Library mcertikos.mm.ShareIntroGenLink

Require Import LinkTemplate.
Require Import MShareIntro.
Require Import ShareIntroGen.
Require Import ShareIntroGenLinkSource.
Require Import MPTNew.
Require Import MPTNewCSource.
Require Import MPTNewCode.

Section WITHCOMPCERTIKOS.
  Context `{compcertikos_prf: CompCertiKOS} `{real_params_prf: RealParams}.
  Context `{multi_oracle_prop: MultiOracleProp}.

  Lemma make_program_find_symbol (CTXT md : module)(m : mem) s :
      (p <- make_program s (CTXT ⊕ (md
              ⊕ SHRDMEMPOOL_LOC ↦ smspool_loc_type) ⊕ ∅) (mptnew ⊕ L64);
       ret (Genv.init_mem p) = OK (Some m)) →
      ∃ b, find_symbol s SHRDMEMPOOL_LOC = Some b ∧
                ∀ pid1 pid2,
                  0 ≤ pid1 < num_proc →
                  0 ≤ pid2 < num_proc →
                  Mem.valid_access m Mint32 b (pid1 × (num_proc × 12) + pid2 × 12) Writable ∧
                  Mem.valid_access m Mint32 b (pid1 × (num_proc × 12) + pid2 × 12 + 4) Writable ∧
                  Mem.valid_access m Mint32 b (pid1 × (num_proc × 12) + pid2 × 12 + 8) Writable.
  Proof.
    intros mkprog; inv_monad´ mkprog.
    assert (mkgenv := make_program_make_globalenv _ _ _ _ mkprog0).
    pose proof mkgenv as mkgenv´.
    eapply make_globalenv_stencil_matches in mkgenv´.
    inv_make_globalenv mkgenv.
    subst.
    rewrite (stencil_matches_symbols _ _ mkgenv´) in ×. inv mkgenv´.
    eexists; split; try eassumption.

    specialize (Genv.init_mem_characterization _ _ Hbvi H0); eauto.
    unfold Genv.perm_globvar; simpl; intros [Hperm _].
    change (Z.max 12582912 0) with 12582912 in Hperm.
    change 12288 with (num_proc × 12); try omega.
    intros; repeat split.
    - unfold Mem.range_perm; intros; apply Hperm.
      simpl in H2.
      omega.
    - replace (pid1 × (num_proc × 12) + pid2 × 12) with ((pid1 × (num_proc × 3) + pid2 × 3) × 4) by omega.
      eexists; reflexivity.
    - unfold Mem.range_perm; intros; apply Hperm.
      simpl in H2.
      omega.
    - replace (pid1 × (num_proc × 12) + pid2 × 12 + 4) with ((pid1 × (num_proc × 3) + pid2 × 3 + 1) × 4) by omega.
      eexists; reflexivity.
    - unfold Mem.range_perm; intros; apply Hperm.
      simpl in H2.
      omega.
    - replace (pid1 × (num_proc × 12) + pid2 × 12 + 8) with ((pid1 × (num_proc × 3) + pid2 × 3 + 2) × 4) by omega.
      eexists; reflexivity.
  Qed.

  Lemma init_correct:
    init_correct_type MShareIntro_module mptnew mshareintro.
  Proof.
    init_correct.

    exploit make_program_find_symbol; eauto.
    intros (b´ & find_symbol_SHRDMEMPOOL_LOC & access).
    assert (b´ = b) by congruence; subst.
    econstructor; try eassumption; intros.
    rewrite 2 ZMap.gi.

    specialize (access _ _ H0 H1).
    destruct access as [ ? [] ].
    assert (readable : Mem.valid_access m2 Mint32 b (pid1 × (num_proc × 12) + pid2 × 12) Readable).
    { eapply Mem.valid_access_implies; try eassumption; constructor. }
    assert (readable4 : Mem.valid_access m2 Mint32 b (pid1 × (num_proc × 12) + pid2 × 12 + 4) Readable).
    { eapply Mem.valid_access_implies; try eassumption; constructor. }
    assert (readable8 : Mem.valid_access m2 Mint32 b (pid1 × (num_proc × 12) + pid2 × 12 + 8) Readable).
    { eapply Mem.valid_access_implies; try eassumption; constructor. }

    destruct (Mem.valid_access_load _ _ _ _ readable) as [ v load ].
    destruct (Mem.valid_access_load _ _ _ _ readable4) as [ v4 load4 ].
    destruct (Mem.valid_access_load _ _ _ _ readable8) as [ v8 load8 ].
    ∃ v, v4, v8; repeat (split; [ eassumption |]).
    constructor.
  Qed.

  Lemma link_correct_aux:
    link_correct_aux_type MShareIntro_module mptnew mshareintro.
  Proof.
    link_correct_aux.
    - link_cfunction
        clear_shared_mem_spec_ref
        MPTNewCode.clear_shared_mem_code_correct.
    - link_cfunction
        get_shared_mem_state_spec_ref
        MPTNewCode.get_shared_mem_state_code_correct.
    - link_cfunction
        get_shared_mem_seen_spec_ref
        MPTNewCode.get_shared_mem_seen_code_correct.
    - link_cfunction
        get_shared_mem_loc_spec_ref
        MPTNewCode.get_shared_mem_loc_code_correct.
    - link_cfunction
        set_shared_mem_state_spec_ref
        MPTNewCode.set_shared_mem_state_code_correct.
    - link_cfunction
        set_shared_mem_seen_spec_ref
        MPTNewCode.set_shared_mem_seen_code_correct.
    - link_cfunction
        set_shared_mem_loc_spec_ref
        MPTNewCode.set_shared_mem_loc_code_correct.
    - apply passthrough_correct.
  Qed.

  Theorem cl_backward_simulation:
    cl_backward_simulation_type MShareIntro_module mptnew mshareintro.
  Proof.
    cl_backward_simulation init_correct link_correct_aux.
  Qed.

  Theorem make_program_exists:
    make_program_exist_type MShareIntro_module mptnew mshareintro.
  Proof.
    make_program_exists link_correct_aux.
  Qed.

End WITHCOMPCERTIKOS.