Library mcertikos.multicore.refins.AsmSingleSemtoEnvSem

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 SingleSemImpl.
Require Import EnvSemImpl.

Require Import FutureTactic.

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 env_step_aux_ge´ :=
      @env_step_aux_ge mem memory_model_ops Hmem Hmwd
                       real_params_ops oracle_ops0 oracle_ops big_ops
                       builtin_idents_norepet_prf pmap zset_op
                       (s_set current_CPU_ID) single_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.

    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 env_step_aux_eq :
      ∀ s t s´,
        env_step_aux_ge (s_set current_CPU_ID) single_oracle ge sten M (Hmakege:=Hmakege) ge s t s´ ↔
        env_step_aux (s_set current_CPU_ID) single_oracle ge sten M (Hmakege:=Hmakege) s t s´.
    Proof.
      intros; split; intros.
      inversion H; auto.
      constructor; auto.
    Qed.

    Definition match_sstate_link := match_sstate current_CPU_ID (hdset := hdseting).

    Hint Unfold match_sstate_link.

    Existing Instance op_general.

    Lemma one_step_single_refines_env_concrete:
      ∀ s s0 s´ t
             (Hone: single_step_aux_ge´ ge s t s´)
             (Hmatch: match_sstate_link s s0),
      ∃ s0´,
        plus (env_step_aux_ge´) ge s0 t s0´
        ∧ match_sstate_link s´ s0´.
    Proof.
      simpl in ×.
      unfold single_step_aux_ge´.
      unfold env_step_aux_ge´.
      intros.
      rewrite single_step_aux_eq in Hone.
      unfold single_step_aux in Hone; simpl in ×.
      unfold match_sstate_link in Hmatch.
      eapply one_step_single_refines_env in Hone; eauto.
      destruct Hone as (s0´ & Hone1 & Hone2).
      ∃ s0´.
      split; auto.
      inv Hone1.
      eapply plus_star_trans.
      eapply plus_one.
      rewrite env_step_aux_eq.
      unfold env_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 env_step_aux_eq.
        unfold env_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_semantics
           (Hmakege := make_program_globalenv (make_program_ops := make_program_ops) _ _ _ _ Hmakep)
           (Genv.globalenv ph) s CTXT ph)
        (env_semantics
           (s_set current_CPU_ID) single_oracle
           (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_sstate_link); intros; eauto; simpl in *; unfold match_sstate_link in *;
        simpl in ×.
      + inv H.
        ∃ (EState current_CPU_ID
                       (pset current_CPU_ID
                             (LState (hdset := hdseting) (Asm.State rs0 m0) true)
                       (pinit (B := s_set current_CPU_ID)
                              (LState (hdset := hdseting) (Asm.State rs0 m0) false))) nil).
        split.
        × constructor; eauto.
        × constructor; eauto.
          rewrite pgss; auto.
          rewrite s_set_in; auto.
      + generalize one_step_single_refines_env_concrete; simpl.
        unfold single_step_aux_ge´.
        unfold env_step_aux_ge´.
        unfold match_sstate_link.
        intros Hstep.
        eapply Hstep in H; eauto.
    -
      eapply single_semantics_receptive.
    -
      eapply env_semantics_determinate; eauto.
  Qed.

End LinkSim.