diff options
Diffstat (limited to 'src/translation/HTLgenproof.v')
-rw-r--r-- | src/translation/HTLgenproof.v | 182 |
1 files changed, 130 insertions, 52 deletions
diff --git a/src/translation/HTLgenproof.v b/src/translation/HTLgenproof.v index 2d2129c..5cdddb2 100644 --- a/src/translation/HTLgenproof.v +++ b/src/translation/HTLgenproof.v @@ -16,9 +16,10 @@ * along with this program. If not, see <https://www.gnu.org/licenses/>. *) +From compcert Require RTL Registers AST. +From compcert Require Import Globalenvs. From coqup Require Import Coquplib HTLgenspec HTLgen Value AssocMap. From coqup Require HTL Verilog. -From compcert Require RTL Registers Globalenvs AST. Import AssocMapNotation. @@ -53,15 +54,14 @@ Inductive match_states : RTL.state -> HTL.state -> Prop := match_states (RTL.Returnstate stack v m) (HTL.Returnstate v'). Hint Constructors match_states : htlproof. -Inductive match_program : RTL.program -> HTL.module -> Prop := - match_program_intro : - forall ge p b m f, - ge = Globalenvs.Genv.globalenv p -> - Globalenvs.Genv.find_symbol ge p.(AST.prog_main) = Some b -> - Globalenvs.Genv.find_funct_ptr ge b = Some (AST.Internal f) -> - tr_module f m -> - match_program p m. -Hint Constructors match_program : 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. + +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. +Qed. Lemma regs_lessdef_add_greater : forall f rs1 rs2 n v, @@ -97,16 +97,6 @@ Proof. Qed. Hint Resolve regs_lessdef_add_match : htlproof. -Lemma valToValue_lessdef : - forall v v', - valToValue v = Some v' <-> - val_value_lessdef v v'. -Proof. - split; intros. - destruct v; try discriminate; constructor. - unfold valToValue in H. inversion H. - Admitted. - (* Need to eventually move posToValue 32 to posToValueAuto, as that has this proof. *) Lemma assumption_32bit : forall v, @@ -142,40 +132,83 @@ Ltac inv_state := inversion TF; match goal with TC : forall _ _, - Maps.PTree.get _ _ = Some _ -> tr_code _ _ _ _ _ _ _, + Maps.PTree.get _ _ = Some _ -> tr_code _ _ _ _ _ _ _ _, H : Maps.PTree.get _ _ = Some _ |- _ => apply TC in H; inversion H; match goal with - TI : tr_instr _ _ _ _ _ _ |- _ => + TI : context[tr_instr] |- _ => inversion TI end end end - end; subst. +end; subst. + +Ltac unfold_func H := + match type of H with + | ?f = _ => unfold f in H; repeat (unfold_match H) + | ?f _ = _ => unfold f in H; repeat (unfold_match H) + | ?f _ _ = _ => unfold f in H; repeat (unfold_match H) + | ?f _ _ _ = _ => unfold f in H; repeat (unfold_match H) + | ?f _ _ _ _ = _ => unfold f in H; repeat (unfold_match H) + end. Section CORRECTNESS. Variable prog : RTL.program. - Variable tprog : HTL.module. + Variable tprog : HTL.program. - Hypothesis TRANSL : match_program prog tprog. + Hypothesis TRANSL : match_prog prog tprog. Let ge : RTL.genv := Globalenvs.Genv.globalenv prog. - Let tge : HTL.genv := HTL.genv_empty. + 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). + + Lemma function_ptr_translated: + forall (b: Values.block) (f: RTL.fundef), + Genv.find_funct_ptr ge b = Some f -> + 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 (cu & tf & P & Q & R); exists tf; auto. + Qed. + + Lemma functions_translated: + forall (v: Values.val) (f: RTL.fundef), + Genv.find_funct ge v = Some f -> + 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 (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). + Hint Resolve senv_preserved : htlproof. Lemma eval_correct : forall sp op rs args m v v' e assoc f, 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 -> - valToValue v = Some v' -> + val_value_lessdef v v' -> Verilog.expr_runp f assoc e v'. Admitted. Lemma eval_cond_correct : forall cond (args : list Registers.reg) s1 c s' i rs args m b f assoc, translate_condition cond args s1 = OK c s' i -> - Op.eval_condition cond (List.map (fun r : BinNums.positive => Registers.Regmap.get r rs) args) m = Some b -> + Op.eval_condition + cond + (List.map (fun r : BinNums.positive => Registers.Regmap.get r rs) args) + m = Some b -> Verilog.expr_runp f assoc c (boolToValue 32 b). Admitted. @@ -216,6 +249,7 @@ Section CORRECTNESS. Proof. induction 1; intros R1 MSTATE; try inv_state. - (* Inop *) + unfold match_prog in TRANSL. econstructor. split. apply Smallstep.plus_one. @@ -232,41 +266,86 @@ Section CORRECTNESS. (* prove match_state *) rewrite assumption_32bit. constructor; auto. - unfold_merge. simpl. apply regs_lessdef_regs. apply greater_than_max_func. + unfold_merge. simpl. apply regs_lessdef_add_greater. apply greater_than_max_func. assumption. unfold state_st_wf. inversion 1. subst. unfold_merge. apply AssocMap.gss. - (* Iop *) - econstructor. - split. + destruct v eqn:?; + try ( + destruct op eqn:?; inversion H21; simpl in H0; repeat (unfold_match H0); + inversion H0; subst; simpl in *; try (unfold_func H4); try (unfold_func H5); + try (unfold_func H6); + try (unfold Op.eval_addressing32 in H6; repeat (unfold_match H6); inversion H6; + unfold_func H3); + + inversion Heql; inversion MASSOC; subst; + assert (HPle : Ple r (RTL.max_reg_function f)) + by (eapply RTL.max_reg_function_use; eauto; simpl; auto); + apply H1 in HPle; inversion HPle; + rewrite H2 in *; discriminate + ). + + + econstructor. split. + apply Smallstep.plus_one. + eapply HTL.step_module; eauto. + econstructor; simpl; trivial. + constructor; trivial. + econstructor; simpl; eauto. + eapply eval_correct; eauto. constructor. + unfold_merge. simpl. + rewrite AssocMap.gso. + apply AssocMap.gss. + apply st_greater_than_res. + + (* match_states *) + assert (pc' = valueToPos (posToValue 32 pc')). auto using assumption_32bit. + rewrite <- H1. + constructor; auto. + unfold_merge. + apply regs_lessdef_add_match. + constructor. + apply regs_lessdef_add_greater. + apply greater_than_max_func. + assumption. + + unfold state_st_wf. intros. inversion H2. subst. + unfold_merge. + rewrite AssocMap.gso. + apply AssocMap.gss. + apply st_greater_than_res. + + + econstructor. split. apply Smallstep.plus_one. eapply HTL.step_module; eauto. econstructor; simpl; trivial. constructor; trivial. econstructor; simpl; eauto. eapply eval_correct; eauto. + constructor. rewrite valueToInt_intToValue. trivial. unfold_merge. simpl. rewrite AssocMap.gso. apply AssocMap.gss. apply st_greater_than_res. - trivial. (* match_states *) - assert (pc' = valueToPos (posToValue 32 pc')). symmetry. apply assumption_32bit. + assert (pc' = valueToPos (posToValue 32 pc')). auto using assumption_32bit. rewrite <- H1. constructor. apply rs0. unfold_merge. - apply regs_add_match. - apply regs_lessdef_regs. - assumption. - apply valToValue_lessdef. - assumption. + apply regs_lessdef_add_match. + constructor. + symmetry. apply valueToInt_intToValue. + apply regs_lessdef_add_greater. + apply greater_than_max_func. + assumption. assumption. unfold state_st_wf. intros. inversion H2. subst. unfold_merge. rewrite AssocMap.gso. apply AssocMap.gss. apply st_greater_than_res. - - econstructor. split. apply Smallstep.plus_one. + + - econstructor. split. apply Smallstep.plus_one. eapply HTL.step_module; eauto. eapply Verilog.stmnt_runp_Vnonblock with (rhsval := if b then posToValue 32 ifso else posToValue 32 ifnot). @@ -291,8 +370,8 @@ Section CORRECTNESS. rewrite assumption_32bit. apply match_state. apply rs0. unfold_merge. - apply regs_lessdef_regs. assumption. - assumption. + apply regs_lessdef_add_greater. apply greater_than_max_func. + assumption. assumption. unfold state_st_wf. intros. inversion H1. subst. unfold_merge. @@ -300,7 +379,7 @@ Section CORRECTNESS. rewrite assumption_32bit. apply match_state. apply rs0. unfold_merge. - apply regs_lessdef_regs. assumption. + apply regs_lessdef_add_greater. apply greater_than_max_func. assumption. assumption. unfold state_st_wf. intros. inversion H1. @@ -366,13 +445,6 @@ Section CORRECTNESS. Admitted. Hint Resolve transl_step_correct : htlproof. - Lemma senv_preserved : - forall id : AST.ident, - Globalenvs.Senv.public_symbol (Smallstep.symbolenv (HTL.semantics tprog)) id = - Globalenvs.Senv.public_symbol (Smallstep.symbolenv (RTL.semantics prog)) id. - Proof. Admitted. - Hint Resolve senv_preserved : htlproof. - Lemma transl_initial_states : forall s1 : Smallstep.state (RTL.semantics prog), Smallstep.initial_state (RTL.semantics prog) s1 -> @@ -389,8 +461,14 @@ Section CORRECTNESS. Proof. Admitted. Hint Resolve transl_final_states : htlproof. - Theorem transf_program_correct: - Smallstep.forward_simulation (RTL.semantics prog) (HTL.semantics tprog). - Proof. eauto with htlproof. Qed. +Theorem transf_program_correct: + Smallstep.forward_simulation (RTL.semantics prog) (HTL.semantics tprog). +Proof. + eapply Smallstep.forward_simulation_plus. + apply senv_preserved. + eexact transl_initial_states. + eexact transl_final_states. + exact transl_step_correct. +Qed. End CORRECTNESS. |