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[kernel-coq] Extend interfaces to contain getters.

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Bug:
Change-Id: If8411f356496017cf371349b3edfae3972725662
Reviewed-on: https://dart-review.googlesource.com/8121
Reviewed-by: Dmitry Stefantsov <dmitryas@google.com>
This commit is contained in:
Samir Jindel 2017-09-26 17:39:15 +00:00
parent 1916dc75e6
commit 1cac4c7924
3 changed files with 119 additions and 101 deletions
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203
pkg/kernel/coq/ObjectModel.v
View file

@ -181,44 +181,52 @@ Record procedure_desc : Type := mk_procedure_desc {
pr_type : function_type;
}.
Record getter_desc : Type := mk_getter_desc {
gt_name : string;
gt_ref : nat;
gt_type : dart_type;
}.
Record interface : Type := mk_interface {
procedures : list procedure_desc;
getters : list getter_desc;
}.
Inductive member_desc : Type :=
| MD_Method : procedure_desc -> member_desc
| MD_Getter : getter_desc -> member_desc
.
(** Type envronment maps class IDs to their interface type. *)
Definition class_env : Type := NatMap.t interface.
(** Function environment maps defined functions to their procedure type. Used
for direct method invocation, direct property get etc. *)
Definition func_env : Type := NatMap.t procedure_desc.
Definition type_env : Type := NatMap.t dart_type.
Fixpoint expression_type
(CE : class_env) (FE : func_env) (TE : type_env) (e : expression) :
(CE : class_env) (TE : type_env) (e : expression) :
option dart_type :=
match e with
| E_Variable_Get (Variable_Get v) => NatMap.find v TE
| E_Property_Get (Property_Get rec prop) =>
rec_type <- expression_type CE FE TE rec;
rec_type <- expression_type CE TE rec;
let (prop_name) := prop in
match rec_type with
| DT_Function_Type _ =>
if string_dec prop_name "call" then [rec_type] else None
| DT_Interface_Type (Interface_Type class) =>
interface <- NatMap.find class CE;
proc_desc <- List.find (fun P =>
if string_dec (pr_name P) prop_name then true else false)
(procedures interface);
[DT_Function_Type (pr_type proc_desc)]
getter <- List.find (fun P =>
if string_dec (gt_name P) prop_name then true else false)
(getters interface);
[gt_type getter]
end
| E_Invocation_Expression (IE_Constructor_Invocation (Constructor_Invocation class)) =>
_ <- NatMap.find class CE;
[DT_Interface_Type (Interface_Type class)]
| E_Invocation_Expression (IE_Method_Invocation (Method_Invocation rec method args _)) =>
rec_type <- expression_type CE FE TE rec;
rec_type <- expression_type CE TE rec;
let (arg_exp) := args in
arg_type <- expression_type CE FE TE arg_exp;
arg_type <- expression_type CE TE arg_exp;
let (method_name) := method in
fun_type <-
match rec_type with
@ -236,16 +244,16 @@ Fixpoint expression_type
end
.
Fixpoint statement_type (CE : class_env) (FE: func_env) (TE : type_env) (s : statement) :
Fixpoint statement_type (CE : class_env) (TE : type_env) (s : statement) :
option (type_env * option dart_type) :=
match s with
| S_Expression_Statement (Expression_Statement e) =>
_ <- expression_type CE FE TE e; [(TE, None)]
_ <- expression_type CE TE e; [(TE, None)]
| S_Return_Statement (Return_Statement re) =>
rt <- expression_type CE FE TE re; [(TE, Some rt)]
rt <- expression_type CE TE re; [(TE, Some rt)]
| S_Variable_Declaration (Variable_Declaration _ _ None) => None
| S_Variable_Declaration (Variable_Declaration var type (Some init)) =>
init_type <- expression_type CE FE TE init;
init_type <- expression_type CE TE init;
if subtype (init_type, type) then
[(NatMap.add var type TE, None)]
else
@ -255,7 +263,7 @@ Fixpoint statement_type (CE : class_env) (FE: func_env) (TE : type_env) (s : sta
match stmts with
| nil => [(TE, None)]
| (s::ss) =>
st <- statement_type CE FE TE s;
st <- statement_type CE TE s;
let (TE', s_rt) := st in
sst <- process_statements TE' ss;
let (TE'', ss_rt) := sst in
@ -263,35 +271,37 @@ Fixpoint statement_type (CE : class_env) (FE: func_env) (TE : type_env) (s : sta
| (None, ss_rt) => [(TE'', ss_rt)]
| (Some rt, None) => [(TE'', Some rt)]
| (Some rt, Some rt') =>
if subtype (rt, rt') then [(TE'', Some rt)] else None
if subtype (rt, rt') then [(TE'', Some rt')] else
if subtype (rt', rt) then [(TE'', Some rt)] else
None
end
end in
process_statements TE stmts
end
.
Definition procedure_type (CE : class_env) (FE: func_env) (p : procedure) : bool :=
Definition procedure_type (CE : class_env) (p : procedure) : bool :=
let (_, _, fn) := p in
let (param, ret_type, body) := fn in
let (param_var, param_type, _) := param in
let TE := NatMap.add param_var param_type (NatMap.empty _) in
match statement_type CE FE TE body with
match statement_type CE TE body with
| Some (_, Some t) => subtype (t, ret_type)
| _ => false
end
.
Definition class_type (CE : class_env) (FE: func_env) (c : class) : bool :=
Definition class_type (CE : class_env) (c : class) : bool :=
let (nn_data, _, procedures) := c in
forallb (procedure_type CE FE) procedures
forallb (procedure_type CE) procedures
.
Section Typing_Equivalence_Homomorphism.
Definition subtype_at (e : expression) :=
forall CE FE TE v s t es,
expression_type CE FE (NatMap.add v s TE) e = [es] /\ s ◁ t ->
exists et, expression_type CE FE (NatMap.add v t TE) e = [et] /\ es ◁ et.
forall CE TE v s t es,
expression_type CE (NatMap.add v s TE) e = [es] /\ s ◁ t ->
exists et, expression_type CE (NatMap.add v t TE) e = [et] /\ es ◁ et.
Hint Resolve NatMap.add_1.
Hint Resolve NatMap.add_2.
@ -334,7 +344,7 @@ Section Typing_Equivalence_Homomorphism.
destruct prop.
unfold expression_type in H1.
fold expression_type in H1.
extract (expression_type CE FE (NatMap.add v s TE) rec) Orig H0.
extract (expression_type CE (NatMap.add v s TE) rec) Orig H0.
(* Go by cases on the original type of the receiver. *)
destruct Orig; [idtac|crush].
@ -346,7 +356,7 @@ Section Typing_Equivalence_Homomorphism.
extract (NatMap.find n CE) iface H3.
destruct iface; [idtac|crush].
simpl in H1.
pose proof (H CE FE TE v s t (DT_Interface_Type (Interface_Type n)) (conj H0 H2)).
pose proof (H CE TE v s t (DT_Interface_Type (Interface_Type n)) (conj H0 H2)).
destruct H4 as [new_rec_type].
destruct H4.
destruct new_rec_type; [idtac|crush].
@ -358,7 +368,7 @@ Section Typing_Equivalence_Homomorphism.
(* Case 2: receiver has function type. *)
destruct f.
force_options.
pose proof (H CE FE TE v s t (DT_Function_Type (Function_Type d d0)) (conj H0 H2)).
pose proof (H CE TE v s t (DT_Function_Type (Function_Type d d0)) (conj H0 H2)).
destruct H3 as [new_rec_type].
destruct H3.
exists new_rec_type.
@ -388,7 +398,7 @@ Section Typing_Equivalence_Homomorphism.
destruct H1.
unfold expression_type in H1.
fold expression_type in H1.
force_expr (expression_type CE FE (NatMap.add v s TE) rec).
force_expr (expression_type CE (NatMap.add v s TE) rec).
destruct d.
(* Case 1: receiver has interface type. *)
@ -402,8 +412,8 @@ Section Typing_Equivalence_Homomorphism.
destruct i.
force_options.
(* The receiver class must be the same. *)
assert (expression_type CE FE (NatMap.add v t TE) rec = [DT_Interface_Type (Interface_Type n0)]).
pose proof (H CE FE TE v s t (DT_Interface_Type (Interface_Type n0)) (conj H4 H2)) as IH_rec.
assert (expression_type CE (NatMap.add v t TE) rec = [DT_Interface_Type (Interface_Type n0)]).
pose proof (H CE TE v s t (DT_Interface_Type (Interface_Type n0)) (conj H4 H2)) as IH_rec.
destruct IH_rec.
destruct H3.
destruct x.
@ -416,7 +426,7 @@ Section Typing_Equivalence_Homomorphism.
fold expression_type.
rewrite H3; simpl.
(* The argument is still well typed. *)
pose proof (H0 CE FE TE v s t d (conj H5 H2)) as IH_arg.
pose proof (H0 CE TE v s t d (conj H5 H2)) as IH_arg.
destruct IH_arg.
destruct H10.
rewrite H10.
@ -434,7 +444,7 @@ Section Typing_Equivalence_Homomorphism.
force_options.
destruct f0.
force_options.
pose proof (H CE FE TE v s t (DT_Function_Type f) (conj H4 H2)).
pose proof (H CE TE v s t (DT_Function_Type f) (conj H4 H2)).
destruct H3.
destruct H3.
destruct x; [crush|idtac].
@ -448,7 +458,7 @@ Section Typing_Equivalence_Homomorphism.
fold expression_type.
rewrite H3.
rewrite bind_some.
pose proof (H0 CE FE TE v s t d (conj H5 H2)).
pose proof (H0 CE TE v s t d (conj H5 H2)).
destruct H12.
destruct H12.
rewrite H12.
@ -477,11 +487,12 @@ End Typing_Equivalence_Homomorphism.
Section Environments.
Definition func_table := NatMap.t member.
(** Function environment maps defined functions to their procedure type. Used
for direct method invocation, direct property get etc. *)
Definition member_env : Type := NatMap.t (member_desc * member).
Definition procedure_dissect (envs: class_env * func_env * func_table) (p : procedure) :=
let (Cs, FT) := envs in
let (CE, FE) := Cs in
Definition procedure_dissect (envs: class_env * member_env) (p : procedure) :=
let (CE, ME) := envs in
let (memb, _, fn) := p in
let (nn, name) := memb in
let (name_str) := name in
@ -490,24 +501,24 @@ Definition procedure_dissect (envs: class_env * func_env * func_table) (p : proc
let (param, ret_type, _) := fn in
let (_, param_type, _) := param in
let proc := mk_procedure_desc name_str id (Function_Type param_type ret_type) in
(proc, (CE, NatMap.add id proc FE, NatMap.add id (M_Procedure p) FT)).
(proc, (CE, NatMap.add id (MD_Method proc, M_Procedure p) ME)).
Definition procedure_to_env p envs := snd (procedure_dissect envs p).
Definition procedure_to_desc envs p := fst (procedure_dissect envs p).
Definition class_to_env (c : class) (envs: class_env * func_env * func_table) :=
Definition class_to_env (c : class) (envs: class_env * member_env) :=
let (nn, name, procs) := c in
let (ref) := nn in
let (id) := ref in
let envs' := List.fold_right procedure_to_env envs procs in
let class_desc := mk_interface (List.map (procedure_to_desc envs') procs) in
let (Cs, FT) := envs' in
let (CE, FE) := Cs in
(NatMap.add id class_desc CE, FE, FT).
let procedures := List.map (procedure_to_desc envs') procs in
let getters := List.map (fun P => mk_getter_desc (pr_name P) (pr_ref P) (DT_Function_Type (pr_type P))) procedures in
let (CE, ME) := envs' in
(NatMap.add id (mk_interface procedures getters) CE, ME).
Definition lib_to_env (l: library) : class_env * func_env * func_table :=
Definition lib_to_env (l: library) : class_env * member_env :=
let (_, classes, top_procs) := l in
let envs := List.fold_right class_to_env (NatMap.empty _, NatMap.empty _, NatMap.empty _) classes in
let envs := List.fold_right class_to_env (NatMap.empty _, NatMap.empty _) classes in
List.fold_right procedure_to_env envs top_procs.
Local Ltac destruct_types :=
@ -519,6 +530,7 @@ Local Ltac destruct_types :=
| [H : named_node_data |- _] => destruct H
| [H : function_node |- _] => destruct H
| [H : procedure_desc |- _] => destruct H
| [H : getter_desc |- _] => destruct H
| [H : name |- _] => destruct H
| [H : reference |- _] => destruct H
| [H : variable_declaration |- _] => destruct H
@ -532,29 +544,23 @@ Proof.
intros.
unfold procedure_to_desc.
unfold procedure_dissect.
destruct env; destruct p.
destruct env'; destruct p.
destruct env; destruct env'.
destruct_types.
crush.
Qed.
Local Definition mono
(envs: class_env * func_env * func_table)
(envs': class_env * func_env * func_table) : Prop :=
let (Cs, FT) := envs in
let (CE, FE) := Cs in
let (Cs', FT') := envs' in
let (CE', FE') := Cs' in
(envs: class_env * member_env)
(envs': class_env * member_env) : Prop :=
let (CE, ME) := envs in
let (CE', ME') := envs' in
(forall n, NatMap.In n CE -> NatMap.In n CE') /\
(forall n, NatMap.In n FE -> NatMap.In n FE') /\
(forall n, NatMap.In n FT -> NatMap.In n FT').
(forall n, NatMap.In n ME -> NatMap.In n ME').
Local Lemma mono_trans : forall x y z, mono x y -> mono y z -> mono x z.
Proof.
intros.
destruct x; destruct p.
destruct y; destruct p.
destruct z; destruct p.
destruct x; destruct y; destruct z.
unfold mono in *.
crush.
Qed.
@ -572,8 +578,7 @@ Proof.
intros.
unfold procedure_dissect in H.
destruct_types.
destruct E1; destruct p.
destruct E2; destruct p.
destruct E1; destruct E2.
unfold mono.
inject H.
crush.
@ -584,13 +589,12 @@ Local Lemma class_mono :
forall E1 E2 c, class_to_env c E1 = E2 -> mono E1 E2.
Proof.
intros.
destruct E1; destruct p.
destruct E2; destruct p.
destruct E1; destruct E2.
unfold class_to_env in H.
destruct_types.
extract_head fold_right in H.
assert (mono (c0, f0, f) H0).
pose proof (foldr_mono mono l (c0, f0, f) procedure_to_env mono_sym mono_trans) as X.
assert (mono (c0, m) H0).
pose proof (foldr_mono mono l (c0, m) procedure_to_env mono_sym mono_trans) as X.
continue_with X.
intros.
unfold procedure_to_env.
@ -600,8 +604,8 @@ Proof.
apply (proc_mono _ _ _ _ (eq_sym HeqP)).
crush.
destruct H0; destruct p.
assert (mono (c, f4, f3) (t, f2, f1)) by
destruct H0.
assert (mono (c, m) (t, m0)) by
(inversion H;
unfold mono;
crush); crush.
@ -610,12 +614,11 @@ Qed.
Local Lemma fold_proc_invar :
forall E1 E2 ps,
List.fold_right procedure_to_env E1 ps = E2 ->
fst (fst E1) = fst (fst E2).
fst E1 = fst E2.
Proof.
intros.
destruct E1 as (Cs, FT); destruct Cs as (CE, FE).
destruct E2 as (Cs', FT'); destruct Cs' as (CE', FE').
pose (x := @foldr_preserve (class_env * func_env * func_table) procedure (fun env => let (X, _) := env in let (CE', _) := X in CE = CE') ps (CE, FE, FT) procedure_to_env).
destruct E1 as (CE, ME); destruct E2 as (CE' , ME').
pose (x := @foldr_preserve (class_env * member_env) procedure (fun env => let (CE', _) := env in CE = CE') ps (CE, ME) procedure_to_env).
continue_with x.
crush.
destruct_types.
@ -628,18 +631,17 @@ Proof.
Qed.
Local Lemma class_env_invar :
forall CE FE FT CE' FE' FT' id id' intf n ps,
forall CE ME CE' ME' id id' intf n ps,
id <> id' ->
class_to_env (Class (Named_Node (Reference id')) n ps) (CE, FE, FT) = (CE', FE', FT') ->
class_to_env (Class (Named_Node (Reference id')) n ps) (CE, ME) = (CE', ME') ->
(NatMap.MapsTo id intf CE' -> NatMap.MapsTo id intf CE).
Proof.
unfold class_to_env.
intros.
extract_head fold_right in H0 as F.
destruct F as (CS, FT_f); destruct CS as (CE_f, FE_f).
destruct F as (CE_f, ME_f).
inversion H0; clear H0.
rewrite H4 in *; clear H4.
rewrite H5 in *; clear H5.
assert (NatMap.MapsTo id intf CE_f).
rewrite <- H3 in H1.
apply (NatMap.add_3 (not_eq_sym H) H1).
@ -650,11 +652,11 @@ Proof.
Qed.
Hint Resolve NatMap.add_1.
Local Lemma program_wf': forall cs CE FE FT class_id intf proc_desc,
List.fold_right class_to_env (NatMap.empty _, NatMap.empty _, NatMap.empty _) cs = ((CE, FE), FT)
Local Lemma program_wf': forall cs CE ME class_id intf proc_desc,
List.fold_right class_to_env (NatMap.empty _, NatMap.empty _) cs = (CE, ME)
-> NatMap.MapsTo class_id intf CE
-> List.In proc_desc (procedures intf)
-> NatMap.In (pr_ref proc_desc) FE /\ NatMap.In (pr_ref proc_desc) FT.
-> NatMap.In (pr_ref proc_desc) ME.
Proof.
intro cs.
induction cs.
@ -685,16 +687,16 @@ Proof.
(* Case 1.1: head class is different. *)
Focus 2.
extract_head fold_right in H as Fold.
destruct Fold as (CS, FT_f); destruct CS as (CE_f, FE_f).
destruct Fold as (CE_f, ME_f).
(* class_id must map to the same interface after applying the previous classes. *)
assert (NatMap.MapsTo class_id intf CE_f).
pose proof (class_env_invar CE_f FE_f FT_f CE FE FT class_id n intf s l (not_eq_sym n0)) as H2.
pose proof (class_env_invar CE_f ME_f CE ME class_id n intf s l (not_eq_sym n0)) as H2.
continue_with H2; crush.
(* Apply the induction hypothesis. *)
pose proof (IHcs CE_f FE_f FT_f class_id intf proc_desc eq_refl H2 H1) as IH.
assert (mono (CE_f, FE_f, FT_f) (CE, FE, FT)).
pose proof (IHcs CE_f ME_f class_id intf proc_desc eq_refl H2 H1) as IH.
assert (mono (CE_f, ME_f) (CE, ME)).
apply (class_mono _ _ ((Class (Named_Node (Reference n)) s l))); crush.
crush.
@ -702,21 +704,24 @@ Proof.
extract_head fold_right in H as Fold.
unfold class_to_env in H.
extract_head fold_right in H as FoldP.
destruct FoldP as (CS, FT_f); destruct CS as (CE_f, FE_f).
destruct FoldP as (CE_f, ME_f).
inversion H; clear H.
rewrite H4 in *; clear H4.
rewrite H5 in *; clear H5.
rewrite e in *; clear e.
assert (NatMap.MapsTo class_id {| procedures := map (procedure_to_desc (CE_f, FE, FT)) l |} CE) by crush.
pose proof (@MoreNatMapFacts.add_3 _ CE class_id intf ({| procedures := map (procedure_to_desc (CE_f, FE, FT)) l |}) (conj H0 H)).
extract_head mk_interface in H3 as I, IEq.
assert (NatMap.MapsTo class_id I CE) by crush.
pose proof (@MoreNatMapFacts.add_3 _ CE class_id intf I (conj H0 H)).
rewrite H2 in *; clear H2.
clear H0.
clear H.
simpl in H1.
clear IHcs.
rewrite IEq in *.
clear IEq.
clear I.
generalize H1.
generalize FoldPEq.
generalize CE_f FE FT.
generalize CE_f ME.
clear H1.
clear FoldPEq.
clear H3.
@ -743,7 +748,7 @@ Proof.
clear H.
simpl in FoldPEq.
extract_head (fold_right procedure_to_env) in FoldPEq as Rest.
destruct Rest; destruct p.
destruct Rest.
unfold procedure_to_env in FoldPEq.
unfold procedure_dissect in FoldPEq.
simpl in FoldPEq.
@ -751,30 +756,32 @@ Proof.
crush.
simpl in FoldPEq.
simpl in IHl.
extract_head fold_right in FoldPEq as InnerFold.
destruct InnerFold as (CS, FT_i); destruct CS as (CE_i, FE_i).
destruct InnerFold as (CE_i, ME_i).
unfold procedure_to_env in FoldPEq.
unfold procedure_dissect in FoldPEq.
destruct_types.
simpl in FoldPEq.
rewrite (proc_desc_noenv (CE_f0, FE0, FT0) (CE_i, FE_i, FT_i)) in H.
pose proof (IHl CE_i FE_i FT_i eq_refl H).
destruct H0.
rewrite (proc_desc_noenv (CE_f0, ME0) (CE_i, ME_i)) in H.
pose proof (IHl CE_i ME_i eq_refl H).
inversion FoldPEq.
clear FoldPEq.
clear H2.
crush.
Qed.
Lemma program_wf: forall l CE FE FT class_id intf proc_desc,
lib_to_env l = ((CE, FE), FT)
Lemma program_wf: forall l CE ME class_id intf proc_desc,
lib_to_env l = (CE, ME)
-> NatMap.MapsTo class_id intf CE
-> List.In proc_desc (procedures intf)
-> NatMap.In (pr_ref proc_desc) FE /\ NatMap.In (pr_ref proc_desc) FT.
-> NatMap.In (pr_ref proc_desc) ME.
Proof.
intros.
destruct l.
unfold lib_to_env in *.
extract_head (fold_right class_to_env) in H as Inner.
destruct Inner as (CS, FT_i); destruct CS as (CE_i, FE_i).
destruct Inner as (CE_i, ME_i).
assert (NatMap.MapsTo class_id intf CE_i).
apply eq_sym in InnerEq.
@ -782,8 +789,8 @@ Proof.
simpl in H.
crush.
pose proof (program_wf' l CE_i FE_i FT_i class_id intf proc_desc (eq_sym InnerEq) H2 H1).
assert (mono (CE_i, FE_i, FT_i) (CE, FE, FT)).
pose proof (program_wf' l CE_i ME_i class_id intf proc_desc (eq_sym InnerEq) H2 H1).
assert (mono (CE_i, ME_i) (CE, ME)).
rewrite <- H.
apply foldr_mono.
exact mono_sym.

8
pkg/kernel/coq/OperationalSemantics.v
View file

@ -372,7 +372,7 @@ Inductive step : configuration -> configuration -> Prop :=
ret_type body ->
env' = env_extend var_id arg_val empty_env ->
next_cont = Exit_Sk ret_cont null_val ->
value_of_type null_val (mk_interface nil) None ->
value_of_type null_val (mk_interface nil nil) None ->
step (Value_Passing_Configuration
(Invocation_Ek rcvr_val name env ret_cont) arg_val)
(Exec_Configuration body env' ret_cont next_cont)
@ -398,7 +398,9 @@ Inductive step : configuration -> configuration -> Prop :=
((pr_name func_proc_desc) = "call")%string ->
value_of_type
func_val
(mk_interface (func_proc_desc :: nil))
(mk_interface (func_proc_desc :: nil)
((mk_getter_desc (pr_name func_proc_desc) (pr_ref func_proc_desc)
(DT_Function_Type (pr_type func_proc_desc))) :: nil))
(Some (DT_Function_Type (pr_type func_proc_desc))) ->
step (Value_Passing_Configuration (Property_Get_Ek name cont) rcvr_val)
(Value_Passing_Configuration cont func_val)
@ -426,7 +428,7 @@ Inductive step : configuration -> configuration -> Prop :=
where ρ' = ρ#[#var = nullVal#]# *)
| Exec_Variable_Declaration_Non_Init :
forall var_id type env ret_cont next_cont null_val env',
value_of_type null_val (mk_interface nil) None ->
value_of_type null_val (mk_interface nil nil) None ->
env' = env_extend var_id null_val env ->
step (Exec_Configuration
(S_Variable_Declaration (Variable_Declaration var_id type None))

9
pkg/kernel/coq/_CoqProject Normal file
View file

@ -0,0 +1,9 @@
-R . Kernel
./Syntax.v
./OperationalSemanticsProof.v
./CommonTactics.v
./Common.v
./SyntaxRaw.v
./ObjectModel.v
./OperationalSemantics.v
./CpdtTactics.v