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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(*i $Id: inductive.mli 11301 2008-08-04 19:41:18Z herbelin $ i*)
(*i*)
open Names
open Univ
open Term
open Declarations
open Environ
(*i*)
(*s Extracting an inductive type from a construction *)
(* [find_m*type env sigma c] coerce [c] to an recursive type (I args).
[find_rectype], [find_inductive] and [find_coinductive]
respectively accepts any recursive type, only an inductive type and
only a coinductive type.
They raise [Not_found] if not convertible to a recursive type. *)
val find_rectype : env -> types -> inductive * constr list
val find_inductive : env -> types -> inductive * constr list
val find_coinductive : env -> types -> inductive * constr list
type mind_specif = mutual_inductive_body * one_inductive_body
(*s Fetching information in the environment about an inductive type.
Raises [Not_found] if the inductive type is not found. *)
val lookup_mind_specif : env -> inductive -> mind_specif
(*s Functions to build standard types related to inductive *)
val ind_subst : mutual_inductive -> mutual_inductive_body -> constr list
val type_of_inductive : env -> mind_specif -> types
val elim_sorts : mind_specif -> sorts_family list
(* Return type as quoted by the user *)
val type_of_constructor : constructor -> mind_specif -> types
(* Return constructor types in normal form *)
val arities_of_constructors : inductive -> mind_specif -> types array
(* Return constructor types in user form *)
val type_of_constructors : inductive -> mind_specif -> types array
(* Transforms inductive specification into types (in nf) *)
val arities_of_specif : mutual_inductive -> mind_specif -> types array
(* [type_case_branches env (I,args) (p:A) c] computes useful types
about the following Cases expression:
<p>Cases (c :: (I args)) of b1..bn end
It computes the type of every branch (pattern variables are
introduced by products), the type for the whole expression, and
the universe constraints generated.
*)
val type_case_branches :
env -> inductive * constr list -> unsafe_judgment -> constr
-> types array * types * constraints
(* Return the arity of an inductive type *)
val mind_arity : one_inductive_body -> Sign.rel_context * sorts_family
val inductive_sort_family : one_inductive_body -> sorts_family
(* Check a [case_info] actually correspond to a Case expression on the
given inductive type. *)
val check_case_info : env -> inductive -> case_info -> unit
(*s Guard conditions for fix and cofix-points. *)
val check_fix : env -> fixpoint -> unit
val check_cofix : env -> cofixpoint -> unit
(*s Support for sort-polymorphic inductive types *)
val type_of_inductive_knowing_parameters :
env -> one_inductive_body -> types array -> types
val max_inductive_sort : sorts array -> universe
val instantiate_universes : env -> Sign.rel_context ->
polymorphic_arity -> types array -> Sign.rel_context * sorts
(***************************************************************)
(* Debug *)
type size = Large | Strict
type subterm_spec =
Subterm of (size * wf_paths)
| Dead_code
| Not_subterm
type guard_env =
{ env : env;
(* dB of last fixpoint *)
rel_min : int;
(* inductive of recarg of each fixpoint *)
inds : inductive array;
(* the recarg information of inductive family *)
recvec : wf_paths array;
(* dB of variables denoting subterms *)
genv : subterm_spec list;
}
val subterm_specif : guard_env -> constr -> subterm_spec
val case_branches_specif : guard_env -> subterm_spec -> inductive ->
constr array -> (guard_env * constr) array
|
