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author | Yann Herklotz <git@yannherklotz.com> | 2023-05-19 18:11:53 +0100 |
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committer | Yann Herklotz <git@yannherklotz.com> | 2023-05-19 18:11:53 +0100 |
commit | c79d1a9dcd5a1ac6bc10492380a77fafa780e7d6 (patch) | |
tree | 44a91ab0a55e6deffd98e7cd387a16a57759d73b /src/hls/GiblePargenproofBackward.v | |
parent | 3be880b441a4d2926c6b14b7bb25a04209fbbca6 (diff) | |
download | vericert-c79d1a9dcd5a1ac6bc10492380a77fafa780e7d6.tar.gz vericert-c79d1a9dcd5a1ac6bc10492380a77fafa780e7d6.zip |
Prepare work on evaluability of instructions
Diffstat (limited to 'src/hls/GiblePargenproofBackward.v')
-rw-r--r-- | src/hls/GiblePargenproofBackward.v | 57 |
1 files changed, 34 insertions, 23 deletions
diff --git a/src/hls/GiblePargenproofBackward.v b/src/hls/GiblePargenproofBackward.v index db0df19..b4442a8 100644 --- a/src/hls/GiblePargenproofBackward.v +++ b/src/hls/GiblePargenproofBackward.v @@ -31,6 +31,7 @@ Require Import vericert.hls.GiblePar. Require Import vericert.hls.Gible. Require Import vericert.hls.GiblePargenproofEquiv. Require Import vericert.hls.GiblePargenproofCommon. +Require Import vericert.hls.GiblePargenproofForward. Require Import vericert.hls.GiblePargen. Require Import vericert.hls.Predicate. Require Import vericert.hls.Abstr. @@ -130,9 +131,8 @@ Definition evaluable_pred_list {G} ctx pr l := (* unfold evaluable_pred_expr in H1. Admitted. *) Lemma evaluable_pred_expr_exists : - forall sp pr f i0 exit_p exit_p' f' i ti p op args dst, - (forall x, sem_pexpr (mk_ctx i0 sp ge) (get_forest_p' x f'.(forest_preds)) (pr !! x)) -> - eval_predf pr exit_p = true -> + forall sp f i0 exit_p exit_p' f' i ti p op args dst, + eval_predf (is_ps i) exit_p = true -> valid_mem (is_mem i0) (is_mem i) -> update (exit_p, f) (RBop p op args dst) = Some (exit_p', f') -> sem (mk_ctx i0 sp ge) f (i, None) -> @@ -141,19 +141,22 @@ Lemma evaluable_pred_expr_exists : exists ti', step_instr ge sp (Iexec ti) (RBop p op args dst) (Iexec ti'). Proof. - intros * HPRED HEVAL VALID_MEM **. cbn -[seq_app] in H. unfold Option.bind in H. destr. inv H. - destruct ti. + intros * HEVAL VALID_MEM **. cbn -[seq_app] in H. unfold Option.bind in H. destr. inv H. + assert (HPRED': sem_predset {| ctx_is := i0; ctx_sp := sp; ctx_ge := ge |} f (is_ps i)) + by now inv H0. + inversion_clear HPRED' as [? ? ? HPRED]. + destruct ti as [is_trs is_tps is_tm]. unfold evaluable_pred_expr in H1. destruct H1 as (r & Heval). rewrite forest_reg_gss in Heval. - exploit sem_pred_expr_prune_predicated2; eauto; intros. cbn in HPRED. - pose proof (truthy_dec pr p) as YH. inversion_clear YH as [YH'|YH']. - - assert (eval_predf pr (dfltp p ∧ exit_p') = true). + exploit sem_pred_expr_prune_predicated2; eauto; intros. + pose proof (truthy_dec (is_ps i) p) as YH. inversion_clear YH as [YH'|YH']. + - assert (eval_predf (is_ps i) (dfltp p ∧ exit_p') = true). { pose proof (truthy_dflt _ _ YH'). rewrite eval_predf_Pand. rewrite H1. now rewrite HEVAL. } exploit sem_pred_expr_app_predicated2; eauto; intros. exploit sem_pred_expr_seq_app_val2; eauto; simplify. unfold pred_ret in *. inv H4. inv H12. - destruct i. exploit sem_merge_list; eauto; intros. + destruct i as [is_rs_1 is_ps_1 is_m_1]. exploit sem_merge_list; eauto; intros. instantiate (1 := args) in H4. eapply sem_pred_expr_ident2 in H4. simplify. exploit sem_pred_expr_ident_det. eapply H5. eapply H4. @@ -164,18 +167,18 @@ Proof. + cbn in *. eapply eval_operation_valid_pointer. symmetry; eauto. unfold ctx_mem in H14. cbn in H14. erewrite <- match_states_list; eauto. + inv H0. - assert (sem_predset {| ctx_is := i0; ctx_sp := sp; ctx_ge := ge |} f pr) + assert (sem_predset {| ctx_is := i0; ctx_sp := sp; ctx_ge := ge |} f (is_ps_1)) by (now constructor). pose proof (sem_predset_det _ _ ltac:(reflexivity) _ _ _ H0 H17). - assert (truthy is_ps0 p). + assert (truthy is_ps_1 p). { eapply truthy_match_state; eassumption. } eapply truthy_match_state; eassumption. - inv YH'. cbn -[seq_app] in H. - assert (eval_predf pr (p0 ∧ exit_p') = false). + assert (eval_predf (is_ps i) (p0 ∧ exit_p') = false). { rewrite eval_predf_Pand. now rewrite H1. } eapply sem_pred_expr_app_predicated_false2 in H; eauto. eexists. eapply exec_RB_falsy. constructor. auto. cbn. - assert (sem_predset {| ctx_is := i0; ctx_sp := sp; ctx_ge := ge |} f pr) + assert (sem_predset {| ctx_is := i0; ctx_sp := sp; ctx_ge := ge |} f (is_ps i)) by (now constructor). inv H0. pose proof (sem_predset_det _ _ ltac:(reflexivity) _ _ _ H4 H8). inv H2. @@ -302,6 +305,8 @@ Proof. Admitted. (* [[id:5e6486bb-fda2-4558-aed8-243a9698de85]] *) Lemma abstr_seq_reverse_correct_fold : forall sp instrs i0 i i' ti cf f' l p p' l' f, + valid_mem (is_mem i0) (is_mem i) -> + eval_predf (is_ps i) p = true -> sem (mk_ctx i0 sp ge) f (i, None) -> mfold_left update' instrs (Some (p, f, l)) = Some (p', f', l') -> evaluable_pred_list (mk_ctx i0 sp ge) f'.(forest_preds) l' -> @@ -311,12 +316,12 @@ Lemma abstr_seq_reverse_correct_fold : SeqBB.step ge sp (Iexec ti) instrs (Iterm ti' cf) /\ state_lessdef i' ti'. Proof. - induction instrs; intros * Y3 Y Y0 Y1 Y2. + induction instrs; intros * YVALID YEVAL Y3 Y Y0 Y1 Y2. - cbn in *. inv Y. - assert (similar {| ctx_is := i0; ctx_sp := sp; ctx_ge := ge |} - {| ctx_is := i0; ctx_sp := sp; ctx_ge := ge |}) + assert (X: similar {| ctx_is := i0; ctx_sp := sp; ctx_ge := ge |} + {| ctx_is := i0; ctx_sp := sp; ctx_ge := ge |}) by reflexivity. - now eapply sem_det in H; [| eapply Y1 | eapply Y3 ]. + now eapply sem_det in X; [| exact Y1 | exact Y3 ]. - cbn -[update] in Y. pose proof Y as YX. apply OptionExtra.mfold_left_Some in YX. inv YX. @@ -330,18 +335,24 @@ Proof. by admit; destruct H as (pred & op & args & dst & EQ); subst a. exploit evaluable_pred_expr_exists; eauto. + (* I have the pred already from sem. *) - admit. admit. admit. intros [t step]. + intros [ti_mid HSTEP]. (* unfold evaluable_pred_list in Y0. *) (* instantiate (1 := forest_preds f'). *) (* eapply in_forest_evaluable; eauto. *) (* (* provable using evaluability in list *) intros [t step]. *) - exploit IHinstrs. 2: { eapply Y. } eauto. auto. eauto. reflexivity. - intros (ti_mid' & Hseq & Hstate). - assert (state_lessdef ti_mid t) by admit. - exists ti_mid'; split; auto. - econstructor; eauto. + pose proof Y3 as YH. + pose proof HSTEP as YHSTEP. + pose proof Y2 as Y2SPLIT; inv Y2SPLIT. + eapply step_exists in YHSTEP. + 2: { symmetry. econstructor; try eassumption; auto. } + inv YHSTEP. inv H1. + exploit sem_update_instr. auto. eauto. eauto. eauto. eauto. auto. intros. + exploit IHinstrs. 3: { eauto. } admit. admit. eauto. admit. eauto. symmetry. + instantiate (1:=ti_mid). admit. intros [ti' [YHH HLD]]. + exists ti'; split; eauto. econstructor; eauto. Admitted. Lemma sem_empty : |