(** As a corollay, in a consistent environment, the rank of a composite type
  is strictly greater than the ranks of its member types. *)

Remark rank_type_members:
  forall ce id t m, In (id, t) m -> (rank_type ce t <= rank_members ce m)%nat.(** Functions can either be defined ([Internal]) or declared as
  external functions ([External]). *)

Inductive fundef : Type :=
  | Internal: F -> fundef
  | External: external_function -> typelist -> type -> calling_convention -> fundef.(** Functions can either be defined ([Internal]) or declared as
  external functions ([External]). *)

Inductive fundef : Type :=
  | Internal: F -> fundef
  | External: external_function -> typelist -> type -> calling_convention -> fundef.(** Functions can either be defined ([Internal]) or declared as
  external functions ([External]). *)

Inductive fundef : Type :=
  | Internal: F -> fundef
  | External: external_function -> typelist -> type -> calling_convention -> fundef.(** A program, or compilation unit, is composed of:
- a list of definitions of functions and global variables;
- the names of functions and global variables that are public (not static);
- the name of the function that acts as entry point ("main" function).
- a list of definitions for structure and union names
- the corresponding composite environment
- a proof that this environment is consistent with the definitions. *)

Record program : Type := {
  prog_defs: list (ident * globdef fundef type);
  prog_public: list ident;
  prog_main: ident;
  prog_types: list composite_definition;
  prog_comp_env: composite_env;
  prog_comp_env_eq: build_composite_env prog_types = OK prog_comp_env
}.(** A program, or compilation unit, is composed of:
- a list of definitions of functions and global variables;
- the names of functions and global variables that are public (not static);
- the name of the function that acts as entry point ("main" function).
- a list of definitions for structure and union names
- the corresponding composite environment
- a proof that this environment is consistent with the definitions. *)

Record program : Type := {
  prog_defs: list (ident * globdef fundef type);
  prog_public: list ident;
  prog_main: ident;
  prog_types: list composite_definition;
  prog_comp_env: composite_env;
  prog_comp_env_eq: build_composite_env prog_types = OK prog_comp_env
}.(** A program, or compilation unit, is composed of:
- a list of definitions of functions and global variables;
- the names of functions and global variables that are public (not static);
- the name of the function that acts as entry point ("main" function).
- a list of definitions for structure and union names
- the corresponding composite environment
- a proof that this environment is consistent with the definitions. *)

Record program : Type := {
  prog_defs: list (ident * globdef fundef type);
  prog_public: list ident;
  prog_main: ident;
  prog_types: list composite_definition;
  prog_comp_env: composite_env;
  prog_comp_env_eq: build_composite_env prog_types = OK prog_comp_env
}.(** A program, or compilation unit, is composed of:
- a list of definitions of functions and global variables;
- the names of functions and global variables that are public (not static);
- the name of the function that acts as entry point ("main" function).
- a list of definitions for structure and union names
- the corresponding composite environment
- a proof that this environment is consistent with the definitions. *)

Record program : Type := {
  prog_defs: list (ident * globdef fundef type);
  prog_public: list ident;
  prog_main: ident;
  prog_types: list composite_definition;
  prog_comp_env: composite_env;
  prog_comp_env_eq: build_composite_env prog_types = OK prog_comp_env
}.(** A program, or compilation unit, is composed of:
- a list of definitions of functions and global variables;
- the names of functions and global variables that are public (not static);
- the name of the function that acts as entry point ("main" function).
- a list of definitions for structure and union names
- the corresponding composite environment
- a proof that this environment is consistent with the definitions. *)

Record program : Type := {
  prog_defs: list (ident * globdef fundef type);
  prog_public: list ident;
  prog_main: ident;
  prog_types: list composite_definition;
  prog_comp_env: composite_env;
  prog_comp_env_eq: build_composite_env prog_types = OK prog_comp_env
}.(** A program, or compilation unit, is composed of:
- a list of definitions of functions and global variables;
- the names of functions and global variables that are public (not static);
- the name of the function that acts as entry point ("main" function).
- a list of definitions for structure and union names
- the corresponding composite environment
- a proof that this environment is consistent with the definitions. *)

Record program : Type := {
  prog_defs: list (ident * globdef fundef type);
  prog_public: list ident;
  prog_main: ident;
  prog_types: list composite_definition;
  prog_comp_env: composite_env;
  prog_comp_env_eq: build_composite_env prog_types = OK prog_comp_env
}.(** A program, or compilation unit, is composed of:
- a list of definitions of functions and global variables;
- the names of functions and global variables that are public (not static);
- the name of the function that acts as entry point ("main" function).
- a list of definitions for structure and union names
- the corresponding composite environment
- a proof that this environment is consistent with the definitions. *)

Record program : Type := {
  prog_defs: list (ident * globdef fundef type);
  prog_public: list ident;
  prog_main: ident;
  prog_types: list composite_definition;
  prog_comp_env: composite_env;
  prog_comp_env_eq: build_composite_env prog_types = OK prog_comp_env
}.Definition program_of_program (p: program) : AST.program fundef type :=
  {| AST.prog_defs := p.(prog_defs);
     AST.prog_public := p.(prog_public);
     AST.prog_main := p.(prog_main) |}.Program Definition make_program (types: list composite_definition)
                                (defs: list (ident * globdef fundef type))
                                (public: list ident)
                                (main: ident) : res program :=
  match build_composite_env types with
  | Error e => Error e
  | OK ce =>
      OK {| prog_defs := defs;
            prog_public := public;
            prog_main := main;
            prog_types := types;
            prog_comp_env := ce;
            prog_comp_env_eq := _ |}
  end.(** * Separate compilation and linking *)

(** ** Linking types *)

Program Instance Linker_types : Linker type := {
  link := fun t1 t2 => if type_eq t1 t2 then Some t1 else None;
  linkorder := fun t1 t2 => t1 = t2
}.(** ** Linking composite definitions *)

Definition check_compat_composite (l: list composite_definition) (cd: composite_definition) : bool :=
  List.forallb
    (fun cd' =>
      if ident_eq (name_composite_def cd') (name_composite_def cd) then composite_def_eq cd cd' else true)
    l.Definition filter_redefs (l1 l2: list composite_definition) :=
  let names1 := map name_composite_def l1 in
  List.filter (fun cd => negb (In_dec ident_eq (name_composite_def cd) names1)) l2.Definition link_composite_defs (l1 l2: list composite_definition): option (list composite_definition) :=
  if List.forallb (check_compat_composite l2) l1
  then Some (l1 ++ filter_redefs l1 l2)
  else None.

(* Specifications: *)
Lemma link_composite_def_inv: forall l1 l2 l, link_composite_defs l1 l2 = Some l -> (forall cd1 cd2, In cd1 l1 -> In cd2 l2 -> name_composite_def cd2 = name_composite_def cd1 -> cd2 = cd1) /\ l = l1 ++ filter_redefs l1 l2 /\ (forall x, In x l <-> In x l1 \/ In x l2).