(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(* This file is a late renaming in May 2000 of constant.ml which
   itself was made for V7.0 in Aug 1999 out of a dispatch by
   Jean-Christophe Filliâtre of Chet Murthy's constants.ml in V5.10.5
   into cooking.ml, declare.ml and constant.ml, ...; renaming done
   because the new contents exceeded in extent what the name
   suggested *)
(* Cleaning and lightening of the kernel by Bruno Barras, Nov 2001 *)
(* Declarations for the module systems added by Jacek Chrzaszcz, Aug 2002 *)
(* Miscellaneous extensions, cleaning or restructurations by Bruno
   Barras, Hugo Herbelin, Jean-Christophe Filliâtre, Pierre Letouzey *)

(* This module defines the types of global declarations. This includes
   global constants/axioms, mutual inductive definitions and the
   module system *)

open Errors
open Util
open Names
open Univ
open Term
open Sign
open Mod_subst

type engagement = ImpredicativeSet

(*s Constants (internal representation) (Definition/Axiom) *)

type polymorphic_arity = {
  poly_param_levels : universe option list;
  poly_level : universe;
}

type constant_type =
  | NonPolymorphicType of types
  | PolymorphicArity of rel_context * polymorphic_arity

type constr_substituted = constr substituted

let from_val = from_val

let force = force subst_mps

let subst_constr_subst = subst_substituted

(** Opaque proof terms are not loaded immediately, but are there
    in a lazy form. Forcing this lazy may trigger some unmarshal of
    the necessary structure. The ['a substituted] type isn't really great
    here, so we store "manually" a substitution list, the younger one at top.
*)

type lazy_constr = constr_substituted Lazy.t * substitution list

let force_lazy_constr (c,l) =
  List.fold_right subst_constr_subst l (Lazy.force c)

let lazy_constr_is_val (c,_) = Lazy.lazy_is_val c

let make_lazy_constr c = (c, [])

let force_opaque lc = force (force_lazy_constr lc)

let opaque_from_val c = (Lazy.lazy_from_val (from_val c), [])

let subst_lazy_constr sub (c,l) = (c,sub::l)

(** Inlining level of parameters at functor applications.
    None means no inlining *)

type inline = int option

(** A constant can have no body (axiom/parameter), or a
    transparent body, or an opaque one *)

type 'a constant_def =
  | Undef of inline
  | Def of 'a
  | OpaqueDef of lazy_constr
  | Primitive of Native.op

type native_name =
  | Linked of string
  | LinkedLazy of string
  | LinkedInteractive of string
  | NotLinked

type constant_body = {
    const_hyps : section_context; (* New: younger hyp at top *)
    const_body : constr_substituted constant_def;
    const_type : constant_type;
    const_body_code : Cemitcodes.to_patch_substituted;
    const_constraints : constraints;
    const_native_name : native_name ref;
    const_inline_code : bool }

let body_of_constant cb = match cb.const_body with
  | Undef _ -> None
  | Def c -> Some c
  | OpaqueDef lc -> Some (force_lazy_constr lc)
  | Primitive _ -> None

let constant_has_body cb = match cb.const_body with
  | Undef _ | Primitive _ -> false
  | Def _ | OpaqueDef _ -> true

let is_opaque cb = match cb.const_body with
  | OpaqueDef _ -> true
  | Undef _ | Def _ | Primitive _ -> false

(* Substitutions of [constant_body] *)

let subst_rel_declaration sub (id,copt,t as x) =
  let copt' = Option.smartmap (subst_mps sub) copt in
  let t' = subst_mps sub t in
  if copt == copt' & t == t' then x else (id,copt',t')

let subst_rel_context sub = list_smartmap (subst_rel_declaration sub)

(* TODO: these substitution functions could avoid duplicating things
   when the substitution have preserved all the fields *)

let subst_const_type sub arity =
  if is_empty_subst sub then arity
  else match arity with
    | NonPolymorphicType s -> NonPolymorphicType (subst_mps sub s)
    | PolymorphicArity (ctx,s) -> PolymorphicArity (subst_rel_context sub ctx,s)

let subst_const_def sub = function
  | Undef inl -> Undef inl
  | Def c -> Def (subst_constr_subst sub c)
  | OpaqueDef lc -> OpaqueDef (subst_lazy_constr sub lc)
  | Primitive op -> Primitive op

let subst_const_body sub cb = {
  const_hyps = (assert (cb.const_hyps=[]); []);
  const_body = subst_const_def sub cb.const_body;
  const_type = subst_const_type sub cb.const_type;
  const_body_code = Cemitcodes.subst_to_patch_subst sub cb.const_body_code;
  const_constraints = cb.const_constraints;
  const_native_name = ref NotLinked;
  const_inline_code = cb.const_inline_code }

(* Hash-consing of [constant_body] *)

let hcons_rel_decl ((n,oc,t) as d) =
  let n' = hcons_name n
  and oc' = Option.smartmap hcons_constr oc
  and t' = hcons_types t
  in if n' == n && oc' == oc && t' == t then d else (n',oc',t')

let hcons_rel_context l = list_smartmap hcons_rel_decl l

let hcons_polyarity ar =
  { poly_param_levels =
      list_smartmap (Option.smartmap hcons_univ) ar.poly_param_levels;
    poly_level = hcons_univ ar.poly_level }

let hcons_const_type = function
  | NonPolymorphicType t ->
    NonPolymorphicType (hcons_constr t)
  | PolymorphicArity (ctx,s) ->
    PolymorphicArity (hcons_rel_context ctx, hcons_polyarity s)

let hcons_const_def = function
  | Undef inl -> Undef inl
  | Def l_constr ->
    let constr = force l_constr in
    Def (from_val (hcons_constr constr))
  | OpaqueDef lc ->
    if lazy_constr_is_val lc then
      let constr = force_opaque lc in
      OpaqueDef (opaque_from_val (hcons_constr constr))
    else OpaqueDef lc

let hcons_const_body cb =
  { cb with
    const_body = hcons_const_def cb.const_body;
    const_type = hcons_const_type cb.const_type;
    const_constraints = hcons_constraints cb.const_constraints }


(*s Inductive types (internal representation with redundant
    information). *)

type recarg =
  | Norec
  | Mrec of inductive
  | Imbr of inductive

let subst_recarg sub r = match r with
  | Norec -> r
  | Mrec (kn,i) -> let kn' = subst_ind sub kn in
      if kn==kn' then r else Mrec (kn',i)
  | Imbr (kn,i) -> let kn' = subst_ind sub kn in
      if kn==kn' then r else Imbr (kn',i)

type wf_paths = recarg Rtree.t

let mk_norec = Rtree.mk_node Norec [||]

let mk_paths r recargs =
  Rtree.mk_node r
    (Array.map (fun l -> Rtree.mk_node Norec (Array.of_list l)) recargs)

let dest_recarg p = fst (Rtree.dest_node p)

(* dest_subterms returns the sizes of each argument of each constructor of
   an inductive object of size [p]. This should never be done for Norec,
   because the number of sons does not correspond to the number of
   constructors.
 *)
let dest_subterms p =
  let (ra,cstrs) = Rtree.dest_node p in
  assert (ra<>Norec);
  Array.map (fun t -> Array.to_list (snd (Rtree.dest_node t))) cstrs

let recarg_length p j =
  let (_,cstrs) = Rtree.dest_node p in
  Array.length (snd (Rtree.dest_node cstrs.(j-1)))

let subst_wf_paths sub p = Rtree.smartmap (subst_recarg sub) p

(**********************************************************************)
(* Representation of mutual inductive types in the kernel             *)
(*
   Inductive I1 (params) : U1 := c11 : T11 | ... | c1p1 : T1p1
   ...
   with      In (params) : Un := cn1 : Tn1 | ... | cnpn : Tnpn
*)

type monomorphic_inductive_arity = {
  mind_user_arity : constr;
  mind_sort : sorts;
}

type inductive_arity =
| Monomorphic of monomorphic_inductive_arity
| Polymorphic of polymorphic_arity

type one_inductive_body = {

(* Primitive datas *)

 (* Name of the type: [Ii] *)
    mind_typename : identifier;

 (* Arity context of [Ii] with parameters: [forall params, Ui] *)
    mind_arity_ctxt : rel_context;

 (* Arity sort, original user arity, and allowed elim sorts, if monomorphic *)
    mind_arity : inductive_arity;

 (* Names of the constructors: [cij] *)
    mind_consnames : identifier array;

 (* Types of the constructors with parameters: [forall params, Tij],
    where the Ik are replaced by de Bruijn index in the context
    I1:forall params, U1 ..  In:forall params, Un *)
    mind_user_lc : types array;

(* Derived datas *)

 (* Number of expected real arguments of the type (no let, no params) *)
    mind_nrealargs : int;

 (* Length of realargs context (with let, no params) *)
    mind_nrealargs_ctxt : int;

 (* List of allowed elimination sorts *)
    mind_kelim : sorts_family list;

 (* Head normalized constructor types so that their conclusion is atomic *)
    mind_nf_lc : types array;

 (* Length of the signature of the constructors (with let, w/o params) *)
    mind_consnrealdecls : int array;

 (* Signature of recursive arguments in the constructors *)
    mind_recargs : wf_paths;

(* Datas for bytecode compilation *)

 (* number of constant constructor *)
    mind_nb_constant : int;

 (* number of no constant constructor *)
    mind_nb_args : int;

    mind_reloc_tbl :  Cbytecodes.reloc_table;

  }

type mutual_inductive_body = {

  (* The component of the mutual inductive block *)
    mind_packets : one_inductive_body array;

  (* Whether the inductive type has been declared as a record *)
    mind_record : bool;

  (* Whether the type is inductive or coinductive *)
    mind_finite : bool;

  (* Number of types in the block *)
    mind_ntypes : int;

  (* Section hypotheses on which the block depends *)
    mind_hyps : section_context;

  (* Number of expected parameters *)
    mind_nparams : int;

  (* Number of recursively uniform (i.e. ordinary) parameters *)
    mind_nparams_rec : int;

  (* The context of parameters (includes let-in declaration) *)
    mind_params_ctxt : rel_context;

  (* Universes constraints enforced by the inductive declaration *)
    mind_constraints : constraints;

  (* Data for native compilation *)
  (* Status of the code (linked or not, and where) *)
    mind_native_name : native_name ref;

  }

let subst_indarity sub = function
| Monomorphic s ->
    Monomorphic {
      mind_user_arity = subst_mps sub s.mind_user_arity;
      mind_sort = s.mind_sort;
    }
| Polymorphic s as x -> x

let subst_mind_packet sub mbp =
  { mind_consnames = mbp.mind_consnames;
    mind_consnrealdecls = mbp.mind_consnrealdecls;
    mind_typename = mbp.mind_typename;
    mind_nf_lc = array_smartmap (subst_mps sub) mbp.mind_nf_lc;
    mind_arity_ctxt = subst_rel_context sub mbp.mind_arity_ctxt;
    mind_arity = subst_indarity sub mbp.mind_arity;
    mind_user_lc = array_smartmap (subst_mps sub) mbp.mind_user_lc;
    mind_nrealargs = mbp.mind_nrealargs;
    mind_nrealargs_ctxt = mbp.mind_nrealargs_ctxt;
    mind_kelim = mbp.mind_kelim;
    mind_recargs = subst_wf_paths sub mbp.mind_recargs (*wf_paths*);
    mind_nb_constant = mbp.mind_nb_constant;
    mind_nb_args = mbp.mind_nb_args;
    mind_reloc_tbl = mbp.mind_reloc_tbl }

let subst_mind sub mib =
  { mind_record = mib.mind_record ;
    mind_finite = mib.mind_finite ;
    mind_ntypes = mib.mind_ntypes ;
    mind_hyps = (assert (mib.mind_hyps=[]); []) ;
    mind_nparams = mib.mind_nparams;
    mind_nparams_rec = mib.mind_nparams_rec;
    mind_params_ctxt =
      map_rel_context (subst_mps sub) mib.mind_params_ctxt;
    mind_packets = array_smartmap (subst_mind_packet sub) mib.mind_packets ;
    mind_constraints = mib.mind_constraints;
    mind_native_name = ref NotLinked }

let hcons_indarity = function
  | Monomorphic a ->
    Monomorphic { mind_user_arity = hcons_constr a.mind_user_arity;
		  mind_sort = hcons_sorts a.mind_sort }
  | Polymorphic a -> Polymorphic (hcons_polyarity a)

let hcons_mind_packet oib =
 { oib with
   mind_typename = hcons_ident oib.mind_typename;
   mind_arity_ctxt = hcons_rel_context oib.mind_arity_ctxt;
   mind_arity = hcons_indarity oib.mind_arity;
   mind_consnames = array_smartmap hcons_ident oib.mind_consnames;
   mind_user_lc = array_smartmap hcons_types oib.mind_user_lc;
   mind_nf_lc = array_smartmap hcons_types oib.mind_nf_lc }

let hcons_mind mib =
  { mib with
    mind_packets = array_smartmap hcons_mind_packet mib.mind_packets;
    mind_params_ctxt = hcons_rel_context mib.mind_params_ctxt;
    mind_constraints = hcons_constraints mib.mind_constraints }

(*s Modules: signature component specifications, module types, and
  module declarations *)

type structure_field_body =
  | SFBconst of constant_body
  | SFBmind of mutual_inductive_body
  | SFBmodule of module_body
  | SFBmodtype of module_type_body

and structure_body = (label * structure_field_body) list

and struct_expr_body =
  | SEBident of module_path
  | SEBfunctor of mod_bound_id * module_type_body * struct_expr_body
  | SEBapply of struct_expr_body * struct_expr_body * constraints
  | SEBstruct of structure_body
  | SEBwith of struct_expr_body * with_declaration_body

and with_declaration_body =
    With_module_body of identifier list * module_path
  | With_definition_body of  identifier list * constant_body

and module_body =
    { mod_mp : module_path;
      mod_expr : struct_expr_body option; 
      mod_type : struct_expr_body;
      mod_type_alg : struct_expr_body option;
      mod_constraints : constraints;
      mod_delta : delta_resolver;
      mod_retroknowledge :  (Native.retro_action * constr) list 
    }

and module_type_body =
    { typ_mp : module_path;
      typ_expr : struct_expr_body;
      typ_expr_alg : struct_expr_body option ;
      typ_constraints : constraints;
      typ_delta :delta_resolver}
