diff options
author | Yann Herklotz <git@yannherklotz.com> | 2020-07-02 11:16:26 +0100 |
---|---|---|
committer | Yann Herklotz <git@yannherklotz.com> | 2020-07-02 11:16:26 +0100 |
commit | 623869a9f902887f6634176ec88f30d27f638dec (patch) | |
tree | 2e624e0d1a38bcd7d952d3f1e575f5c1fd02a670 /src/translation | |
parent | 4c475a386caeaee3e3ef7682840c738cecdee941 (diff) | |
parent | aa28022035b16417aaafa36a450461c5133a44b4 (diff) | |
download | vericert-kvx-623869a9f902887f6634176ec88f30d27f638dec.tar.gz vericert-kvx-623869a9f902887f6634176ec88f30d27f638dec.zip |
Merge branch 'dev-nadesh-merge' into dev-nadeshdev-nadesh
Diffstat (limited to 'src/translation')
-rw-r--r-- | src/translation/HTLgen.v | 129 | ||||
-rw-r--r-- | src/translation/HTLgenproof.v | 2049 | ||||
-rw-r--r-- | src/translation/HTLgenspec.v | 116 | ||||
-rw-r--r-- | src/translation/Veriloggen.v | 9 | ||||
-rw-r--r-- | src/translation/Veriloggenproof.v | 60 |
5 files changed, 2009 insertions, 354 deletions
diff --git a/src/translation/HTLgen.v b/src/translation/HTLgen.v index c96d4c7..4cde0c8 100644 --- a/src/translation/HTLgen.v +++ b/src/translation/HTLgen.v @@ -17,7 +17,7 @@ *) From compcert Require Import Maps. -From compcert Require Errors Globalenvs. +From compcert Require Errors Globalenvs Integers. From compcert Require Import AST RTL. From coqup Require Import Verilog HTL Coquplib AssocMap Value Statemonad. @@ -131,7 +131,7 @@ Lemma declare_reg_state_incr : s.(st_st) s.(st_freshreg) s.(st_freshstate) - (AssocMap.set r (i, Scalar sz) s.(st_scldecls)) + (AssocMap.set r (i, VScalar sz) s.(st_scldecls)) s.(st_arrdecls) s.(st_datapath) s.(st_controllogic)). @@ -142,7 +142,7 @@ Definition declare_reg (i : option io) (r : reg) (sz : nat) : mon unit := s.(st_st) s.(st_freshreg) s.(st_freshstate) - (AssocMap.set r (i, Scalar sz) s.(st_scldecls)) + (AssocMap.set r (i, VScalar sz) s.(st_scldecls)) s.(st_arrdecls) s.(st_datapath) s.(st_controllogic)) @@ -280,19 +280,39 @@ Definition translate_condition (c : Op.condition) (args : list reg) : mon expr : | _, _ => error (Errors.msg "Htlgen: condition instruction not implemented: other") end. +Definition check_address_parameter_signed (p : Z) : bool := + Z.eqb (Z.modulo p 4) 0 + && Z.leb Integers.Ptrofs.min_signed p + && Z.leb p Integers.Ptrofs.max_signed. + +Definition check_address_parameter_unsigned (p : Z) : bool := + Z.eqb (Z.modulo p 4) 0 + && Z.leb p Integers.Ptrofs.max_unsigned. + Definition translate_eff_addressing (a: Op.addressing) (args: list reg) : mon expr := - match a, args with - | Op.Aindexed off, r1::nil => ret (boplitz Vadd r1 off) - | Op.Aindexed2 off, r1::r2::nil => ret (Vbinop Vadd (Vvar r1) (boplitz Vadd r2 off)) + match a, args with (* TODO: We should be more methodical here; what are the possibilities?*) + | Op.Aindexed off, r1::nil => + if (check_address_parameter_signed off) + then ret (boplitz Vadd r1 off) + else error (Errors.msg "Veriloggen: translate_eff_addressing (Aindexed): address misaligned") | Op.Ascaled scale offset, r1::nil => - ret (Vbinop Vadd (boplitz Vmul r1 scale) (Vlit (ZToValue 32 offset))) - | Op.Aindexed2scaled scale offset, r1::r2::nil => - ret (Vbinop Vadd (boplitz Vadd r1 offset) (boplitz Vmul r2 scale)) - (* Stack arrays/referenced variables *) + if (check_address_parameter_signed scale) && (check_address_parameter_signed offset) + then ret (Vbinop Vadd (boplitz Vmul r1 scale) (Vlit (ZToValue 32 offset))) + else error (Errors.msg "Veriloggen: translate_eff_addressing (Ascaled): address misaligned") + | Op.Aindexed2 offset, r1::r2::nil => + if (check_address_parameter_signed offset) + then ret (Vbinop Vadd (Vvar r1) (boplitz Vadd r2 offset)) + else error (Errors.msg "Veriloggen: translate_eff_addressing (Aindexed2): address misaligned") + | Op.Aindexed2scaled scale offset, r1::r2::nil => (* Typical for dynamic array addressing *) + if (check_address_parameter_signed scale) && (check_address_parameter_signed offset) + then ret (Vbinop Vadd (boplitz Vadd r1 offset) (boplitz Vmul r2 scale)) + else error (Errors.msg "Veriloggen: translate_eff_addressing (Aindexed2scaled): address misaligned") | Op.Ainstack a, nil => (* We need to be sure that the base address is aligned *) - let a := Integers.Ptrofs.unsigned a in (* FIXME: Assuming stack offsets are +ve; is this ok? *) - ret (Vlit (ZToValue 32 a)) - | _, _ => error (Errors.msg "Htlgen: eff_addressing instruction not implemented: other") + let a := Integers.Ptrofs.unsigned a in + if (check_address_parameter_unsigned a) + then ret (Vlit (ZToValue 32 a)) + else error (Errors.msg "Veriloggen: translate_eff_addressing (Ainstack): address misaligned") + | _, _ => error (Errors.msg "Veriloggen: translate_eff_addressing unsuported addressing") end. (** Translate an instruction to a statement. FIX mulhs mulhu *) @@ -374,24 +394,24 @@ Definition add_branch_instr (e: expr) (n n1 n2: node) : mon unit := Definition translate_arr_access (mem : AST.memory_chunk) (addr : Op.addressing) (args : list reg) (stack : reg) : mon expr := - match addr, args with (* TODO: We should be more methodical here; what are the possibilities?*) - | Op.Aindexed off, r1::nil => (* FIXME: Cannot guarantee alignment *) - ret (Vvari stack (Vbinop Vadd (boplitz Vdiv r1 4) (Vlit (ZToValue 32 (off / 4))))) - | Op.Ascaled scale offset, r1::nil => - if ((Z.eqb (Z.modulo scale 4) 0) && (Z.eqb (Z.modulo offset 4) 0)) - then ret (Vvari stack (Vbinop Vadd (boplitz Vmul r1 (scale / 4)) (Vlit (ZToValue 32 (offset / 4))))) - else error (Errors.msg "Htlgen: translate_arr_access address misaligned") - | Op.Aindexed2scaled scale offset, r1::r2::nil => (* Typical for dynamic array addressing *) - if ((Z.eqb (Z.modulo scale 4) 0) && (Z.eqb (Z.modulo offset 4) 0)) + match mem, addr, args with (* TODO: We should be more methodical here; what are the possibilities?*) + | Mint32, Op.Aindexed off, r1::nil => + if (check_address_parameter_signed off) + then ret (Vvari stack (Vbinop Vdivu (boplitz Vadd r1 off) (Vlit (ZToValue 32 4)))) + else error (Errors.msg "HTLgen: translate_arr_access address misaligned") + | Mint32, Op.Aindexed2scaled scale offset, r1::r2::nil => (* Typical for dynamic array addressing *) + if (check_address_parameter_signed scale) && (check_address_parameter_signed offset) then ret (Vvari stack - (Vbinop Vadd (Vbinop Vadd (boplitz Vdiv r1 4) (Vlit (ZToValue 32 (offset / 4)))) - (boplitz Vmul r2 (scale / 4)))) - else error (Errors.msg "Htlgen: translate_arr_access address misaligned") - | Op.Ainstack a, nil => (* We need to be sure that the base address is aligned *) - let a := Integers.Ptrofs.unsigned a in (* FIXME: Assuming stack offsets are +ve; is this ok? *) - if (Z.eq_dec (Z.modulo a 4) 0) then ret (Vvari stack (Vlit (ZToValue 32 (a / 4)))) - else error (Errors.msg "Htlgen: eff_addressing misaligned stack offset") - | _, _ => error (Errors.msg "Htlgen: translate_arr_access unsupported addressing") + (Vbinop Vdivu + (Vbinop Vadd (boplitz Vadd r1 offset) (boplitz Vmul r2 scale)) + (ZToValue 32 4))) + else error (Errors.msg "HTLgen: translate_arr_access address misaligned") + | Mint32, Op.Ainstack a, nil => (* We need to be sure that the base address is aligned *) + let a := Integers.Ptrofs.unsigned a in + if (check_address_parameter_unsigned a) + then ret (Vvari stack (Vlit (ZToValue 32 (a / 4)))) + else error (Errors.msg "HTLgen: eff_addressing misaligned stack offset") + | _, _, _ => error (Errors.msg "HTLgen: translate_arr_access unsuported addressing") end. Fixpoint enumerate (i : nat) (ns : list node) {struct ns} : list (nat * node) := @@ -418,10 +438,10 @@ Definition transf_instr (fin rtrn stack: reg) (ni: node * instruction) : mon uni | Iload mem addr args dst n' => do src <- translate_arr_access mem addr args stack; do _ <- declare_reg None dst 32; - add_instr n n' (block dst src) + add_instr n n' (nonblock dst src) | Istore mem addr args src n' => do dst <- translate_arr_access mem addr args stack; - add_instr n n' (Vblock dst (Vvar src)) (* TODO: Could juse use add_instr? reg exists. *) + add_instr n n' (Vnonblock dst (Vvar src)) (* TODO: Could juse use add_instr? reg exists. *) | Icall _ _ _ _ _ => error (Errors.msg "Calls are not implemented.") | Itailcall _ _ _ => error (Errors.msg "Tailcalls are not implemented.") | Ibuiltin _ _ _ _ => error (Errors.msg "Builtin functions not implemented.") @@ -447,7 +467,7 @@ Lemma create_reg_state_incr: s.(st_st) (Pos.succ (st_freshreg s)) (st_freshstate s) - (AssocMap.set s.(st_freshreg) (i, Scalar sz) s.(st_scldecls)) + (AssocMap.set s.(st_freshreg) (i, VScalar sz) s.(st_scldecls)) s.(st_arrdecls) (st_datapath s) (st_controllogic s)). @@ -459,7 +479,7 @@ Definition create_reg (i : option io) (sz : nat) : mon reg := s.(st_st) (Pos.succ r) (st_freshstate s) - (AssocMap.set s.(st_freshreg) (i, Scalar sz) s.(st_scldecls)) + (AssocMap.set s.(st_freshreg) (i, VScalar sz) s.(st_scldecls)) (st_arrdecls s) (st_datapath s) (st_controllogic s)) @@ -472,27 +492,31 @@ Lemma create_arr_state_incr: (Pos.succ (st_freshreg s)) (st_freshstate s) s.(st_scldecls) - (AssocMap.set s.(st_freshreg) (i, Array sz ln) s.(st_arrdecls)) + (AssocMap.set s.(st_freshreg) (i, VArray sz ln) s.(st_arrdecls)) (st_datapath s) (st_controllogic s)). Proof. constructor; simpl; auto with htlh. Qed. -Definition create_arr (i : option io) (sz : nat) (ln : nat) : mon reg := +Definition create_arr (i : option io) (sz : nat) (ln : nat) : mon (reg * nat) := fun s => let r := s.(st_freshreg) in - OK r (mkstate + OK (r, ln) (mkstate s.(st_st) (Pos.succ r) (st_freshstate s) s.(st_scldecls) - (AssocMap.set s.(st_freshreg) (i, Array sz ln) s.(st_arrdecls)) + (AssocMap.set s.(st_freshreg) (i, VArray sz ln) s.(st_arrdecls)) (st_datapath s) (st_controllogic s)) (create_arr_state_incr s sz ln i). +Definition stack_correct (sz : Z) : bool := + (0 <=? sz) && (sz <? Integers.Ptrofs.modulus) && (Z.modulo sz 4 =? 0). + Definition transf_module (f: function) : mon module := + if stack_correct f.(fn_stacksize) then do fin <- create_reg (Some Voutput) 1; do rtrn <- create_reg (Some Voutput) 32; - do stack <- create_arr None 32 (Z.to_nat (f.(fn_stacksize) / 4)); + do (stack, stack_len) <- create_arr None 32 (Z.to_nat (f.(fn_stacksize) / 4)); do _ <- collectlist (transf_instr fin rtrn stack) (Maps.PTree.elements f.(RTL.fn_code)); do _ <- collectlist (fun r => declare_reg (Some Vinput) r 32) f.(RTL.fn_params); do start <- create_reg (Some Vinput) 1; @@ -506,20 +530,22 @@ Definition transf_module (f: function) : mon module := f.(fn_entrypoint) current_state.(st_st) stack + stack_len fin rtrn start rst clk current_state.(st_scldecls) - current_state.(st_arrdecls)). + current_state.(st_arrdecls)) + else error (Errors.msg "Stack size misalignment."). Definition max_state (f: function) : state := let st := Pos.succ (max_reg_function f) in mkstate st (Pos.succ st) (Pos.succ (max_pc_function f)) - (AssocMap.set st (None, Scalar 32) (st_scldecls (init_state st))) + (AssocMap.set st (None, VScalar 32) (st_scldecls (init_state st))) (st_arrdecls (init_state st)) (st_datapath (init_state st)) (st_controllogic (init_state st)). @@ -529,7 +555,7 @@ Definition transl_module (f : function) : Errors.res module := Definition transl_fundef := transf_partial_fundef transl_module. -Definition transl_program (p : RTL.program) := transform_partial_program transl_fundef p. +(* Definition transl_program (p : RTL.program) := transform_partial_program transl_fundef p. *) (*Definition transl_main_fundef f : Errors.res HTL.fundef := match f with @@ -546,11 +572,18 @@ Definition transl_program (p: RTL.program) : Errors.res HTL.program := (fun i v => Errors.OK v) p. *) -(*Definition main_is_internal (p : RTL.program): Prop := +Definition main_is_internal (p : RTL.program) : bool := let ge := Globalenvs.Genv.globalenv p in - forall b m, - Globalenvs.Genv.find_symbol ge p.(AST.prog_main) = Some b -> - Globalenvs.Genv.find_funct_ptr ge b = Some (AST.Internal m). + match Globalenvs.Genv.find_symbol ge p.(AST.prog_main) with + | Some b => + match Globalenvs.Genv.find_funct_ptr ge b with + | Some (AST.Internal _) => true + | _ => false + end + | _ => false + end. -Definition tranls_program_with_proof (p : RTL.program) : Errors.res { p' : HTL.program | main_is_internal p }. -*) +Definition transl_program (p : RTL.program) : Errors.res HTL.program := + if main_is_internal p + then transform_partial_program transl_fundef p + else Errors.Error (Errors.msg "Main function is not Internal."). diff --git a/src/translation/HTLgenproof.v b/src/translation/HTLgenproof.v index 9786d23..6e470d5 100644 --- a/src/translation/HTLgenproof.v +++ b/src/translation/HTLgenproof.v @@ -18,9 +18,11 @@ From compcert Require RTL Registers AST Integers. From compcert Require Import Globalenvs Memory. -From coqup Require Import Coquplib HTLgenspec HTLgen Value AssocMap. +From coqup Require Import Coquplib HTLgenspec HTLgen Value AssocMap Array IntegerExtra ZExtra. From coqup Require HTL Verilog. +Require Import Lia. + Local Open Scope assocmap. Hint Resolve Smallstep.forward_simulation_plus : htlproof. @@ -42,44 +44,80 @@ Definition state_st_wf (m : HTL.module) (s : HTL.state) := asa!(m.(HTL.mod_st)) = Some (posToValue 32 st). Hint Unfold state_st_wf : htlproof. -Inductive match_stacks : list RTL.stackframe -> list HTL.stackframe -> Prop := -| match_stacks_nil : - match_stacks nil nil -| match_stacks_cons : - forall cs lr r f sp pc rs m assoc - (TF : tr_module f m) - (ST: match_stacks cs lr) - (MA: match_assocmaps f rs assoc), - match_stacks (RTL.Stackframe r f sp pc rs :: cs) - (HTL.Stackframe r m pc assoc :: lr). - -Inductive match_arrs (m : HTL.module) : RTL.function -> mem -> AssocMap.t (list value) -> Prop := -| match_arr : forall mem asa stack sp f sz, - sz = f.(RTL.fn_stacksize) -> - asa ! (m.(HTL.mod_stk)) = Some stack -> +Inductive match_arrs (m : HTL.module) (f : RTL.function) (sp : Values.val) (mem : mem) : + Verilog.assocmap_arr -> Prop := +| match_arr : forall asa stack, + asa ! (m.(HTL.mod_stk)) = Some stack /\ + stack.(arr_length) = Z.to_nat (f.(RTL.fn_stacksize) / 4) /\ (forall ptr, - 0 <= ptr < sz -> - nth_error stack (Z.to_nat ptr) = - (Coquplib.Option.bind (Mem.loadv AST.Mint32 mem - (Values.Val.offset_ptr sp (Integers.Ptrofs.repr ptr))) - valToValue)) -> - match_arrs m f mem asa. + 0 <= ptr < Z.of_nat m.(HTL.mod_stk_len) -> + opt_val_value_lessdef (Mem.loadv AST.Mint32 mem + (Values.Val.offset_ptr sp (Integers.Ptrofs.repr (4 * ptr)))) + (Option.default (NToValue 32 0) + (Option.join (array_get_error (Z.to_nat ptr) stack)))) -> + match_arrs m f sp mem asa. + +Definition stack_based (v : Values.val) (sp : Values.block) : Prop := + match v with + | Values.Vptr sp' off => sp' = sp + | _ => True + end. + +Definition reg_stack_based_pointers (sp : Values.block) (rs : Registers.Regmap.t Values.val) : Prop := + forall r, stack_based (Registers.Regmap.get r rs) sp. + +Definition arr_stack_based_pointers (spb : Values.block) (m : mem) (stack_length : Z) + (sp : Values.val) : Prop := + forall ptr, + 0 <= ptr < (stack_length / 4) -> + stack_based (Option.default + Values.Vundef + (Mem.loadv AST.Mint32 m + (Values.Val.offset_ptr sp (Integers.Ptrofs.repr (4 * ptr))))) + spb. + +Definition stack_bounds (sp : Values.val) (hi : Z) (m : mem) : Prop := + forall ptr v, + hi <= ptr <= Integers.Ptrofs.max_unsigned -> + Z.modulo ptr 4 = 0 -> + Mem.loadv AST.Mint32 m (Values.Val.offset_ptr sp (Integers.Ptrofs.repr ptr )) = None /\ + Mem.storev AST.Mint32 m (Values.Val.offset_ptr sp (Integers.Ptrofs.repr ptr )) v = None. + +Inductive match_frames : list RTL.stackframe -> list HTL.stackframe -> Prop := +| match_frames_nil : + match_frames nil nil. +(* | match_frames_cons : *) +(* forall cs lr r f sp sp' pc rs m asr asa *) +(* (TF : tr_module f m) *) +(* (ST: match_frames mem cs lr) *) +(* (MA: match_assocmaps f rs asr) *) +(* (MARR : match_arrs m f sp mem asa) *) +(* (SP : sp = Values.Vptr sp' (Integers.Ptrofs.repr 0)) *) +(* (RSBP: reg_stack_based_pointers sp' rs) *) +(* (ASBP: arr_stack_based_pointers sp' mem (f.(RTL.fn_stacksize)) sp) *) +(* (BOUNDS : stack_bounds sp (f.(RTL.fn_stacksize)) mem), *) +(* match_frames mem (RTL.Stackframe r f sp pc rs :: cs) *) +(* (HTL.Stackframe r m pc asr asa :: lr). *) Inductive match_states : RTL.state -> HTL.state -> Prop := -| match_state : forall asa asr sf f sp rs mem m st res +| match_state : forall asa asr sf f sp sp' rs mem m st res (MASSOC : match_assocmaps f rs asr) (TF : tr_module f m) (WF : state_st_wf m (HTL.State res m st asr asa)) - (MS : match_stacks sf res) - (MA : match_arrs m f mem asa), + (MF : match_frames sf res) + (MARR : match_arrs m f sp mem asa) + (SP : sp = Values.Vptr sp' (Integers.Ptrofs.repr 0)) + (RSBP : reg_stack_based_pointers sp' rs) + (ASBP : arr_stack_based_pointers sp' mem (f.(RTL.fn_stacksize)) sp) + (BOUNDS : stack_bounds sp (f.(RTL.fn_stacksize)) mem), match_states (RTL.State sf f sp st rs mem) (HTL.State res m st asr asa) | match_returnstate : forall - v v' stack m res - (MS : match_stacks stack res), + v v' stack mem res + (MF : match_frames stack res), val_value_lessdef v v' -> - match_states (RTL.Returnstate stack v m) (HTL.Returnstate res v') + match_states (RTL.Returnstate stack v mem) (HTL.Returnstate res v') | match_initial_call : forall f m m0 (TF : tr_module f m), @@ -87,12 +125,23 @@ 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 : @@ -129,6 +178,94 @@ Proof. Qed. Hint Resolve regs_lessdef_add_match : htlproof. +Lemma list_combine_none : + forall n l, + length l = n -> + list_combine Verilog.merge_cell (list_repeat None n) l = l. +Proof. + induction n; intros; crush. + - symmetry. apply length_zero_iff_nil. auto. + - destruct l; crush. + rewrite list_repeat_cons. + crush. f_equal. + eauto. +Qed. + +Lemma combine_none : + forall n a, + a.(arr_length) = n -> + arr_contents (combine Verilog.merge_cell (arr_repeat None n) a) = arr_contents a. +Proof. + intros. + unfold combine. + crush. + + rewrite <- (arr_wf a) in H. + apply list_combine_none. + assumption. +Qed. + +Lemma list_combine_lookup_first : + forall l1 l2 n, + length l1 = length l2 -> + nth_error l1 n = Some None -> + nth_error (list_combine Verilog.merge_cell l1 l2) n = nth_error l2 n. +Proof. + induction l1; intros; crush. + + rewrite nth_error_nil in H0. + discriminate. + + destruct l2 eqn:EQl2. crush. + simpl in H. invert H. + destruct n; simpl in *. + invert H0. simpl. reflexivity. + eauto. +Qed. + +Lemma combine_lookup_first : + forall a1 a2 n, + a1.(arr_length) = a2.(arr_length) -> + array_get_error n a1 = Some None -> + array_get_error n (combine Verilog.merge_cell a1 a2) = array_get_error n a2. +Proof. + intros. + + unfold array_get_error in *. + apply list_combine_lookup_first; eauto. + rewrite a1.(arr_wf). rewrite a2.(arr_wf). + assumption. +Qed. + +Lemma list_combine_lookup_second : + forall l1 l2 n x, + length l1 = length l2 -> + nth_error l1 n = Some (Some x) -> + nth_error (list_combine Verilog.merge_cell l1 l2) n = Some (Some x). +Proof. + induction l1; intros; crush; auto. + + destruct l2 eqn:EQl2. crush. + simpl in H. invert H. + destruct n; simpl in *. + invert H0. simpl. reflexivity. + eauto. +Qed. + +Lemma combine_lookup_second : + forall a1 a2 n x, + a1.(arr_length) = a2.(arr_length) -> + array_get_error n a1 = Some (Some x) -> + array_get_error n (combine Verilog.merge_cell a1 a2) = Some (Some x). +Proof. + intros. + + unfold array_get_error in *. + apply list_combine_lookup_second; eauto. + rewrite a1.(arr_wf). rewrite a2.(arr_wf). + assumption. +Qed. + (* Need to eventually move posToValue 32 to posToValueAuto, as that has this proof. *) Lemma assumption_32bit : forall v, @@ -198,6 +335,17 @@ Proof. constructor. Qed. +Lemma arr_lookup_some: + forall (z : Z) (r0 : Registers.reg) (r : Verilog.reg) (asr : assocmap) (asa : Verilog.assocmap_arr) + (stack : Array (option value)) (H5 : asa ! r = Some stack) n, + exists x, Verilog.arr_assocmap_lookup asa r n = Some x. +Proof. + intros z r0 r asr asa stack H5 n. + eexists. + unfold Verilog.arr_assocmap_lookup. rewrite H5. reflexivity. +Qed. +Hint Resolve arr_lookup_some : htlproof. + Section CORRECTNESS. Variable prog : RTL.program. @@ -205,13 +353,16 @@ Section CORRECTNESS. Hypothesis TRANSL : match_prog prog tprog. -(* Let ge : RTL.genv := Globalenvs.Genv.globalenv prog. + 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), @@ -219,7 +370,7 @@ 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. @@ -229,21 +380,21 @@ 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. @@ -281,171 +432,1470 @@ Section CORRECTNESS. exists asr' asa', HTL.step tge (HTL.State res m st asr asa) Events.E0 (HTL.State res m st asr' asa'). - Theorem transl_step_correct: - forall (S1 : RTL.state) t S2, - RTL.step ge S1 t S2 -> - forall (R1 : HTL.state), - match_states S1 R1 -> - exists R2, Smallstep.plus HTL.step tge R1 t R2 /\ match_states S2 R2. + Opaque combine. + + Ltac tac0 := + match goal with + | [ |- context[valueToPos (posToValue 32 _)] ] => rewrite assumption_32bit + + | [ |- context[Verilog.merge_arrs _ _] ] => unfold Verilog.merge_arrs + | [ |- context[Verilog.merge_arr] ] => unfold Verilog.merge_arr + | [ |- context[Verilog.merge_regs _ _] ] => unfold Verilog.merge_regs; crush; unfold_merge + | [ |- context[reg_stack_based_pointers] ] => unfold reg_stack_based_pointers; intros + | [ |- context[Verilog.arr_assocmap_set _ _ _ _] ] => unfold Verilog.arr_assocmap_set + + | [ |- context[HTL.empty_stack] ] => unfold HTL.empty_stack + + | [ |- context[_ # ?d <- _ ! ?d] ] => rewrite AssocMap.gss + | [ |- context[_ # ?d <- _ ! ?s] ] => rewrite AssocMap.gso + | [ |- context[(AssocMap.empty _) ! _] ] => rewrite AssocMap.gempty + + | [ |- context[array_get_error _ (combine Verilog.merge_cell (arr_repeat None _) _)] ] => + rewrite combine_lookup_first + + | [ |- state_st_wf _ _ ] => unfold state_st_wf; inversion 1 + | [ |- context[match_states _ _] ] => econstructor; auto + | [ |- match_arrs _ _ _ _ _ ] => econstructor; auto + | [ |- match_assocmaps _ _ _ # _ <- (posToValue 32 _) ] => + apply regs_lessdef_add_greater; [> apply greater_than_max_func | assumption] + + | [ H : ?asa ! ?r = Some _ |- Verilog.arr_assocmap_lookup ?asa ?r _ = Some _ ] => + unfold Verilog.arr_assocmap_lookup; setoid_rewrite H; f_equal + | [ |- context[(AssocMap.combine _ _ _) ! _] ] => + try (rewrite AssocMap.gcombine; [> | reflexivity]) + + | [ |- context[Registers.Regmap.get ?d (Registers.Regmap.set ?d _ _)] ] => + rewrite Registers.Regmap.gss + | [ |- context[Registers.Regmap.get ?s (Registers.Regmap.set ?d _ _)] ] => + destruct (Pos.eq_dec s d) as [EQ|EQ]; + [> rewrite EQ | rewrite Registers.Regmap.gso; auto] + + | [ H : opt_val_value_lessdef _ _ |- _ ] => invert H + | [ H : context[Z.of_nat (Z.to_nat _)] |- _ ] => rewrite Z2Nat.id in H; [> solve crush |] + | [ H : _ ! _ = Some _ |- _] => setoid_rewrite H + end. + + Ltac small_tac := repeat (crush; try array; try ptrofs); crush; auto. + Ltac big_tac := repeat (crush; try array; try ptrofs; try tac0); crush; auto. + + Lemma transl_inop_correct: + forall (s : list RTL.stackframe) (f : RTL.function) (sp : Values.val) (pc : positive) + (rs : RTL.regset) (m : mem) (pc' : RTL.node), + (RTL.fn_code f) ! pc = Some (RTL.Inop pc') -> + forall R1 : HTL.state, + match_states (RTL.State s f sp pc rs m) R1 -> + exists R2 : HTL.state, + Smallstep.plus HTL.step tge R1 Events.E0 R2 /\ match_states (RTL.State s f sp pc' rs m) R2. Proof. - induction 1; intros R1 MSTATE; try inv_state. - - (* Inop *) - unfold match_prog in TRANSL. - econstructor. - split. - apply Smallstep.plus_one. + intros s f sp pc rs m pc' H R1 MSTATE. + inv_state. + + unfold match_prog in TRANSL. + econstructor. + split. + apply Smallstep.plus_one. + eapply HTL.step_module; eauto. + apply assumption_32bit. + (* processing of state *) + econstructor. + crush. + econstructor. + econstructor. + econstructor. + + all: invert MARR; big_tac. + Unshelve. + constructor. + Qed. + Hint Resolve transl_inop_correct : htlproof. + + Lemma transl_iop_correct: + forall (s : list RTL.stackframe) (f : RTL.function) (sp : Values.val) (pc : positive) + (rs : Registers.Regmap.t Values.val) (m : mem) (op : Op.operation) (args : list Registers.reg) + (res0 : Registers.reg) (pc' : RTL.node) (v : Values.val), + (RTL.fn_code f) ! pc = Some (RTL.Iop op args res0 pc') -> + Op.eval_operation ge sp op (map (fun r : positive => Registers.Regmap.get r rs) args) m = Some v -> + forall R1 : HTL.state, + match_states (RTL.State s f sp pc rs m) R1 -> + exists R2 : HTL.state, + Smallstep.plus HTL.step tge R1 Events.E0 R2 /\ + match_states (RTL.State s f sp pc' (Registers.Regmap.set res0 v rs) m) R2. + Proof. + intros s f sp pc rs m op args res0 pc' v H H0. + + (* Iop *) + (* 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. *) + + (* (* match_states *) *) + (* assert (pc' = valueToPos (posToValue 32 pc')). auto using assumption_32bit. *) + (* rewrite <- H1. *) + (* constructor. *) + (* unfold_merge. *) + (* 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. *) + (* assumption. *) + Admitted. + Hint Resolve transl_iop_correct : htlproof. + + Ltac tac := + repeat match goal with + | [ _ : error _ _ = OK _ _ _ |- _ ] => discriminate + | [ _ : context[if (?x && ?y) then _ else _] |- _ ] => + let EQ1 := fresh "EQ" in + let EQ2 := fresh "EQ" in + destruct x eqn:EQ1; destruct y eqn:EQ2; simpl in * + | [ _ : context[if ?x then _ else _] |- _ ] => + let EQ := fresh "EQ" in + destruct x eqn:EQ; simpl in * + | [ H : ret _ _ = _ |- _ ] => invert H + | [ _ : context[match ?x with | _ => _ end] |- _ ] => destruct x + end. + + Ltac inv_arr_access := + match goal with + | [ _ : translate_arr_access ?chunk ?addr ?args _ _ = OK ?c _ _ |- _] => + destruct c, chunk, addr, args; crush; tac; crush + end. + + Lemma transl_iload_correct: + forall (s : list RTL.stackframe) (f : RTL.function) (sp : Values.val) (pc : positive) + (rs : Registers.Regmap.t Values.val) (m : mem) (chunk : AST.memory_chunk) + (addr : Op.addressing) (args : list Registers.reg) (dst : Registers.reg) + (pc' : RTL.node) (a v : Values.val), + (RTL.fn_code f) ! pc = Some (RTL.Iload chunk addr args dst pc') -> + Op.eval_addressing ge sp addr (map (fun r : positive => Registers.Regmap.get r rs) args) = Some a -> + Mem.loadv chunk m a = Some v -> + forall R1 : HTL.state, + match_states (RTL.State s f sp pc rs m) R1 -> + exists R2 : HTL.state, + Smallstep.plus HTL.step tge R1 Events.E0 R2 /\ + match_states (RTL.State s f sp pc' (Registers.Regmap.set dst v rs) m) R2. + Proof. + intros s f sp pc rs m chunk addr args dst pc' a v H H0 H1 R1 MSTATE. + inv_state. inv_arr_access. + + + (** Preamble *) + invert MARR. crush. + + unfold Op.eval_addressing in H0. + destruct (Archi.ptr64) eqn:ARCHI; crush. + + unfold reg_stack_based_pointers in RSBP. + pose proof (RSBP r0) as RSBPr0. + + destruct (Registers.Regmap.get r0 rs) eqn:EQr0; crush. + + rewrite ARCHI in H1. crush. + subst. + + pose proof MASSOC as MASSOC'. + invert MASSOC'. + pose proof (H0 r0). + assert (HPler0 : Ple r0 (RTL.max_reg_function f)) + by (eapply RTL.max_reg_function_use; eauto; crush; eauto). + apply H6 in HPler0. + invert HPler0; try congruence. + rewrite EQr0 in H8. + invert H8. + clear H0. clear H6. + + unfold check_address_parameter_signed in *; + unfold check_address_parameter_unsigned in *; crush. + + remember (Integers.Ptrofs.add (Integers.Ptrofs.repr (valueToZ asr # r0)) + (Integers.Ptrofs.of_int (Integers.Int.repr z))) as OFFSET. + + (** Modular preservation proof *) + assert (Integers.Ptrofs.unsigned OFFSET mod 4 = 0) as MOD_PRESERVE. + { rewrite HeqOFFSET. + apply PtrofsExtra.add_mod; crush; try lia. + exists 1073741824. reflexivity. (* FIXME: This is sadness inducing. *) + rewrite Integers.Ptrofs.signed_repr; try assumption. + admit. (* FIXME: Register bounds. *) + apply PtrofsExtra.of_int_mod. + rewrite Integers.Int.signed_repr; crush. } + + (** Read bounds proof *) + assert (Integers.Ptrofs.unsigned OFFSET < f.(RTL.fn_stacksize)) as READ_BOUND_HIGH. + { destruct (Integers.Ptrofs.unsigned OFFSET <? f.(RTL.fn_stacksize)) eqn:EQ; crush; auto. + unfold stack_bounds in BOUNDS. + exploit (BOUNDS (Integers.Ptrofs.unsigned OFFSET)); auto. + split; try lia; apply Integers.Ptrofs.unsigned_range_2. + small_tac. } + + (** Normalisation proof *) + assert (Integers.Ptrofs.repr + (4 * Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4))) = OFFSET) + as NORMALISE. + { replace 4 with (Integers.Ptrofs.unsigned (Integers.Ptrofs.repr 4)) at 1 by reflexivity. + rewrite <- PtrofsExtra.mul_unsigned. + apply PtrofsExtra.mul_divu; crush; auto. } + + (** Normalised bounds proof *) + assert (0 <= + Integers.Ptrofs.unsigned (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4)) + < (RTL.fn_stacksize f / 4)) + as NORMALISE_BOUND. + { split. + apply Integers.Ptrofs.unsigned_range_2. + assert (forall x y, Integers.Ptrofs.divu x y = Integers.Ptrofs.divu x y ) by reflexivity. + unfold Integers.Ptrofs.divu at 2 in H0. + rewrite H0. clear H0. + rewrite Integers.Ptrofs.unsigned_repr; crush. + apply Zmult_lt_reg_r with (p := 4); try lia. + repeat rewrite ZLib.div_mul_undo; try lia. + apply Z.div_pos; small_tac. + apply Z.div_le_upper_bound; small_tac. } + + inversion NORMALISE_BOUND as [ NORMALISE_BOUND_LOW NORMALISE_BOUND_HIGH ]; + clear NORMALISE_BOUND. + + (** Start of proof proper *) + eexists. split. + eapply Smallstep.plus_one. eapply HTL.step_module; eauto. - (* processing of state *) + apply assumption_32bit. + econstructor. econstructor. econstructor. crush. + econstructor. econstructor. econstructor. crush. + econstructor. econstructor. + econstructor. econstructor. econstructor. econstructor. + econstructor. econstructor. econstructor. econstructor. + + all: big_tac. + + 1: { apply st_greater_than_res. } + 2: { apply st_greater_than_res. } + + (** Match assocmaps *) + apply regs_lessdef_add_match; big_tac. + + (** Equality proof *) + match goal with + | [ |- context [valueToNat ?x] ] => + assert (Z.to_nat + (Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu + OFFSET + (Integers.Ptrofs.repr 4))) + = + valueToNat x) + as EXPR_OK by admit + end. + rewrite <- EXPR_OK. + + specialize (H7 (Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu + OFFSET + (Integers.Ptrofs.repr 4)))). + exploit H7; big_tac. + + (** RSBP preservation *) + unfold arr_stack_based_pointers in ASBP. + specialize (ASBP (Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4)))). + exploit ASBP; big_tac. + rewrite NORMALISE in H0. rewrite H1 in H0. assumption. + + + (** Preamble *) + invert MARR. crush. + + unfold Op.eval_addressing in H0. + destruct (Archi.ptr64) eqn:ARCHI; crush. + + unfold reg_stack_based_pointers in RSBP. + pose proof (RSBP r0) as RSBPr0. + pose proof (RSBP r1) as RSBPr1. + + destruct (Registers.Regmap.get r0 rs) eqn:EQr0; + destruct (Registers.Regmap.get r1 rs) eqn:EQr1; crush. + + rewrite ARCHI in H1. crush. + subst. + clear RSBPr1. + + pose proof MASSOC as MASSOC'. + invert MASSOC'. + pose proof (H0 r0). + pose proof (H0 r1). + assert (HPler0 : Ple r0 (RTL.max_reg_function f)) + by (eapply RTL.max_reg_function_use; eauto; crush; eauto). + assert (HPler1 : Ple r1 (RTL.max_reg_function f)) + by (eapply RTL.max_reg_function_use; eauto; simpl; auto). + apply H6 in HPler0. + apply H8 in HPler1. + invert HPler0; invert HPler1; try congruence. + rewrite EQr0 in H10. + rewrite EQr1 in H12. + invert H10. invert H12. + clear H0. clear H6. clear H8. + + unfold check_address_parameter_signed in *; + unfold check_address_parameter_unsigned in *; crush. + + remember (Integers.Ptrofs.add (Integers.Ptrofs.repr (valueToZ asr # r0)) + (Integers.Ptrofs.of_int + (Integers.Int.add (Integers.Int.mul (valueToInt asr # r1) (Integers.Int.repr z)) + (Integers.Int.repr z0)))) as OFFSET. + + (** Modular preservation proof *) + assert (Integers.Ptrofs.unsigned OFFSET mod 4 = 0) as MOD_PRESERVE. + { rewrite HeqOFFSET. + apply PtrofsExtra.add_mod; crush; try lia. + exists 1073741824. reflexivity. (* FIXME: This is sadness inducing. *) + rewrite Integers.Ptrofs.signed_repr; try assumption. + admit. (* FIXME: Register bounds. *) + apply PtrofsExtra.of_int_mod. + apply IntExtra.add_mod; crush; try lia. + exists 1073741824. reflexivity. (* FIXME: This is sadness inducing. *) + apply IntExtra.mul_mod; crush; try lia. + exists 1073741824. reflexivity. (* FIXME: This is sadness inducing. *) + admit. (* FIXME: Register bounds. *) + rewrite Integers.Int.signed_repr; crush. + rewrite Integers.Int.signed_repr; crush. } + + (** Read bounds proof *) + assert (Integers.Ptrofs.unsigned OFFSET < f.(RTL.fn_stacksize)) as READ_BOUND_HIGH. + { destruct (Integers.Ptrofs.unsigned OFFSET <? f.(RTL.fn_stacksize)) eqn:EQ; crush; auto. + unfold stack_bounds in BOUNDS. + exploit (BOUNDS (Integers.Ptrofs.unsigned OFFSET)); auto. + split; try lia; apply Integers.Ptrofs.unsigned_range_2. + small_tac. } + + (** Normalisation proof *) + assert (Integers.Ptrofs.repr + (4 * Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4))) = OFFSET) + as NORMALISE. + { replace 4 with (Integers.Ptrofs.unsigned (Integers.Ptrofs.repr 4)) at 1 by reflexivity. + rewrite <- PtrofsExtra.mul_unsigned. + apply PtrofsExtra.mul_divu; crush. } + + (** Normalised bounds proof *) + assert (0 <= + Integers.Ptrofs.unsigned (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4)) + < (RTL.fn_stacksize f / 4)) + as NORMALISE_BOUND. + { split. + apply Integers.Ptrofs.unsigned_range_2. + assert (forall x y, Integers.Ptrofs.divu x y = Integers.Ptrofs.divu x y ) by reflexivity. + unfold Integers.Ptrofs.divu at 2 in H0. + rewrite H0. clear H0. + rewrite Integers.Ptrofs.unsigned_repr; crush. + apply Zmult_lt_reg_r with (p := 4); try lia. + repeat rewrite ZLib.div_mul_undo; try lia. + apply Z.div_pos; small_tac. + apply Z.div_le_upper_bound; lia. } + + inversion NORMALISE_BOUND as [ NORMALISE_BOUND_LOW NORMALISE_BOUND_HIGH ]; + clear NORMALISE_BOUND. + + (** Start of proof proper *) + eexists. split. + eapply Smallstep.plus_one. + eapply HTL.step_module; eauto. + apply assumption_32bit. + econstructor. econstructor. econstructor. crush. + econstructor. econstructor. econstructor. crush. + econstructor. econstructor. econstructor. + econstructor. econstructor. econstructor. econstructor. econstructor. - simpl. trivial. + eapply Verilog.erun_Vbinop with (EQ := ?[EQ6]). + econstructor. econstructor. econstructor. econstructor. + econstructor. econstructor. econstructor. econstructor. + econstructor. econstructor. + + all: big_tac. + + 1: { apply st_greater_than_res. } + 2: { apply st_greater_than_res. } + + (** Match assocmaps *) + apply regs_lessdef_add_match; big_tac. + + (** Equality proof *) + match goal with + | [ |- context [valueToNat ?x] ] => + assert (Z.to_nat + (Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu + OFFSET + (Integers.Ptrofs.repr 4))) + = + valueToNat x) + as EXPR_OK by admit + end. + rewrite <- EXPR_OK. + + specialize (H7 (Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu + OFFSET + (Integers.Ptrofs.repr 4)))). + exploit H7; big_tac. + + (** RSBP preservation *) + unfold arr_stack_based_pointers in ASBP. + specialize (ASBP (Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4)))). + exploit ASBP; big_tac. + rewrite NORMALISE in H0. rewrite H1 in H0. assumption. + + + invert MARR. crush. + + unfold Op.eval_addressing in H0. + destruct (Archi.ptr64) eqn:ARCHI; crush. + rewrite ARCHI in H0. crush. + + unfold check_address_parameter_unsigned in *; + unfold check_address_parameter_signed in *; crush. + + assert (Integers.Ptrofs.repr 0 = Integers.Ptrofs.zero) as ZERO by reflexivity. + rewrite ZERO in H1. clear ZERO. + rewrite Integers.Ptrofs.add_zero_l in H1. + + remember i0 as OFFSET. + + (** Modular preservation proof *) + rename H0 into MOD_PRESERVE. + + (** Read bounds proof *) + assert (Integers.Ptrofs.unsigned OFFSET < f.(RTL.fn_stacksize)) as READ_BOUND_HIGH. + { destruct (Integers.Ptrofs.unsigned OFFSET <? f.(RTL.fn_stacksize)) eqn:EQ; crush; auto. + unfold stack_bounds in BOUNDS. + exploit (BOUNDS (Integers.Ptrofs.unsigned OFFSET)); big_tac. } + + (** Normalisation proof *) + assert (Integers.Ptrofs.repr + (4 * Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4))) = OFFSET) + as NORMALISE. + { replace 4 with (Integers.Ptrofs.unsigned (Integers.Ptrofs.repr 4)) at 1 by reflexivity. + rewrite <- PtrofsExtra.mul_unsigned. + apply PtrofsExtra.mul_divu; crush. } + + (** Normalised bounds proof *) + assert (0 <= + Integers.Ptrofs.unsigned (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4)) + < (RTL.fn_stacksize f / 4)) + as NORMALISE_BOUND. + { split. + apply Integers.Ptrofs.unsigned_range_2. + assert (forall x y, Integers.Ptrofs.divu x y = Integers.Ptrofs.divu x y ) by reflexivity. + unfold Integers.Ptrofs.divu at 2 in H0. + rewrite H0. clear H0. + rewrite Integers.Ptrofs.unsigned_repr; crush. + apply Zmult_lt_reg_r with (p := 4); try lia. + repeat rewrite ZLib.div_mul_undo; try lia. + apply Z.div_pos; small_tac. + apply Z.div_le_upper_bound; lia. } + + inversion NORMALISE_BOUND as [ NORMALISE_BOUND_LOW NORMALISE_BOUND_HIGH ]; + clear NORMALISE_BOUND. + + (** Start of proof proper *) + eexists. split. + eapply Smallstep.plus_one. + eapply HTL.step_module; eauto. + apply assumption_32bit. + econstructor. econstructor. econstructor. crush. + econstructor. econstructor. econstructor. econstructor. crush. + + all: big_tac. + + 1: { apply st_greater_than_res. } + 2: { apply st_greater_than_res. } + + (** Match assocmaps *) + apply regs_lessdef_add_match; big_tac. + + (** Equality proof *) + match goal with + | [ |- context [valueToNat ?x] ] => + assert (Z.to_nat + (Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu + OFFSET + (Integers.Ptrofs.repr 4))) + = + valueToNat x) + as EXPR_OK by admit + end. + rewrite <- EXPR_OK. + + specialize (H7 (Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu + OFFSET + (Integers.Ptrofs.repr 4)))). + exploit H7; big_tac. + + (** RSBP preservation *) + unfold arr_stack_based_pointers in ASBP. + specialize (ASBP (Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu OFFSET (Integers.Ptrofs.repr 4)))). + exploit ASBP; big_tac. + rewrite NORMALISE in H0. rewrite H1 in H0. assumption. + Admitted. + Hint Resolve transl_iload_correct : htlproof. + + Lemma transl_istore_correct: + forall (s : list RTL.stackframe) (f : RTL.function) (sp : Values.val) (pc : positive) + (rs : Registers.Regmap.t Values.val) (m : mem) (chunk : AST.memory_chunk) + (addr : Op.addressing) (args : list Registers.reg) (src : Registers.reg) + (pc' : RTL.node) (a : Values.val) (m' : mem), + (RTL.fn_code f) ! pc = Some (RTL.Istore chunk addr args src pc') -> + Op.eval_addressing ge sp addr (map (fun r : positive => Registers.Regmap.get r rs) args) = Some a -> + Mem.storev chunk m a (Registers.Regmap.get src rs) = Some m' -> + forall R1 : HTL.state, + match_states (RTL.State s f sp pc rs m) R1 -> + exists R2 : HTL.state, + Smallstep.plus HTL.step tge R1 Events.E0 R2 /\ match_states (RTL.State s f sp pc' rs m') R2. + Proof. + intros s f sp pc rs m chunk addr args src pc' a m' H H0 H1 R1 MSTATES. + inv_state. inv_arr_access. + + + (** Preamble *) + invert MARR. crush. + + unfold Op.eval_addressing in H0. + destruct (Archi.ptr64) eqn:ARCHI; crush. + + unfold reg_stack_based_pointers in RSBP. + pose proof (RSBP r0) as RSBPr0. + + destruct (Registers.Regmap.get r0 rs) eqn:EQr0; crush. + + rewrite ARCHI in H1. crush. + subst. + + pose proof MASSOC as MASSOC'. + invert MASSOC'. + pose proof (H0 r0). + assert (HPler0 : Ple r0 (RTL.max_reg_function f)) + by (eapply RTL.max_reg_function_use; eauto; crush; eauto). + apply H6 in HPler0. + invert HPler0; try congruence. + rewrite EQr0 in H8. + invert H8. + clear H0. clear H6. + + unfold check_address_parameter_unsigned in *; + unfold check_address_parameter_signed in *; crush. + + remember (Integers.Ptrofs.add (Integers.Ptrofs.repr (valueToZ asr # r0)) + (Integers.Ptrofs.of_int (Integers.Int.repr z))) as OFFSET. + + (** Modular preservation proof *) + assert (Integers.Ptrofs.unsigned OFFSET mod 4 = 0) as MOD_PRESERVE. + { rewrite HeqOFFSET. + apply PtrofsExtra.add_mod; crush; try lia. + exists 1073741824. reflexivity. (* FIXME: This is sadness inducing. *) + rewrite Integers.Ptrofs.signed_repr; try assumption. + admit. (* FIXME: Register bounds. *) + apply PtrofsExtra.of_int_mod. + rewrite Integers.Int.signed_repr; crush. } + + (** Write bounds proof *) + assert (Integers.Ptrofs.unsigned OFFSET < f.(RTL.fn_stacksize)) as WRITE_BOUND_HIGH. + { destruct (Integers.Ptrofs.unsigned OFFSET <? f.(RTL.fn_stacksize)) eqn:EQ; crush; auto. + unfold stack_bounds in BOUNDS. + exploit (BOUNDS (Integers.Ptrofs.unsigned OFFSET) (Registers.Regmap.get src rs)); big_tac. + apply Integers.Ptrofs.unsigned_range_2. } + + (** Start of proof proper *) + eexists. split. + eapply Smallstep.plus_one. + eapply HTL.step_module; eauto. + apply assumption_32bit. + econstructor. econstructor. econstructor. + eapply Verilog.stmnt_runp_Vnonblock_arr. crush. econstructor. + eapply Verilog.erun_Vbinop with (EQ := ?[EQ7]). + eapply Verilog.erun_Vbinop with (EQ := ?[EQ8]). econstructor. econstructor. + econstructor. econstructor. econstructor. econstructor. + econstructor. econstructor. econstructor. econstructor. - (* prove stval *) - unfold merge_assocmap. - unfold_merge. simpl. apply AssocMap.gss. + all: crush. - (* prove match_state *) + (** State Lookup *) + unfold Verilog.merge_regs. + crush. + unfold_merge. + apply AssocMap.gss. + + (** Match states *) rewrite assumption_32bit. - constructor; auto. - unfold_merge. simpl. apply regs_lessdef_add_greater. apply greater_than_max_func. + econstructor; eauto. + + (** Match assocmaps *) + unfold Verilog.merge_regs. crush. unfold_merge. + apply regs_lessdef_add_greater. apply greater_than_max_func. assumption. - unfold state_st_wf. inversion 1. subst. unfold_merge. apply AssocMap.gss. - - (* Iop *) - (* 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. *) - - (* (* match_states *) *) - (* assert (pc' = valueToPos (posToValue 32 pc')). auto using assumption_32bit. *) - (* rewrite <- H1. *) - (* constructor. *) - (* unfold_merge. *) - (* 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. *) - (* assumption. *) - admit. - - - admit. - - admit. - - - eexists. split. apply Smallstep.plus_one. - eapply HTL.step_module; eauto. - eapply Verilog.stmnt_runp_Vnonblock_reg with - (rhsval := if b then posToValue 32 ifso else posToValue 32 ifnot). + (** States well formed *) + unfold state_st_wf. inversion 1. crush. + unfold Verilog.merge_regs. + unfold_merge. + apply AssocMap.gss. + + (** Equality proof *) + match goal with + | [ |- context [valueToNat ?x] ] => + assert (Z.to_nat + (Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu + OFFSET + (Integers.Ptrofs.repr 4))) + = + valueToNat x) + as EXPR_OK by admit + end. + + assert (Integers.Ptrofs.repr 0 = Integers.Ptrofs.zero) as ZERO by reflexivity. + inversion MASSOC; revert HeqOFFSET; subst; clear MASSOC; intros HeqOFFSET. + + econstructor. + repeat split; crush. + unfold HTL.empty_stack. + crush. + unfold Verilog.merge_arrs. + + rewrite AssocMap.gcombine. + 2: { reflexivity. } + unfold Verilog.arr_assocmap_set. + rewrite AssocMap.gss. + unfold Verilog.merge_arr. + rewrite AssocMap.gss. + setoid_rewrite H5. + reflexivity. + + rewrite combine_length. + rewrite <- array_set_len. + unfold arr_repeat. crush. + apply list_repeat_len. + + rewrite <- array_set_len. + unfold arr_repeat. crush. + rewrite list_repeat_len. + rewrite H4. reflexivity. + + remember (Integers.Ptrofs.add (Integers.Ptrofs.repr (valueToZ asr # r0)) + (Integers.Ptrofs.of_int (Integers.Int.repr z))) as OFFSET. + + destruct (4 * ptr ==Z Integers.Ptrofs.unsigned OFFSET). + + erewrite Mem.load_store_same. + 2: { rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite e. + rewrite Integers.Ptrofs.unsigned_repr. + exact H1. + apply Integers.Ptrofs.unsigned_range_2. } constructor. + erewrite combine_lookup_second. + simpl. + assert (Ple src (RTL.max_reg_function f)) + by (eapply RTL.max_reg_function_use; eauto; simpl; auto); + apply H0 in H13. + destruct (Registers.Regmap.get src rs) eqn:EQ_SRC; constructor; invert H13; eauto. + + rewrite <- array_set_len. + unfold arr_repeat. crush. + rewrite list_repeat_len. auto. + + assert (4 * ptr / 4 = Integers.Ptrofs.unsigned OFFSET / 4) by (f_equal; assumption). + rewrite Z.mul_comm in H13. + rewrite Z_div_mult in H13; try lia. + replace 4 with (Integers.Ptrofs.unsigned (Integers.Ptrofs.repr 4)) in H13 by reflexivity. + rewrite <- PtrofsExtra.divu_unsigned in H13; unfold_constants; try lia. + rewrite H13. rewrite EXPR_OK. + rewrite array_get_error_set_bound. + reflexivity. + unfold arr_length, arr_repeat. simpl. + rewrite list_repeat_len. lia. + + erewrite Mem.load_store_other with (m1 := m). + 2: { exact H1. } + 2: { right. + rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite Integers.Ptrofs.unsigned_repr. + simpl. + destruct (Z_le_gt_dec (4 * ptr + 4) (Integers.Ptrofs.unsigned OFFSET)); eauto. + right. + apply ZExtra.mod_0_bounds; try lia. + apply ZLib.Z_mod_mult'. + rewrite Z2Nat.id in H19; try lia. + apply Zmult_lt_compat_r with (p := 4) in H19; try lia. + rewrite ZLib.div_mul_undo in H19; try lia. + split; try lia. + apply Z.le_trans with (m := RTL.fn_stacksize f); crush; lia. + } + + rewrite <- EXPR_OK. + rewrite PtrofsExtra.divu_unsigned; auto; try (unfold_constants; lia). + destruct (ptr ==Z Integers.Ptrofs.unsigned OFFSET / 4). + apply Z.mul_cancel_r with (p := 4) in e; try lia. + rewrite ZLib.div_mul_undo in e; try lia. + rewrite combine_lookup_first. + eapply H7; eauto. + + rewrite <- array_set_len. + unfold arr_repeat. crush. + rewrite list_repeat_len. auto. + rewrite array_gso. + unfold array_get_error. + unfold arr_repeat. + crush. + apply list_repeat_lookup. + lia. + unfold_constants. + intro. + apply Z2Nat.inj_iff in H13; try lia. + apply Z.div_pos; try lia. + apply Integers.Ptrofs.unsigned_range. + + assert (Integers.Ptrofs.repr 0 = Integers.Ptrofs.zero) as ZERO by reflexivity. + unfold arr_stack_based_pointers. + intros. + destruct (4 * ptr ==Z Integers.Ptrofs.unsigned OFFSET). + + crush. + erewrite Mem.load_store_same. + 2: { rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite e. + rewrite Integers.Ptrofs.unsigned_repr. + exact H1. + apply Integers.Ptrofs.unsigned_range_2. } + crush. + destruct (Registers.Regmap.get src rs) eqn:EQ_SRC; try constructor. + destruct (Archi.ptr64); try discriminate. + pose proof (RSBP src). rewrite EQ_SRC in H0. + assumption. simpl. - destruct b. - eapply Verilog.erun_Vternary_true. - eapply eval_cond_correct; eauto. - constructor. - apply boolToValue_ValueToBool. - eapply Verilog.erun_Vternary_false. - eapply eval_cond_correct; eauto. - constructor. - apply boolToValue_ValueToBool. - constructor. + erewrite Mem.load_store_other with (m1 := m). + 2: { exact H1. } + 2: { right. + rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite Integers.Ptrofs.unsigned_repr. + simpl. + destruct (Z_le_gt_dec (4 * ptr + 4) (Integers.Ptrofs.unsigned OFFSET)); eauto. + right. + apply ZExtra.mod_0_bounds; try lia. + apply ZLib.Z_mod_mult'. + invert H0. + apply Zmult_lt_compat_r with (p := 4) in H14; try lia. + rewrite ZLib.div_mul_undo in H14; try lia. + split; try lia. + apply Z.le_trans with (m := RTL.fn_stacksize f); crush; lia. + } + apply ASBP; assumption. + + unfold stack_bounds in *. intros. + simpl. + assert (Integers.Ptrofs.repr 0 = Integers.Ptrofs.zero) as ZERO by reflexivity. + erewrite Mem.load_store_other with (m1 := m). + 2: { exact H1. } + 2: { right. right. simpl. + rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite Integers.Ptrofs.unsigned_repr; crush; try lia. + apply ZExtra.mod_0_bounds; crush; try lia. } + crush. + exploit (BOUNDS ptr); try lia. intros. crush. + exploit (BOUNDS ptr v); try lia. intros. + invert H0. + match goal with | |- ?x = _ => destruct x eqn:EQ end; try reflexivity. + assert (Mem.valid_access m AST.Mint32 sp' + (Integers.Ptrofs.unsigned + (Integers.Ptrofs.add (Integers.Ptrofs.repr 0) + (Integers.Ptrofs.repr ptr))) Writable). + { pose proof H1. eapply Mem.store_valid_access_2 in H0. + exact H0. eapply Mem.store_valid_access_3. eassumption. } + pose proof (Mem.valid_access_store m AST.Mint32 sp' + (Integers.Ptrofs.unsigned + (Integers.Ptrofs.add (Integers.Ptrofs.repr 0) + (Integers.Ptrofs.repr ptr))) v). + apply X in H0. invert H0. congruence. + + + (** Preamble *) + invert MARR. crush. + + unfold Op.eval_addressing in H0. + destruct (Archi.ptr64) eqn:ARCHI; crush. + + unfold reg_stack_based_pointers in RSBP. + pose proof (RSBP r0) as RSBPr0. + pose proof (RSBP r1) as RSBPr1. + + destruct (Registers.Regmap.get r0 rs) eqn:EQr0; + destruct (Registers.Regmap.get r1 rs) eqn:EQr1; crush. + + rewrite ARCHI in H1. crush. + subst. + clear RSBPr1. + + pose proof MASSOC as MASSOC'. + invert MASSOC'. + pose proof (H0 r0). + pose proof (H0 r1). + assert (HPler0 : Ple r0 (RTL.max_reg_function f)) + by (eapply RTL.max_reg_function_use; eauto; crush; eauto). + assert (HPler1 : Ple r1 (RTL.max_reg_function f)) + by (eapply RTL.max_reg_function_use; eauto; simpl; auto). + apply H6 in HPler0. + apply H8 in HPler1. + invert HPler0; invert HPler1; try congruence. + rewrite EQr0 in H10. + rewrite EQr1 in H12. + invert H10. invert H12. + clear H0. clear H6. clear H8. + + unfold check_address_parameter_signed in *; + unfold check_address_parameter_unsigned in *; crush. + + remember (Integers.Ptrofs.add (Integers.Ptrofs.repr (valueToZ asr # r0)) + (Integers.Ptrofs.of_int + (Integers.Int.add (Integers.Int.mul (valueToInt asr # r1) (Integers.Int.repr z)) + (Integers.Int.repr z0)))) as OFFSET. + + (** Modular preservation proof *) + assert (Integers.Ptrofs.unsigned OFFSET mod 4 = 0) as MOD_PRESERVE. + { rewrite HeqOFFSET. + apply PtrofsExtra.add_mod; crush; try lia. + exists 1073741824. reflexivity. (* FIXME: This is sadness inducing. *) + rewrite Integers.Ptrofs.signed_repr; try assumption. + admit. (* FIXME: Register bounds. *) + apply PtrofsExtra.of_int_mod. + apply IntExtra.add_mod; crush; try lia. + exists 1073741824. reflexivity. (* FIXME: This is sadness inducing. *) + apply IntExtra.mul_mod; crush; try lia. + exists 1073741824. reflexivity. (* FIXME: This is sadness inducing. *) + admit. (* FIXME: Register bounds. *) + rewrite Integers.Int.signed_repr; crush; try split; try assumption. + rewrite Integers.Int.signed_repr; crush; try split; try assumption. + } + + (** Write bounds proof *) + assert (Integers.Ptrofs.unsigned OFFSET < f.(RTL.fn_stacksize)) as WRITE_BOUND_HIGH. + { destruct (Integers.Ptrofs.unsigned OFFSET <? f.(RTL.fn_stacksize)) eqn:EQ; crush; auto. + unfold stack_bounds in BOUNDS. + exploit (BOUNDS (Integers.Ptrofs.unsigned OFFSET) (Registers.Regmap.get src rs)); auto. + split; try lia; apply Integers.Ptrofs.unsigned_range_2. + small_tac. } + + (** Start of proof proper *) + eexists. split. + eapply Smallstep.plus_one. + eapply HTL.step_module; eauto. + apply assumption_32bit. + econstructor. econstructor. econstructor. + eapply Verilog.stmnt_runp_Vnonblock_arr. crush. + econstructor. + eapply Verilog.erun_Vbinop with (EQ := ?[EQ9]). + eapply Verilog.erun_Vbinop with (EQ := ?[EQ10]). + eapply Verilog.erun_Vbinop with (EQ := ?[EQ11]). + econstructor. econstructor. econstructor. econstructor. + econstructor. + eapply Verilog.erun_Vbinop with (EQ := ?[EQ12]). + econstructor. econstructor. econstructor. econstructor. + econstructor. econstructor. econstructor. econstructor. + econstructor. econstructor. econstructor. econstructor. + + all: crush. + + (** State Lookup *) + unfold Verilog.merge_regs. + crush. unfold_merge. apply AssocMap.gss. - destruct b. + (** Match states *) rewrite assumption_32bit. - apply match_state. - unfold_merge. + econstructor; eauto. + + (** Match assocmaps *) + unfold Verilog.merge_regs. crush. unfold_merge. apply regs_lessdef_add_greater. apply greater_than_max_func. - assumption. assumption. + assumption. - unfold state_st_wf. intros. inversion H1. - subst. unfold_merge. + (** States well formed *) + unfold state_st_wf. inversion 1. crush. + unfold Verilog.merge_regs. + unfold_merge. apply AssocMap.gss. - assumption. + (** Equality proof *) + assert (Z.to_nat + (Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu + OFFSET + (Integers.Ptrofs.repr 4))) + = + valueToNat (vdiv + (vplus (vplus asr # r0 (ZToValue 32 z0) ?EQ11) (vmul asr # r1 (ZToValue 32 z) ?EQ12) + ?EQ10) (ZToValue 32 4) ?EQ9)) + as EXPR_OK by admit. + + assert (Integers.Ptrofs.repr 0 = Integers.Ptrofs.zero) as ZERO by reflexivity. + inversion MASSOC; revert HeqOFFSET; subst; clear MASSOC; intros HeqOFFSET. + + econstructor. + repeat split; crush. + unfold HTL.empty_stack. + crush. + unfold Verilog.merge_arrs. + + rewrite AssocMap.gcombine. + 2: { reflexivity. } + unfold Verilog.arr_assocmap_set. + rewrite AssocMap.gss. + unfold Verilog.merge_arr. + rewrite AssocMap.gss. + setoid_rewrite H5. + reflexivity. + + rewrite combine_length. + rewrite <- array_set_len. + unfold arr_repeat. crush. + apply list_repeat_len. + + rewrite <- array_set_len. + unfold arr_repeat. crush. + rewrite list_repeat_len. + rewrite H4. reflexivity. + + remember (Integers.Ptrofs.add (Integers.Ptrofs.repr (valueToZ asr # r0)) + (Integers.Ptrofs.of_int + (Integers.Int.add (Integers.Int.mul (valueToInt asr # r1) (Integers.Int.repr z)) + (Integers.Int.repr z0)))) as OFFSET. + destruct (4 * ptr ==Z Integers.Ptrofs.unsigned OFFSET). + + erewrite Mem.load_store_same. + 2: { rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite e. + rewrite Integers.Ptrofs.unsigned_repr. + exact H1. + apply Integers.Ptrofs.unsigned_range_2. } + constructor. + erewrite combine_lookup_second. + simpl. + assert (Ple src (RTL.max_reg_function f)) + by (eapply RTL.max_reg_function_use; eauto; simpl; auto); + apply H0 in H20. + destruct (Registers.Regmap.get src rs) eqn:EQ_SRC; constructor; invert H20; eauto. + + rewrite <- array_set_len. + unfold arr_repeat. crush. + rewrite list_repeat_len. auto. + + assert (4 * ptr / 4 = Integers.Ptrofs.unsigned OFFSET / 4) by (f_equal; assumption). + rewrite Z.mul_comm in H20. + rewrite Z_div_mult in H20; try lia. + replace 4 with (Integers.Ptrofs.unsigned (Integers.Ptrofs.repr 4)) in H20 by reflexivity. + rewrite <- PtrofsExtra.divu_unsigned in H20; unfold_constants; try lia. + rewrite H20. rewrite EXPR_OK. + rewrite array_get_error_set_bound. + reflexivity. + unfold arr_length, arr_repeat. simpl. + rewrite list_repeat_len. lia. + + erewrite Mem.load_store_other with (m1 := m). + 2: { exact H1. } + 2: { right. + rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite Integers.Ptrofs.unsigned_repr. + simpl. + destruct (Z_le_gt_dec (4 * ptr + 4) (Integers.Ptrofs.unsigned OFFSET)); eauto. + right. + apply ZExtra.mod_0_bounds; try lia. + apply ZLib.Z_mod_mult'. + rewrite Z2Nat.id in H22; try lia. + apply Zmult_lt_compat_r with (p := 4) in H22; try lia. + rewrite ZLib.div_mul_undo in H22; try lia. + split; try lia. + apply Z.le_trans with (m := RTL.fn_stacksize f); crush; lia. + } + + rewrite <- EXPR_OK. + rewrite PtrofsExtra.divu_unsigned; auto; try (unfold_constants; lia). + destruct (ptr ==Z Integers.Ptrofs.unsigned OFFSET / 4). + apply Z.mul_cancel_r with (p := 4) in e; try lia. + rewrite ZLib.div_mul_undo in e; try lia. + rewrite combine_lookup_first. + eapply H7; eauto. + + rewrite <- array_set_len. + unfold arr_repeat. crush. + rewrite list_repeat_len. auto. + rewrite array_gso. + unfold array_get_error. + unfold arr_repeat. + crush. + apply list_repeat_lookup. + lia. + unfold_constants. + intro. + apply Z2Nat.inj_iff in H20; try lia. + apply Z.div_pos; try lia. + apply Integers.Ptrofs.unsigned_range. + + assert (Integers.Ptrofs.repr 0 = Integers.Ptrofs.zero) as ZERO by reflexivity. + unfold arr_stack_based_pointers. + intros. + destruct (4 * ptr ==Z Integers.Ptrofs.unsigned OFFSET). + + crush. + erewrite Mem.load_store_same. + 2: { rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite e. + rewrite Integers.Ptrofs.unsigned_repr. + exact H1. + apply Integers.Ptrofs.unsigned_range_2. } + crush. + destruct (Registers.Regmap.get src rs) eqn:EQ_SRC; try constructor. + destruct (Archi.ptr64); try discriminate. + pose proof (RSBP src). rewrite EQ_SRC in H0. assumption. - rewrite assumption_32bit. - apply match_state. + simpl. + erewrite Mem.load_store_other with (m1 := m). + 2: { exact H1. } + 2: { right. + rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite Integers.Ptrofs.unsigned_repr. + simpl. + destruct (Z_le_gt_dec (4 * ptr + 4) (Integers.Ptrofs.unsigned OFFSET)); eauto. + right. + apply ZExtra.mod_0_bounds; try lia. + apply ZLib.Z_mod_mult'. + invert H0. + apply Zmult_lt_compat_r with (p := 4) in H21; try lia. + rewrite ZLib.div_mul_undo in H21; try lia. + split; try lia. + apply Z.le_trans with (m := RTL.fn_stacksize f); crush; lia. + } + apply ASBP; assumption. + + unfold stack_bounds in *. intros. + simpl. + assert (Integers.Ptrofs.repr 0 = Integers.Ptrofs.zero) as ZERO by reflexivity. + erewrite Mem.load_store_other with (m1 := m). + 2: { exact H1. } + 2: { right. right. simpl. + rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite Integers.Ptrofs.unsigned_repr; crush; try lia. + apply ZExtra.mod_0_bounds; crush; try lia. } + crush. + exploit (BOUNDS ptr); try lia. intros. crush. + exploit (BOUNDS ptr v); try lia. intros. + invert H0. + match goal with | |- ?x = _ => destruct x eqn:EQ end; try reflexivity. + assert (Mem.valid_access m AST.Mint32 sp' + (Integers.Ptrofs.unsigned + (Integers.Ptrofs.add (Integers.Ptrofs.repr 0) + (Integers.Ptrofs.repr ptr))) Writable). + { pose proof H1. eapply Mem.store_valid_access_2 in H0. + exact H0. eapply Mem.store_valid_access_3. eassumption. } + pose proof (Mem.valid_access_store m AST.Mint32 sp' + (Integers.Ptrofs.unsigned + (Integers.Ptrofs.add (Integers.Ptrofs.repr 0) + (Integers.Ptrofs.repr ptr))) v). + apply X in H0. invert H0. congruence. + + + invert MARR. crush. + + unfold Op.eval_addressing in H0. + destruct (Archi.ptr64) eqn:ARCHI; crush. + rewrite ARCHI in H0. crush. + + unfold check_address_parameter_unsigned in *; + unfold check_address_parameter_signed in *; crush. + + assert (Integers.Ptrofs.repr 0 = Integers.Ptrofs.zero) as ZERO by reflexivity. + rewrite ZERO in H1. clear ZERO. + rewrite Integers.Ptrofs.add_zero_l in H1. + + remember i0 as OFFSET. + + (** Modular preservation proof *) + rename H0 into MOD_PRESERVE. + + (** Write bounds proof *) + assert (Integers.Ptrofs.unsigned OFFSET < f.(RTL.fn_stacksize)) as WRITE_BOUND_HIGH. + { destruct (Integers.Ptrofs.unsigned OFFSET <? f.(RTL.fn_stacksize)) eqn:EQ; crush; auto. + unfold stack_bounds in BOUNDS. + exploit (BOUNDS (Integers.Ptrofs.unsigned OFFSET) (Registers.Regmap.get src rs)); auto. + crush. + replace (Integers.Ptrofs.repr 0) with (Integers.Ptrofs.zero) by reflexivity. + small_tac. } + + (** Start of proof proper *) + eexists. split. + eapply Smallstep.plus_one. + eapply HTL.step_module; eauto. + apply assumption_32bit. + econstructor. econstructor. econstructor. + eapply Verilog.stmnt_runp_Vnonblock_arr. crush. + econstructor. econstructor. econstructor. econstructor. + + all: crush. + + (** State Lookup *) + unfold Verilog.merge_regs. + crush. unfold_merge. - apply regs_lessdef_add_greater. apply greater_than_max_func. assumption. + apply AssocMap.gss. + + (** Match states *) + rewrite assumption_32bit. + econstructor; eauto. + + (** Match assocmaps *) + unfold Verilog.merge_regs. crush. unfold_merge. + apply regs_lessdef_add_greater. apply greater_than_max_func. assumption. - unfold state_st_wf. intros. inversion H1. - subst. unfold_merge. + (** States well formed *) + unfold state_st_wf. inversion 1. crush. + unfold Verilog.merge_regs. + unfold_merge. apply AssocMap.gss. - assumption. + (** Equality proof *) + assert (Z.to_nat + (Integers.Ptrofs.unsigned + (Integers.Ptrofs.divu + OFFSET + (Integers.Ptrofs.repr 4))) + = + valueToNat (ZToValue 32 (Integers.Ptrofs.unsigned OFFSET / 4))) + as EXPR_OK by admit. + + assert (Integers.Ptrofs.repr 0 = Integers.Ptrofs.zero) as ZERO by reflexivity. + inversion MASSOC; revert HeqOFFSET; subst; clear MASSOC; intros HeqOFFSET. + + econstructor. + repeat split; crush. + unfold HTL.empty_stack. + crush. + unfold Verilog.merge_arrs. + + rewrite AssocMap.gcombine. + 2: { reflexivity. } + unfold Verilog.arr_assocmap_set. + rewrite AssocMap.gss. + unfold Verilog.merge_arr. + rewrite AssocMap.gss. + setoid_rewrite H5. + reflexivity. + + rewrite combine_length. + rewrite <- array_set_len. + unfold arr_repeat. crush. + apply list_repeat_len. + + rewrite <- array_set_len. + unfold arr_repeat. crush. + rewrite list_repeat_len. + rewrite H4. reflexivity. + + remember i0 as OFFSET. + destruct (4 * ptr ==Z Integers.Ptrofs.unsigned OFFSET). + + erewrite Mem.load_store_same. + 2: { rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite e. + rewrite Integers.Ptrofs.unsigned_repr. + exact H1. + apply Integers.Ptrofs.unsigned_range_2. } + constructor. + erewrite combine_lookup_second. + simpl. + assert (Ple src (RTL.max_reg_function f)) + by (eapply RTL.max_reg_function_use; eauto; simpl; auto); + apply H0 in H8. + destruct (Registers.Regmap.get src rs) eqn:EQ_SRC; constructor; invert H8; eauto. + + rewrite <- array_set_len. + unfold arr_repeat. crush. + rewrite list_repeat_len. auto. + + assert (4 * ptr / 4 = Integers.Ptrofs.unsigned OFFSET / 4) by (f_equal; assumption). + rewrite Z.mul_comm in H8. + rewrite Z_div_mult in H8; try lia. + replace 4 with (Integers.Ptrofs.unsigned (Integers.Ptrofs.repr 4)) in H8 by reflexivity. + rewrite <- PtrofsExtra.divu_unsigned in H8; unfold_constants; try lia. + rewrite H8. rewrite EXPR_OK. + rewrite array_get_error_set_bound. + reflexivity. + unfold arr_length, arr_repeat. simpl. + rewrite list_repeat_len. lia. + + erewrite Mem.load_store_other with (m1 := m). + 2: { exact H1. } + 2: { right. + rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite Integers.Ptrofs.unsigned_repr. + simpl. + destruct (Z_le_gt_dec (4 * ptr + 4) (Integers.Ptrofs.unsigned OFFSET)); eauto. + right. + apply ZExtra.mod_0_bounds; try lia. + apply ZLib.Z_mod_mult'. + rewrite Z2Nat.id in H12; try lia. + apply Zmult_lt_compat_r with (p := 4) in H12; try lia. + rewrite ZLib.div_mul_undo in H12; try lia. + split; try lia. + apply Z.le_trans with (m := RTL.fn_stacksize f); crush; lia. + } + + rewrite <- EXPR_OK. + rewrite PtrofsExtra.divu_unsigned; auto; try (unfold_constants; lia). + destruct (ptr ==Z Integers.Ptrofs.unsigned OFFSET / 4). + apply Z.mul_cancel_r with (p := 4) in e; try lia. + rewrite ZLib.div_mul_undo in e; try lia. + rewrite combine_lookup_first. + eapply H7; eauto. + + rewrite <- array_set_len. + unfold arr_repeat. crush. + rewrite list_repeat_len. auto. + rewrite array_gso. + unfold array_get_error. + unfold arr_repeat. + crush. + apply list_repeat_lookup. + lia. + unfold_constants. + intro. + apply Z2Nat.inj_iff in H8; try lia. + apply Z.div_pos; try lia. + apply Integers.Ptrofs.unsigned_range. + + assert (Integers.Ptrofs.repr 0 = Integers.Ptrofs.zero) as ZERO by reflexivity. + unfold arr_stack_based_pointers. + intros. + destruct (4 * ptr ==Z Integers.Ptrofs.unsigned OFFSET). + + crush. + erewrite Mem.load_store_same. + 2: { rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite e. + rewrite Integers.Ptrofs.unsigned_repr. + exact H1. + apply Integers.Ptrofs.unsigned_range_2. } + crush. + destruct (Registers.Regmap.get src rs) eqn:EQ_SRC; try constructor. + destruct (Archi.ptr64); try discriminate. + pose proof (RSBP src). rewrite EQ_SRC in H0. assumption. - - (* Return *) - econstructor. split. + simpl. + erewrite Mem.load_store_other with (m1 := m). + 2: { exact H1. } + 2: { right. + rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite Integers.Ptrofs.unsigned_repr. + simpl. + destruct (Z_le_gt_dec (4 * ptr + 4) (Integers.Ptrofs.unsigned OFFSET)); eauto. + right. + apply ZExtra.mod_0_bounds; try lia. + apply ZLib.Z_mod_mult'. + invert H0. + apply Zmult_lt_compat_r with (p := 4) in H10; try lia. + rewrite ZLib.div_mul_undo in H10; try lia. + split; try lia. + apply Z.le_trans with (m := RTL.fn_stacksize f); crush; lia. + } + apply ASBP; assumption. + + unfold stack_bounds in *. intros. + simpl. + assert (Integers.Ptrofs.repr 0 = Integers.Ptrofs.zero) as ZERO by reflexivity. + erewrite Mem.load_store_other with (m1 := m). + 2: { exact H1. } + 2: { right. right. simpl. + rewrite ZERO. + rewrite Integers.Ptrofs.add_zero_l. + rewrite Integers.Ptrofs.unsigned_repr; crush; try lia. + apply ZExtra.mod_0_bounds; crush; try lia. } + crush. + exploit (BOUNDS ptr); try lia. intros. crush. + exploit (BOUNDS ptr v); try lia. intros. + invert H0. + match goal with | |- ?x = _ => destruct x eqn:EQ end; try reflexivity. + assert (Mem.valid_access m AST.Mint32 sp' + (Integers.Ptrofs.unsigned + (Integers.Ptrofs.add (Integers.Ptrofs.repr 0) + (Integers.Ptrofs.repr ptr))) Writable). + { pose proof H1. eapply Mem.store_valid_access_2 in H0. + exact H0. eapply Mem.store_valid_access_3. eassumption. } + pose proof (Mem.valid_access_store m AST.Mint32 sp' + (Integers.Ptrofs.unsigned + (Integers.Ptrofs.add (Integers.Ptrofs.repr 0) + (Integers.Ptrofs.repr ptr))) v). + apply X in H0. invert H0. congruence. + Admitted. + Hint Resolve transl_istore_correct : htlproof. + + Lemma transl_icond_correct: + forall (s : list RTL.stackframe) (f : RTL.function) (sp : Values.val) (pc : positive) + (rs : Registers.Regmap.t Values.val) (m : mem) (cond : Op.condition) (args : list Registers.reg) + (ifso ifnot : RTL.node) (b : bool) (pc' : RTL.node), + (RTL.fn_code f) ! pc = Some (RTL.Icond cond args ifso ifnot) -> + Op.eval_condition cond (map (fun r : positive => Registers.Regmap.get r rs) args) m = Some b -> + pc' = (if b then ifso else ifnot) -> + forall R1 : HTL.state, + match_states (RTL.State s f sp pc rs m) R1 -> + exists R2 : HTL.state, + Smallstep.plus HTL.step tge R1 Events.E0 R2 /\ match_states (RTL.State s f sp pc' rs m) R2. + Proof. + intros s f sp pc rs m cond args ifso ifnot b pc' H H0 H1 R1 MSTATE. + inv_state. + + eexists. split. apply Smallstep.plus_one. + eapply HTL.step_module; eauto. + apply assumption_32bit. + eapply Verilog.stmnt_runp_Vnonblock_reg with + (rhsval := if b then posToValue 32 ifso else posToValue 32 ifnot). + constructor. + + simpl. + destruct b. + eapply Verilog.erun_Vternary_true. + eapply eval_cond_correct; eauto. + constructor. + apply boolToValue_ValueToBool. + eapply Verilog.erun_Vternary_false. + eapply eval_cond_correct; eauto. + constructor. + apply boolToValue_ValueToBool. + constructor. + + big_tac. + + invert MARR. + destruct b; rewrite assumption_32bit; big_tac. + + Unshelve. + constructor. + Qed. + Hint Resolve transl_icond_correct : htlproof. + + Lemma transl_ijumptable_correct: + forall (s : list RTL.stackframe) (f : RTL.function) (sp : Values.val) (pc : positive) + (rs : Registers.Regmap.t Values.val) (m : mem) (arg : Registers.reg) (tbl : list RTL.node) + (n : Integers.Int.int) (pc' : RTL.node), + (RTL.fn_code f) ! pc = Some (RTL.Ijumptable arg tbl) -> + Registers.Regmap.get arg rs = Values.Vint n -> + list_nth_z tbl (Integers.Int.unsigned n) = Some pc' -> + forall R1 : HTL.state, + match_states (RTL.State s f sp pc rs m) R1 -> + exists R2 : HTL.state, + Smallstep.plus HTL.step tge R1 Events.E0 R2 /\ match_states (RTL.State s f sp pc' rs m) R2. + Proof. + intros s f sp pc rs m arg tbl n pc' H H0 H1 R1 MSTATE. + Admitted. + Hint Resolve transl_ijumptable_correct : htlproof. + + Lemma transl_ireturn_correct: + forall (s : list RTL.stackframe) (f : RTL.function) (stk : Values.block) + (pc : positive) (rs : RTL.regset) (m : mem) (or : option Registers.reg) + (m' : mem), + (RTL.fn_code f) ! pc = Some (RTL.Ireturn or) -> + Mem.free m stk 0 (RTL.fn_stacksize f) = Some m' -> + forall R1 : HTL.state, + match_states (RTL.State s f (Values.Vptr stk Integers.Ptrofs.zero) pc rs m) R1 -> + exists R2 : HTL.state, + Smallstep.plus HTL.step tge R1 Events.E0 R2 /\ + match_states (RTL.Returnstate s (Registers.regmap_optget or Values.Vundef rs) m') R2. + Proof. + intros s f stk pc rs m or m' H H0 R1 MSTATE. + inv_state. + + - econstructor. split. eapply Smallstep.plus_two. - + eapply HTL.step_module; eauto. + apply assumption_32bit. constructor. econstructor; simpl; trivial. econstructor; simpl; trivial. @@ -453,45 +1903,41 @@ Section CORRECTNESS. econstructor; simpl; trivial. constructor. - constructor. - constructor. + constructor. constructor. - unfold_merge. simpl. - rewrite AssocMap.gso. - rewrite AssocMap.gso. - unfold state_st_wf in WF. eapply WF. reflexivity. - apply st_greater_than_res. apply st_greater_than_res. + unfold state_st_wf in WF; big_tac; eauto. + apply st_greater_than_res. + apply st_greater_than_res. apply HTL.step_finish. + unfold Verilog.merge_regs. unfold_merge; simpl. rewrite AssocMap.gso. apply AssocMap.gss. apply finish_not_return. apply AssocMap.gss. rewrite Events.E0_left. reflexivity. - constructor. - assumption. + + constructor; auto. constructor. + (* FIXME: Duplication *) - econstructor. split. eapply Smallstep.plus_two. eapply HTL.step_module; eauto. + apply assumption_32bit. constructor. econstructor; simpl; trivial. econstructor; simpl; trivial. + constructor. constructor. constructor. + constructor. constructor. constructor. - constructor. constructor. - - constructor. - econstructor; simpl; trivial. - apply Verilog.erun_Vvar. trivial. - unfold_merge. simpl. - rewrite AssocMap.gso. - rewrite AssocMap.gso. - unfold state_st_wf in WF. eapply WF. trivial. - apply st_greater_than_res. apply st_greater_than_res. trivial. + unfold state_st_wf in WF; big_tac; eauto. + apply st_greater_than_res. + apply st_greater_than_res. apply HTL.step_finish. + unfold Verilog.merge_regs. unfold_merge. rewrite AssocMap.gso. apply AssocMap.gss. @@ -499,46 +1945,158 @@ Section CORRECTNESS. apply AssocMap.gss. rewrite Events.E0_left. trivial. - constructor. assumption. simpl. inversion MASSOC. subst. + constructor; auto. + + simpl. inversion MASSOC. subst. unfold find_assocmap, AssocMapExt.get_default. rewrite AssocMap.gso. apply H1. eapply RTL.max_reg_function_use. eauto. simpl; tauto. apply st_greater_than_res. - - inversion MSTATE; subst. inversion TF; subst. - econstructor. split. apply Smallstep.plus_one. - eapply HTL.step_call. + Unshelve. + all: constructor. + Qed. + Hint Resolve transl_ireturn_correct : htlproof. + + Lemma transl_callstate_correct: + forall (s : list RTL.stackframe) (f : RTL.function) (args : list Values.val) + (m : mem) (m' : Mem.mem') (stk : Values.block), + Mem.alloc m 0 (RTL.fn_stacksize f) = (m', stk) -> + forall R1 : HTL.state, + match_states (RTL.Callstate s (AST.Internal f) args m) R1 -> + exists R2 : HTL.state, + Smallstep.plus HTL.step tge R1 Events.E0 R2 /\ + match_states + (RTL.State s f (Values.Vptr stk Integers.Ptrofs.zero) (RTL.fn_entrypoint f) + (RTL.init_regs args (RTL.fn_params f)) m') R2. + Proof. + intros s f args m m' stk H R1 MSTATE. - constructor. apply regs_lessdef_add_greater. - apply greater_than_max_func. - apply init_reg_assoc_empty. assumption. unfold state_st_wf. - intros. inv H1. apply AssocMap.gss. constructor. + inversion MSTATE; subst. inversion TF; subst. + econstructor. split. apply Smallstep.plus_one. + eapply HTL.step_call. crush. - admit. + apply match_state with (sp' := stk); eauto. - - inversion MSTATE; subst. inversion MS; subst. econstructor. - split. apply Smallstep.plus_one. - constructor. + all: big_tac. - constructor; auto. constructor; auto. apply regs_lessdef_add_match; auto. - apply regs_lessdef_add_greater. apply greater_than_max_func. auto. + apply regs_lessdef_add_greater. + apply greater_than_max_func. + apply init_reg_assoc_empty. - unfold state_st_wf. intros. inv H. rewrite AssocMap.gso. - rewrite AssocMap.gss. trivial. apply st_greater_than_res. + constructor. - admit. + destruct (Mem.load AST.Mint32 m' stk + (Integers.Ptrofs.unsigned (Integers.Ptrofs.add + Integers.Ptrofs.zero + (Integers.Ptrofs.repr (4 * ptr))))) eqn:LOAD. + pose proof Mem.load_alloc_same as LOAD_ALLOC. + pose proof H as ALLOC. + eapply LOAD_ALLOC in ALLOC. + 2: { exact LOAD. } + ptrofs. rewrite LOAD. + rewrite ALLOC. + repeat constructor. + + ptrofs. rewrite LOAD. + repeat constructor. + + unfold reg_stack_based_pointers. intros. + unfold RTL.init_regs; crush. + destruct (RTL.fn_params f); + rewrite Registers.Regmap.gi; constructor. + + unfold arr_stack_based_pointers. intros. + crush. + destruct (Mem.load AST.Mint32 m' stk + (Integers.Ptrofs.unsigned (Integers.Ptrofs.add + Integers.Ptrofs.zero + (Integers.Ptrofs.repr (4 * ptr))))) eqn:LOAD. + pose proof Mem.load_alloc_same as LOAD_ALLOC. + pose proof H as ALLOC. + eapply LOAD_ALLOC in ALLOC. + 2: { exact LOAD. } + rewrite ALLOC. + repeat constructor. + constructor. - Unshelve. - exact (AssocMap.empty value). - exact (AssocMap.empty value). - admit. - admit. - (* exact (ZToValue 32 0). *) - (* exact (AssocMap.empty value). *) - (* exact (AssocMap.empty value). *) - (* exact (AssocMap.empty value). *) - (* exact (AssocMap.empty value). *) - Admitted. - Hint Resolve transl_step_correct : htlproof. + Transparent Mem.alloc. (* TODO: Since there are opaque there's probably a lemma. *) + Transparent Mem.load. + Transparent Mem.store. + unfold stack_bounds. + split. + + unfold Mem.alloc in H. + invert H. + crush. + unfold Mem.load. + intros. + match goal with | |- context[if ?x then _ else _] => destruct x end; try congruence. + invert v0. unfold Mem.range_perm in H3. + unfold Mem.perm in H3. crush. + unfold Mem.perm_order' in H3. + small_tac. + exploit (H3 ptr). rewrite Integers.Ptrofs.unsigned_repr; small_tac. intros. + rewrite Maps.PMap.gss in H8. + match goal with | H8 : context[if ?x then _ else _] |- _ => destruct x eqn:EQ end; try contradiction. + crush. + apply proj_sumbool_true in H10. lia. + + unfold Mem.alloc in H. + invert H. + crush. + unfold Mem.store. + intros. + match goal with | |- context[if ?x then _ else _] => destruct x end; try congruence. + invert v0. unfold Mem.range_perm in H3. + unfold Mem.perm in H3. crush. + unfold Mem.perm_order' in H3. + small_tac. + exploit (H3 ptr). rewrite Integers.Ptrofs.unsigned_repr; small_tac. intros. + rewrite Maps.PMap.gss in H8. + match goal with | H8 : context[if ?x then _ else _] |- _ => destruct x eqn:EQ end; try contradiction. + crush. + apply proj_sumbool_true in H10. lia. + Opaque Mem.alloc. + Opaque Mem.load. + Opaque Mem.store. + Qed. + Hint Resolve transl_callstate_correct : htlproof. + + Lemma transl_returnstate_correct: + forall (res0 : Registers.reg) (f : RTL.function) (sp : Values.val) (pc : RTL.node) + (rs : RTL.regset) (s : list RTL.stackframe) (vres : Values.val) (m : mem) + (R1 : HTL.state), + match_states (RTL.Returnstate (RTL.Stackframe res0 f sp pc rs :: s) vres m) R1 -> + exists R2 : HTL.state, + Smallstep.plus HTL.step tge R1 Events.E0 R2 /\ + match_states (RTL.State s f sp pc (Registers.Regmap.set res0 vres rs) m) R2. + Proof. + intros res0 f sp pc rs s vres m R1 MSTATE. + inversion MSTATE. inversion MF. + Qed. + Hint Resolve transl_returnstate_correct : htlproof. + + Lemma option_inv : + forall A x y, + @Some A x = Some y -> x = y. + Proof. intros. inversion H. trivial. Qed. + + Lemma main_tprog_internal : + forall b, + Globalenvs.Genv.find_symbol tge tprog.(AST.prog_main) = Some b -> + exists f, Genv.find_funct_ptr (Genv.globalenv tprog) b = Some (AST.Internal f). + Proof. + intros. + destruct TRANSL. unfold main_is_internal in H1. + repeat (unfold_match H1). replace b with b0. + exploit function_ptr_translated; eauto. intros [tf [A B]]. + unfold transl_fundef, AST.transf_partial_fundef, Errors.bind in B. + unfold_match B. inv B. econstructor. apply A. + + apply option_inv. rewrite <- Heqo. rewrite <- H. + rewrite symbols_preserved. replace (AST.prog_main tprog) with (AST.prog_main prog). + trivial. symmetry; eapply Linking.match_program_main; eauto. + Qed. (* Had to admit proof because currently there is no way to force main to be Internal. *) Lemma transl_initial_states : @@ -548,20 +2106,35 @@ 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. + exploit main_tprog_internal; eauto; intros. + rewrite symbols_preserved. replace (AST.prog_main tprog) with (AST.prog_main prog). + apply Heqo. symmetry; eapply Linking.match_program_main; eauto. + inversion H5. 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 H6. + constructor. - apply transl_module_correct. auto. - Qed.*) + apply transl_module_correct. + assert (Some (AST.Internal x) = Some (AST.Internal m)). + replace (AST.fundef HTL.module) with (HTL.fundef). + rewrite <- H6. setoid_rewrite <- A. trivial. + trivial. inv H7. assumption. + Qed. Hint Resolve transl_initial_states : htlproof. Lemma transl_final_states : @@ -572,18 +2145,26 @@ Section CORRECTNESS. Smallstep.final_state (RTL.semantics prog) s1 r -> Smallstep.final_state (HTL.semantics tprog) s2 r. Proof. - intros. inv H0. inv H. inv H4. inv MS. constructor. trivial. + intros. inv H0. inv H. inv H4. invert MF. constructor. reflexivity. Qed. - Hint Resolve transl_final_states : htlproof.*) + Hint Resolve transl_final_states : htlproof. -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.*) -Admitted. + Theorem transl_step_correct: + forall (S1 : RTL.state) t S2, + RTL.step ge S1 t S2 -> + forall (R1 : HTL.state), + match_states S1 R1 -> + exists R2, Smallstep.plus HTL.step tge R1 t R2 /\ match_states S2 R2. + Proof. + induction 1; eauto with htlproof; (intros; inv_state). + Qed. + Hint Resolve transl_step_correct : htlproof. + + Theorem transf_program_correct: + Smallstep.forward_simulation (RTL.semantics prog) (HTL.semantics tprog). + Proof. + eapply Smallstep.forward_simulation_plus; eauto with htlproof. + apply senv_preserved. + Qed. End CORRECTNESS. diff --git a/src/translation/HTLgenspec.v b/src/translation/HTLgenspec.v index 887a696..0cdecba 100644 --- a/src/translation/HTLgenspec.v +++ b/src/translation/HTLgenspec.v @@ -113,41 +113,13 @@ Ltac monadInv H := statemachine that is created by the translation contains the correct translations for each of the elements *) -Inductive tr_op : Op.operation -> list reg -> expr -> Prop := -| tr_op_Omove : forall r, tr_op Op.Omove (r::nil) (Vvar r) -| tr_op_Ointconst : forall n l, tr_op (Op.Ointconst n) l (Vlit (intToValue n)) -| tr_op_Oneg : forall r, tr_op Op.Oneg (r::nil) (Vunop Vneg (Vvar r)) -| tr_op_Osub : forall r1 r2, tr_op Op.Osub (r1::r2::nil) (bop Vsub r1 r2) -| tr_op_Omul : forall r1 r2, tr_op Op.Omul (r1::r2::nil) (bop Vmul r1 r2) -| tr_op_Omulimm : forall r n, tr_op (Op.Omulimm n) (r::nil) (boplit Vmul r n) -| tr_op_Odiv : forall r1 r2, tr_op Op.Odiv (r1::r2::nil) (bop Vdiv r1 r2) -| tr_op_Odivu : forall r1 r2, tr_op Op.Odivu (r1::r2::nil) (bop Vdivu r1 r2) -| tr_op_Omod : forall r1 r2, tr_op Op.Omod (r1::r2::nil) (bop Vmod r1 r2) -| tr_op_Omodu : forall r1 r2, tr_op Op.Omodu (r1::r2::nil) (bop Vmodu r1 r2) -| tr_op_Oand : forall r1 r2, tr_op Op.Oand (r1::r2::nil) (bop Vand r1 r2) -| tr_op_Oandimm : forall n r, tr_op (Op.Oandimm n) (r::nil) (boplit Vand r n) -| tr_op_Oor : forall r1 r2, tr_op Op.Oor (r1::r2::nil) (bop Vor r1 r2) -| tr_op_Oorimm : forall n r, tr_op (Op.Oorimm n) (r::nil) (boplit Vor r n) -| tr_op_Oxor : forall r1 r2, tr_op Op.Oxor (r1::r2::nil) (bop Vxor r1 r2) -| tr_op_Oxorimm : forall n r, tr_op (Op.Oxorimm n) (r::nil) (boplit Vxor r n) -| tr_op_Onot : forall r, tr_op Op.Onot (r::nil) (Vunop Vnot (Vvar r)) -| tr_op_Oshl : forall r1 r2, tr_op Op.Oshl (r1::r2::nil) (bop Vshl r1 r2) -| tr_op_Oshlimm : forall n r, tr_op (Op.Oshlimm n) (r::nil) (boplit Vshl r n) -| tr_op_Oshr : forall r1 r2, tr_op Op.Oshr (r1::r2::nil) (bop Vshr r1 r2) -| tr_op_Oshrimm : forall n r, tr_op (Op.Oshrimm n) (r::nil) (boplit Vshr r n) -| tr_op_Ocmp : forall c l e s s' i, translate_condition c l s = OK e s' i -> tr_op (Op.Ocmp c) l e -| tr_op_Olea : forall a l e s s' i, translate_eff_addressing a l s = OK e s' i -> tr_op (Op.Olea a) l e -| tr_op_Oleal : forall a l e s s' i, translate_eff_addressing a l s = OK e s' i -> tr_op (Op.Oleal a) l e -| tr_op_Ocast32signed : forall r, tr_op (Op.Ocast32signed) (r::nil) (Vvar r). -Hint Constructors tr_op : htlspec. - Inductive tr_instr (fin rtrn st stk : reg) : RTL.instruction -> stmnt -> stmnt -> Prop := | tr_instr_Inop : forall n, tr_instr fin rtrn st stk (RTL.Inop n) Vskip (state_goto st n) | tr_instr_Iop : - forall n op args e dst, - tr_op op args e -> + forall n op args dst s s' e i, + translate_instr op args s = OK e s' i -> tr_instr fin rtrn st stk (RTL.Iop op args dst n) (Vnonblock (Vvar dst) e) (state_goto st n) | tr_instr_Icond : forall n1 n2 cond args s s' i c, @@ -163,12 +135,16 @@ Inductive tr_instr (fin rtrn st stk : reg) : RTL.instruction -> stmnt -> stmnt - | tr_instr_Iload : forall mem addr args s s' i c dst n, translate_arr_access mem addr args stk s = OK c s' i -> - tr_instr fin rtrn st stk (RTL.Iload mem addr args dst n) (block dst c) (state_goto st n) + tr_instr fin rtrn st stk (RTL.Iload mem addr args dst n) (nonblock dst c) (state_goto st n) | tr_instr_Istore : forall mem addr args s s' i c src n, translate_arr_access mem addr args stk s = OK c s' i -> - tr_instr fin rtrn st stk (RTL.Istore mem addr args src n) (Vblock c (Vvar src)) - (state_goto st n). + tr_instr fin rtrn st stk (RTL.Istore mem addr args src n) (Vnonblock c (Vvar src)) + (state_goto st n) +| tr_instr_Ijumptable : + forall cexpr tbl r, + cexpr = tbl_to_case_expr st tbl -> + tr_instr fin rtrn st stk (RTL.Ijumptable r tbl) (Vskip) (Vcase (Vvar r) cexpr (Some Vskip)). Hint Constructors tr_instr : htlspec. Inductive tr_code (c : RTL.code) (pc : RTL.node) (i : RTL.instruction) (stmnts trans : PTree.t stmnt) @@ -184,14 +160,17 @@ Hint Constructors tr_code : htlspec. Inductive tr_module (f : RTL.function) : module -> Prop := tr_module_intro : - forall data control fin rtrn st stk m start rst clk scldecls arrdecls, + forall data control fin rtrn st stk stk_len m start rst clk scldecls arrdecls, (forall pc i, Maps.PTree.get pc f.(RTL.fn_code) = Some i -> - tr_code f.(RTL.fn_code) pc i data control fin rtrn st stk) -> + tr_code f.(RTL.fn_code) pc i data control fin rtrn st stk) -> + stk_len = Z.to_nat (f.(RTL.fn_stacksize) / 4) -> + Z.modulo (f.(RTL.fn_stacksize)) 4 = 0 -> + 0 <= f.(RTL.fn_stacksize) < Integers.Ptrofs.modulus -> m = (mkmodule f.(RTL.fn_params) data control f.(RTL.fn_entrypoint) - st stk fin rtrn start rst clk scldecls arrdecls) -> + st stk stk_len fin rtrn start rst clk scldecls arrdecls) -> tr_module f m. Hint Constructors tr_module : htlspec. @@ -315,21 +294,6 @@ Ltac rewrite_states := remember (?x ?s) as c1; remember (?x ?s') as c2; try subst end. -Lemma translate_instr_tr_op : - forall op args s s' e i, - translate_instr op args s = OK e s' i -> - tr_op op args e. -Proof. -(* intros. - destruct op eqn:?; eauto with htlspec; try discriminate; simpl in *; - try (match goal with - [ H: match ?args with _ => _ end _ = _ _ _ |- _ ] => - repeat (destruct args; try discriminate) - end); - monadInv H; constructor. -Qed.*) Admitted. (* FIXME: Currently admitted because added Osel *) -Hint Resolve translate_instr_tr_op : htlspec. - Ltac unfold_match H := match type of H with | context[match ?g with _ => _ end] => destruct g eqn:?; try discriminate @@ -343,7 +307,7 @@ Ltac inv_add_instr' H := end; repeat unfold_match H; inversion H. Ltac inv_add_instr := - match goal with + lazymatch goal with | H: context[add_instr_skip _ _ _] |- _ => inv_add_instr' H | H: context[add_instr_skip _ _] |- _ => @@ -356,6 +320,10 @@ Ltac inv_add_instr := inv_add_instr' H | H: context[add_branch_instr _ _ _ _] |- _ => monadInv H; inv_incr; inv_add_instr + | H: context[add_node_skip _ _ _] |- _ => + inv_add_instr' H + | H: context[add_node_skip _ _] |- _ => + monadInv H; inv_incr; inv_add_instr end. Ltac destruct_optional := @@ -370,7 +338,7 @@ Lemma iter_expand_instr_spec : c!pc = Some instr -> tr_code c pc instr s'.(st_datapath) s'.(st_controllogic) fin rtrn s'.(st_st) stack). Proof. -(* induction l; simpl; intros; try contradiction. + induction l; simpl; intros; try contradiction. destruct a as [pc1 instr1]; simpl in *. inv H0. monadInv H. inv_incr. destruct (peq pc pc1). - subst. @@ -383,15 +351,13 @@ Proof. + destruct o with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence. + destruct o0 with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence. - + inversion H2. inversion H14. unfold nonblock. assert (HST: st_st s4 = st_st s2) by congruence. rewrite HST. - constructor. eapply translate_instr_tr_op. apply EQ1. - eapply in_map with (f := fst) in H14. contradiction. + + inversion H2. inversion H14. unfold nonblock. replace (st_st s4) with (st_st s2) by congruence. + econstructor. apply EQ1. eapply in_map with (f := fst) in H14. contradiction. + destruct o with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence. + destruct o0 with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence. - + inversion H2. inversion H14. rewrite <- e2. assert (HST: st_st s2 = st_st s0) by congruence. - rewrite HST. econstructor. apply EQ1. - eapply in_map with (f := fst) in H14. contradiction. + + inversion H2. inversion H14. rewrite <- e2. replace (st_st s2) with (st_st s0) by congruence. + econstructor. apply EQ1. eapply in_map with (f := fst) in H14. contradiction. + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. @@ -409,6 +375,12 @@ Proof. eauto with htlspec. * apply in_map with (f := fst) in H2. contradiction. + + destruct o with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence. + + destruct o0 with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence. + + inversion H2. + * inversion H14. constructor. congruence. + * apply in_map with (f := fst) in H14. contradiction. + + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence. + inversion H2. @@ -428,10 +400,16 @@ Proof. - eapply IHl. apply EQ0. assumption. destruct H2. inversion H2. subst. contradiction. intros. specialize H1 with pc0 instr0. destruct H1. tauto. trivial. - destruct H2. inv H2. contradiction. assumption. assumption.*) -Admitted. + destruct H2. inv H2. contradiction. assumption. assumption. +Qed. Hint Resolve iter_expand_instr_spec : htlspec. +Lemma create_arr_inv : forall w x y z a b c d, + create_arr w x y z = OK (a, b) c d -> y = b. +Proof. + inversion 1. reflexivity. +Qed. + Theorem transl_module_correct : forall f m, transl_module f = Errors.OK m -> tr_module f m. @@ -444,12 +422,22 @@ Proof. inversion s; subst. unfold transf_module in *. - monadInv Heqr. - econstructor; simpl; trivial. + unfold stack_correct in *. + destruct (0 <=? RTL.fn_stacksize f) eqn:STACK_BOUND_LOW; + destruct (RTL.fn_stacksize f <? Integers.Ptrofs.modulus) eqn:STACK_BOUND_HIGH; + destruct (RTL.fn_stacksize f mod 4 =? 0) eqn:STACK_ALIGN; + crush; + monadInv Heqr. + + (* TODO: We should be able to fold this into the automation. *) + pose proof (create_arr_inv _ _ _ _ _ _ _ _ EQ0) as STK_LEN. + rewrite <- STK_LEN. + + econstructor; simpl; auto. intros. inv_incr. assert (EQ3D := EQ3). - destruct x3. + destruct x4. apply collect_declare_datapath_trans in EQ3. apply collect_declare_controllogic_trans in EQ3D. assert (STC: st_controllogic s10 = st_controllogic s3) by congruence. diff --git a/src/translation/Veriloggen.v b/src/translation/Veriloggen.v index efe3565..b550ff9 100644 --- a/src/translation/Veriloggen.v +++ b/src/translation/Veriloggen.v @@ -29,13 +29,13 @@ Fixpoint transl_list (st : list (node * Verilog.stmnt)) {struct st} : list (expr Fixpoint scl_to_Vdecl (scldecl : list (reg * (option io * scl_decl))) {struct scldecl} : list module_item := match scldecl with - | (r, (io, Scalar sz))::scldecl' => Vdeclaration (Vdecl io r sz) :: scl_to_Vdecl scldecl' + | (r, (io, VScalar sz))::scldecl' => Vdeclaration (Vdecl io r sz) :: scl_to_Vdecl scldecl' | nil => nil end. Fixpoint arr_to_Vdeclarr (arrdecl : list (reg * (option io * arr_decl))) {struct arrdecl} : list module_item := match arrdecl with - | (r, (io, Array sz l))::arrdecl' => Vdeclaration (Vdeclarr io r sz l) :: arr_to_Vdeclarr arrdecl' + | (r, (io, VArray sz l))::arrdecl' => Vdeclaration (Vdeclarr io r sz l) :: arr_to_Vdeclarr arrdecl' | nil => nil end. @@ -43,10 +43,10 @@ Definition transl_module (m : HTL.module) : Verilog.module := let case_el_ctrl := transl_list (PTree.elements m.(mod_controllogic)) in let case_el_data := transl_list (PTree.elements m.(mod_datapath)) in let body := - Valways (Vposedge m.(mod_clk)) (Vcase (Vvar m.(mod_st)) case_el_data (Some Vskip)) - :: Valways (Vposedge m.(mod_clk)) (Vcond (Vbinop Veq (Vvar m.(mod_reset)) (ZToValue 1 1)) + Valways (Vposedge m.(mod_clk)) (Vcond (Vbinop Veq (Vvar m.(mod_reset)) (ZToValue 1 1)) (Vnonblock (Vvar m.(mod_st)) (posToValue 32 m.(mod_entrypoint))) (Vcase (Vvar m.(mod_st)) case_el_ctrl (Some Vskip))) + :: Valways (Vposedge m.(mod_clk)) (Vcase (Vvar m.(mod_st)) case_el_data (Some Vskip)) :: (arr_to_Vdeclarr (AssocMap.elements m.(mod_arrdecls)) ++ scl_to_Vdecl (AssocMap.elements m.(mod_scldecls))) in Verilog.mkmodule m.(mod_start) @@ -56,6 +56,7 @@ Definition transl_module (m : HTL.module) : Verilog.module := m.(mod_return) m.(mod_st) m.(mod_stk) + m.(mod_stk_len) m.(mod_params) body m.(mod_entrypoint). diff --git a/src/translation/Veriloggenproof.v b/src/translation/Veriloggenproof.v index 6c58c56..ca4ecab 100644 --- a/src/translation/Veriloggenproof.v +++ b/src/translation/Veriloggenproof.v @@ -16,16 +16,68 @@ * along with this program. If not, see <https://www.gnu.org/licenses/>. *) -From compcert Require Import Smallstep. -From coqup Require HTL Verilog. +From compcert Require Import Smallstep Linking. +From coqup Require HTL. +From coqup Require Import Coquplib Veriloggen Verilog. + +Definition match_prog (prog : HTL.program) (tprog : Verilog.program) := + match_program (fun cu f tf => tf = transl_fundef f) eq prog tprog. + +Lemma transf_program_match: + forall prog, match_prog prog (transl_program prog). +Proof. + intros. eapply match_transform_program_contextual. auto. +Qed. + +Inductive match_stacks : list HTL.stackframe -> list stackframe -> Prop := +| match_stack : + forall res m pc reg_assoc arr_assoc hstk vstk, + match_stacks hstk vstk -> + match_stacks (HTL.Stackframe res m pc reg_assoc arr_assoc :: hstk) + (Stackframe res (transl_module m) pc + reg_assoc arr_assoc :: vstk) +| match_stack_nil : match_stacks nil nil. + +Inductive match_states : HTL.state -> state -> Prop := +| match_state : + forall m st reg_assoc arr_assoc hstk vstk, + match_stacks hstk vstk -> + match_states (HTL.State hstk m st reg_assoc arr_assoc) + (State vstk (transl_module m) st reg_assoc arr_assoc) +| match_returnstate : + forall v hstk vstk, + match_stacks hstk vstk -> + match_states (HTL.Returnstate hstk v) (Returnstate vstk v) +| match_initial_call : + forall m, + match_states (HTL.Callstate nil m nil) (Callstate nil (transl_module m) nil). Section CORRECTNESS. Variable prog: HTL.program. - Variable tprog: Verilog.program. + Variable tprog: program. + + Hypothesis TRANSL : match_prog prog tprog. + + Let ge : HTL.genv := Globalenvs.Genv.globalenv prog. + Let tge : genv := Globalenvs.Genv.globalenv tprog. + + Theorem transl_step_correct : + forall (S1 : HTL.state) t S2, + HTL.step ge S1 t S2 -> + forall (R1 : state), + match_states S1 R1 -> + exists R2, Smallstep.plus step tge R1 t R2 /\ match_states S2 R2. + Proof. +(* induction 1; intros R1 MSTATE; inv MSTATE; econstructor; split. + - apply Smallstep.plus_one. econstructor. eassumption. trivial. + * econstructor. econstructor.*) + Admitted. Theorem transf_program_correct: forward_simulation (HTL.semantics prog) (Verilog.semantics tprog). - Admitted. + Admitted. + End CORRECTNESS. + |