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(* *************************************************************)
(* *)
(* The Compcert verified compiler *)
(* *)
(* Sylvain Boulmé Grenoble-INP, VERIMAG *)
(* Justus Fasse UGA, VERIMAG *)
(* Xavier Leroy INRIA Paris-Rocquencourt *)
(* David Monniaux CNRS, VERIMAG *)
(* Cyril Six Kalray *)
(* *)
(* Copyright Kalray. Copyright VERIMAG. All rights reserved. *)
(* This file is distributed under the terms of the INRIA *)
(* Non-Commercial License Agreement. *)
(* *)
(* *************************************************************)
Require Import Coqlib Errors.
Require Import Integers Floats AST Linking.
Require Import Values Memory Events Globalenvs Smallstep.
Require Import Op Locations Machblock Conventions PseudoAsmblock Asmblock.
Require Machblockgenproof Asmblockgenproof.
Require Import Asmgen.
Module Asmblock_PRESERVATION.
Import Asmblock_TRANSF.
Definition match_prog (p: Asmblock.program) (tp: Asm.program) :=
match_program (fun _ f tf => transf_fundef f = OK tf) eq p tp.
Lemma transf_program_match:
forall p tp, transf_program p = OK tp -> match_prog p tp.
Proof.
intros. eapply match_transform_partial_program; eauto.
Qed.
Section PRESERVATION.
Variable prog: Asmblock.program.
Variable tprog: Asm.program.
Hypothesis TRANSF: match_prog prog tprog.
Let ge := Genv.globalenv prog.
Let tge := Genv.globalenv tprog.
Definition lk :aarch64_linker := {| Asmblock.symbol_low:=Asm.symbol_low tge; Asmblock.symbol_high:=Asm.symbol_high tge|}.
Lemma symbols_preserved:
forall (s: ident), Genv.find_symbol tge s = Genv.find_symbol ge s.
Proof (Genv.find_symbol_match TRANSF).
Lemma symbol_addresses_preserved:
forall (s: ident) (ofs: ptrofs),
Genv.symbol_address tge s ofs = Genv.symbol_address ge s ofs.
Proof.
intros; unfold Genv.symbol_address; rewrite symbols_preserved; reflexivity.
Qed.
Lemma senv_preserved:
Senv.equiv ge tge.
Proof (Genv.senv_match TRANSF).
Lemma symbol_high_low: forall (id: ident) (ofs: ptrofs),
Val.addl (Asmblock.symbol_high lk id ofs) (Asmblock.symbol_low lk id ofs) = Genv.symbol_address ge id ofs.
Proof.
unfold lk; simpl. intros; rewrite Asm.symbol_high_low; unfold Genv.symbol_address;
rewrite symbols_preserved; reflexivity.
Qed.
Lemma functions_translated:
forall b f,
Genv.find_funct_ptr ge b = Some f ->
exists tf,
Genv.find_funct_ptr tge b = Some tf /\ transf_fundef f = OK tf.
Proof (Genv.find_funct_ptr_transf_partial TRANSF).
(* Asmblock and Asm share the same definition of state *)
Definition match_states (s1 s2 : state) := s1 = s2.
Lemma transf_initial_states:
forall s1, Asmblock.initial_state prog s1 ->
exists s2, Asm.initial_state tprog s2 /\ match_states s1 s2.
Proof.
intros ? INIT_s1.
inversion INIT_s1 as (m, ?, ge0, rs). unfold ge0 in *.
econstructor; split.
- econstructor.
eapply (Genv.init_mem_transf_partial TRANSF); eauto.
- rewrite (match_program_main TRANSF); rewrite symbol_addresses_preserved.
unfold rs; reflexivity.
Qed.
Lemma transf_final_states:
forall s1 s2 r,
match_states s1 s2 -> Asmblock.final_state s1 r -> Asm.final_state s2 r.
Proof.
intros s1 s2 r MATCH FINAL_s1.
inv FINAL_s1; inv MATCH; constructor; assumption.
Qed.
Lemma step_simulation s1 t s1':
Asmblock.step lk ge s1 t s1' ->
forall s2, match_states s1 s2 ->
(exists s2', plus Asm.step tge s2 t s2' /\ match_states s1' s2').
Proof.
intros STEP s2 MATCH.
inv STEP; simpl; exploit functions_translated; eauto;
intros (tf0 & FINDtf & TRANSf);
monadInv TRANSf.
- (* internal step *) admit.
- (* external step *)
eexists; split.
+ apply plus_one.
rewrite <- MATCH.
exploit external_call_symbols_preserved; eauto. apply senv_preserved.
intros ?.
eapply Asm.exec_step_external; eauto.
+ econstructor; eauto.
Admitted.
Lemma transf_program_correct:
forward_simulation (Asmblock.semantics lk prog) (Asm.semantics tprog).
Proof.
eapply forward_simulation_plus.
- apply senv_preserved.
- eexact transf_initial_states.
- eexact transf_final_states.
- (* TODO step_simulation *) admit.
Admitted.
End PRESERVATION.
End Asmblock_PRESERVATION.
Local Open Scope linking_scope.
Definition block_passes :=
mkpass Machblockgenproof.match_prog
::: mkpass PseudoAsmblockproof.match_prog
::: mkpass Asmblockgenproof.match_prog
::: mkpass Asmblock_PRESERVATION.match_prog
::: pass_nil _.
Definition match_prog := pass_match (compose_passes block_passes).
Lemma transf_program_match:
forall p tp, Asmgen.transf_program p = OK tp -> match_prog p tp.
Proof.
intros p tp H.
unfold Asmgen.transf_program in H. apply bind_inversion in H. destruct H.
inversion_clear H. apply bind_inversion in H1. destruct H1.
inversion_clear H. inversion H2. remember (Machblockgen.transf_program p) as mbp.
unfold match_prog; simpl.
exists mbp; split. apply Machblockgenproof.transf_program_match; auto.
exists x; split. apply PseudoAsmblockproof.transf_program_match; auto.
exists x0; split. apply Asmblockgenproof.transf_program_match; auto.
exists tp; split. apply Asmblock_PRESERVATION.transf_program_match; auto. auto.
Qed.
(** Return Address Offset *)
Definition return_address_offset: Mach.function -> Mach.code -> ptrofs -> Prop :=
Machblockgenproof.Mach_return_address_offset (PseudoAsmblockproof.rao Asmblockgenproof.next).
Lemma return_address_exists:
forall f sg ros c, is_tail (Mach.Mcall sg ros :: c) f.(Mach.fn_code) ->
exists ra, return_address_offset f c ra.
Proof.
intros; eapply Machblockgenproof.Mach_return_address_exists; eauto.
Admitted.
Section PRESERVATION.
Variable prog: Mach.program.
Variable tprog: Asm.program.
Hypothesis TRANSF: match_prog prog tprog.
Let ge := Genv.globalenv prog.
Let tge := Genv.globalenv tprog.
Theorem transf_program_correct:
forward_simulation (Mach.semantics return_address_offset prog) (Asm.semantics tprog).
Proof.
unfold match_prog in TRANSF. simpl in TRANSF.
inv TRANSF. inv H. inv H1. inv H. inv H2. inv H. inv H3. inv H.
eapply compose_forward_simulations.
{ exploit Machblockgenproof.transf_program_correct; eauto. }
eapply compose_forward_simulations.
+ apply PseudoAsmblockproof.transf_program_correct; eauto.
- intros; apply Asmblockgenproof.next_progress.
- intros; eapply Asmblockgenproof.functions_bound_max_pos; eauto.
{ intros; eapply Asmblock_PRESERVATION.symbol_high_low; eauto. }
+ eapply compose_forward_simulations. apply Asmblockgenproof.transf_program_correct; eauto.
{ intros; eapply Asmblock_PRESERVATION.symbol_high_low; eauto. }
apply Asmblock_PRESERVATION.transf_program_correct. eauto.
Qed.
End PRESERVATION.
Instance TransfAsm: TransfLink match_prog := pass_match_link (compose_passes block_passes).
(*******************************************)
(* Stub actually needed by driver/Compiler *)
Module Asmgenproof0.
Definition return_address_offset := return_address_offset.
End Asmgenproof0.
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