diff options
Diffstat (limited to 'backend')
| -rw-r--r-- | backend/Selection.v | 53 | ||||
| -rw-r--r-- | backend/Selectionproof.v | 157 | ||||
| -rw-r--r-- | backend/SplitLongproof.v | 133 |
3 files changed, 231 insertions, 112 deletions
diff --git a/backend/Selection.v b/backend/Selection.v index 4154659c..c9771d99 100644 --- a/backend/Selection.v +++ b/backend/Selection.v @@ -24,7 +24,7 @@ Require String. Require Import Coqlib Maps. -Require Import AST Errors Integers Globalenvs Switch. +Require Import AST Errors Integers Globalenvs Builtins Switch. Require Cminor. Require Import Op CminorSel Cminortyping. Require Import SelectOp SplitLong SelectLong SelectDiv. @@ -162,6 +162,13 @@ Definition sel_binop (op: Cminor.binary_operation) (arg1 arg2: expr) : expr := | Cminor.Ocmplu c => cmplu c arg1 arg2 end. +Definition sel_select (ty: typ) (cnd ifso ifnot: expr) : expr := + let (cond, args) := condition_of_expr cnd in + match SelectOp.select ty cond args ifso ifnot with + | Some a => a + | None => Econdition (condexpr_of_expr cnd) ifso ifnot + end. + (** Conversion from Cminor expression to Cminorsel expressions *) Fixpoint sel_expr (a: Cminor.expr) : expr := @@ -231,6 +238,43 @@ Definition sel_builtin_res (optid: option ident) : builtin_res ident := | Some id => BR id end. +(** Known builtin functions *) + +Function sel_known_builtin (bf: builtin_function) (args: exprlist) := + match bf, args with + | BI_platform b, _ => + SelectOp.platform_builtin b args + | BI_standard (BI_select ty), a1 ::: a2 ::: a3 ::: Enil => + Some (sel_select ty a1 a2 a3) + | BI_standard BI_fabs, a1 ::: Enil => + Some (SelectOp.absf a1) + | _, _ => + None + end. + +(** Builtin functions in general *) + +Definition sel_builtin_default (optid: option ident) (ef: external_function) + (args: list Cminor.expr) := + Sbuiltin (sel_builtin_res optid) ef + (sel_builtin_args args (Machregs.builtin_constraints ef)). + +Definition sel_builtin (optid: option ident) (ef: external_function) + (args: list Cminor.expr) := + match optid, ef with + | Some id, EF_builtin name sg => + match lookup_builtin_function name sg with + | Some bf => + match sel_known_builtin bf (sel_exprlist args) with + | Some a => Sassign id a + | None => sel_builtin_default optid ef args + end + | None => sel_builtin_default optid ef args + end + | _, _ => + sel_builtin_default optid ef args + end. + (** Conversion of Cminor [switch] statements to decision trees. *) Parameter compile_switch: Z -> nat -> table -> comptree. @@ -342,13 +386,10 @@ Fixpoint sel_stmt (ki: known_idents) (env: typenv) (s: Cminor.stmt) : res stmt : OK (match classify_call fn with | Call_default => Scall optid sg (inl _ (sel_expr fn)) (sel_exprlist args) | Call_imm id => Scall optid sg (inr _ id) (sel_exprlist args) - | Call_builtin ef => Sbuiltin (sel_builtin_res optid) ef - (sel_builtin_args args - (Machregs.builtin_constraints ef)) + | Call_builtin ef => sel_builtin optid ef args end) | Cminor.Sbuiltin optid ef args => - OK (Sbuiltin (sel_builtin_res optid) ef - (sel_builtin_args args (Machregs.builtin_constraints ef))) + OK (sel_builtin optid ef args) | Cminor.Stailcall sg fn args => OK (match classify_call fn with | Call_imm id => Stailcall sg (inr _ id) (sel_exprlist args) diff --git a/backend/Selectionproof.v b/backend/Selectionproof.v index 50875086..ee3ed358 100644 --- a/backend/Selectionproof.v +++ b/backend/Selectionproof.v @@ -14,7 +14,8 @@ Require Import FunInd. Require Import Coqlib Maps. -Require Import AST Linking Errors Integers Values Memory Events Globalenvs Smallstep. +Require Import AST Linking Errors Integers. +Require Import Values Memory Builtins Events Globalenvs Smallstep. Require Import Switch Cminor Op CminorSel Cminortyping. Require Import SelectOp SelectDiv SplitLong SelectLong Selection. Require Import SelectOpproof SelectDivproof SplitLongproof SelectLongproof. @@ -216,19 +217,16 @@ Lemma eval_condition_of_expr: forall a le v b, eval_expr tge sp e m le a v -> Val.bool_of_val v b -> - let (cond, al) := condition_of_expr a in exists vl, - eval_exprlist tge sp e m le al vl - /\ eval_condition cond vl m = Some b. + eval_exprlist tge sp e m le (snd (condition_of_expr a)) vl + /\ eval_condition (fst (condition_of_expr a)) vl m = Some b. Proof. - intros until a. functional induction (condition_of_expr a); intros. -(* compare *) - inv H. simpl in H6. inv H6. apply Val.bool_of_val_of_optbool in H0. - exists vl; auto. -(* default *) - exists (v :: nil); split. - econstructor. auto. constructor. - simpl. inv H0. auto. + intros a; functional induction (condition_of_expr a); intros; simpl. +- inv H. exists vl; split; auto. + simpl in H6. inv H6. apply Val.bool_of_val_of_optbool in H0. auto. +- exists (v :: nil); split. + constructor; auto; constructor. + inv H0; simpl; auto. Qed. Lemma eval_load: @@ -353,6 +351,52 @@ Proof. exists v; split; auto. eapply eval_cmplu; eauto. Qed. +Lemma eval_sel_select: + forall le a1 a2 a3 v1 v2 v3 b ty, + eval_expr tge sp e m le a1 v1 -> + eval_expr tge sp e m le a2 v2 -> + eval_expr tge sp e m le a3 v3 -> + Val.bool_of_val v1 b -> + exists v, eval_expr tge sp e m le (sel_select ty a1 a2 a3) v + /\ Val.lessdef (Val.select (Some b) v2 v3 ty) v. +Proof. + unfold sel_select; intros. + specialize (eval_condition_of_expr _ _ _ _ H H2). + destruct (condition_of_expr a1) as [cond args]; simpl fst; simpl snd. intros (vl & A & B). + destruct (select ty cond args a2 a3) as [a|] eqn:SEL. +- eapply eval_select; eauto. +- exists (if b then v2 else v3); split. + econstructor; eauto. eapply eval_condexpr_of_expr; eauto. destruct b; auto. + apply Val.lessdef_normalize. +Qed. + +(** Known built-in functions *) + +Lemma eval_sel_known_builtin: + forall bf args a vl v le, + sel_known_builtin bf args = Some a -> + eval_exprlist tge sp e m le args vl -> + builtin_function_sem bf vl = Some v -> + exists v', eval_expr tge sp e m le a v' /\ Val.lessdef v v'. +Proof. + intros until le; intros SEL ARGS SEM. + destruct bf as [bf|bf]; simpl in SEL. +- destruct bf; try discriminate. ++ (* select *) + inv ARGS; try discriminate. inv H0; try discriminate. inv H2; try discriminate. inv H3; try discriminate. + inv SEL. + simpl in SEM. destruct v1; inv SEM. + replace (Val.normalize (if Int.eq i Int.zero then v2 else v0) t) + with (Val.select (Some (negb (Int.eq i Int.zero))) v0 v2 t) + by (destruct (Int.eq i Int.zero); reflexivity). + eapply eval_sel_select; eauto. constructor. ++ (* fabs *) + inv ARGS; try discriminate. inv H0; try discriminate. + inv SEL. + simpl in SEM; inv SEM. apply eval_absf; auto. +- eapply eval_platform_builtin; eauto. +Qed. + End CMCONSTR. (** Recognition of calls to built-in functions *) @@ -793,6 +837,51 @@ Proof. intros. destruct oid; simpl; auto. apply set_var_lessdef; auto. Qed. +Lemma sel_builtin_default_correct: + forall optid ef al sp e1 m1 vl t v m2 e1' m1' f k, + Cminor.eval_exprlist ge sp e1 m1 al vl -> + external_call ef ge vl m1 t v m2 -> + env_lessdef e1 e1' -> Mem.extends m1 m1' -> + exists e2' m2', + step tge (State f (sel_builtin_default optid ef al) k sp e1' m1') + t (State f Sskip k sp e2' m2') + /\ env_lessdef (set_optvar optid v e1) e2' + /\ Mem.extends m2 m2'. +Proof. + intros. unfold sel_builtin_default. + exploit sel_builtin_args_correct; eauto. intros (vl' & A & B). + exploit external_call_mem_extends; eauto. intros (v' & m2' & D & E & F & _). + econstructor; exists m2'; split. + econstructor. eexact A. eapply external_call_symbols_preserved. eexact senv_preserved. eexact D. + split; auto. apply sel_builtin_res_correct; auto. +Qed. + +Lemma sel_builtin_correct: + forall optid ef al sp e1 m1 vl t v m2 e1' m1' f k, + Cminor.eval_exprlist ge sp e1 m1 al vl -> + external_call ef ge vl m1 t v m2 -> + env_lessdef e1 e1' -> Mem.extends m1 m1' -> + exists e2' m2', + step tge (State f (sel_builtin optid ef al) k sp e1' m1') + t (State f Sskip k sp e2' m2') + /\ env_lessdef (set_optvar optid v e1) e2' + /\ Mem.extends m2 m2'. +Proof. + intros. + exploit sel_exprlist_correct; eauto. intros (vl' & A & B). + exploit external_call_mem_extends; eauto. intros (v' & m2' & D & E & F & _). + unfold sel_builtin. + destruct optid as [id|]; eauto using sel_builtin_default_correct. + destruct ef; eauto using sel_builtin_default_correct. + destruct (lookup_builtin_function name sg) as [bf|] eqn:LKUP; eauto using sel_builtin_default_correct. + destruct (sel_known_builtin bf (sel_exprlist al)) as [a|] eqn:SKB; eauto using sel_builtin_default_correct. + simpl in D. red in D. rewrite LKUP in D. inv D. + exploit eval_sel_known_builtin; eauto. intros (v'' & U & V). + econstructor; exists m2'; split. + econstructor. eexact U. + split; auto. apply set_var_lessdef; auto. apply Val.lessdef_trans with v'; auto. +Qed. + (** If-conversion *) Lemma classify_stmt_sound_1: @@ -982,19 +1071,18 @@ Inductive match_states: Cminor.state -> CminorSel.state -> Prop := match_states (Cminor.Returnstate v k m) (Returnstate v' k' m') - | match_builtin_1: forall cunit hf ef args args' optid f sp e k m al f' e' k' m' env + | match_builtin_1: forall cunit hf ef args optid f sp e k m al f' e' k' m' env (LINK: linkorder cunit prog) (HF: helper_functions_declared cunit hf) (TF: sel_function (prog_defmap cunit) hf f = OK f') (TYF: type_function f = OK env) (MC: match_cont cunit hf (known_id f) env k k') - (LDA: Val.lessdef_list args args') + (EA: Cminor.eval_exprlist ge sp e m al args) (LDE: env_lessdef e e') - (ME: Mem.extends m m') - (EA: list_forall2 (CminorSel.eval_builtin_arg tge sp e' m') al args'), + (ME: Mem.extends m m'), match_states (Cminor.Callstate (External ef) args (Cminor.Kcall optid f sp e k) m) - (State f' (Sbuiltin (sel_builtin_res optid) ef al) k' sp e' m') + (State f' (sel_builtin optid ef al) k' sp e' m') | match_builtin_2: forall cunit hf v v' optid f sp e k m f' e' m' k' env (LINK: linkorder cunit prog) (HF: helper_functions_declared cunit hf) @@ -1002,11 +1090,11 @@ Inductive match_states: Cminor.state -> CminorSel.state -> Prop := (TYF: type_function f = OK env) (MC: match_cont cunit hf (known_id f) env k k') (LDV: Val.lessdef v v') - (LDE: env_lessdef e e') + (LDE: env_lessdef (set_optvar optid v e) e') (ME: Mem.extends m m'), match_states (Cminor.Returnstate v (Cminor.Kcall optid f sp e k) m) - (State f' Sskip k' sp (set_builtin_res (sel_builtin_res optid) v' e') m'). + (State f' Sskip k' sp e' m'). Remark call_cont_commut: forall cunit hf ki env k k', @@ -1078,6 +1166,14 @@ Proof. destruct (ident_eq id id0). conclude. discriminate. Qed. +Remark sel_builtin_nolabel: + forall (hf: helper_functions) optid ef args, nolabel' (sel_builtin optid ef args). +Proof. + unfold sel_builtin; intros; red; intros. + destruct optid; auto. destruct ef; auto. destruct lookup_builtin_function; auto. + destruct sel_known_builtin; auto. +Qed. + Remark find_label_commut: forall cunit hf ki env lbl s k s' k', match_cont cunit hf ki env k k' -> @@ -1093,8 +1189,11 @@ Proof. unfold store. destruct (addressing m (sel_expr e)); simpl; auto. (* call *) destruct (classify_call (prog_defmap cunit) e); simpl; auto. + rewrite sel_builtin_nolabel; auto. (* tailcall *) destruct (classify_call (prog_defmap cunit) e); simpl; auto. +(* builtin *) + rewrite sel_builtin_nolabel; auto. (* seq *) exploit (IHs1 (Cminor.Kseq s2 k)). constructor; eauto. eauto. destruct (Cminor.find_label lbl s1 (Cminor.Kseq s2 k)) as [[sx kx] | ]; @@ -1188,9 +1287,7 @@ Proof. eapply match_cont_call with (cunit := cunit) (hf := hf); eauto. + (* turned into Sbuiltin *) intros EQ. subst fd. - exploit sel_builtin_args_correct; eauto. intros [vargs' [C D]]. - right; left; split. simpl. omega. split. auto. - econstructor; eauto. + right; left; split. simpl; omega. split; auto. econstructor; eauto. - (* Stailcall *) exploit Mem.free_parallel_extends; eauto. intros [m2' [P Q]]. erewrite <- stackspace_function_translated in P by eauto. @@ -1207,12 +1304,8 @@ Proof. eapply match_callstate with (cunit := cunit'); eauto. eapply call_cont_commut; eauto. - (* Sbuiltin *) - exploit sel_builtin_args_correct; eauto. intros [vargs' [P Q]]. - exploit external_call_mem_extends; eauto. - intros [vres' [m2 [A [B [C D]]]]]. - left; econstructor; split. - econstructor. eauto. eapply external_call_symbols_preserved; eauto. apply senv_preserved. - econstructor; eauto. apply sel_builtin_res_correct; auto. + exploit sel_builtin_correct; eauto. intros (e2' & m2' & P & Q & R). + left; econstructor; split. eexact P. econstructor; eauto. - (* Seq *) left; econstructor; split. constructor. @@ -1303,11 +1396,8 @@ Proof. econstructor. eapply external_call_symbols_preserved; eauto. apply senv_preserved. econstructor; eauto. - (* external call turned into a Sbuiltin *) - exploit external_call_mem_extends; eauto. - intros [vres' [m2 [A [B [C D]]]]]. - left; econstructor; split. - econstructor. eauto. eapply external_call_symbols_preserved; eauto. apply senv_preserved. - econstructor; eauto. + exploit sel_builtin_correct; eauto. intros (e2' & m2' & P & Q & R). + left; econstructor; split. eexact P. econstructor; eauto. - (* return *) inv MC. left; econstructor; split. @@ -1315,7 +1405,6 @@ Proof. econstructor; eauto. destruct optid; simpl; auto. apply set_var_lessdef; auto. - (* return of an external call turned into a Sbuiltin *) right; left; split. simpl; omega. split. auto. econstructor; eauto. - apply sel_builtin_res_correct; auto. Qed. Lemma sel_initial_states: diff --git a/backend/SplitLongproof.v b/backend/SplitLongproof.v index f1e8b590..18c1f18d 100644 --- a/backend/SplitLongproof.v +++ b/backend/SplitLongproof.v @@ -15,42 +15,13 @@ Require Import String. Require Import Coqlib Maps. Require Import AST Errors Integers Floats. -Require Import Values Memory Globalenvs Events Cminor Op CminorSel. +Require Import Values Memory Globalenvs Builtins Events Cminor Op CminorSel. Require Import SelectOp SelectOpproof SplitLong. Local Open Scope cminorsel_scope. Local Open Scope string_scope. -(** * Axiomatization of the helper functions *) - -Definition external_implements (name: string) (sg: signature) (vargs: list val) (vres: val) : Prop := - forall F V (ge: Genv.t F V) m, - external_call (EF_runtime name sg) ge vargs m E0 vres m. - -Definition builtin_implements (name: string) (sg: signature) (vargs: list val) (vres: val) : Prop := - forall F V (ge: Genv.t F V) m, - external_call (EF_builtin name sg) ge vargs m E0 vres m. - -Axiom i64_helpers_correct : - (forall x z, Val.longoffloat x = Some z -> external_implements "__compcert_i64_dtos" sig_f_l (x::nil) z) - /\ (forall x z, Val.longuoffloat x = Some z -> external_implements "__compcert_i64_dtou" sig_f_l (x::nil) z) - /\ (forall x z, Val.floatoflong x = Some z -> external_implements "__compcert_i64_stod" sig_l_f (x::nil) z) - /\ (forall x z, Val.floatoflongu x = Some z -> external_implements "__compcert_i64_utod" sig_l_f (x::nil) z) - /\ (forall x z, Val.singleoflong x = Some z -> external_implements "__compcert_i64_stof" sig_l_s (x::nil) z) - /\ (forall x z, Val.singleoflongu x = Some z -> external_implements "__compcert_i64_utof" sig_l_s (x::nil) z) - /\ (forall x, builtin_implements "__builtin_negl" sig_l_l (x::nil) (Val.negl x)) - /\ (forall x y, builtin_implements "__builtin_addl" sig_ll_l (x::y::nil) (Val.addl x y)) - /\ (forall x y, builtin_implements "__builtin_subl" sig_ll_l (x::y::nil) (Val.subl x y)) - /\ (forall x y, builtin_implements "__builtin_mull" sig_ii_l (x::y::nil) (Val.mull' x y)) - /\ (forall x y z, Val.divls x y = Some z -> external_implements "__compcert_i64_sdiv" sig_ll_l (x::y::nil) z) - /\ (forall x y z, Val.divlu x y = Some z -> external_implements "__compcert_i64_udiv" sig_ll_l (x::y::nil) z) - /\ (forall x y z, Val.modls x y = Some z -> external_implements "__compcert_i64_smod" sig_ll_l (x::y::nil) z) - /\ (forall x y z, Val.modlu x y = Some z -> external_implements "__compcert_i64_umod" sig_ll_l (x::y::nil) z) - /\ (forall x y, external_implements "__compcert_i64_shl" sig_li_l (x::y::nil) (Val.shll x y)) - /\ (forall x y, external_implements "__compcert_i64_shr" sig_li_l (x::y::nil) (Val.shrlu x y)) - /\ (forall x y, external_implements "__compcert_i64_sar" sig_li_l (x::y::nil) (Val.shrl x y)) - /\ (forall x y, external_implements "__compcert_i64_umulh" sig_ll_l (x::y::nil) (Val.mullhu x y)) - /\ (forall x y, external_implements "__compcert_i64_smulh" sig_ll_l (x::y::nil) (Val.mullhs x y)). +(** * Properties of the helper functions *) Definition helper_declared {F V: Type} (p: AST.program (AST.fundef F) V) (id: ident) (name: string) (sg: signature) : Prop := (prog_defmap p)!id = Some (Gfun (External (EF_runtime name sg))). @@ -84,60 +55,67 @@ Variable sp: val. Variable e: env. Variable m: mem. -Ltac UseHelper := decompose [Logic.and] i64_helpers_correct; eauto. Ltac DeclHelper := red in HELPERS; decompose [Logic.and] HELPERS; eauto. Lemma eval_helper: - forall le id name sg args vargs vres, + forall bf le id name sg args vargs vres, eval_exprlist ge sp e m le args vargs -> helper_declared prog id name sg -> - external_implements name sg vargs vres -> + lookup_builtin_function name sg = Some bf -> + builtin_function_sem bf vargs = Some vres -> eval_expr ge sp e m le (Eexternal id sg args) vres. Proof. intros. red in H0. apply Genv.find_def_symbol in H0. destruct H0 as (b & P & Q). rewrite <- Genv.find_funct_ptr_iff in Q. - econstructor; eauto. + econstructor; eauto. + simpl. red. rewrite H1. constructor; auto. Qed. Corollary eval_helper_1: - forall le id name sg arg1 varg1 vres, + forall bf le id name sg arg1 varg1 vres, eval_expr ge sp e m le arg1 varg1 -> helper_declared prog id name sg -> - external_implements name sg (varg1::nil) vres -> + lookup_builtin_function name sg = Some bf -> + builtin_function_sem bf (varg1 :: nil) = Some vres -> eval_expr ge sp e m le (Eexternal id sg (arg1 ::: Enil)) vres. Proof. intros. eapply eval_helper; eauto. constructor; auto. constructor. Qed. Corollary eval_helper_2: - forall le id name sg arg1 arg2 varg1 varg2 vres, + forall bf le id name sg arg1 arg2 varg1 varg2 vres, eval_expr ge sp e m le arg1 varg1 -> eval_expr ge sp e m le arg2 varg2 -> helper_declared prog id name sg -> - external_implements name sg (varg1::varg2::nil) vres -> + lookup_builtin_function name sg = Some bf -> + builtin_function_sem bf (varg1 :: varg2 :: nil) = Some vres -> eval_expr ge sp e m le (Eexternal id sg (arg1 ::: arg2 ::: Enil)) vres. Proof. intros. eapply eval_helper; eauto. constructor; auto. constructor; auto. constructor. Qed. Remark eval_builtin_1: - forall le id sg arg1 varg1 vres, + forall bf le id sg arg1 varg1 vres, eval_expr ge sp e m le arg1 varg1 -> - builtin_implements id sg (varg1::nil) vres -> + lookup_builtin_function id sg = Some bf -> + builtin_function_sem bf (varg1 :: nil) = Some vres -> eval_expr ge sp e m le (Ebuiltin (EF_builtin id sg) (arg1 ::: Enil)) vres. Proof. - intros. econstructor. econstructor. eauto. constructor. apply H0. + intros. econstructor. econstructor. eauto. constructor. + simpl. red. rewrite H0. constructor. auto. Qed. Remark eval_builtin_2: - forall le id sg arg1 arg2 varg1 varg2 vres, + forall bf le id sg arg1 arg2 varg1 varg2 vres, eval_expr ge sp e m le arg1 varg1 -> eval_expr ge sp e m le arg2 varg2 -> - builtin_implements id sg (varg1::varg2::nil) vres -> + lookup_builtin_function id sg = Some bf -> + builtin_function_sem bf (varg1 :: varg2 :: nil) = Some vres -> eval_expr ge sp e m le (Ebuiltin (EF_builtin id sg) (arg1 ::: arg2 ::: Enil)) vres. Proof. - intros. econstructor. constructor; eauto. constructor; eauto. constructor. apply H1. + intros. econstructor. constructor; eauto. constructor; eauto. constructor. + simpl. red. rewrite H1. constructor. auto. Qed. Definition unary_constructor_sound (cstr: expr -> expr) (sem: val -> val) : Prop := @@ -386,9 +364,10 @@ Qed. Theorem eval_negl: unary_constructor_sound negl Val.negl. Proof. unfold negl; red; intros. destruct (is_longconst a) eqn:E. - econstructor; split. apply eval_longconst. +- econstructor; split. apply eval_longconst. exploit is_longconst_sound; eauto. intros EQ; subst x. simpl. auto. - econstructor; split. eapply eval_builtin_1; eauto. UseHelper. auto. +- exists (Val.negl x); split; auto. + eapply (eval_builtin_1 (BI_standard BI_negl)); eauto. Qed. Theorem eval_notl: unary_constructor_sound notl Val.notl. @@ -410,7 +389,7 @@ Theorem eval_longoffloat: exists v, eval_expr ge sp e m le (longoffloat a) v /\ Val.lessdef y v. Proof. intros; unfold longoffloat. econstructor; split. - eapply eval_helper_1; eauto. DeclHelper. UseHelper. auto. + eapply (eval_helper_1 (BI_standard BI_i64_dtos)); eauto. DeclHelper. auto. auto. Qed. Theorem eval_longuoffloat: @@ -420,7 +399,7 @@ Theorem eval_longuoffloat: exists v, eval_expr ge sp e m le (longuoffloat a) v /\ Val.lessdef y v. Proof. intros; unfold longuoffloat. econstructor; split. - eapply eval_helper_1; eauto. DeclHelper. UseHelper. auto. + eapply (eval_helper_1 (BI_standard BI_i64_dtou)); eauto. DeclHelper. auto. auto. Qed. Theorem eval_floatoflong: @@ -429,8 +408,9 @@ Theorem eval_floatoflong: Val.floatoflong x = Some y -> exists v, eval_expr ge sp e m le (floatoflong a) v /\ Val.lessdef y v. Proof. - intros; unfold floatoflong. econstructor; split. - eapply eval_helper_1; eauto. DeclHelper. UseHelper. auto. + intros; unfold floatoflong. exists y; split; auto. + eapply (eval_helper_1 (BI_standard BI_i64_stod)); eauto. DeclHelper. auto. + simpl. destruct x; simpl in H0; inv H0; auto. Qed. Theorem eval_floatoflongu: @@ -439,8 +419,9 @@ Theorem eval_floatoflongu: Val.floatoflongu x = Some y -> exists v, eval_expr ge sp e m le (floatoflongu a) v /\ Val.lessdef y v. Proof. - intros; unfold floatoflongu. econstructor; split. - eapply eval_helper_1; eauto. DeclHelper. UseHelper. auto. + intros; unfold floatoflongu. exists y; split; auto. + eapply (eval_helper_1 (BI_standard BI_i64_utod)); eauto. DeclHelper. auto. + simpl. destruct x; simpl in H0; inv H0; auto. Qed. Theorem eval_longofsingle: @@ -477,8 +458,9 @@ Theorem eval_singleoflong: Val.singleoflong x = Some y -> exists v, eval_expr ge sp e m le (singleoflong a) v /\ Val.lessdef y v. Proof. - intros; unfold singleoflong. econstructor; split. - eapply eval_helper_1; eauto. DeclHelper. UseHelper. auto. + intros; unfold singleoflong. exists y; split; auto. + eapply (eval_helper_1 (BI_standard BI_i64_stof)); eauto. DeclHelper. auto. + simpl. destruct x; simpl in H0; inv H0; auto. Qed. Theorem eval_singleoflongu: @@ -487,8 +469,9 @@ Theorem eval_singleoflongu: Val.singleoflongu x = Some y -> exists v, eval_expr ge sp e m le (singleoflongu a) v /\ Val.lessdef y v. Proof. - intros; unfold singleoflongu. econstructor; split. - eapply eval_helper_1; eauto. DeclHelper. UseHelper. auto. + intros; unfold singleoflongu. exists y; split; auto. + eapply (eval_helper_1 (BI_standard BI_i64_utof)); eauto. DeclHelper. auto. + simpl. destruct x; simpl in H0; inv H0; auto. Qed. Theorem eval_andl: binary_constructor_sound andl Val.andl. @@ -615,7 +598,9 @@ Proof. simpl. erewrite <- Int64.decompose_shl_2. instantiate (1 := Int64.hiword i). rewrite Int64.ofwords_recompose. auto. auto. + (* n >= 64 *) - econstructor; split. eapply eval_helper_2; eauto. EvalOp. DeclHelper. UseHelper. auto. + econstructor; split. + eapply eval_helper_2; eauto. EvalOp. DeclHelper. reflexivity. reflexivity. + auto. Qed. Theorem eval_shll: binary_constructor_sound shll Val.shll. @@ -626,7 +611,7 @@ Proof. exploit is_intconst_sound; eauto. intros EQ; subst y; clear H0. eapply eval_shllimm; eauto. - (* General case *) - econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto. + econstructor; split. eapply eval_helper_2; eauto. DeclHelper. reflexivity. reflexivity. auto. Qed. Lemma eval_shrluimm: @@ -660,7 +645,9 @@ Proof. simpl. erewrite <- Int64.decompose_shru_2. instantiate (1 := Int64.loword i). rewrite Int64.ofwords_recompose. auto. auto. + (* n >= 64 *) - econstructor; split. eapply eval_helper_2; eauto. EvalOp. DeclHelper. UseHelper. auto. + econstructor; split. + eapply eval_helper_2; eauto. EvalOp. DeclHelper. reflexivity. reflexivity. + auto. Qed. Theorem eval_shrlu: binary_constructor_sound shrlu Val.shrlu. @@ -671,7 +658,7 @@ Proof. exploit is_intconst_sound; eauto. intros EQ; subst y; clear H0. eapply eval_shrluimm; eauto. - (* General case *) - econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto. + econstructor; split. eapply eval_helper_2; eauto. DeclHelper. reflexivity. reflexivity. auto. Qed. Lemma eval_shrlimm: @@ -709,7 +696,9 @@ Proof. erewrite <- Int64.decompose_shr_2. instantiate (1 := Int64.loword i). rewrite Int64.ofwords_recompose. auto. auto. + (* n >= 64 *) - econstructor; split. eapply eval_helper_2; eauto. EvalOp. DeclHelper. UseHelper. auto. + econstructor; split. + eapply eval_helper_2; eauto. EvalOp. DeclHelper. reflexivity. reflexivity. + auto. Qed. Theorem eval_shrl: binary_constructor_sound shrl Val.shrl. @@ -720,7 +709,7 @@ Proof. exploit is_intconst_sound; eauto. intros EQ; subst y; clear H0. eapply eval_shrlimm; eauto. - (* General case *) - econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto. + econstructor; split. eapply eval_helper_2; eauto. DeclHelper. reflexivity. reflexivity. auto. Qed. Theorem eval_addl: Archi.ptr64 = false -> binary_constructor_sound addl Val.addl. @@ -730,7 +719,7 @@ Proof. assert (DEFAULT: exists v, eval_expr ge sp e m le default v /\ Val.lessdef (Val.addl x y) v). { - econstructor; split. eapply eval_builtin_2; eauto. UseHelper. auto. + econstructor; split. eapply eval_builtin_2; eauto. reflexivity. reflexivity. auto. } destruct (is_longconst a) as [p|] eqn:LC1; destruct (is_longconst b) as [q|] eqn:LC2. @@ -753,7 +742,7 @@ Proof. assert (DEFAULT: exists v, eval_expr ge sp e m le default v /\ Val.lessdef (Val.subl x y) v). { - econstructor; split. eapply eval_builtin_2; eauto. UseHelper. auto. + econstructor; split. eapply eval_builtin_2; eauto. reflexivity. reflexivity. auto. } destruct (is_longconst a) as [p|] eqn:LC1; destruct (is_longconst b) as [q|] eqn:LC2. @@ -784,7 +773,7 @@ Proof. exploit eval_add. eexact E2. eexact E3. intros [v5 [E5 L5]]. exploit eval_add. eexact E5. eexact E4. intros [v6 [E6 L6]]. exists (Val.longofwords v6 (Val.loword p)); split. - EvalOp. eapply eval_builtin_2; eauto. UseHelper. + EvalOp. eapply eval_builtin_2; eauto. reflexivity. reflexivity. intros. unfold le1, p in *; subst; simpl in *. inv L3. inv L4. inv L5. simpl in L6. inv L6. simpl. f_equal. symmetry. apply Int64.decompose_mul. @@ -832,14 +821,14 @@ Theorem eval_mullhu: forall n, unary_constructor_sound (fun a => mullhu a n) (fun v => Val.mullhu v (Vlong n)). Proof. unfold mullhu; intros; red; intros. econstructor; split; eauto. - eapply eval_helper_2; eauto. apply eval_longconst. DeclHelper; eauto. UseHelper. + eapply eval_helper_2; eauto. apply eval_longconst. DeclHelper. reflexivity. reflexivity. Qed. Theorem eval_mullhs: forall n, unary_constructor_sound (fun a => mullhs a n) (fun v => Val.mullhs v (Vlong n)). Proof. unfold mullhs; intros; red; intros. econstructor; split; eauto. - eapply eval_helper_2; eauto. apply eval_longconst. DeclHelper; eauto. UseHelper. + eapply eval_helper_2; eauto. apply eval_longconst. DeclHelper. reflexivity. reflexivity. Qed. Theorem eval_shrxlimm: @@ -881,7 +870,7 @@ Theorem eval_divlu_base: exists v, eval_expr ge sp e m le (divlu_base a b) v /\ Val.lessdef z v. Proof. intros; unfold divlu_base. - econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto. + econstructor; split. eapply eval_helper_2; eauto. DeclHelper. reflexivity. eassumption. auto. Qed. Theorem eval_modlu_base: @@ -892,7 +881,7 @@ Theorem eval_modlu_base: exists v, eval_expr ge sp e m le (modlu_base a b) v /\ Val.lessdef z v. Proof. intros; unfold modlu_base. - econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto. + econstructor; split. eapply eval_helper_2; eauto. DeclHelper. reflexivity. eassumption. auto. Qed. Theorem eval_divls_base: @@ -903,7 +892,7 @@ Theorem eval_divls_base: exists v, eval_expr ge sp e m le (divls_base a b) v /\ Val.lessdef z v. Proof. intros; unfold divls_base. - econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto. + econstructor; split. eapply eval_helper_2; eauto. DeclHelper. reflexivity. eassumption. auto. Qed. Theorem eval_modls_base: @@ -914,7 +903,7 @@ Theorem eval_modls_base: exists v, eval_expr ge sp e m le (modls_base a b) v /\ Val.lessdef z v. Proof. intros; unfold modls_base. - econstructor; split. eapply eval_helper_2; eauto. DeclHelper. UseHelper. auto. + econstructor; split. eapply eval_helper_2; eauto. DeclHelper. reflexivity. eassumption. auto. Qed. Remark decompose_cmpl_eq_zero: |