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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
open Constr
open Environ
(***********************************************************************
s Reduction functions *)
(* None of these functions do eta reduction *)
val whd_betaiotazeta : env -> constr -> constr
val whd_all : env -> constr -> constr
val whd_allnolet : env -> constr -> constr
val whd_betaiota : env -> constr -> constr
val nf_betaiota : env -> constr -> constr
(***********************************************************************
s conversion functions *)
exception NotConvertible
type 'a kernel_conversion_function = env -> 'a -> 'a -> unit
type 'a extended_conversion_function =
?l2r:bool -> ?reds:TransparentState.t -> env ->
?evars:((existential->constr option) * UGraph.t) ->
'a -> 'a -> unit
type conv_pb = CONV | CUMUL
type 'a universe_compare =
{ (* Might raise NotConvertible *)
compare_sorts : env -> conv_pb -> Sorts.t -> Sorts.t -> 'a -> 'a;
compare_instances: flex:bool -> Univ.Instance.t -> Univ.Instance.t -> 'a -> 'a;
compare_cumul_instances : conv_pb -> Univ.Variance.t array ->
Univ.Instance.t -> Univ.Instance.t -> 'a -> 'a }
type 'a universe_state = 'a * 'a universe_compare
type ('a,'b) generic_conversion_function = env -> 'b universe_state -> 'a -> 'a -> 'b
type 'a infer_conversion_function = env -> UGraph.t -> 'a -> 'a -> Univ.Constraint.t
val get_cumulativity_constraints : conv_pb -> Univ.Variance.t array ->
Univ.Instance.t -> Univ.Instance.t -> Univ.Constraint.t
val inductive_cumulativity_arguments : (Declarations.mutual_inductive_body * int) -> int
val constructor_cumulativity_arguments : (Declarations.mutual_inductive_body * int * int) -> int
val sort_cmp_universes : env -> conv_pb -> Sorts.t -> Sorts.t ->
'a * 'a universe_compare -> 'a * 'a universe_compare
(* [flex] should be true for constants, false for inductive types and
constructors. *)
val convert_instances : flex:bool -> Univ.Instance.t -> Univ.Instance.t ->
'a * 'a universe_compare -> 'a * 'a universe_compare
(** These two never raise UnivInconsistency, inferred_universes
just gathers the constraints. *)
val checked_universes : UGraph.t universe_compare
val inferred_universes : (UGraph.t * Univ.Constraint.t) universe_compare
(** These two functions can only raise NotConvertible *)
val conv : constr extended_conversion_function
val conv_leq : types extended_conversion_function
(** These conversion functions are used by module subtyping, which needs to infer
universe constraints inside the kernel *)
val infer_conv : ?l2r:bool -> ?evars:(existential->constr option) ->
?ts:TransparentState.t -> constr infer_conversion_function
val infer_conv_leq : ?l2r:bool -> ?evars:(existential->constr option) ->
?ts:TransparentState.t -> types infer_conversion_function
(** Depending on the universe state functions, this might raise
[UniverseInconsistency] in addition to [NotConvertible] (for better error
messages). *)
val generic_conv : conv_pb -> l2r:bool -> (existential->constr option) ->
TransparentState.t -> (constr,'a) generic_conversion_function
val default_conv : conv_pb -> ?l2r:bool -> types kernel_conversion_function
val default_conv_leq : ?l2r:bool -> types kernel_conversion_function
(************************************************************************)
(** Builds an application node, reducing beta redexes it may produce. *)
val beta_applist : constr -> constr list -> constr
(** Builds an application node, reducing beta redexes it may produce. *)
val beta_appvect : constr -> constr array -> constr
(** Builds an application node, reducing beta redexe it may produce. *)
val beta_app : constr -> constr -> constr
(** Pseudo-reduction rule Prod(x,A,B) a --> B[x\a] *)
val hnf_prod_applist : env -> types -> constr list -> types
(** In [hnf_prod_applist_assum n c args], [c] is supposed to (whd-)reduce to
the form [∀Γ.t] with [Γ] of length [n] and possibly with let-ins; it
returns [t] with the assumptions of [Γ] instantiated by [args] and
the local definitions of [Γ] expanded. *)
val hnf_prod_applist_assum : env -> int -> types -> constr list -> types
(** Compatibility alias for Term.lambda_appvect_assum *)
val betazeta_appvect : int -> constr -> constr array -> constr
(***********************************************************************
s Recognizing products and arities modulo reduction *)
val dest_prod : env -> types -> Constr.rel_context * types
val dest_prod_assum : env -> types -> Constr.rel_context * types
val dest_lam : env -> constr -> Constr.rel_context * constr
val dest_lam_assum : env -> constr -> Constr.rel_context * constr
exception NotArity
val dest_arity : env -> types -> Term.arity (* raises NotArity if not an arity *)
val is_arity : env -> types -> bool
val eta_expand : env -> constr -> types -> constr
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