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(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(* $Id$ *)
open Pp
open Util
open Names
open Nameops
open Term
open Termops
open Reductionops
open Inductiveops
open Evd
open Environ
open Proof_trees
open Clenv
open Pattern
open Matching
open Coqlib
open Declarations
(* I implemented the following functions which test whether a term t
is an inductive but non-recursive type, a general conjuction, a
general disjunction, or a type with no constructors.
They are more general than matching with or_term, and_term, etc,
since they do not depend on the name of the type. Hence, they
also work on ad-hoc disjunctions introduced by the user.
-- Eduardo (6/8/97). *)
type 'a matching_function = constr -> 'a option
type testing_function = constr -> bool
let op2bool = function Some _ -> true | None -> false
let match_with_non_recursive_type t =
match kind_of_term t with
| App _ ->
let (hdapp,args) = decompose_app t in
(match kind_of_term hdapp with
| Ind ind ->
if not (Global.lookup_mind (fst ind)).mind_finite then
Some (hdapp,args)
else
None
| _ -> None)
| _ -> None
let is_non_recursive_type t = op2bool (match_with_non_recursive_type t)
(* A general conjunction type is a non-recursive inductive type with
only one constructor. *)
let match_with_conjunction t =
let (hdapp,args) = decompose_app t in
match kind_of_term hdapp with
| Ind ind ->
let (mib,mip) = Global.lookup_inductive ind in
if (Array.length mip.mind_consnames = 1)
&& (not (mis_is_recursive (ind,mib,mip)))
&& (mip.mind_nrealargs = 0)
then
Some (hdapp,args)
else
None
| _ -> None
let is_conjunction t = op2bool (match_with_conjunction t)
(* A general disjunction type is a non-recursive inductive type all
whose constructors have a single argument. *)
let match_with_disjunction t =
let (hdapp,args) = decompose_app t in
match kind_of_term hdapp with
| Ind ind ->
let car = mis_constr_nargs ind in
if array_for_all (fun ar -> ar = 1) car &&
(let (mib,mip) = Global.lookup_inductive ind in
not (mis_is_recursive (ind,mib,mip)))
then
Some (hdapp,args)
else
None
| _ -> None
let is_disjunction t = op2bool (match_with_disjunction t)
let match_with_empty_type t =
let (hdapp,args) = decompose_app t in
match (kind_of_term hdapp) with
| Ind ind ->
let (mib,mip) = Global.lookup_inductive ind in
let nconstr = Array.length mip.mind_consnames in
if nconstr = 0 then Some hdapp else None
| _ -> None
let is_empty_type t = op2bool (match_with_empty_type t)
let match_with_unit_type t =
let (hdapp,args) = decompose_app t in
match (kind_of_term hdapp) with
| Ind ind ->
let (mib,mip) = Global.lookup_inductive ind in
let constr_types = mip.mind_nf_lc in
let nconstr = Array.length mip.mind_consnames in
let zero_args c =
nb_prod c = mip.mind_nparams in
if nconstr = 1 && array_for_all zero_args constr_types then
Some hdapp
else
None
| _ -> None
let is_unit_type t = op2bool (match_with_unit_type t)
(* Checks if a given term is an application of an
inductive binary relation R, so that R has only one constructor
establishing its reflexivity. *)
(* ["(A : ?)(x:A)(? A x x)"] and ["(x : ?)(? x x)"] *)
let x = Name (id_of_string "x")
let y = Name (id_of_string "y")
let name_A = Name (id_of_string "A")
let coq_refl_rel1_pattern =
PProd
(name_A, PMeta None,
PProd (x, PRel 1, PApp (PMeta None, [|PRel 2; PRel 1; PRel 1|])))
let coq_refl_rel2_pattern =
PProd (x, PMeta None, PApp (PMeta None, [|PRel 1; PRel 1|]))
let coq_refl_reljm_pattern =
PProd
(name_A, PMeta None,
PProd (x, PRel 1, PApp (PMeta None, [|PRel 2; PRel 1; PRel 2;PRel 1|])))
let match_with_equation t =
let (hdapp,args) = decompose_app t in
match (kind_of_term hdapp) with
| Ind ind ->
let (mib,mip) = Global.lookup_inductive ind in
let constr_types = mip.mind_nf_lc in
let nconstr = Array.length mip.mind_consnames in
if nconstr = 1 &&
(is_matching coq_refl_rel1_pattern constr_types.(0) ||
is_matching coq_refl_rel2_pattern constr_types.(0) ||
is_matching coq_refl_reljm_pattern constr_types.(0))
then
Some (hdapp,args)
else
None
| _ -> None
let is_equation t = op2bool (match_with_equation t)
(* ["(?1 -> ?2)"] *)
let imp a b = PProd (Anonymous, a, b)
let coq_arrow_pattern = imp (PMeta (Some 1)) (PMeta (Some 2))
let match_with_nottype t =
try
match matches coq_arrow_pattern t with
| [(1,arg);(2,mind)] ->
if is_empty_type mind then Some (mind,arg) else None
| _ -> anomaly "Incorrect pattern matching"
with PatternMatchingFailure -> None
let is_nottype t = op2bool (match_with_nottype t)
let is_imp_term c =
match kind_of_term c with
| Prod (_,_,b) -> not (dependent (mkRel 1) b)
| _ -> false
let rec has_nodep_prod_after n c =
match kind_of_term c with
| Prod (_,_,b) ->
( n>0 || not (dependent (mkRel 1) b))
&& (has_nodep_prod_after (n-1) b)
| _ -> true
let has_nodep_prod = has_nodep_prod_after 0
let match_with_nodep_ind t =
let (hdapp,args) = decompose_app t in
match (kind_of_term hdapp) with
| Ind ind ->
let (mib,mip) = Global.lookup_inductive ind in
let constr_types = mip.mind_nf_lc in
let nodep_constr = has_nodep_prod_after mip.mind_nparams in
if array_for_all nodep_constr constr_types then
Some (hdapp,args)
else
None
| _ -> None
let is_nodep_ind t=op2bool (match_with_nodep_ind t)
|