Imported Upstream version 8.8.2upstream/8.8.2

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-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-open Names
-open Term
-
-(** This module defines the internal representation of global
-   declarations. This includes global constants/axioms, mutual
-   inductive definitions, modules and module types *)
-
-type set_predicativity = ImpredicativeSet | PredicativeSet
-
-type engagement = set_predicativity
-
-(** {6 Representation of constants (Definition/Axiom) } *)
-
-(** Non-universe polymorphic mode polymorphism (Coq 8.2+): inductives
-    and constants hiding inductives are implicitely polymorphic when
-    applied to parameters, on the universes appearing in the whnf of
-    their parameters and their conclusion, in a template style.
-    
-    In truely universe polymorphic mode, we always use RegularArity.
-*)
-
-type template_arity = {
-  template_param_levels : Univ.universe_level option list;
-  template_level : Univ.universe;
-}
-
-type ('a, 'b) declaration_arity = 
-  | RegularArity of 'a
-  | TemplateArity of 'b
-
-type constant_type = (types, Context.Rel.t * template_arity) declaration_arity
-
-(** 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 *)
-
-(** Projections are a particular kind of constant: 
-    always transparent. *)
-
-type projection_body = {
-  proj_ind : mutual_inductive;
-  proj_npars : int;
-  proj_arg : int;
-  proj_type : types; (* Type under params *)
-  proj_eta : constr * types; (* Eta-expanded term and type *)
-  proj_body : constr; (* For compatibility with VMs only, the match version *)
-}
-
-type constant_def =
-  | Undef of inline
-  | Def of constr Mod_subst.substituted
-  | OpaqueDef of Opaqueproof.opaque
-
-type constant_universes = Univ.universe_context
-
-(** The [typing_flags] are instructions to the type-checker which
-    modify its behaviour. The typing flags used in the type-checking
-    of a constant are tracked in their {!constant_body} so that they
-    can be displayed to the user. *)
-type typing_flags = {
-  check_guarded : bool; (** If [false] then fixed points and co-fixed
-                            points are assumed to be total. *)
-  check_universes : bool; (** If [false] universe constraints are not checked *)
-}
-
-(* some contraints are in constant_constraints, some other may be in
- * the OpaueDef *)
-type constant_body = {
-    const_hyps : Context.section_context; (** New: younger hyp at top *)
-    const_body : constant_def;
-    const_type : constant_type;
-    const_body_code : Cemitcodes.to_patch_substituted option;
-    const_polymorphic : bool; (** Is it polymorphic or not *)
-    const_universes : constant_universes;
-    const_proj : projection_body option;
-    const_inline_code : bool;
-    const_typing_flags : typing_flags; (** The typing options which
-                                           were used for
-                                           type-checking. *)
-}
-
-(** {6 Representation of mutual inductive types in the kernel } *)
-
-type recarg =
-  | Norec
-  | Mrec of inductive
-  | Imbr of inductive
-
-type wf_paths = recarg Rtree.t
-
-(**
-{v
-   Inductive I1 (params) : U1 := c11 : T11 | ... | c1p1 : T1p1
-   ...
-   with      In (params) : Un := cn1 : Tn1 | ... | cnpn : Tnpn
-v}
-*)
-
-(** Record information:
-    If the record is not primitive, then None
-    Otherwise, we get:
-    - The identifier for the binder name of the record in primitive projections.
-    - The constants associated to each projection.
-    - The checked projection bodies. *)
-
-type record_body = (Id.t * constant array * projection_body array) option
-
-type regular_inductive_arity = {
-  mind_user_arity : types;
-  mind_sort : sorts;
-}
-
-type inductive_arity = (regular_inductive_arity, template_arity) declaration_arity
-
-type one_inductive_body = {
-(** {8 Primitive datas } *)
-
-    mind_typename : Id.t; (** Name of the type: [Ii] *)
-
-    mind_arity_ctxt : Context.Rel.t; (** Arity context of [Ii] with parameters: [forall params, Ui] *)
-
-    mind_arity : inductive_arity; (** Arity sort and original user arity *)
-
-    mind_consnames : Id.t array; (** Names of the constructors: [cij] *)
-
-    mind_user_lc : types 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 *)
-
-(** {8 Derived datas } *)
-
-    mind_nrealargs : int; (** Number of expected real arguments of the type (no let, no params) *)
-
-    mind_nrealdecls : int; (** Length of realargs context (with let, no params) *)
-
-    mind_kelim : sorts_family list; (** List of allowed elimination sorts *)
-
-    mind_nf_lc : types array; (** Head normalized constructor types so that their conclusion exposes the inductive type *)
-
-    mind_consnrealargs : int array;
- (** Number of expected proper arguments of the constructors (w/o params) *)
-
-    mind_consnrealdecls : int array;
- (** Length of the signature of the constructors (with let, w/o params) *)
-
-    mind_recargs : wf_paths; (** Signature of recursive arguments in the constructors *)
-
-(** {8 Datas for bytecode compilation } *)
-
-    mind_nb_constant : int; (** number of constant constructor *)
-
-    mind_nb_args : int; (** number of no constant constructor *)
-
-    mind_reloc_tbl :  Cbytecodes.reloc_table;
-  }
-
-type mutual_inductive_body = {
-
-    mind_packets : one_inductive_body array;  (** The component of the mutual inductive block *)
-
-    mind_record : record_body option; (** The record information *)
-
-    mind_finite : Decl_kinds.recursivity_kind;  (** Whether the type is inductive or coinductive *)
-
-    mind_ntypes : int;  (** Number of types in the block *)
-
-    mind_hyps : Context.section_context;  (** Section hypotheses on which the block depends *)
-
-    mind_nparams : int;  (** Number of expected parameters including non-uniform ones (i.e. length of mind_params_ctxt w/o let-in) *)
-
-    mind_nparams_rec : int;  (** Number of recursively uniform (i.e. ordinary) parameters *)
-
-    mind_params_ctxt : Context.Rel.t;  (** The context of parameters (includes let-in declaration) *)
-
-    mind_polymorphic : bool; (** Is it polymorphic or not *)
-
-    mind_universes : Univ.universe_context; (** Local universe variables and constraints *)
-
-    mind_private : bool option; (** allow pattern-matching: Some true ok, Some false blocked *)
-
-    mind_typing_flags : typing_flags; (** typing flags at the time of the inductive creation *)
-}
-
-(** {6 Module declarations } *)
-
-(** Functor expressions are forced to be on top of other expressions *)
-
-type ('ty,'a) functorize =
-  | NoFunctor of 'a
-  | MoreFunctor of MBId.t * 'ty * ('ty,'a) functorize
-
-(** The fully-algebraic module expressions : names, applications, 'with ...'.
-    They correspond to the user entries of non-interactive modules.
-    They will be later expanded into module structures in [Mod_typing],
-    and won't play any role into the kernel after that : they are kept
-    only for short module printing and for extraction. *)
-
-type with_declaration =
-  | WithMod of Id.t list * module_path
-  | WithDef of Id.t list * constr Univ.in_universe_context
-
-type module_alg_expr =
-  | MEident of module_path
-  | MEapply of module_alg_expr * module_path
-  | MEwith of module_alg_expr * with_declaration
-
-(** A component of a module structure *)
-
-type structure_field_body =
-  | SFBconst of constant_body
-  | SFBmind of mutual_inductive_body
-  | SFBmodule of module_body
-  | SFBmodtype of module_type_body
-
-(** A module structure is a list of labeled components.
-
-    Note : we may encounter now (at most) twice the same label in
-    a [structure_body], once for a module ([SFBmodule] or [SFBmodtype])
-    and once for an object ([SFBconst] or [SFBmind]) *)
-
-and structure_body = (Label.t * structure_field_body) list
-
-(** A module signature is a structure, with possibly functors on top of it *)
-
-and module_signature = (module_type_body,structure_body) functorize
-
-(** A module expression is an algebraic expression, possibly functorized. *)
-
-and module_expression = (module_type_body,module_alg_expr) functorize
-
-and module_implementation =
-  | Abstract (** no accessible implementation *)
-  | Algebraic of module_expression (** non-interactive algebraic expression *)
-  | Struct of module_signature (** interactive body *)
-  | FullStruct (** special case of [Struct] : the body is exactly [mod_type] *)
-
-and module_body =
-  { mod_mp : module_path; (** absolute path of the module *)
-    mod_expr : module_implementation; (** implementation *)
-    mod_type : module_signature; (** expanded type *)
-    mod_type_alg : module_expression option; (** algebraic type *)
-    mod_constraints : Univ.ContextSet.t; (**
-      set of all universes constraints in the module  *)
-    mod_delta : Mod_subst.delta_resolver; (**
-      quotiented set of equivalent constants and inductive names *)
-    mod_retroknowledge : Retroknowledge.action list }
-
-(** For a module, there are five possible situations:
-    - [Declare Module M : T] then [mod_expr = Abstract; mod_type_alg = Some T]
-    - [Module M := E] then [mod_expr = Algebraic E; mod_type_alg = None]
-    - [Module M : T := E] then [mod_expr = Algebraic E; mod_type_alg = Some T]
-    - [Module M. ... End M] then [mod_expr = FullStruct; mod_type_alg = None]
-    - [Module M : T. ... End M] then [mod_expr = Struct; mod_type_alg = Some T]
-    And of course, all these situations may be functors or not. *)
-
-(** A [module_type_body] is just a [module_body] with no
-    implementation ([mod_expr] always [Abstract]) and also
-    an empty [mod_retroknowledge]. Its [mod_type_alg] contains
-    the algebraic definition of this module type, or [None]
-    if it has been built interactively. *)
-
-and module_type_body = module_body
-
-(** Extra invariants :
-
-    - No [MEwith] inside a [mod_expr] implementation : the 'with' syntax
-      is only supported for module types
-
-    - A module application is atomic, for instance ((M N) P) :
-      * the head of [MEapply] can only be another [MEapply] or a [MEident]
-      * the argument of [MEapply] is now directly forced to be a [module_path].
-*)