Library mcertikos.multicore.refins.AsmBigSemtoSingleSem
Require Import Coqlib.
Require Import Maps.
Require Import ASTExtra.
Require Import Integers.
Require Import Floats.
Require Import Values.
Require Import Events.
Require Import Globalenvs.
Require Import Conventions.
Require Import AuxLemma.
Require Import GlobIdent.
Require Import Smallstep.
Require Import CommonTactic.
Require Import Coq.Logic.FunctionalExtensionality.
Require Import AuxFunctions.
Require Import LAsm.
Require Import GlobalOracle.
Require Import liblayers.compat.CompatLayers.
Require Import MBoot.
Require Import RealParams.
Require Import AbstractDataType.
Require Import FlatMemory.
Require Import Decision.
Require Import LAsmModuleSem.
Require Import Soundness.
Require Import CompatExternalCalls.
Require Import LinkTactic.
Require Import I64Layer.
Require Import StencilImpl.
Require Import MakeProgram.
Require Import MakeProgramImpl.
Require Import LAsmModuleSemAux.
Require Import liblayers.compat.CompatGenSem.
Require Import TacticsForTesting.
Require Import Concurrent_Linking_Lib.
Require Import Concurrent_Linking_Def.
Require Import Concurrent_Linking_Prop.
Require Import HWSemImpl.
Require Import ConcurrentOracle.
Require Import BigSemImpl.
Require Import SingleSemImpl.
Section LinkwithLAsm.
Context `{Hmem: Mem.MemoryModelX}.
Context `{Hmwd: UseMemWithData mem}.
Context `{real_params: RealParams}.
Context `{multi_oracle_prop: MultiOracleProp}.
Context `{builtin_idents_norepet_prf: CompCertBuiltins.BuiltinIdentsNorepet}.
Notation LDATA := RData.
Notation LDATAOps := (cdata (cdata_ops := mboot_data_ops) LDATA).
Local Open Scope Z_scope.
Context `{pmap: PartialMap}.
Context `{zset_op: ZSet_operation}.
Existing Instance hdseting.
Existing Instance op_sep.
Context `{mc_oracle_cond: MCLinkOracleCond (mem := mem) (memory_model_ops := memory_model_ops) (Hmwd := Hmwd)
(Hmem := Hmem) (real_params_ops := real_params_ops)
(oracle_ops0 := oracle_ops0) (oracle_ops := oracle_ops) (big_ops := big_ops)
(builtin_idents_norepet_prf := builtin_idents_norepet_prf)
(zset_op := zset_op) (pmap := pmap)}.
Section WITH_GE.
Variables (ge: genv) (sten: stencil) (M: module).
Context {Hmakege: make_globalenv (module_ops:= LAsm.module_ops) (mkp_ops:= make_program_ops)
sten M (mboot ⊕ L64) = ret ge}.
Definition single_big_step_aux_ge´ :=
@single_big_step_aux_ge mem memory_model_ops Hmem Hmwd
real_params_ops oracle_ops0 oracle_ops big_ops
builtin_idents_norepet_prf fair zset_op mc_oracle
ge sten M Hmakege.
Definition single_step_aux_ge´ :=
@single_step_aux_ge mem memory_model_ops Hmem Hmwd
real_params_ops oracle_ops0 oracle_ops big_ops
builtin_idents_norepet_prf zset_op mc_oracle
ge sten M Hmakege.
Definition match_bsstate_link (s_h: single_state) (s_l: single_state) : Prop :=
match_bsstate (hdset := hdseting) s_h s_l.
Hint Unfold match_bsstate_link.
Lemma single_big_step_aux_eq :
∀ (ge:genv) sten M
(Hmakege: make_globalenv sten M (mboot ⊕ L64) = ret ge)
s t s´,
single_big_step_aux_ge ge sten M (Hmakege:=Hmakege) ge s t s´ ↔
single_big_step_aux ge sten M (Hmakege:=Hmakege) s t s´.
Proof.
intros; split; intros.
inversion H; auto.
constructor; auto.
Qed.
Lemma single_step_aux_eq :
∀ (ge:genv) sten M
(Hmakege: make_globalenv sten M (mboot ⊕ L64) = ret ge)
s t s´,
single_step_aux_ge ge sten M (Hmakege:=Hmakege) ge s t s´ ↔
single_step_aux ge sten M (Hmakege:=Hmakege) s t s´.
Proof.
intros; split; intros.
inversion H; auto.
constructor; auto.
Qed.
Lemma one_step_single_refines_big_concrete:
∀ s s0 s´ t
(Hone: single_big_step_aux_ge´ ge s t s´)
(Hmatch: match_bsstate_link s s0),
∃ s0´,
plus (single_step_aux_ge´) ge s0 t s0´
∧ match_bsstate_link s´ s0´.
Proof.
simpl in ×.
unfold single_step_aux_ge´.
unfold single_big_step_aux_ge´.
intros.
rewrite single_big_step_aux_eq in Hone.
unfold single_big_step_aux in Hone; simpl in ×.
unfold match_bsstate_link in ×.
assert (core_set current_CPU_ID = true).
{ eapply current_CPU_ID_in_core_set. }
eapply one_step_single_refines_big in Hone; eauto; [ | inv mc_oracle_cond; auto].
destruct Hone as (s_l´ & Hone & Htwo).
∃ s_l´.
split; auto.
inv Hone.
eapply plus_star_trans.
eapply plus_one.
rewrite single_step_aux_eq.
unfold single_step_aux; simpl; eauto.
instantiate (1:= t2).
simpl.
generalize dependent H1.
clear.
{ induction 1.
constructor.
eapply star_trans.
eapply star_one.
rewrite single_step_aux_eq.
unfold single_step_aux.
exact H.
eauto.
eauto. }
eauto.
Qed.
End WITH_GE.
End LinkwithLAsm.
Section LinkSim.
Context `{Hmem: Mem.MemoryModelX}.
Context `{Hmwd: UseMemWithData mem}.
Context `{real_params: RealParams}.
Context `{multi_oracle_prop: MultiOracleProp}.
Context `{builtin_idents_norepet_prf: CompCertBuiltins.BuiltinIdentsNorepet}.
Notation LDATA := RData.
Notation LDATAOps := (cdata (cdata_ops := mboot_data_ops) LDATA).
Local Open Scope Z_scope.
Context `{pmap: PartialMap}.
Context `{zset_op: ZSet_operation}.
Context `{mc_oracle_cond: MCLinkOracleCond (mem := mem) (memory_model_ops := memory_model_ops) (Hmwd := Hmwd)
(Hmem := Hmem) (real_params_ops := real_params_ops)
(oracle_ops0 := oracle_ops0) (oracle_ops := oracle_ops) (big_ops := big_ops)
(builtin_idents_norepet_prf := builtin_idents_norepet_prf)
(zset_op := zset_op) (pmap := pmap)}.
Theorem cl_backward_simulation:
∀ (s: stencil) (CTXT: LAsm.module) (ph: AST.program fundef unit)
(Hmakep: make_program (module_ops:= LAsm.module_ops) s CTXT (mboot ⊕ L64) = OK ph),
backward_simulation
(single_big_semantics
(Hmakege := make_program_globalenv (make_program_ops := make_program_ops) _ _ _ _ Hmakep)
(Genv.globalenv ph) s CTXT ph)
(single_semantics
(Hmakege := make_program_globalenv (make_program_ops := make_program_ops) _ _ _ _ Hmakep)
(Genv.globalenv ph) s CTXT ph).
Proof.
intros. apply forward_to_backward_simulation; eauto.
- eapply forward_simulation_plus with
(match_states:= match_bsstate_link); intros; eauto; simpl in *; unfold match_bsstate_link in *;
simpl in ×.
+ inv H.
∃ (SState current_CPU_ID (LState (hdset := hdseting) (Asm.State rs0 m0) true) nil).
split.
× constructor; eauto.
× constructor; auto.
split; [constructor | split].
{ eapply current_CPU_ID_in_core_set. }
{ constructor. }
{ intro contra; inv contra. }
{ simpl.
split; [auto | intro contra; inv contra]. }
+ generalize one_step_single_refines_big_concrete; simpl.
unfold single_big_step_aux_ge´.
unfold single_big_step_aux_ge´.
intros Hstep.
unfold match_bsstate in ×.
eapply Hstep in H; eauto.
-
eapply single_big_semantics_receptive.
-
eapply single_semantics_determinate; eauto.
Qed.
End LinkSim.