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inductiveops.mli
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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
open Names
open Term
open Declarations
open Environ
open Evd
(** The following three functions are similar to the ones defined in
Inductive, but they expect an env *)
val type_of_inductive : env -> pinductive -> types
(** Return type as quoted by the user *)
val type_of_constructor : env -> pconstructor -> types
val type_of_constructors : env -> pinductive -> types array
(** Return constructor types in normal form *)
val arities_of_constructors : env -> pinductive -> types array
(** An inductive type with its parameters (transparently supports
reasoning either with only recursively uniform parameters or with all
parameters including the recursively non-uniform ones *)
type inductive_family
val make_ind_family : inductive puniverses * constr list -> inductive_family
val dest_ind_family : inductive_family -> inductive puniverses * constr list
val map_ind_family : (constr -> constr) -> inductive_family -> inductive_family
val liftn_inductive_family : int -> int -> inductive_family -> inductive_family
val lift_inductive_family : int -> inductive_family -> inductive_family
val substnl_ind_family :
constr list -> int -> inductive_family -> inductive_family
(** An inductive type with its parameters and real arguments *)
type inductive_type = IndType of inductive_family * EConstr.constr list
val make_ind_type : inductive_family * EConstr.constr list -> inductive_type
val dest_ind_type : inductive_type -> inductive_family * EConstr.constr list
val map_inductive_type : (EConstr.constr -> EConstr.constr) -> inductive_type -> inductive_type
val liftn_inductive_type : int -> int -> inductive_type -> inductive_type
val lift_inductive_type : int -> inductive_type -> inductive_type
val substnl_ind_type : EConstr.constr list -> int -> inductive_type -> inductive_type
val mkAppliedInd : inductive_type -> EConstr.constr
val mis_is_recursive_subset : int list -> wf_paths -> bool
val mis_is_recursive :
inductive * mutual_inductive_body * one_inductive_body -> bool
val mis_nf_constructor_type :
pinductive * mutual_inductive_body * one_inductive_body -> int -> constr
(** {6 Extract information from an inductive name} *)
(** @return number of constructors *)
val nconstructors : inductive -> int
val nconstructors_env : env -> inductive -> int
(** @return arity of constructors excluding parameters, excluding local defs *)
val constructors_nrealargs : inductive -> int array
val constructors_nrealargs_env : env -> inductive -> int array
(** @return arity of constructors excluding parameters, including local defs *)
val constructors_nrealdecls : inductive -> int array
val constructors_nrealdecls_env : env -> inductive -> int array
(** @return the arity, excluding params, excluding local defs *)
val inductive_nrealargs : inductive -> int
val inductive_nrealargs_env : env -> inductive -> int
(** @return the arity, excluding params, including local defs *)
val inductive_nrealdecls : inductive -> int
val inductive_nrealdecls_env : env -> inductive -> int
(** @return the arity, including params, excluding local defs *)
val inductive_nallargs : inductive -> int
val inductive_nallargs_env : env -> inductive -> int
(** @return the arity, including params, including local defs *)
val inductive_nalldecls : inductive -> int
val inductive_nalldecls_env : env -> inductive -> int
(** @return nb of params without local defs *)
val inductive_nparams : inductive -> int
val inductive_nparams_env : env -> inductive -> int
(** @return nb of params with local defs *)
val inductive_nparamdecls : inductive -> int
val inductive_nparamdecls_env : env -> inductive -> int
(** @return params context *)
val inductive_paramdecls : pinductive -> Context.Rel.t
val inductive_paramdecls_env : env -> pinductive -> Context.Rel.t
(** @return full arity context, hence with letin *)
val inductive_alldecls : pinductive -> Context.Rel.t
val inductive_alldecls_env : env -> pinductive -> Context.Rel.t
(** {7 Extract information from a constructor name} *)
(** @return param + args without letin *)
val constructor_nallargs : constructor -> int
val constructor_nallargs_env : env -> constructor -> int
(** @return param + args with letin *)
val constructor_nalldecls : constructor -> int
val constructor_nalldecls_env : env -> constructor -> int
(** @return args without letin *)
val constructor_nrealargs : constructor -> int
val constructor_nrealargs_env : env -> constructor -> int
(** @return args with letin *)
val constructor_nrealdecls : constructor -> int
val constructor_nrealdecls_env : env -> constructor -> int
(** Is there local defs in params or args ? *)
val constructor_has_local_defs : constructor -> bool
val inductive_has_local_defs : inductive -> bool
val allowed_sorts : env -> inductive -> sorts_family list
(** (Co)Inductive records with primitive projections do not have eta-conversion,
hence no dependent elimination. *)
val has_dependent_elim : mutual_inductive_body -> bool
(** Primitive projections *)
val projection_nparams : projection -> int
val projection_nparams_env : env -> projection -> int
val type_of_projection_knowing_arg : env -> evar_map -> Projection.t ->
EConstr.t -> EConstr.types -> types
(** Extract information from an inductive family *)
type constructor_summary = {
cs_cstr : pconstructor; (* internal name of the constructor plus universes *)
cs_params : constr list; (* parameters of the constructor in current ctx *)
cs_nargs : int; (* length of arguments signature (letin included) *)
cs_args : Context.Rel.t; (* signature of the arguments (letin included) *)
cs_concl_realargs : constr array; (* actual realargs in the concl of cstr *)
}
val lift_constructor : int -> constructor_summary -> constructor_summary
val get_constructor :
pinductive * mutual_inductive_body * one_inductive_body * constr list ->
int -> constructor_summary
val get_constructors : env -> inductive_family -> constructor_summary array
val get_projections : env -> inductive_family -> constant array option
(** [get_arity] returns the arity of the inductive family instantiated
with the parameters; if recursively non-uniform parameters are not
part of the inductive family, they appears in the arity *)
val get_arity : env -> inductive_family -> Context.Rel.t * sorts_family
val build_dependent_constructor : constructor_summary -> constr
val build_dependent_inductive : env -> inductive_family -> constr
val make_arity_signature : env -> evar_map -> bool -> inductive_family -> EConstr.rel_context
val make_arity : env -> evar_map -> bool -> inductive_family -> sorts -> EConstr.types
val build_branch_type : env -> evar_map -> bool -> constr -> constructor_summary -> types
(** Raise [Not_found] if not given a valid inductive type *)
val extract_mrectype : evar_map -> EConstr.t -> (inductive * EConstr.EInstance.t) * EConstr.constr list
val find_mrectype : env -> evar_map -> EConstr.types -> (inductive * EConstr.EInstance.t) * EConstr.constr list
val find_mrectype_vect : env -> evar_map -> EConstr.types -> (inductive * EConstr.EInstance.t) * EConstr.constr array
val find_rectype : env -> evar_map -> EConstr.types -> inductive_type
val find_inductive : env -> evar_map -> EConstr.types -> (inductive * EConstr.EInstance.t) * constr list
val find_coinductive : env -> evar_map -> EConstr.types -> (inductive * EConstr.EInstance.t) * constr list
(********************)
(** Builds the case predicate arity (dependent or not) *)
val arity_of_case_predicate :
env -> inductive_family -> bool -> sorts -> types
val type_case_branches_with_names :
env -> evar_map -> pinductive * EConstr.constr list -> constr -> constr -> types array * types
(** Annotation for cases *)
val make_case_info : env -> inductive -> case_style -> case_info
(** Make a case or substitute projections if the inductive type is a record
with primitive projections.
Fail with an error if the elimination is dependent while the
inductive type does not allow dependent elimination. *)
val make_case_or_project :
env -> evar_map -> inductive_family -> case_info ->
(* pred *) EConstr.constr -> (* term *) EConstr.constr -> (* branches *) EConstr.constr array -> EConstr.constr
(*i Compatibility
val make_default_case_info : env -> case_style -> inductive -> case_info
i*)
(********************)
val type_of_inductive_knowing_conclusion :
env -> evar_map -> Inductive.mind_specif puniverses -> EConstr.types -> evar_map * EConstr.types
(********************)
val control_only_guard : env -> types -> unit
(* inference of subtyping condition for inductive types *)
(* for debugging purposes only to be removed *)
val infer_inductive_subtyping_arity_constructor : Environ.env * Evd.evar_map * Univ.Constraint.t ->
(Term.constr -> Term.constr) ->
Term.types -> bool -> Context.Rel.t -> Environ.env * Evd.evar_map * Univ.Constraint.t
val infer_inductive_subtyping : Environ.env -> Evd.evar_map -> Entries.mutual_inductive_entry ->
Entries.mutual_inductive_entry