Library mcertikos.proc.ThreadInitGen
*********************************************************************** * * * The CertiKOS Certified Kit Operating System * * * * The FLINT Group, Yale University * * * * Copyright The FLINT Group, Yale University. All rights reserved. * * This file is distributed under the terms of the Yale University * * Non-Commercial License Agreement. * * * ***********************************************************************
This file provide the contextual refinement proof between PThreadIntro layer and PThreadInit 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 LayerCalculusLemma.
Require Import AbstractDataType.
Require Import ThreadInitGenSpec.
Require Import PThreadIntro.
Require Import PThreadInit.
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 LayerCalculusLemma.
Require Import AbstractDataType.
Require Import ThreadInitGenSpec.
Require Import PThreadIntro.
Require Import PThreadInit.
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 (cdata_ops := pthreadinit_data_ops) HDATA).
Notation LDATAOps := (cdata (cdata_ops := mshareintro_data_ops) LDATA).
Section WITHMEM.
Context `{Hstencil: Stencil}.
Context `{Hmem: Mem.MemoryModel}.
Context `{Hmwd: UseMemWithData mem}.
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 (cdata_ops := pthreadinit_data_ops) HDATA).
Notation LDATAOps := (cdata (cdata_ops := mshareintro_data_ops) LDATA).
Section WITHMEM.
Context `{Hstencil: Stencil}.
Context `{Hmem: Mem.MemoryModel}.
Context `{Hmwd: UseMemWithData mem}.
Relation between raw data at two layers
Record relate_RData (f: meminj) (hadt: LDATA) (ladt: LDATA) :=
mkrelate_RData {
flatmem_re: FlatMem.flatmem_inj (HP hadt) (HP ladt);
vmxinfo_re: vmxinfo hadt = vmxinfo 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;
pb_re: pb hadt = pb ladt;
kctxt_re: kctxt_inj f num_proc (kctxt hadt) (kctxt ladt);
tcb_re: tcb hadt = tcb 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 hadt = in_intr ladt;
drv_serial_re: drv_serial hadt = drv_serial 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
}.
mkrelate_RData {
flatmem_re: FlatMem.flatmem_inj (HP hadt) (HP ladt);
vmxinfo_re: vmxinfo hadt = vmxinfo 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;
pb_re: pb hadt = pb ladt;
kctxt_re: kctxt_inj f num_proc (kctxt hadt) (kctxt ladt);
tcb_re: tcb hadt = tcb 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 hadt = in_intr ladt;
drv_serial_re: drv_serial hadt = drv_serial 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.
End Rel_Property.
Global Instance rel_prf: CompatRel HDATAOps LDATAOps.
Proof.
constructor; intros; simpl; trivial.
eapply relate_incr; eauto.
Qed.
∀ 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.
End Rel_Property.
Global Instance rel_prf: CompatRel HDATAOps LDATAOps.
Proof.
constructor; intros; simpl; trivial.
eapply relate_incr; eauto.
Qed.
Section Exists.
Lemma thread_init_exist:
∀ habd habd´ labd i f,
ObjQueue.thread_init_spec i habd = ret habd´
→ relate_RData f habd labd
→ ∃ labd´, thread_init_spec i labd = Some labd´
∧ relate_RData f habd´ labd´
∧ kernel_mode labd.
Proof.
unfold ObjQueue.thread_init_spec, thread_init_spec, sharedmem_init_spec,
thread_init_spec.
intros until f. exist_simpl.
Qed.
End Exists.
Section FRESH_PRIM.
Lemma thread_init_spec_ref:
compatsim (crel HDATA LDATA) (gensem ObjQueue.thread_init_spec) thread_init_spec_low.
Proof.
compatsim_simpl (@match_AbData).
exploit thread_init_exist; eauto 1.
intros [labd´ [HP [HM Hkern]]].
refine_split; try econstructor; eauto. constructor.
Qed.
End FRESH_PRIM.
Section PASSTHROUGH_RPIM.
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) pthreadinit_passthrough pthreadintro.
Proof.
sim_oplus.
- apply fload_sim.
- apply fstore_sim.
- apply flatmem_copy_sim.
- apply vmxinfo_get_sim.
- apply palloc_sim.
- apply pfree_sim.
- apply setPT_sim.
- apply ptRead_sim.
- apply ptResv_sim.
- apply kctxt_new_sim.
- apply shared_mem_status_sim.
- apply offer_shared_mem_sim.
- apply get_state_sim.
- apply get_prev_sim.
- apply get_next_sim.
- apply set_state_sim.
- apply set_prev_sim.
- apply set_next_sim.
- apply ptin_sim.
- apply ptout_sim.
- apply container_get_quota_sim.
- apply container_get_usage_sim.
- apply container_can_consume_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.
- apply cli_sim.
- apply sti_sim.
- apply cons_buf_read_sim.
- apply serial_putc_sim.
- apply serial_intr_disable_sim.
- apply serial_intr_enable_sim.
- layer_sim_simpl.
+ eapply load_correct2.
+ eapply store_correct2.
Qed.
End PASSTHROUGH_RPIM.
End OneStep_Forward_Relation.
End WITHMEM.
End Refinement.
Lemma thread_init_exist:
∀ habd habd´ labd i f,
ObjQueue.thread_init_spec i habd = ret habd´
→ relate_RData f habd labd
→ ∃ labd´, thread_init_spec i labd = Some labd´
∧ relate_RData f habd´ labd´
∧ kernel_mode labd.
Proof.
unfold ObjQueue.thread_init_spec, thread_init_spec, sharedmem_init_spec,
thread_init_spec.
intros until f. exist_simpl.
Qed.
End Exists.
Section FRESH_PRIM.
Lemma thread_init_spec_ref:
compatsim (crel HDATA LDATA) (gensem ObjQueue.thread_init_spec) thread_init_spec_low.
Proof.
compatsim_simpl (@match_AbData).
exploit thread_init_exist; eauto 1.
intros [labd´ [HP [HM Hkern]]].
refine_split; try econstructor; eauto. constructor.
Qed.
End FRESH_PRIM.
Section PASSTHROUGH_RPIM.
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) pthreadinit_passthrough pthreadintro.
Proof.
sim_oplus.
- apply fload_sim.
- apply fstore_sim.
- apply flatmem_copy_sim.
- apply vmxinfo_get_sim.
- apply palloc_sim.
- apply pfree_sim.
- apply setPT_sim.
- apply ptRead_sim.
- apply ptResv_sim.
- apply kctxt_new_sim.
- apply shared_mem_status_sim.
- apply offer_shared_mem_sim.
- apply get_state_sim.
- apply get_prev_sim.
- apply get_next_sim.
- apply set_state_sim.
- apply set_prev_sim.
- apply set_next_sim.
- apply ptin_sim.
- apply ptout_sim.
- apply container_get_quota_sim.
- apply container_get_usage_sim.
- apply container_can_consume_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.
- apply cli_sim.
- apply sti_sim.
- apply cons_buf_read_sim.
- apply serial_putc_sim.
- apply serial_intr_disable_sim.
- apply serial_intr_enable_sim.
- layer_sim_simpl.
+ eapply load_correct2.
+ eapply store_correct2.
Qed.
End PASSTHROUGH_RPIM.
End OneStep_Forward_Relation.
End WITHMEM.
End Refinement.