(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
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(*i $Id: inductive.mli 11301 2008-08-04 19:41:18Z herbelin $ i*)

(*i*)
open Names
open Univ
open Term
open Declarations
open Environ
(*i*)

(*s Extracting an inductive type from a construction *)

(* [find_m*type env sigma c] coerce [c] to an recursive type (I args).
   [find_rectype], [find_inductive] and [find_coinductive]
   respectively accepts any recursive type, only an inductive type and
   only a coinductive type.
   They raise [Not_found] if not convertible to a recursive type. *)

val find_rectype     : env -> types -> inductive * constr list
val find_inductive   : env -> types -> inductive * constr list
val find_coinductive : env -> types -> inductive * constr list

type mind_specif = mutual_inductive_body * one_inductive_body

(*s Fetching information in the environment about an inductive type.
    Raises [Not_found] if the inductive type is not found. *)
val lookup_mind_specif : env -> inductive -> mind_specif

(*s Functions to build standard types related to inductive *)
val ind_subst : mutual_inductive -> mutual_inductive_body -> constr list

val type_of_inductive : env -> mind_specif -> types

val elim_sorts : mind_specif -> sorts_family list

(* Return type as quoted by the user *)
val type_of_constructor : constructor -> mind_specif -> types

(* Return constructor types in normal form *)
val arities_of_constructors : inductive -> mind_specif -> types array

(* Return constructor types in user form *)
val type_of_constructors : inductive -> mind_specif -> types array

(* Transforms inductive specification into types (in nf) *)
val arities_of_specif : mutual_inductive -> mind_specif -> types array 


(* [type_case_branches env (I,args) (p:A) c] computes useful types
   about the following Cases expression:
      <p>Cases (c :: (I args)) of b1..bn end
   It computes the type of every branch (pattern variables are
   introduced by products), the type for the whole expression, and
   the universe constraints generated.
 *)
val type_case_branches :
  env -> inductive * constr list -> unsafe_judgment -> constr
    -> types array * types * constraints

(* Return the arity of an inductive type *)
val mind_arity : one_inductive_body -> Sign.rel_context * sorts_family

val inductive_sort_family : one_inductive_body -> sorts_family

(* Check a [case_info] actually correspond to a Case expression on the
   given inductive type. *)
val check_case_info : env -> inductive -> case_info -> unit

(*s Guard conditions for fix and cofix-points. *)
val check_fix : env -> fixpoint -> unit
val check_cofix : env -> cofixpoint -> unit

(*s Support for sort-polymorphic inductive types *)

val type_of_inductive_knowing_parameters :
  env -> one_inductive_body -> types array -> types

val max_inductive_sort : sorts array -> universe

val instantiate_universes : env -> Sign.rel_context ->
    polymorphic_arity -> types array -> Sign.rel_context * sorts

(***************************************************************)
(* Debug *)

type size = Large | Strict
type subterm_spec =
    Subterm of (size * wf_paths)
  | Dead_code
  | Not_subterm
type guard_env =
  { env     : env;
    (* dB of last fixpoint *)
    rel_min : int;
    (* inductive of recarg of each fixpoint *)
    inds    : inductive array;
    (* the recarg information of inductive family *)
    recvec  : wf_paths array;
    (* dB of variables denoting subterms *)
    genv    : subterm_spec list;
  }

val subterm_specif : guard_env -> constr -> subterm_spec
val case_branches_specif : guard_env -> subterm_spec -> inductive ->
  constr array -> (guard_env * constr) array
