Library mcertikos.ipc.IPCIntroGenLink

Require Import HAsmLinkTemplate.
Require Import PIPCIntro.
Require Import IPCIntroGen.
Require Import IPCIntroGenLinkSource.
Require Import PHThread.
Require Import PHThreadCSource.
Require Import PHThreadCode.
Require Import LAsmModuleSemSpec.

Require Import GlobalOracleProp.
Require Import SingleOracle.

Section WITHCOMPCERTIKOS.

  Context `{single_oracle_prop: SingleOracleProp}.
  Context `{real_params : RealParams}.
  Context `{multi_oracle_prop: MultiOracleProp}.
  Context `{compcertkos: CompCertiKOS}.
  Context `{multi_oracle_link: !MultiOracleLink}.


  Notation HDATA := AbstractDataType.RData.
  Notation LDATA := AbstractDataType.RData.

  Notation HDATAOps := (cdata (cdata_ops := pipcintro_data_ops) HDATA).
  Notation LDATAOps := (cdata (cdata_ops := phthread_data_ops) LDATA).

  Definition oplus_monotonic := PseudoJoin.oplus_monotonic
    (A := compatlayer (cdata _ (cdata_ops := phthread_data_ops))).
  Definition oplus_sim_monotonic := PseudoJoin.oplus_sim_monotonic.
  Definition right_upper_bound := Structures.right_upper_bound
    (A := compatlayer (cdata _ (cdata_ops := phthread_data_ops))).
  Definition left_upper_bound := Structures.left_upper_bound
    (A := compatlayer (cdata _ (cdata_ops := phthread_data_ops))).

  Lemma init_correct:
    init_correct_type PIPCIntro_module phthread pipcintro.
  Proof.
    init_correct.
    - destruct (init_data_low_level_invariant (genv_next s)); eauto.
    - destruct (init_data_low_level_invariant (genv_next s)); eauto.
      repeat intro.
      edestruct kctxt_INJECT; eauto.
    - destruct (init_data_low_level_invariant (genv_next s)); eauto.
      repeat intro.
      edestruct uctxt_INJECT; eauto.
    - destruct (init_data_low_level_invariant (genv_next s)); eauto.
      repeat intro.
      assert (vmcs2 = vmcs1) as Hvmcs by congruence.
      rewrite Hvmcs.
      specialize (VMCS_INJECT vmid vmcs1 H0 H1).
      destruct VMCS_INJECT; eauto.
      constructor.
      intro.
      edestruct H3; eauto.
    - destruct (init_data_low_level_invariant (genv_next s)); eauto.
      repeat intro.
      assert (vmx2 = vmx1) as Hvmx by congruence.
      rewrite Hvmx.
      specialize (VMX_INJECT vmid vmx1 H0 H1).
      destruct VMX_INJECT; eauto.
      constructor.
      intro.
      edestruct H3; eauto.
  Qed.

  Lemma link_correct_aux:
    link_correct_aux_type PIPCIntro_module phthread pipcintro.
  Proof.
    link_correct_aux.
    - link_cfunction
         syncsendto_chan_pre_spec_ref
         PIPCINTROCODE.syncsendto_chan_pre_code_correct.
    - link_cfunction
         tryreceive_chan_spec_ref
         PIPCINTROCODE.tryreceive_chan_code_correct.
    - apply passthrough_correct.
  Qed.

  Theorem cl_backward_simulation:
    cl_backward_simulation_type PIPCIntro_module phthread pipcintro.
  Proof.
    cl_backward_simulation init_correct link_correct_aux.
  Qed.

  Theorem make_program_exists:
    make_program_exist_type PIPCIntro_module phthread pipcintro.
  Proof.
    make_program_exists link_correct_aux.
  Qed.

End WITHCOMPCERTIKOS.