kctxt_ra_spec, kctxt_sp_spec, pt_new_spec.
intros until f; intros HP HR; inv HR. simpl.
intros HH Hsys Hsys' Hincr.
revert HP. subrewrite'. intros HQ.
subdestruct; simpl.
destruct HH; rewrite <- AC_re0 in Hdestruct3.
assert (Hpos:= cvalid_child_id_pos _ valid_container _ Hdestruct3
(Z.of_nat (length (cchildren (ZMap.get id (AC labd)))))).
rewrite zeq_false.
subrewrite'. rewrite zlt_lt_true; simpl.
subrewrite'. rewrite zlt_lt_true; simpl.
- inv HQ. refine_split'; eauto 2.
econstructor; eauto 2; simpl.
rewrite ZMap.gss; rewrite ZMap.set2.
unfold kctxt_inj in *; kctxt_inj_simpl.
+ destruct Hsys' as [id' Hsys'].
eapply stencil_find_symbol_inject'; eauto.
+ rewrite Int.add_zero; trivial.
+ eapply stencil_find_symbol_inject'; eauto.
+ rewrite Int.add_zero; trivial.
- omega.
- omega.
- omega.
Qed.
End Exists.
Section FRESH_PRIM.
Lemma kctxt_new_spec_ref:
compatsim (crel HDATA LDATA) (dnew_compatsem ObjThread.kctxt_new_spec)
kctxt_new_spec_low.
Proof.
compatsim_simpl (@match_AbData).
exploit kctxt_new_exist; eauto 1.
intros (labd' & HP & HM & Hkern).
destruct H8 as [fun_id Hsymbol].
exploit (stencil_find_symbol_inject' s ι fun_id b'); eauto.
intros HFB.
refine_split; try econstructor; eauto. constructor.
Qed.
End FRESH_PRIM.
Section PASSTHROUGH_PRIM.
Global Instance: (LoadStoreProp (hflatmem_store:= flatmem_store) (lflatmem_store:= flatmem_store)).
Proof.
accessor_prop_tac.
- eapply flatmem_store_exists; eauto.
Qed.
Lemma passthrough_correct:
sim (crel HDATA LDATA) pkcontextnew_passthrough pkcontext.
Proof.
sim_oplus.
- apply fload_sim.
- apply fstore_sim.
- apply flatmem_copy_sim.
- apply vmxinfo_get_sim.
- apply device_output_sim.
- apply pfree_sim.
- apply setPT_sim.
- apply ptRead_sim.
- apply ptResv_sim.
- apply sharedmem_init_sim.
- apply shared_mem_status_sim.
- apply offer_shared_mem_sim.
- apply ptin_sim.
- apply ptout_sim.
- apply clearCR2_sim.
- apply container_get_nchildren_sim.
- apply container_get_quota_sim.
- apply container_get_usage_sim.
- apply container_can_consume_sim.
- apply alloc_sim.
- apply trapin_sim.
- apply trapout_sim.
- apply hostin_sim.
- apply hostout_sim.
- apply trap_info_get_sim.
- apply trap_info_ret_sim.
- apply kctxt_switch_sim.
- layer_sim_simpl.
+ eapply load_correct2.
+ eapply store_correct2.
Qed.
End PASSTHROUGH_PRIM.
End OneStep_Forward_Relation.
End WITHMEM.
End Refinement.