(************************************************************************)
(*  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: reduction.mli 10840 2008-04-23 21:29:34Z herbelin $ i*)

(*i*)
open Term
open Environ
open Closure
(*i*)

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(*s Reduction functions *)

val whd_betaiotazeta        : constr -> constr
val whd_betadeltaiota       : env -> constr -> constr
val whd_betadeltaiota_nolet : env -> constr -> constr

val nf_betaiota      : constr -> constr

(************************************************************************)
(*s conversion functions *)

exception NotConvertible
exception NotConvertibleVect of int
type 'a conversion_function = env -> 'a -> 'a -> Univ.constraints
type 'a trans_conversion_function = Names.transparent_state -> env -> 'a -> 'a -> Univ.constraints

type conv_pb = CONV | CUMUL

val sort_cmp : 
    conv_pb -> sorts -> sorts -> Univ.constraints -> Univ.constraints

val conv_sort      : sorts conversion_function
val conv_sort_leq  : sorts conversion_function

val trans_conv_cmp       : conv_pb -> constr trans_conversion_function

val trans_conv           : constr trans_conversion_function
val trans_conv_leq       : types trans_conversion_function

val conv_cmp       : conv_pb -> constr conversion_function

val conv           : constr conversion_function
val conv_leq       : types conversion_function
val conv_leq_vecti : types array conversion_function

(* option for conversion *)
val set_vm_conv : (conv_pb -> types conversion_function) -> unit
val vm_conv : conv_pb -> types conversion_function

val set_default_conv : (conv_pb -> types conversion_function) -> unit
val default_conv     : conv_pb -> types conversion_function
val default_conv_leq : types conversion_function

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(* Builds an application node, reducing beta redexes it may produce. *) 
val beta_appvect : constr -> constr array -> constr

(* Pseudo-reduction rule  Prod(x,A,B) a --> B[x\a] *)
val hnf_prod_applist : env -> types -> constr list -> types


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(*s Recognizing products and arities modulo reduction *)

val dest_prod       : env -> types -> Sign.rel_context * types
val dest_prod_assum : env -> types -> Sign.rel_context * types

val dest_arity : env -> types -> Sign.arity
val is_arity   : env -> types -> bool