Library mcertikos.multicore.refins.AsmSplitSemtoBig2Sem
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 SplitSemImpl.
Require Import Big2SemImpl.
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_split_step_aux_ge´ :=
@single_split_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_big2_step_aux_ge´ :=
@single_big2_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.
Lemma single_split_step_aux_eq :
∀ s t s´,
single_split_step_aux_ge ge sten M (Hmakege:=Hmakege) ge s t s´ ↔
single_split_step_aux ge sten M (Hmakege:=Hmakege) s t s´.
Proof.
intros; split; intros.
inversion H; auto.
constructor; auto.
Qed.
Lemma single_big2_step_aux_eq :
∀ s t s´,
single_big2_step_aux_ge ge sten M (Hmakege:=Hmakege) ge s t s´ ↔
single_big2_step_aux ge sten M (Hmakege:=Hmakege) s t s´.
Proof.
intros; split; intros.
inversion H; auto.
constructor; auto.
Qed.
Lemma one_step_big2_refines_split_concrete:
∀ s s0 s´ t
(Hone: single_split_step_aux_ge´ ge s t s´)
(Hmatch: match_srstate (hdset := hdseting) s s0),
∃ s0´,
plus single_big2_step_aux_ge´ ge s0 t s0´
∧ match_srstate (hdset := hdseting) s´ s0´.
Proof.
simpl in ×.
unfold single_split_step_aux_ge´.
unfold single_big2_step_aux_ge´.
intros.
rewrite single_split_step_aux_eq in Hone.
unfold single_split_step_aux in Hone; simpl in ×.
eapply one_step_big2_refines_split with (o := single_oracle) in Hone; eauto.
destruct Hone as (s0´ & Hone1 & Hone2).
∃ s0´.
split; auto.
inv Hone1.
eapply plus_star_trans.
eapply plus_one.
rewrite single_big2_step_aux_eq.
unfold single_big2_step_aux; simpl; eauto.
instantiate (1:= t2).
simpl.
generalize dependent H0.
clear H Hmatch Hone2.
{ induction 1.
constructor.
eapply star_trans.
eapply star_one.
rewrite single_big2_step_aux_eq.
unfold single_big2_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_split_semantics
(Hmakege := make_program_globalenv (make_program_ops := make_program_ops) _ _ _ _ Hmakep)
(Genv.globalenv ph) s CTXT ph)
(single_big2_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_srstate (hdset := hdseting)); intros; eauto; simpl in ×.
+ inv H.
∃ (RState (hdset := hdseting) (Asm.State rs0 m0) nil).
split.
× constructor; eauto.
× constructor; eauto.
+ generalize one_step_big2_refines_split_concrete; simpl.
unfold single_split_step_aux_ge´.
unfold single_big2_step_aux_ge´.
intros Hstep.
eapply Hstep in H; eauto.
-
eapply single_split_semantics_receptive.
-
eapply single_big2_semantics_determinate; eauto.
Qed.
End LinkSim.