diff options
Diffstat (limited to 'src/translation/HTLgenproof.v')
| -rw-r--r-- | src/translation/HTLgenproof.v | 69 |
1 files changed, 54 insertions, 15 deletions
diff --git a/src/translation/HTLgenproof.v b/src/translation/HTLgenproof.v index a502453..24191ae 100644 --- a/src/translation/HTLgenproof.v +++ b/src/translation/HTLgenproof.v @@ -113,12 +113,23 @@ Inductive match_states : RTL.state -> HTL.state -> Prop := Hint Constructors match_states : htlproof. Definition match_prog (p: RTL.program) (tp: HTL.program) := - Linking.match_program (fun cu f tf => transl_fundef f = Errors.OK tf) eq p tp. + Linking.match_program (fun cu f tf => transl_fundef f = Errors.OK tf) eq p tp /\ + main_is_internal p = true. + +Definition match_prog_matches : + forall p tp, + match_prog p tp -> + Linking.match_program (fun cu f tf => transl_fundef f = Errors.OK tf) eq p tp. + Proof. intros. unfold match_prog in H. tauto. Qed. Lemma transf_program_match: forall p tp, HTLgen.transl_program p = Errors.OK tp -> match_prog p tp. Proof. - intros. apply Linking.match_transform_partial_program; auto. + intros. unfold transl_program in H. + destruct (main_is_internal p) eqn:?; try discriminate. + unfold match_prog. split. + apply Linking.match_transform_partial_program; auto. + assumption. Qed. Lemma regs_lessdef_add_greater : @@ -258,13 +269,16 @@ Section CORRECTNESS. Hypothesis TRANSL : match_prog prog tprog. + Lemma TRANSL' : + Linking.match_program (fun cu f tf => transl_fundef f = Errors.OK tf) eq prog tprog. + Proof. intros; apply match_prog_matches; assumption. Qed. + Let ge : RTL.genv := Globalenvs.Genv.globalenv prog. Let tge : HTL.genv := Globalenvs.Genv.globalenv tprog. Lemma symbols_preserved: forall (s: AST.ident), Genv.find_symbol tge s = Genv.find_symbol ge s. - Proof - (Genv.find_symbol_transf_partial TRANSL). + Proof. intros. eapply (Genv.find_symbol_match TRANSL'). Qed. Lemma function_ptr_translated: forall (b: Values.block) (f: RTL.fundef), @@ -272,7 +286,7 @@ Section CORRECTNESS. exists tf, Genv.find_funct_ptr tge b = Some tf /\ transl_fundef f = Errors.OK tf. Proof. - intros. exploit (Genv.find_funct_ptr_match TRANSL); eauto. + intros. exploit (Genv.find_funct_ptr_match TRANSL'); eauto. intros (cu & tf & P & Q & R); exists tf; auto. Qed. @@ -282,21 +296,21 @@ Section CORRECTNESS. exists tf, Genv.find_funct tge v = Some tf /\ transl_fundef f = Errors.OK tf. Proof. - intros. exploit (Genv.find_funct_match TRANSL); eauto. + intros. exploit (Genv.find_funct_match TRANSL'); eauto. intros (cu & tf & P & Q & R); exists tf; auto. Qed. Lemma senv_preserved: Senv.equiv (Genv.to_senv ge) (Genv.to_senv tge). Proof - (Genv.senv_transf_partial TRANSL). + (Genv.senv_transf_partial TRANSL'). Hint Resolve senv_preserved : htlproof. Lemma eval_correct : - forall sp op rs args m v v' e asr asa f, + forall sp op rs args m v v' e asr asa f s s' i, Op.eval_operation ge sp op (List.map (fun r : BinNums.positive => Registers.Regmap.get r rs) args) m = Some v -> - tr_op op args e -> + translate_instr op args s = OK e s' i -> val_value_lessdef v v' -> Verilog.expr_runp f asr asa e v'. Admitted. @@ -380,7 +394,7 @@ Section CORRECTNESS. 2: { reflexivity. } rewrite AssocMap.gss. unfold Verilog.merge_arr. - setoid_rewrite H3. + setoid_rewrite H5. reflexivity. rewrite combine_length. @@ -1155,6 +1169,7 @@ Section CORRECTNESS. assumption. + - admit. - (* Return *) econstructor. split. eapply Smallstep.plus_two. @@ -1269,6 +1284,17 @@ Section CORRECTNESS. Admitted. Hint Resolve transl_step_correct : htlproof. + Lemma main_tprog_internal : + forall b f, + Globalenvs.Genv.find_symbol tge tprog.(AST.prog_main) = Some b -> + Genv.find_funct_ptr (Genv.globalenv tprog) b = Some (AST.Internal f). + Admitted. + + Lemma option_inv : + forall A x y, + @Some A x = Some y -> x = y. + Proof. intros. inversion H. trivial. Qed. + (* Had to admit proof because currently there is no way to force main to be Internal. *) Lemma transl_initial_states : forall s1 : Smallstep.state (RTL.semantics prog), @@ -1277,20 +1303,33 @@ Section CORRECTNESS. Smallstep.initial_state (HTL.semantics tprog) s2 /\ match_states s1 s2. Proof. induction 1. + destruct TRANSL. unfold main_is_internal in H4. + repeat (unfold_match H4). + assert (f = AST.Internal f1). apply option_inv. + rewrite <- Heqo0. rewrite <- H1. replace b with b0. + auto. apply option_inv. rewrite <- H0. rewrite <- Heqo. + trivial. exploit function_ptr_translated; eauto. intros [tf [A B]]. unfold transl_fundef, Errors.bind in B. + unfold AST.transf_partial_fundef, Errors.bind in B. repeat (unfold_match B). inversion B. subst. econstructor; split. econstructor. - apply (Genv.init_mem_transf_partial TRANSL); eauto. + apply (Genv.init_mem_transf_partial TRANSL'); eauto. replace (AST.prog_main tprog) with (AST.prog_main prog). rewrite symbols_preserved; eauto. symmetry; eapply Linking.match_program_main; eauto. - Admitted. - (*eexact A. trivial. + apply main_tprog_internal. replace ge0 with ge in * by auto. + replace b0 with b in *. rewrite symbols_preserved. + replace (AST.prog_main tprog) with (AST.prog_main prog). + assumption. + symmetry; eapply Linking.match_program_main; eauto. + apply option_inv. rewrite <- H0. rewrite <- Heqo. + trivial. + constructor. - apply transl_module_correct. auto. - Qed.*) + apply transl_module_correct. eassumption. + Qed. Hint Resolve transl_initial_states : htlproof. Lemma transl_final_states : |