Module Inductiveops

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

Return type as quoted by the user

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.pinductive * Declarations.mutual_inductive_body * Declarations.one_inductive_body) -> int -> 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 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.mutual_inductive_body -> 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

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 * Sorts.family

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 -> Sorts.t -> EConstr.types
val build_branch_type : Environ.env -> Evd.evar_map -> bool -> Constr.constr -> constructor_summary -> Constr.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 arity_of_case_predicate : Environ.env -> inductive_family -> bool -> Sorts.t -> Constr.types

Builds the case predicate arity (dependent or not)

val type_case_branches_with_names : Environ.env -> Evd.evar_map -> (Constr.pinductive * EConstr.constr list) -> Constr.constr -> Constr.constr -> EConstr.types array * Constr.types
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 make_case_invert : Environ.env -> inductive_type -> Constr.case_info -> (EConstr.constr, EConstr.EInstance.t) Constr.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 -> Inductive.mind_specif Univ.puniverses -> EConstr.types -> Evd.evar_map * EConstr.types
val control_only_guard : Environ.env -> Evd.evar_map -> EConstr.types -> unit