diff options
Diffstat (limited to 'common/Events.v')
| -rw-r--r-- | common/Events.v | 217 |
1 files changed, 167 insertions, 50 deletions
diff --git a/common/Events.v b/common/Events.v index b2335b96..28bb992a 100644 --- a/common/Events.v +++ b/common/Events.v @@ -24,6 +24,7 @@ Require Import Floats. Require Import Values. Require Import Memory. Require Import Globalenvs. +Require Import Builtins. (** * Events and traces *) @@ -622,7 +623,7 @@ Record extcall_properties (sem: extcall_sem) (sg: signature) : Prop := ec_well_typed: forall ge vargs m1 t vres m2, sem ge vargs m1 t vres m2 -> - Val.has_type vres (proj_sig_res sg); + Val.has_rettype vres sg.(sig_res); (** The semantics is invariant under change of global environment that preserves symbols. *) ec_symbols_preserved: @@ -648,9 +649,12 @@ Record extcall_properties (sem: extcall_sem) (sg: signature) : Prop := (** External call cannot modify memory unless they have [Max, Writable] permissions. *) ec_readonly: - forall ge vargs m1 t vres m2, + forall ge vargs m1 t vres m2 b ofs n bytes, sem ge vargs m1 t vres m2 -> - Mem.unchanged_on (loc_not_writable m1) m1 m2; + Mem.valid_block m1 b -> + Mem.loadbytes m2 b ofs n = Some bytes -> + (forall i, ofs <= i < ofs + n -> ~Mem.perm m1 b i Max Writable) -> + Mem.loadbytes m1 b ofs n = Some bytes; (** External calls must commute with memory extensions, in the following sense. *) @@ -770,12 +774,12 @@ Qed. Lemma volatile_load_ok: forall chunk, extcall_properties (volatile_load_sem chunk) - (mksignature (Tptr :: nil) (Some (type_of_chunk chunk)) cc_default). + (mksignature (Tptr :: nil) (rettype_of_chunk chunk) cc_default). Proof. intros; constructor; intros. (* well typed *) -- unfold proj_sig_res; simpl. inv H. inv H0. apply Val.load_result_type. - eapply Mem.load_type; eauto. +- inv H. inv H0. apply Val.load_result_rettype. + eapply Mem.load_rettype; eauto. (* symbols *) - inv H0. constructor. eapply volatile_load_preserved; eauto. (* valid blocks *) @@ -783,7 +787,7 @@ Proof. (* max perms *) - inv H; auto. (* readonly *) -- inv H. apply Mem.unchanged_on_refl. +- inv H; auto. (* mem extends *) - inv H. inv H1. inv H6. inv H4. exploit volatile_load_extends; eauto. intros [v' [A B]]. @@ -832,14 +836,27 @@ Proof. rewrite C; auto. Qed. +Lemma unchanged_on_readonly: + forall m1 m2 b ofs n bytes, + Mem.unchanged_on (loc_not_writable m1) m1 m2 -> + Mem.valid_block m1 b -> + Mem.loadbytes m2 b ofs n = Some bytes -> + (forall i, ofs <= i < ofs + n -> ~Mem.perm m1 b i Max Writable) -> + Mem.loadbytes m1 b ofs n = Some bytes. +Proof. + intros. + rewrite <- H1. symmetry. + apply Mem.loadbytes_unchanged_on_1 with (P := loc_not_writable m1); auto. +Qed. + Lemma volatile_store_readonly: forall ge chunk1 m1 b1 ofs1 v t m2, volatile_store ge chunk1 m1 b1 ofs1 v t m2 -> Mem.unchanged_on (loc_not_writable m1) m1 m2. Proof. intros. inv H. - apply Mem.unchanged_on_refl. - eapply Mem.store_unchanged_on; eauto. +- apply Mem.unchanged_on_refl. +- eapply Mem.store_unchanged_on; eauto. exploit Mem.store_valid_access_3; eauto. intros [P Q]. intros. unfold loc_not_writable. red; intros. elim H2. apply Mem.perm_cur_max. apply P. auto. @@ -921,7 +938,7 @@ Qed. Lemma volatile_store_ok: forall chunk, extcall_properties (volatile_store_sem chunk) - (mksignature (Tptr :: type_of_chunk chunk :: nil) None cc_default). + (mksignature (Tptr :: type_of_chunk chunk :: nil) Tvoid cc_default). Proof. intros; constructor; intros. (* well typed *) @@ -933,7 +950,7 @@ Proof. (* perms *) - inv H. inv H2. auto. eauto with mem. (* readonly *) -- inv H. eapply volatile_store_readonly; eauto. +- inv H. eapply unchanged_on_readonly; eauto. eapply volatile_store_readonly; eauto. (* mem extends*) - inv H. inv H1. inv H6. inv H7. inv H4. exploit volatile_store_extends; eauto. intros [m2' [A [B C]]]. @@ -966,7 +983,7 @@ Inductive extcall_malloc_sem (ge: Senv.t): Lemma extcall_malloc_ok: extcall_properties extcall_malloc_sem - (mksignature (Tptr :: nil) (Some Tptr) cc_default). + (mksignature (Tptr :: nil) Tptr cc_default). Proof. assert (UNCHANGED: forall (P: block -> Z -> Prop) m lo hi v m' b m'', @@ -983,7 +1000,7 @@ Proof. } constructor; intros. (* well typed *) -- inv H. unfold proj_sig_res, Tptr; simpl. destruct Archi.ptr64; auto. +- inv H. simpl. unfold Tptr; destruct Archi.ptr64; auto. (* symbols preserved *) - inv H0; econstructor; eauto. (* valid block *) @@ -993,7 +1010,7 @@ Proof. rewrite dec_eq_false. auto. apply Mem.valid_not_valid_diff with m1; eauto with mem. (* readonly *) -- inv H. eapply UNCHANGED; eauto. +- inv H. eapply unchanged_on_readonly; eauto. (* mem extends *) - inv H. inv H1. inv H7. assert (SZ: v2 = Vptrofs sz). @@ -1044,38 +1061,43 @@ Qed. Inductive extcall_free_sem (ge: Senv.t): list val -> mem -> trace -> val -> mem -> Prop := - | extcall_free_sem_intro: forall b lo sz m m', + | extcall_free_sem_ptr: forall b lo sz m m', Mem.load Mptr m b (Ptrofs.unsigned lo - size_chunk Mptr) = Some (Vptrofs sz) -> Ptrofs.unsigned sz > 0 -> Mem.free m b (Ptrofs.unsigned lo - size_chunk Mptr) (Ptrofs.unsigned lo + Ptrofs.unsigned sz) = Some m' -> - extcall_free_sem ge (Vptr b lo :: nil) m E0 Vundef m'. + extcall_free_sem ge (Vptr b lo :: nil) m E0 Vundef m' + | extcall_free_sem_null: forall m, + extcall_free_sem ge (Vnullptr :: nil) m E0 Vundef m. Lemma extcall_free_ok: extcall_properties extcall_free_sem - (mksignature (Tptr :: nil) None cc_default). + (mksignature (Tptr :: nil) Tvoid cc_default). Proof. constructor; intros. (* well typed *) -- inv H. unfold proj_sig_res. simpl. auto. +- inv H; simpl; auto. (* symbols preserved *) - inv H0; econstructor; eauto. (* valid block *) -- inv H. eauto with mem. +- inv H; eauto with mem. (* perms *) -- inv H. eapply Mem.perm_free_3; eauto. +- inv H; eauto using Mem.perm_free_3. (* readonly *) -- inv H. eapply Mem.free_unchanged_on; eauto. - intros. red; intros. elim H3. +- eapply unchanged_on_readonly; eauto. inv H. ++ eapply Mem.free_unchanged_on; eauto. + intros. red; intros. elim H6. apply Mem.perm_cur_max. apply Mem.perm_implies with Freeable; auto with mem. eapply Mem.free_range_perm; eauto. ++ apply Mem.unchanged_on_refl. (* mem extends *) -- inv H. inv H1. inv H8. inv H6. +- inv H. ++ inv H1. inv H8. inv H6. exploit Mem.load_extends; eauto. intros [v' [A B]]. assert (v' = Vptrofs sz). { unfold Vptrofs in *; destruct Archi.ptr64; inv B; auto. } subst v'. exploit Mem.free_parallel_extends; eauto. intros [m2' [C D]]. - exists Vundef; exists m2'; intuition. + exists Vundef; exists m2'; intuition auto. econstructor; eauto. eapply Mem.free_unchanged_on; eauto. unfold loc_out_of_bounds; intros. @@ -1083,8 +1105,14 @@ Proof. { apply Mem.perm_cur_max. apply Mem.perm_implies with Freeable; auto with mem. eapply Mem.free_range_perm. eexact H4. eauto. } tauto. ++ inv H1. inv H5. replace v2 with Vnullptr. + exists Vundef; exists m1'; intuition auto. + constructor. + apply Mem.unchanged_on_refl. + unfold Vnullptr in *; destruct Archi.ptr64; inv H3; auto. (* mem inject *) -- inv H0. inv H2. inv H7. inv H9. +- inv H0. ++ inv H2. inv H7. inv H9. exploit Mem.load_inject; eauto. intros [v' [A B]]. assert (v' = Vptrofs sz). { unfold Vptrofs in *; destruct Archi.ptr64; inv B; auto. } @@ -1098,7 +1126,7 @@ Proof. intro EQ. exploit Mem.free_parallel_inject; eauto. intros (m2' & C & D). exists f, Vundef, m2'; split. - apply extcall_free_sem_intro with (sz := sz) (m' := m2'). + apply extcall_free_sem_ptr with (sz := sz) (m' := m2'). rewrite EQ. rewrite <- A. f_equal. omega. auto. auto. rewrite ! EQ. rewrite <- C. f_equal; omega. @@ -1111,14 +1139,19 @@ Proof. apply P. omega. split. auto. red; intros. congruence. ++ inv H2. inv H6. replace v' with Vnullptr. + exists f, Vundef, m1'; intuition auto using Mem.unchanged_on_refl. + constructor. + red; intros; congruence. + unfold Vnullptr in *; destruct Archi.ptr64; inv H4; auto. (* trace length *) - inv H; simpl; omega. (* receptive *) -- assert (t1 = t2). inv H; inv H0; auto. subst t2. +- assert (t1 = t2) by (inv H; inv H0; auto). subst t2. exists vres1; exists m1; auto. (* determ *) -- inv H; inv H0. - assert (EQ1: Vptrofs sz0 = Vptrofs sz) by congruence. +- inv H; inv H0; try (unfold Vnullptr in *; destruct Archi.ptr64; discriminate). ++ assert (EQ1: Vptrofs sz0 = Vptrofs sz) by congruence. assert (EQ2: sz0 = sz). { unfold Vptrofs in EQ1; destruct Archi.ptr64 eqn:SF. rewrite <- (Ptrofs.of_int64_to_int64 SF sz0), <- (Ptrofs.of_int64_to_int64 SF sz). congruence. @@ -1126,6 +1159,7 @@ Proof. } subst sz0. split. constructor. intuition congruence. ++ split. constructor. intuition auto. Qed. (** ** Semantics of [memcpy] operations. *) @@ -1146,11 +1180,11 @@ Inductive extcall_memcpy_sem (sz al: Z) (ge: Senv.t): Lemma extcall_memcpy_ok: forall sz al, extcall_properties (extcall_memcpy_sem sz al) - (mksignature (Tptr :: Tptr :: nil) None cc_default). + (mksignature (Tptr :: Tptr :: nil) Tvoid cc_default). Proof. intros. constructor. - (* return type *) - intros. inv H. constructor. + intros. inv H. exact I. - (* change of globalenv *) intros. inv H0. econstructor; eauto. - (* valid blocks *) @@ -1158,8 +1192,9 @@ Proof. - (* perms *) intros. inv H. eapply Mem.perm_storebytes_2; eauto. - (* readonly *) - intros. inv H. eapply Mem.storebytes_unchanged_on; eauto. - intros; red; intros. elim H8. + intros. inv H. eapply unchanged_on_readonly; eauto. + eapply Mem.storebytes_unchanged_on; eauto. + intros; red; intros. elim H11. apply Mem.perm_cur_max. eapply Mem.storebytes_range_perm; eauto. - (* extensions *) intros. inv H. @@ -1208,7 +1243,7 @@ Proof. assert (RPDST: Mem.range_perm m1 bdst (Ptrofs.unsigned odst) (Ptrofs.unsigned odst + sz) Cur Nonempty). replace sz with (Z.of_nat (length bytes)). eapply Mem.range_perm_implies. eapply Mem.storebytes_range_perm; eauto. auto with mem. - rewrite LEN. apply nat_of_Z_eq. omega. + rewrite LEN. apply Z2Nat.id. omega. assert (PSRC: Mem.perm m1 bsrc (Ptrofs.unsigned osrc) Cur Nonempty). apply RPSRC. omega. assert (PDST: Mem.perm m1 bdst (Ptrofs.unsigned odst) Cur Nonempty). @@ -1257,7 +1292,7 @@ Inductive extcall_annot_sem (text: string) (targs: list typ) (ge: Senv.t): Lemma extcall_annot_ok: forall text targs, extcall_properties (extcall_annot_sem text targs) - (mksignature targs None cc_default). + (mksignature targs Tvoid cc_default). Proof. intros; constructor; intros. (* well typed *) @@ -1270,7 +1305,7 @@ Proof. (* perms *) - inv H; auto. (* readonly *) -- inv H. apply Mem.unchanged_on_refl. +- inv H; auto. (* mem extends *) - inv H. exists Vundef; exists m1'; intuition. @@ -1302,11 +1337,11 @@ Inductive extcall_annot_val_sem (text: string) (targ: typ) (ge: Senv.t): Lemma extcall_annot_val_ok: forall text targ, extcall_properties (extcall_annot_val_sem text targ) - (mksignature (targ :: nil) (Some targ) cc_default). + (mksignature (targ :: nil) targ cc_default). Proof. intros; constructor; intros. (* well typed *) -- inv H. unfold proj_sig_res; simpl. eapply eventval_match_type; eauto. +- inv H. eapply eventval_match_type; eauto. (* symbols *) - destruct H as (A & B & C). inv H0. econstructor; eauto. eapply eventval_match_preserved; eauto. @@ -1315,7 +1350,7 @@ Proof. (* perms *) - inv H; auto. (* readonly *) -- inv H. apply Mem.unchanged_on_refl. +- inv H; auto. (* mem extends *) - inv H. inv H1. inv H6. exists v2; exists m1'; intuition. @@ -1346,7 +1381,7 @@ Inductive extcall_debug_sem (ge: Senv.t): Lemma extcall_debug_ok: forall targs, extcall_properties extcall_debug_sem - (mksignature targs None cc_default). + (mksignature targs Tvoid cc_default). Proof. intros; constructor; intros. (* well typed *) @@ -1358,7 +1393,7 @@ Proof. (* perms *) - inv H; auto. (* readonly *) -- inv H. apply Mem.unchanged_on_refl. +- inv H; auto. (* mem extends *) - inv H. exists Vundef; exists m1'; intuition. @@ -1377,12 +1412,68 @@ Proof. split. constructor. auto. Qed. +(** ** Semantics of known built-in functions. *) + +(** Some built-in functions and runtime support functions have known semantics + as defined in the [Builtin] modules. + These built-in functions have no observable effects and do not access memory. *) + +Inductive known_builtin_sem (bf: builtin_function) (ge: Senv.t): + list val -> mem -> trace -> val -> mem -> Prop := + | known_builtin_sem_intro: forall vargs vres m, + builtin_function_sem bf vargs = Some vres -> + known_builtin_sem bf ge vargs m E0 vres m. + +Lemma known_builtin_ok: forall bf, + extcall_properties (known_builtin_sem bf) (builtin_function_sig bf). +Proof. + intros. set (bsem := builtin_function_sem bf). constructor; intros. +(* well typed *) +- inv H. + specialize (bs_well_typed _ bsem vargs). + unfold val_opt_has_rettype, bsem; rewrite H0. + auto. +(* symbols *) +- inv H0. econstructor; eauto. +(* valid blocks *) +- inv H; auto. +(* perms *) +- inv H; auto. +(* readonly *) +- inv H; auto. +(* mem extends *) +- inv H. fold bsem in H2. apply val_inject_list_lessdef in H1. + specialize (bs_inject _ bsem _ _ _ H1). + unfold val_opt_inject; rewrite H2; intros. + destruct (bsem vargs') as [vres'|] eqn:?; try contradiction. + exists vres', m1'; intuition auto using Mem.extends_refl, Mem.unchanged_on_refl. + constructor; auto. + apply val_inject_lessdef; auto. +(* mem injects *) +- inv H0. fold bsem in H3. + specialize (bs_inject _ bsem _ _ _ H2). + unfold val_opt_inject; rewrite H3; intros. + destruct (bsem vargs') as [vres'|] eqn:?; try contradiction. + exists f, vres', m1'; intuition auto using Mem.extends_refl, Mem.unchanged_on_refl. + constructor; auto. + red; intros; congruence. +(* trace length *) +- inv H; simpl; omega. +(* receptive *) +- inv H; inv H0. exists vres1, m1; constructor; auto. +(* determ *) +- inv H; inv H0. + split. constructor. intuition congruence. +Qed. + (** ** Semantics of external functions. *) -(** For functions defined outside the program ([EF_external], - [EF_builtin] and [EF_runtime]), we do not define their - semantics, but only assume that it satisfies - [extcall_properties]. *) +(** For functions defined outside the program ([EF_external]), + we do not define their semantics, but only assume that it satisfies + [extcall_properties]. + We do the same for built-in functions and runtime support functions that + are not described in [Builtins]. +*) Parameter external_functions_sem: String.string -> signature -> extcall_sem. @@ -1398,6 +1489,22 @@ Axiom inline_assembly_properties: (** ** Combined semantics of external calls *) +Definition builtin_or_external_sem name sg := + match lookup_builtin_function name sg with + | Some bf => known_builtin_sem bf + | None => external_functions_sem name sg + end. + +Lemma builtin_or_external_sem_ok: forall name sg, + extcall_properties (builtin_or_external_sem name sg) sg. +Proof. + unfold builtin_or_external_sem; intros. + destruct (lookup_builtin_function name sg) as [bf|] eqn:L. +- exploit lookup_builtin_function_sig; eauto. intros EQ; subst sg. + apply known_builtin_ok. +- apply external_functions_properties. +Qed. + (** Combining the semantics given above for the various kinds of external calls, we define the predicate [external_call] that relates: - the external function being invoked @@ -1412,8 +1519,8 @@ This predicate is used in the semantics of all CompCert languages. *) Definition external_call (ef: external_function): extcall_sem := match ef with | EF_external name sg => external_functions_sem name sg - | EF_builtin name sg => external_functions_sem name sg - | EF_runtime name sg => external_functions_sem name sg + | EF_builtin name sg => builtin_or_external_sem name sg + | EF_runtime name sg => builtin_or_external_sem name sg | EF_vload chunk => volatile_load_sem chunk | EF_vstore chunk => volatile_store_sem chunk | EF_malloc => extcall_malloc_sem @@ -1431,8 +1538,8 @@ Theorem external_call_spec: Proof. intros. unfold external_call, ef_sig; destruct ef. apply external_functions_properties. - apply external_functions_properties. - apply external_functions_properties. + apply builtin_or_external_sem_ok. + apply builtin_or_external_sem_ok. apply volatile_load_ok. apply volatile_store_ok. apply extcall_malloc_ok. @@ -1444,7 +1551,7 @@ Proof. apply extcall_debug_ok. Qed. -Definition external_call_well_typed ef := ec_well_typed (external_call_spec ef). +Definition external_call_well_typed_gen ef := ec_well_typed (external_call_spec ef). Definition external_call_symbols_preserved ef := ec_symbols_preserved (external_call_spec ef). Definition external_call_valid_block ef := ec_valid_block (external_call_spec ef). Definition external_call_max_perm ef := ec_max_perm (external_call_spec ef). @@ -1455,6 +1562,16 @@ Definition external_call_trace_length ef := ec_trace_length (external_call_spec Definition external_call_receptive ef := ec_receptive (external_call_spec ef). Definition external_call_determ ef := ec_determ (external_call_spec ef). +(** Corollary of [external_call_well_typed_gen]. *) + +Lemma external_call_well_typed: + forall ef ge vargs m1 t vres m2, + external_call ef ge vargs m1 t vres m2 -> + Val.has_type vres (proj_sig_res (ef_sig ef)). +Proof. + intros. apply Val.has_proj_rettype. eapply external_call_well_typed_gen; eauto. +Qed. + (** Corollary of [external_call_valid_block]. *) Lemma external_call_nextblock: |