(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(* The following definitions are used by the function
   [assumptions] which gives as an output the set of all
   axioms and sections variables on which a given term depends
   in a context (expectingly the Global context) *)

(* Initial author: Arnaud Spiwack
   Module-traversing code: Pierre Letouzey *)

open Pp
open Errors
open Util
open Names
open Term
open Declarations
open Mod_subst
open Globnames

type context_object =
  | Variable of Id.t (* A section variable or a Let definition *)
  | Axiom of constant      (* An axiom or a constant. *)
  | Opaque of constant     (* An opaque constant. *)
  | Transparent of constant

(* Defines a set of [assumption] *)
module OrderedContextObject =
struct
  type t = context_object
  let compare x y =
      match x , y with
      | Variable i1 , Variable i2 -> Id.compare i1 i2
      | Axiom k1 , Axiom k2 -> con_ord k1 k2
      | Opaque k1 , Opaque k2 -> con_ord k1 k2
      | Transparent k1 , Transparent k2 -> con_ord k1 k2
      | Axiom _ , Variable _ -> 1
      | Opaque _ , Variable _
      | Opaque _ , Axiom _ -> 1
      | Transparent _ , Variable _
      | Transparent _ , Axiom _
      | Transparent _ , Opaque _ -> 1
      | _ , _ -> -1
end

module ContextObjectSet = Set.Make (OrderedContextObject)
module ContextObjectMap = Map.Make (OrderedContextObject)

(** For a constant c in a module sealed by an interface (M:T and
    not M<:T), [Global.lookup_constant] may return a [constant_body]
    without body. We fix this by looking in the implementation
    of the module *)

let modcache = ref (MPmap.empty : structure_body MPmap.t)

let rec search_mod_label lab = function
  | [] -> raise Not_found
  | (l, SFBmodule mb) :: _ when Label.equal l lab -> mb
  | _ :: fields -> search_mod_label lab fields

let rec search_cst_label lab = function
  | [] -> raise Not_found
  | (l, SFBconst cb) :: _ when Label.equal l lab -> cb
  | _ :: fields -> search_cst_label lab fields

(* TODO: using [empty_delta_resolver] below is probably slightly incorrect. But:
    a) I don't see currently what should be used instead
    b) this shouldn't be critical for Print Assumption. At worse some
       constants will have a canonical name which is non-canonical,
       leading to failures in [Global.lookup_constant], but our own
       [lookup_constant] should work.
*)

let rec fields_of_functor f subs mp0 args = function
  |NoFunctor a -> f subs mp0 args a
  |MoreFunctor (mbid,_,e) ->
    match args with
    | [] -> assert false (* we should only encounter applied functors *)
    | mpa :: args ->
      let subs = add_mbid mbid mpa empty_delta_resolver (*TODO*) subs in
      fields_of_functor f subs mp0 args e

let rec lookup_module_in_impl mp =
  try Global.lookup_module mp
  with Not_found ->
    (* The module we search might not be exported by its englobing module(s).
       We access the upper layer, and then do a manual search *)
    match mp with
      | MPfile _ | MPbound _ ->
	raise Not_found (* should have been found by [lookup_module] *)
      | MPdot (mp',lab') ->
	let fields = memoize_fields_of_mp mp' in
	search_mod_label lab' fields

and memoize_fields_of_mp mp =
  try MPmap.find mp !modcache
  with Not_found ->
    let l = fields_of_mp mp in
    modcache := MPmap.add mp l !modcache;
    l

and fields_of_mp mp =
  let mb = lookup_module_in_impl mp in
  let fields,inner_mp,subs = fields_of_mb empty_subst mb [] in
  let subs =
    if mp_eq inner_mp mp then subs
    else add_mp inner_mp mp mb.mod_delta subs
  in
  Modops.subst_structure subs fields

and fields_of_mb subs mb args = match mb.mod_expr with
  |Algebraic expr -> fields_of_expression subs mb.mod_mp args expr
  |Struct sign -> fields_of_signature subs mb.mod_mp args sign
  |Abstract|FullStruct -> fields_of_signature subs mb.mod_mp args mb.mod_type

(** The Abstract case above corresponds to [Declare Module] *)

and fields_of_signature x =
  fields_of_functor
    (fun subs mp0 args struc ->
      assert (List.is_empty args);
      (struc, mp0, subs)) x

and fields_of_expr subs mp0 args = function
  |MEident mp ->
    let mb = lookup_module_in_impl (subst_mp subs mp) in
    fields_of_mb subs mb args
  |MEapply (me1,mp2) -> fields_of_expr subs mp0 (mp2::args) me1
  |MEwith _ -> assert false (* no 'with' in [mod_expr] *)

and fields_of_expression x = fields_of_functor fields_of_expr x

let lookup_constant_in_impl cst fallback =
  try
    let mp,dp,lab = repr_kn (canonical_con cst) in
    let fields = memoize_fields_of_mp mp in
    (* A module found this way is necessarily closed, in particular
       our constant cannot be in an opened section : *)
    search_cst_label lab fields
  with Not_found ->
    (* Either:
       - The module part of the constant isn't registered yet :
         we're still in it, so the [constant_body] found earlier
         (if any) was a true axiom.
       - The label has not been found in the structure. This is an error *)
    match fallback with
      | Some cb -> cb
      | None -> anomaly (str "Print Assumption: unknown constant " ++ pr_con cst)

let lookup_constant cst =
  try
    let cb = Global.lookup_constant cst in
    if Declareops.constant_has_body cb then cb
    else lookup_constant_in_impl cst (Some cb)
  with Not_found -> lookup_constant_in_impl cst None

(** Graph traversal of an object, collecting on the way the dependencies of
    traversed objects *)
let rec traverse accu t = match kind_of_term t with
| Var id ->
  let body () = match Global.lookup_named id with (_, body, _) -> body in
  traverse_object accu body (VarRef id)
| Const (kn, _) ->
  let body () = Global.body_of_constant_body (lookup_constant kn) in
  traverse_object accu body (ConstRef kn)
| Ind (ind, _) ->
  traverse_object accu (fun () -> None) (IndRef ind)
| Construct (cst, _) ->
  traverse_object accu (fun () -> None) (ConstructRef cst)
| Meta _ | Evar _ -> assert false
| _ -> Constr.fold traverse accu t

and traverse_object (curr, data) body obj =
  let data =
    if Refmap.mem obj data then data
    else match body () with
    | None -> Refmap.add obj Refset.empty data
    | Some body ->
      let (contents, data) = traverse (Refset.empty, data) body in
      Refmap.add obj contents data
  in
  (Refset.add obj curr, data)

let traverse t =
  let () = modcache := MPmap.empty in
  traverse (Refset.empty, Refmap.empty) t

(** Hopefully bullet-proof function to recover the type of a constant. It just
    ignores all the universe stuff. There are many issues that can arise when
    considering terms out of any valid environment, so use with caution. *)
let type_of_constant cb = match cb.Declarations.const_type with
| Declarations.RegularArity ty -> ty
| Declarations.TemplateArity (ctx, arity) ->
  Term.mkArity (ctx, Sorts.sort_of_univ arity.Declarations.template_level)

let assumptions ?(add_opaque=false) ?(add_transparent=false) st t =
  let (idts, knst) = st in
  (** Only keep the transitive dependencies *)
  let (_, graph) = traverse t in
  let fold obj _ accu = match obj with
  | VarRef id ->
    let (_, body, t) = Global.lookup_named id in
    if Option.is_empty body then ContextObjectMap.add (Variable id) t accu
    else accu
  | ConstRef kn ->
    let cb = lookup_constant kn in
    if not (Declareops.constant_has_body cb) then
      let t = type_of_constant cb in
      ContextObjectMap.add (Axiom kn) t accu
    else if add_opaque && (Declareops.is_opaque cb || not (Cpred.mem kn knst)) then
      let t = type_of_constant cb in
      ContextObjectMap.add (Opaque kn) t accu
    else if add_transparent then
      let t = type_of_constant cb in
      ContextObjectMap.add (Transparent kn) t accu
    else
      accu
  | IndRef _ | ConstructRef _ -> accu
  in
  Refmap.fold fold graph ContextObjectMap.empty