bedrock.lang.cpp.syntax.translation_unit

(*
 * Copyright (c) 2020-2024 BedRock Systems, Inc.
 * This software is distributed under the terms of the BedRock Open-Source License.
 * See the LICENSE-BedRock file in the repository root for details.
 *)
Require Import stdpp.fin_maps.
Require Import bedrock.prelude.base.
Require Import bedrock.prelude.bytestring_core.
Require Import bedrock.prelude.avl.
Require Import bedrock.lang.cpp.syntax.core.
Require Import bedrock.lang.cpp.syntax.types.
Require Import bedrock.lang.cpp.syntax.decl.
Require Import bedrock.lang.cpp.syntax.namemap.
Export decl.

#[local] Set Primitive Projections.

#[local] Tactic Notation "solve_decision" := intros; solve_decision.

Variant GlobDecl' {lang} : Set :=
  | Gtype (* this is a type declaration, but not a definition *)
  | Gunion (_ : Union' lang) (* union body *)
  | Gstruct (_ : Struct' lang) (* struct body *)
  | Genum (_ : type' lang) (_ : list ident) (* *)
  | Gconstant (_ : type' lang) (init : option (Expr' lang)) (* used for enumerator constants*)
  | Gtypedef (_ : type' lang)
  | Gunsupported (_ : bs).
#[global] Arguments GlobDecl' : clear implicits.
#[global] Arguments Gunion _ & _ : assert.
#[global] Arguments Gstruct _ & _ : assert.
#[global] Arguments Genum _ & _ _ : assert.
#[global] Arguments Gconstant _ & _ _ : assert.
#[global] Arguments Gtypedef _ & _ : assert.
#[global] Arguments Gunsupported _ & _ : assert.
#[global] Instance: forall {lang}, EqDecision (GlobDecl' lang).
Proof. solve_decision. Defined.
Notation GlobDecl := (GlobDecl' lang.cpp).

Definition type_table : Type := NM.t GlobDecl.

Module global_init.
  Variant t {lang : lang.t} : Set :=
  | Init (_ : Expr' lang)
  | ImplicitInit
    (* ^^ This arises because template instantiations are only carried out
          as much as they are needed. For example,
       <<
       template<typename T, T v>
       struct integral_constant {
         static constexpr T value = v;
       };
       void test() {
         // this line forces the declaration, but not the initialization.
         auto x = sizeof(integral_constant<bool, true>::value);
         // this line forces the initialization of the value.
         auto y = integral_constant<bool, true>::value;
       }
       >>
     *)
  | NoInit
  | Delayed (* for <<static>> variables declared in functions.
               These are initialized during the first call to the function *)
  | Extern.
  #[global] Arguments t _ : clear implicits.
  #[global] Instance t_eq {lang} : EqDecision (t lang).
  Proof. solve_decision. Defined.

  Import UPoly.
  #[universes(polymorphic)]
  Definition fmap {lang lang' : lang.t} `{FMap M} (f : Expr' lang -> Expr' lang')
    (gi : global_init.t lang) : global_init.t lang' :=
    match gi with
    | global_init.Init e => global_init.Init $ f e
    | global_init.ImplicitInit => global_init.ImplicitInit
    | global_init.NoInit => global_init.NoInit
    | global_init.Delayed => global_init.Delayed
    | global_init.Extern => global_init.Extern
    end.

  #[universes(polymorphic)]
  Definition traverse {lang lang' : lang.t} `{MRet M, Ap M} (f : Expr' lang -> M (Expr' lang'))
    (gi : global_init.t lang) : M (global_init.t lang') :=
    match gi with
    | global_init.Init e => global_init.Init <$> f e
    | global_init.ImplicitInit => mret global_init.ImplicitInit
    | global_init.NoInit => mret global_init.NoInit
    | global_init.Delayed => mret global_init.Delayed
    | global_init.Extern => mret global_init.Extern
    end.
End global_init.

(* Values in Object files. These can be externed. *)
Variant ObjValue' {lang} : Set :=
| Ovar (_ : type' lang) (_ : global_init.t lang)
| Ofunction (_ : Func' lang)
| Omethod (_ : Method' lang)
| Oconstructor (_ : Ctor' lang)
| Odestructor (_ : Dtor' lang).
#[global] Arguments ObjValue' : clear implicits.
#[global] Arguments Ovar _ & _ _ : assert.
#[global] Arguments Ofunction _ & _ : assert.
#[global] Arguments Omethod _ & _ : assert.
#[global] Arguments Oconstructor _ & _ : assert.
#[global] Arguments Odestructor _ & _ : assert.
#[global] Instance: forall {lang}, EqDecision (ObjValue' lang).
Proof. solve_decision. Defined.
Notation ObjValue := (ObjValue' lang.cpp).

Definition type_of_classname {lang} : classname' lang -> type' lang :=
  match lang with
  | lang.cpp => Tnamed
  | lang.temp => fun x => x
  end.

Definition type_of_value {lang} (o : ObjValue' lang) : type' lang :=
  normalize_type
  match o with
  | Ovar t _ => t
  | Ofunction f => Tfunction {| ft_cc := f.(f_cc) ; ft_arity := f.(f_arity) ; ft_return := f.(f_return) ; ft_params := snd <$> f.(f_params) |}
  | Omethod m =>
    Tmember_func (Tqualified m.(m_this_qual) (type_of_classname m.(m_class)))
                 $ Tfunction {| ft_cc := m.(m_cc) ; ft_arity := m.(m_arity) ; ft_return := m.(m_return) ; ft_params := snd <$> m.(m_params) |}

  | Oconstructor c =>
    Tmember_func (type_of_classname c.(c_class)) $ Tfunction {| ft_cc := c.(c_cc) ; ft_arity := c.(c_arity) ; ft_return := Tvoid ; ft_params := snd <$> c.(c_params) |}
  | Odestructor d =>
    Tmember_func (type_of_classname d.(d_class)) $ Tfunction {| ft_cc := d.(d_cc) ; ft_arity := Ar_Definite ; ft_return := Tvoid ; ft_params := nil |}
  end.

Definition symbol_table : Type := NM.t ObjValue.

Variant GlobalInit' {lang} : Set :=
  (* initialization by an expression *)
| ExprInit (_ : Expr' lang)
  (* zero initialization *)
| ZeroInit
  (* declaration will be initialized from within a function.
     The C++ standard states that these need to be initialized
     in a concurrency-safe way; however, in practice it is common
     to disable this functionality in embedded code using
     -fno-threadsafe-statics. The boolean attached to this
     determines whether *the compiler* guarantees there is at most
     a single call to this constructor.

     See https://eel.is/c++draft/stmt.dcl3 *)
| FunctionInit (at_most_once : bool).
#[global] Arguments GlobalInit' : clear implicits.
#[global] Arguments ExprInit _ & _ : assert.
#[global] Instance: forall {lang}, EqDecision (GlobalInit' lang).
Proof. solve_decision. Defined.
Notation GlobalInit := (GlobalInit' lang.cpp).

Record GlobalInitializer' {lang} : Set := Build_GlobalInitializer
  { g_name : obj_name' lang
  ; g_type : type' lang
  ; g_init : GlobalInit' lang
  }.
#[global] Arguments GlobalInitializer' : clear implicits.
#[global] Arguments Build_GlobalInitializer _ & _ _ _ : assert.
#[global] Instance: forall {lang}, EqDecision (GlobalInitializer' lang).
Proof. solve_decision. Defined.
Notation GlobalInitializer := (GlobalInitializer' lang.cpp).

Definition InitializerBlock' lang : Set :=
  list (GlobalInitializer' lang).
Notation InitializerBlock := (InitializerBlock' lang.cpp).
#[global] Instance InitializerBlock_empty {lang} : Empty (InitializerBlock' lang) :=
  nil.

Definition alias_table : Type := NM.t type.

Record translation_unit : Type := {
  symbols : symbol_table;
  types : type_table;
  aliases : alias_table; (* we eschew <<Gtypedef>> for now *)
  initializer : InitializerBlock;
  byte_order : endian;
}.

(*
(** These Lookup instances come with no theory; use instead the unfolding
    lemmas below and the `fin_maps` theory. *)
[global] Instance global_lookup : Lookup globname GlobDecl translation_unit := fun k m => m.(types) !! k. global Instance symbol_lookup : Lookup obj_name ObjValue translation_unit :=
  fun k m => m.(symbols) !! k.

Lemma tu_lookup_globals (t : translation_unit) (n : globname) :
  t !! n = t.(types) !! n.
Proof. done. Qed.

Lemma tu_lookup_symbols (t : translation_unit) (n : obj_name) :
  t !! n = t.(symbols) !! n.
Proof. done. Qed.
*)

Fixpoint is_trivially_destructible (tu : translation_unit) (ty : type) {struct ty} : bool :=
  qual_norm (fun _ t =>
               match t with
               | Tref _ | Trv_ref _
               | Tnum _ _ | Tchar_ _
               | Tvoid | Tbool | Tptr _
               | Tenum _
               | Tmember_pointer _ _
               | Tfloat_ _
               | Tnullptr => true
               | Tnamed nm =>
                   match tu.(types) !! nm with
                   | Some (Gunion u) => u.(u_trivially_destructible)
                   | Some (Gstruct s) => s.(s_trivially_destructible)
                   | _ => false
                   end
               | Tarray ety _ => is_trivially_destructible tu ety
               | _ => false
               end) ty.

(* [global] Remove Hints IM_lookup : typeclass_instances. (* TODO: structurd name lookup *) *)

Fixpoint ref_to_type (t : type) : option type :=
  match t with
  | Tref t
  | Trv_ref t => Some t
  | Tqualified _ t => ref_to_type t
  | _ => None
  end.

(* Not a reference type *)
Notation not_ref_type t := (ref_to_type t = None).

Section with_type_table.
  Variable te : type_table.
  (*
  To traverse a type definition and compute, say, its list of subobjects,
  we require that the type is _complete_, as in the usual sense.

  This definition is adapted from Krebbers'15, Definition 3.3.5, with needed
  adjustments for C++.

  Unlike Krebbers:
  - our type_table are not ordered
  - complete_named takes a proof of complete_decl to simplify its use for consumers,
    so we'd naively recheck a struct wherever needed; but an actual checker can
    be smarter (it could use a state monad carrying a map of known-complete types).

  The C++ standard defines and constrains "(in)complete type"s at
  https://eel.is/c++draft/basic.types.generaldef:object_type,incompletely-defined, and constraints it at https://eel.is/c++draft/basic.scope.pdecl6,
  https://eel.is/c++draft/class.memdef:data_member, https://eel.is/c++draft/basic.def.odr12,
  https://eel.is/c++draft/basic.def5. *)

  (* Check that g : GlobDecl is complete in environment te. *)
  Inductive complete_decl : GlobDecl -> Prop :=
  (* We intentionally omit Krebbers' clauses checking the aggregate is not
  empty: empty aggregates are legal in full C/C++ (see
  cpp2v-tests/test_translation_unit_validity.cpp). *)
  | complete_Struct {st : Struct}
              (_ : forall (b : name) li, In (b, li) st.(s_bases) -> complete_type (Tnamed b))
              (_ : forall m, In m st.(s_fields) -> complete_type m.(mem_type))
    : complete_decl (Gstruct st)
  | complete_Union {u}
              (_ : forall m, In m u.(u_fields) -> complete_type m.(mem_type))
    : complete_decl (Gunion u)
  | complete_enum {t consts} (_ : complete_type t)
    : complete_decl (Genum t consts)
  (* No need for typedefs since those are forbidden in `Tnamed`, `Gtype` isn't
  legal, `Gconstant` is illegal and wouldn't make sense. *)

  (* Basic types. This excludes references (as checked by complete_basic_type_not_ref). *)
  with complete_basic_type : type -> Prop :=
  | complete_float sz : complete_basic_type (Tfloat_ sz)
  | complete_int sgn sz : complete_basic_type (Tnum sgn sz)
  | complete_bool : complete_basic_type Tbool
  | complete_nullptr : complete_basic_type Tnullptr
  | complete_char c : complete_basic_type (Tchar_ c)

  (* t can in turn be a pointer type *)
  | complete_ptr {t} : complete_pointee_type t -> complete_basic_type (Tptr t)

  (* complete_pointee_type t says that a pointer/reference to t is complete.
     This excludes references (as checked by complete_pointee_type_not_ref)
     since they cannot be nested. *)
  with complete_pointee_type : type -> Prop :=
  | complete_pt_qualified {q t} (_ : complete_pointee_type t)
    : complete_pointee_type (Tqualified q t)
  (*
    Pointers to array are only legal if the array is complete, at least
    in C, since they cannot actually be indexed or created.
    This rejects the invalid C:

    struct T; int foo(struct T x[][10]);

    However, C++ compilers appear to accept this code, which we cover
    in wellscoped_array.
    *)
  | complete_pt_array t n
    (_ : (n <> 0)%N) (* From Krebbers. Probably needed to reject T[][]. *)
    (_ : complete_type t) :
    complete_pointee_type (Tarray t n)
  | complete_pt_named {n decl} :
    (* This check could not appear in a Krebbers-style definition.
       And it is not needed to enable computation on complete types.
     *)
    te !! n = Some decl ->
    complete_pointee_type (Tnamed n)
  | complete_pt_enum {n ty branches} :
    (* This check could not appear in a Krebbers-style definition.
       And it is not needed to enable computation on complete types.
     *)
    te !! n = Some (Genum ty branches) ->
    complete_basic_type ty ->
    complete_pointee_type (Tenum n)

  (* Beware:
  Tfunction represents a function type; somewhat counterintuitively,
  a pointer to a function type is complete even if the argument/return types
  are not complete but only well-scoped, you're just forbidden from
  actually invoking the pointer; this follows Krebbers'15 3.3.5. *)
  | complete_pt_function {cc ret args}
      (_ : wellscoped_type ret)
      (_ : wellscoped_types args)
    : complete_pointee_type (Tfunction $ FunctionType (ft_cc:=cc) ret args)
  | complete_pt_basic t :
    complete_basic_type t ->
    complete_pointee_type t
  | complete_pointee_void : complete_pointee_type Tvoid
  (* complete_type t says that type t is well-formed, that is, complete. *)
  with complete_type : type -> Prop :=
  | complete_qualified {q t} (_ : complete_type t)
    : complete_type (Tqualified q t)
  (* Reference types. This setup forbids references to references. *)
  | complete_ref {t} : complete_pointee_type t -> complete_type (Tref t)
  | complete_rv_ref {t} : complete_pointee_type t -> complete_type (Trv_ref t)
  (*
  A reference to a struct/union named n is well-formed if its definition is.
  TODO: instead of checking that n points to a well-formed definition
  _at each occurrence_, check it once, when adding it to our
  analogue of a type environment, that is type_table.
  However, that might require replacing type_table by a _sequence_ of
  declarations, instead of an unordered dictionary.
  *)
  | complete_named {n decl} (_ : te !! n = Some decl)
                    (_ : complete_decl decl) :
    complete_type (Tnamed n)
  | complete_array {t n}
    (_ : (n <> 0)%N) (* Needed? from Krebbers*)
    (_ : complete_type t) :
    complete_type (Tarray t n)
  | complete_member_pointer {n t} (_ : not_ref_type t)
      (_ : complete_pointee_type (Tnamed n))
      (_ : complete_pointee_type t)
    : complete_type (Tmember_pointer (Tnamed n) t)
  | complete_function {cc ar ret args} :
    (*
    We could probably omit this constructor, and consider function types as not
    complete; "complete function types" do not exist in the standard, and
    complete_symbol_table does not use the concept.
     *)
    complete_pointee_type (Tfunction $ FunctionType (ft_cc:=cc) (ft_arity:=ar) ret args) ->
    complete_type (Tfunction $ FunctionType (ft_cc:=cc) (ft_arity:=ar) ret args)
  | complete_basic t :
    complete_basic_type t ->
    complete_type t
  

  with wellscoped_type : type -> Prop :=
  | wellscoped_qualified {q t} (_ : wellscoped_type t)
    : wellscoped_type (Tqualified q t)
  | wellscoped_array t n
    (_ : (n <> 0)%N) : (* From Krebbers. Probably needed to reject T[][]. *)
    wellscoped_type t ->
    wellscoped_type (Tarray t n)
  | wellscoped_pointee t :
    complete_pointee_type t ->
    wellscoped_type t
  (* covers references. *)
  | wellscoped_complete {t} :
    complete_type t ->
    wellscoped_type t
  with wellscoped_types : list type -> Prop :=
  | wellscoped_nil : wellscoped_types []
  | wellscoped_cons t ts :
    wellscoped_type t ->
    wellscoped_types ts ->
    wellscoped_types (t :: ts).

  Inductive valid_decl : GlobDecl -> Prop :=
  | valid_typedef t :
    (*
    All typedefs in use have been inlined at their use-site, so we don't enforce
    their validity.

    In addition, we can't enforce their validity because `clang` produces
    builtin typedefs with ill-scoped bodies, such as
    (Dtypedef "__NSConstantString" (Tnamed "_Z22__NSConstantString_tag")) :: ... :: (Dtypedef "__builtin_va_list" (Tarray (Tnamed "_Z13__va_list_tag") 1)) ::. *)
    (* wellscoped_type t -> *)
    valid_decl (Gtypedef t)
  | valid_type : valid_decl Gtype
  | valid_const t oe :
    (* Potentially redundant. *)
    wellscoped_type t ->
    valid_decl (Gconstant t oe)
  | valid_complete_decl g :
    complete_decl g -> valid_decl g.
End with_type_table.

Scheme complete_decl_mut_ind := Minimality for complete_decl Sort Prop
with complete_basic_type_mut_ind := Minimality for complete_basic_type Sort Prop
with complete_pointee_type_mut_ind := Minimality for complete_pointee_type Sort Prop
with complete_type_mut_ind := Minimality for complete_type Sort Prop
with wellscoped_type_mut_ind := Minimality for wellscoped_type Sort Prop
with wellscoped_types_mut_ind := Minimality for wellscoped_types Sort Prop.

Combined Scheme complete_mut_ind from complete_decl_mut_ind, complete_basic_type_mut_ind,
  complete_pointee_type_mut_ind, complete_type_mut_ind,
  wellscoped_type_mut_ind, wellscoped_types_mut_ind.

Lemma complete_basic_type_not_ref te t : complete_basic_type te t → not_ref_type t.
Proof. by inversion 1. Qed.
Lemma complete_pointee_type_not_ref te t : complete_pointee_type te t → not_ref_type t.
Proof. induction 1; by [eapply complete_basic_type_not_ref | ]. Qed.

Lemma complete_type_not_ref_ref te t1 t2 : complete_type te t1 → ref_to_type t1 = Some t2 → not_ref_type t2.
Proof.
  induction 1 => Hsome; simplify_eq/=; generalize dependent te => te;
    try by [exact: complete_pointee_type_not_ref| tauto].
  move => /complete_basic_type_not_ref; naive_solver.
Qed.

Definition complete_type_table (te : type_table) :=
  map_Forall (fun _key d => valid_decl te d) te.

Definition complete_symbol_table (te : type_table) (syms : symbol_table) :=
  map_Forall (fun _key d => complete_pointee_type te (type_of_value d)) syms.

Definition complete_translation_unit (te : type_table) (syms : symbol_table) :=
  complete_type_table te /\ complete_symbol_table te syms.

(*
[global] Instance complete_type_table_dec te : Decision (complete_type_table te). Proof. apply: map_Forall_dec. (* unshelve eapply map_Forall_dec; try apply _. *)
*)

(*
TODOs for FM-216:
1. prove complete_type_table_dec above with an efficient checker.
2. add bool_decide (complete_type_table types = true) to translation_unit;
   that's automatically proof-irrelevant, and proofs are just cheap eq_refl.
3. add any helper lemmas, say for proving equality of translation_unit from
   equality of the relevant componets.

Twist: the "decision procedure" likely requires fuel; find how to adapt the
above plan. We'll likely end up with a boolean checker proven correct.

Question: do we need complete_symbol_table? This is not expected.

Goal: enable recursion on proofs of complete_type_table, e.g. for defining
anyR (FM-215).
*)