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|
(* $Id$ *)
(*i*)
open Names
open Univ
open Term
open Sign
(*i*)
(* Inductive types (internal representation). *)
type recarg =
| Param of int
| Norec
| Mrec of int
| Imbr of inductive_path * (recarg list)
type mutual_inductive_packet = {
mind_consnames : identifier array;
mind_typename : identifier;
mind_lc : constr;
mind_arity : typed_type;
mind_kelim : sorts list;
mind_listrec : (recarg list) array;
mind_finite : bool }
type mutual_inductive_body = {
mind_kind : path_kind;
mind_ntypes : int;
mind_hyps : typed_type signature;
mind_packets : mutual_inductive_packet array;
mind_constraints : constraints;
mind_singl : constr option;
mind_nparams : int }
val mind_type_finite : mutual_inductive_body -> int -> bool
(*s To give a more efficient access to the informations related to a given
inductive type, we introduce the following type [mind_specif], which
contains all the informations about the inductive type, including its
instanciation arguments. *)
type mind_specif = {
mis_sp : section_path;
mis_mib : mutual_inductive_body;
mis_tyi : int;
mis_args : constr array;
mis_mip : mutual_inductive_packet }
val mis_ntypes : mind_specif -> int
val mis_nconstr : mind_specif -> int
val mis_nparams : mind_specif -> int
val mis_kelim : mind_specif -> sorts list
val mis_recargs : mind_specif -> (recarg list) array array
val mis_recarg : mind_specif -> (recarg list) array
val mis_typename : mind_specif -> identifier
val is_recursive : int list -> recarg list array -> bool
val mis_is_recursive : mind_specif -> bool
val mis_consnames : mind_specif -> identifier array
val mind_nth_type_packet :
mutual_inductive_body -> int -> mutual_inductive_packet
(*s This type gathers useful informations about some instance of a constructor
relatively to some implicit context (the current one)
If [cs_cstr] is a constructor in [(I p1...pm a1...an)] then
[cs_params] is [p1...pm] and the type of [MutConstruct(cs_cstr)
p1...pn] is [(cs_args)(I p1...pm cs_concl_realargs)] where [cs_args]
and [cs_params] are relative to the current env and [cs_concl_realargs]
is relative to the current env enriched by [cs_args]
*)
type constructor_summary = {
cs_cstr : constructor;
cs_params : constr list;
cs_nargs : int;
cs_args : (name * constr) list;
cs_concl_realargs : constr array
}
(*s A variant of [mind_specif_of_mind] with pre-splitted args
Invariant: We have \par
[Hnf (fullmind)] = [DOPN(AppL,[|MutInd mind;..params..;..realargs..|])] \par
with [mind] = [((sp,i),localvars)] for some [sp, i, localvars].
[make_constrs] is a receipt to build constructor instantiated by
local vars and params; it is a closure which does not need to be
lifted; it must be applied to [mind] and [params] to get the constructors
correctly lifted and instantiated
[make_arity] is a receipt to build the arity instantiated by local
vars and by params; it is a closure which does not need to be
lifted. Arity is pre-decomposed into its real parameters and its
sort; it must be applied to [mind] and [params] to get the arity
correctly lifted and instantiated
*)
type inductive_summary = {
fullmind : constr;
mind : inductive;
params : constr list;
realargs : constr list;
nparams : int;
nrealargs : int;
nconstr : int;
make_arity : inductive -> constr list -> (name * constr) list * sorts;
make_constrs : inductive -> constr list -> constructor_summary array
}
(*s Declaration of inductive types. *)
type mutual_inductive_entry = {
mind_entry_nparams : int;
mind_entry_finite : bool;
mind_entry_inds : (identifier * constr * identifier list * constr) list }
(*s The different kinds of errors that may result of a malformed inductive
definition. *)
type inductive_error =
| NonPos of name list * constr * constr
| NotEnoughArgs of name list * constr * constr
| NotConstructor of name list * constr * constr
| NonPar of name list * constr * int * constr * constr
| SameNamesTypes of identifier
| SameNamesConstructors of identifier * identifier
| NotAnArity of identifier
| BadEntry
exception InductiveError of inductive_error
(*s The following functions are utility functions to check and to
decompose a declaration. *)
(* [mind_check_names] checks the names of an inductive types declaration
i.e. that all the types and constructors names are distinct.
It raises an exception [InductiveError _] if it is not the case. *)
val mind_check_names : mutual_inductive_entry -> unit
(* [mind_extract_and_check_params] extracts the parameters of an inductive
types declaration. It raises an exception [InductiveError _] if there is
not enough abstractions in any of the terms of the field
[mind_entry_inds]. *)
val mind_extract_and_check_params :
mutual_inductive_entry -> (name * constr) list
val mind_extract_params : int -> constr -> (name * constr) list * constr
val mind_check_lc : (name * constr) list -> mutual_inductive_entry -> unit
val inductive_of_constructor : constructor -> inductive
val ith_constructor_of_inductive : inductive -> int -> constructor
val inductive_path_of_constructor_path : constructor_path -> inductive_path
val ith_constructor_path_of_inductive_path :
inductive_path -> int -> constructor_path
(* This builds [(ci params (Rel 1)...(Rel ci_nargs))] which is the argument
of predicate in a cases branch *)
val build_dependent_constructor : constructor_summary -> constr
(* This builds [(I params (Rel 1)...(Rel nrealargs))] which is the argument
of predicate in a cases branch *)
val build_dependent_inductive : inductive_summary -> constr
|
