diff options
Diffstat (limited to 'backend/CSE3analysisproof.v')
| -rw-r--r-- | backend/CSE3analysisproof.v | 74 |
1 files changed, 56 insertions, 18 deletions
diff --git a/backend/CSE3analysisproof.v b/backend/CSE3analysisproof.v index 66b199cc..1e5b88c3 100644 --- a/backend/CSE3analysisproof.v +++ b/backend/CSE3analysisproof.v @@ -699,6 +699,27 @@ Section SOUNDNESS. + congruence. Qed. + Lemma arglist_idem_write: + forall { A : Type} args (rs : Regmap.t A) dst, + (rs # dst <- (rs # dst)) ## args = rs ## args. + Proof. + induction args; trivial. + intros. cbn. + f_equal; trivial. + apply Regmap.gsident. + Qed. + + Lemma sem_rhs_idem_write: + forall sop args rs dst m v, + sem_rhs sop args rs m v -> + sem_rhs sop args (rs # dst <- (rs # dst)) m v. + Proof. + intros. + unfold sem_rhs in *. + rewrite arglist_idem_write. + assumption. + Qed. + Theorem oper2_sound: forall no dst sop args rel rs m v, sem_rel rel rs m -> @@ -726,6 +747,17 @@ Section SOUNDNESS. rewrite Regmap.gss. apply sem_rhs_depends_on_args_only; auto. } + intros INi. + destruct (PSet.contains rel e) eqn:CONTAINSe. + { pose proof (REL e {| eq_lhs := dst; eq_op := sop; eq_args := args |} CONTAINSe H) as RELe. + pose proof (REL i eq CONTAINS INi) as RELi. + unfold sem_eq in *. + cbn in RELe. + replace v with (rs # dst) by (eapply sem_rhs_det; eassumption). + rewrite Regmap.gsident. + apply sem_rhs_idem_write. + assumption. + } rewrite PSet.gaddo in CONTAINS by congruence. apply (kill_reg_sound rel rs m dst v REL i eq); auto. Qed. @@ -821,24 +853,24 @@ Section SOUNDNESS. subst. rewrite <- (forward_move_sound rel rs m r) by auto. apply move_sound; auto. - - destruct (is_trivial_sym_op sop). - { - apply kill_reg_sound; auto. - } - destruct rhs_find as [src |] eqn:RHS_FIND. + - destruct rhs_find as [src |] eqn:RHS_FIND. + destruct (Compopts.optim_CSE3_glb tt). * apply sem_rel_glb; split. - ** pose proof (rhs_find_sound no sop (forward_move_l (ctx:=ctx) rel args) rel src rs m REL RHS_FIND) as SOUND. - eapply forward_move_rhs_sound in RHS. - 2: eassumption. + ** pose proof (rhs_find_sound no sop args rel src rs m REL RHS_FIND) as SOUND. rewrite <- (sem_rhs_det SOUND RHS). apply move_sound; auto. + ** apply sem_rel_glb; split. + *** apply oper1_sound; auto. + *** apply oper1_sound; auto. + apply forward_move_rhs_sound; auto. + * apply sem_rel_glb; split. + ** apply oper1_sound; auto. ** apply oper1_sound; auto. apply forward_move_rhs_sound; auto. - * ** apply oper1_sound; auto. - apply forward_move_rhs_sound; auto. - + apply oper1_sound; auto. - apply forward_move_rhs_sound; auto. + + apply sem_rel_glb; split. + * apply oper1_sound; auto. + * apply oper1_sound; auto. + apply forward_move_rhs_sound; auto. Qed. Hint Resolve oper_sound : cse3. @@ -927,22 +959,28 @@ Section SOUNDNESS. Hint Resolve store1_sound : cse3. + Theorem store_sound: forall no chunk addr args a src rel tenv rs m m', sem_rel rel rs m -> wt_regset tenv rs -> eval_addressing genv sp addr (rs ## args) = Some a -> Mem.storev chunk m a (rs#src) = Some m' -> - sem_rel (store (ctx:=ctx) no chunk addr args src (tenv (forward_move (ctx:=ctx) rel src)) rel) rs m'. + sem_rel (store (ctx:=ctx) no tenv chunk addr args src rel) rs m'. Proof. unfold store. intros until m'. intros REL WT ADDR STORE. - rewrite <- forward_move_l_sound with (rel:=rel) (m:=m) in ADDR by trivial. - rewrite <- forward_move_sound with (rel:=rel) (m:=m) in STORE by trivial. - apply store1_sound with (a := a) (m := m); trivial. - (* rewrite forward_move_sound with (rel:=rel) (m:=m) in STORE by trivial. - assumption. *) + apply sem_rel_glb; split. + - apply sem_rel_glb; split. + * apply store1_sound with (a := a) (m := m); trivial. + * rewrite <- forward_move_l_sound with (rel:=rel) (m:=m) in ADDR by trivial. + apply store1_sound with (a := a) (m := m); trivial. + - rewrite <- forward_move_sound with (rel:=rel) (m:=m) in STORE by trivial. + apply sem_rel_glb; split. + * apply store1_sound with (a := a) (m := m); trivial. + * rewrite <- forward_move_l_sound with (rel:=rel) (m:=m) in ADDR by trivial. + apply store1_sound with (a := a) (m := m); trivial. Qed. Hint Resolve store_sound : cse3. |