Inductiveops (coq-core.Inductiveops)

val type_of_inductive : Environ.env -> Constr.pinductive -> Constr.types

val e_type_of_inductive : 
  Environ.env ->
  Evd.evar_map ->
  Names.inductive EConstr.puniverses ->
  EConstr.types

val type_of_constructor : Environ.env -> Constr.pconstructor -> Constr.types

Return type as quoted by the user

val e_type_of_constructor : 
  Environ.env ->
  Evd.evar_map ->
  Names.constructor EConstr.puniverses ->
  EConstr.types

val type_of_constructors : 
  Environ.env ->
  Constr.pinductive ->
  Constr.types array

val arities_of_constructors : 
  Environ.env ->
  Constr.pinductive ->
  Constr.types array

Return constructor types in normal form

type inductive_family

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

val make_ind_family : 
  (Names.inductive Univ.puniverses * Constr.constr list) ->
  inductive_family

val dest_ind_family : 
  inductive_family ->
  Names.inductive Univ.puniverses * Constr.constr list

val map_ind_family : 
  ( Constr.constr -> 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.constr list ->
  int ->
  inductive_family ->
  inductive_family

val relevance_of_inductive_family : 
  Environ.env ->
  inductive_family ->
  Sorts.relevance

type inductive_type =

| IndType of inductive_family * EConstr.constr list

An inductive type with its parameters and real arguments

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 ind_of_ind_type : inductive_type -> Names.inductive

val relevance_of_inductive_type : 
  Environ.env ->
  inductive_type ->
  Sorts.relevance

val mkAppliedInd : inductive_type -> EConstr.constr

val mis_is_recursive_subset : int list -> Declarations.wf_paths -> bool

val mis_is_recursive : 
  (Names.inductive
   * Declarations.mutual_inductive_body
   * Declarations.one_inductive_body) ->
  bool

val mis_nf_constructor_type : 
  Constr.pconstructor ->
  (Declarations.mutual_inductive_body * Declarations.one_inductive_body) ->
  Constr.constr

Extract information from an inductive name

val nconstructors : Environ.env -> Names.inductive -> int

returns
number of constructors

val nconstructors_env : Environ.env -> Names.inductive -> int

val constructors_nrealargs : Environ.env -> Names.inductive -> int array

returns
arity of constructors excluding parameters, excluding local defs

val constructors_nrealargs_env : Environ.env -> Names.inductive -> int array

val constructors_nrealdecls : Environ.env -> Names.inductive -> int array

returns
arity of constructors excluding parameters, including local defs

val constructors_nrealdecls_env : Environ.env -> Names.inductive -> int array

val inductive_nrealargs : Environ.env -> Names.inductive -> int

returns
the arity, excluding params, excluding local defs

val inductive_nrealargs_env : Environ.env -> Names.inductive -> int

val inductive_nrealdecls : Environ.env -> Names.inductive -> int

returns
the arity, excluding params, including local defs

val inductive_nrealdecls_env : Environ.env -> Names.inductive -> int

val inductive_nallargs : Environ.env -> Names.inductive -> int

returns
the arity, including params, excluding local defs

val inductive_nallargs_env : Environ.env -> Names.inductive -> int

val inductive_nalldecls : Environ.env -> Names.inductive -> int

returns
the arity, including params, including local defs

val inductive_nalldecls_env : Environ.env -> Names.inductive -> int

val inductive_nparams : Environ.env -> Names.inductive -> int

returns
nb of params without local defs

val inductive_nparams_env : Environ.env -> Names.inductive -> int

val inductive_nparamdecls : Environ.env -> Names.inductive -> int

returns
nb of params with local defs

val inductive_nparamdecls_env : Environ.env -> Names.inductive -> int

val inductive_paramdecls : 
  Environ.env ->
  Constr.pinductive ->
  Constr.rel_context

returns
params context

val inductive_paramdecls_env : 
  Environ.env ->
  Constr.pinductive ->
  Constr.rel_context

val inductive_alldecls : Environ.env -> Constr.pinductive -> Constr.rel_context

returns
full arity context, hence with letin

val inductive_alldecls_env : 
  Environ.env ->
  Constr.pinductive ->
  Constr.rel_context

Extract information from a constructor name

val constructor_nallargs : Environ.env -> Names.constructor -> int

returns
param + args without letin

val constructor_nallargs_env : Environ.env -> Names.constructor -> int

val constructor_nalldecls : Environ.env -> Names.constructor -> int

returns
param + args with letin

val constructor_nalldecls_env : Environ.env -> Names.constructor -> int

val constructor_nrealargs : Environ.env -> Names.constructor -> int

returns
args without letin

val constructor_nrealargs_env : Environ.env -> Names.constructor -> int

val constructor_nrealdecls : Environ.env -> Names.constructor -> int

returns
args with letin

val constructor_nrealdecls_env : Environ.env -> Names.constructor -> int

val inductive_alltags : Environ.env -> Names.inductive -> bool list

returns
tags of all decls: true = assumption, false = letin

val constructor_alltags : Environ.env -> Names.constructor -> bool list

val constructor_has_local_defs : Environ.env -> Names.constructor -> bool

Is there local defs in params or args ?

val inductive_has_local_defs : Environ.env -> Names.inductive -> bool

val sorts_below : Sorts.family -> Sorts.family list

val top_allowed_sort : Environ.env -> Names.inductive -> Sorts.family

val has_dependent_elim : Declarations.mind_specif -> bool

(Co)Inductive records with primitive projections do not have eta-conversion, hence no dependent elimination.

val type_of_projection_knowing_arg : 
  Environ.env ->
  Evd.evar_map ->
  Names.Projection.t ->
  EConstr.t ->
  EConstr.types ->
  Constr.types

Primitive projections

Extract information from an inductive family

type constructor_summary = {

cs_cstr : Constr.pconstructor;

cs_params : Constr.constr list;

cs_nargs : int;

cs_args : Constr.rel_context;

cs_concl_realargs : Constr.constr array;

}

val lift_constructor : int -> constructor_summary -> constructor_summary

val get_constructor : 
  (Constr.pinductive
   * Declarations.mutual_inductive_body
   * Declarations.one_inductive_body
   * Constr.constr list) ->
  int ->
  constructor_summary

val get_constructors : 
  Environ.env ->
  inductive_family ->
  constructor_summary array

val get_arity : Environ.env -> inductive_family -> Constr.rel_context

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 build_dependent_constructor : constructor_summary -> Constr.constr

val build_dependent_inductive : 
  Environ.env ->
  inductive_family ->
  Constr.constr

val make_arity_signature : 
  Environ.env ->
  Evd.evar_map ->
  bool ->
  inductive_family ->
  EConstr.rel_context

val make_arity : 
  Environ.env ->
  Evd.evar_map ->
  bool ->
  inductive_family ->
  EConstr.ESorts.t ->
  EConstr.types

val extract_mrectype : 
  Evd.evar_map ->
  EConstr.t ->
  (Names.inductive * EConstr.EInstance.t) * EConstr.constr list

Raise Not_found if not given a valid inductive type

val find_mrectype : 
  Environ.env ->
  Evd.evar_map ->
  EConstr.types ->
  (Names.inductive * EConstr.EInstance.t) * EConstr.constr list

val find_mrectype_vect : 
  Environ.env ->
  Evd.evar_map ->
  EConstr.types ->
  (Names.inductive * EConstr.EInstance.t) * EConstr.constr array

val find_rectype : 
  Environ.env ->
  Evd.evar_map ->
  EConstr.types ->
  inductive_type

val find_inductive : 
  Environ.env ->
  Evd.evar_map ->
  EConstr.types ->
  (Names.inductive * EConstr.EInstance.t) * Constr.constr list

val find_coinductive : 
  Environ.env ->
  Evd.evar_map ->
  EConstr.types ->
  (Names.inductive * EConstr.EInstance.t) * Constr.constr list

val instantiate_constructor_params : 
  Constr.pconstructor ->
  Declarations.mind_specif ->
  Constr.constr list ->
  Constr.constr

instantiate_constructor_params cstr mind params instantiates the type of the given constructor with parameters params

val arity_of_case_predicate : 
  Environ.env ->
  inductive_family ->
  bool ->
  Sorts.t ->
  Constr.types

Builds the case predicate arity (dependent or not)

val make_case_info : 
  Environ.env ->
  Names.inductive ->
  Sorts.relevance ->
  Constr.case_style ->
  Constr.case_info

Annotation for cases

val make_case_or_project : 
  Environ.env ->
  Evd.evar_map ->
  inductive_type ->
  Constr.case_info ->
  EConstr.constr ->
  EConstr.constr ->
  EConstr.constr array ->
  EConstr.constr

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 simple_make_case_or_project : 
  Environ.env ->
  Evd.evar_map ->
  Constr.case_info ->
  EConstr.constr ->
  EConstr.case_invert ->
  EConstr.constr ->
  EConstr.constr array ->
  EConstr.constr

Sometimes make_case_or_project is nicer to call with a pre-built case_invert than inductive_type.

val make_case_invert : 
  Environ.env ->
  inductive_type ->
  Constr.case_info ->
  EConstr.case_invert

val compute_projections : 
  Environ.env ->
  Names.inductive ->
  (Constr.constr * Constr.types) array

Given a primitive record type, for every field computes the eta-expanded projection and its type.

val type_of_inductive_knowing_conclusion : 
  Environ.env ->
  Evd.evar_map ->
  Declarations.mind_specif Univ.puniverses ->
  EConstr.types ->
  Evd.evar_map * EConstr.types

val control_only_guard : Environ.env -> Evd.evar_map -> EConstr.types -> unit