path: root/library/coqlib.ml

(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

open CErrors
open Util
open Pp
open Names
open Libnames
open Globnames
open Nametab

let coq = Libnames.coq_string (* "Coq" *)

(************************************************************************)
(* Generic functions to find Coq objects *)

type message = string

let make_dir l = DirPath.make (List.rev_map Id.of_string l)

let find_reference locstr dir s =
  let dp = make_dir dir in
  let sp = Libnames.make_path dp (Id.of_string s) in
  try Nametab.global_of_path sp
  with Not_found ->
    (* Following bug 5066 we are more permissive with the handling
       of not found errors here *)
    user_err ~hdr:locstr
      Pp.(str "cannot find " ++ Libnames.pr_path sp ++
          str "; maybe library " ++ DirPath.print dp ++
          str " has to be required first.")

let coq_reference locstr dir s = find_reference locstr (coq::dir) s

let has_suffix_in_dirs dirs ref =
  let dir = dirpath (path_of_global ref) in
  List.exists (fun d -> is_dirpath_prefix_of d dir) dirs

let gen_reference_in_modules locstr dirs s =
  let dirs = List.map make_dir dirs in
  let qualid = qualid_of_string s in
  let all = Nametab.locate_all qualid in
  let all = List.sort_uniquize RefOrdered_env.compare all in
  let these = List.filter (has_suffix_in_dirs dirs) all in
  match these with
    | [x] -> x
    | [] ->
	anomaly ~label:locstr (str "cannot find " ++ str s ++
	str " in module" ++ str (if List.length dirs > 1 then "s " else " ") ++
        prlist_with_sep pr_comma DirPath.print dirs ++ str ".")
    | l ->
      anomaly ~label:locstr
	(str "ambiguous name " ++ str s ++ str " can represent " ++
	   prlist_with_sep pr_comma
	   (fun x -> Libnames.pr_path (Nametab.path_of_global x)) l ++
	   str " in module" ++ str (if List.length dirs > 1 then "s " else " ") ++
           prlist_with_sep pr_comma DirPath.print dirs ++ str ".")

(* For tactics/commands requiring vernacular libraries *)

let check_required_library d =
  let dir = make_dir d in
  if Library.library_is_loaded dir then ()
  else
    let in_current_dir = match Lib.current_mp () with
      | MPfile dp -> DirPath.equal dir dp
      | _ -> false
    in
    if not in_current_dir then
(* Loading silently ...
    let m, prefix = List.sep_last d' in
    read_library
     (Loc.ghost,make_qualid (DirPath.make (List.rev prefix)) m)
*)
(* or failing ...*)
      user_err ~hdr:"Coqlib.check_required_library"
        (str "Library " ++ DirPath.print dir ++ str " has to be required first.")

(************************************************************************)
(* Specific Coq objects *)

let init_reference dir s =
  let d = coq::"Init"::dir in
  check_required_library d; find_reference "Coqlib" d s

let logic_reference dir s =
  let d = coq::"Logic"::dir in
  check_required_library d; find_reference "Coqlib" d s

let arith_dir = [coq;"Arith"]
let arith_modules = [arith_dir]

let numbers_dir = [coq;"Numbers"]
let parith_dir = [coq;"PArith"]
let narith_dir = [coq;"NArith"]
let zarith_dir = [coq;"ZArith"]

let zarith_base_modules = [numbers_dir;parith_dir;narith_dir;zarith_dir]

let init_dir = [coq;"Init"]
let init_modules = [
  init_dir@["Datatypes"];
  init_dir@["Logic"];
  init_dir@["Specif"];
  init_dir@["Logic_Type"];
  init_dir@["Nat"];
  init_dir@["Peano"];
  init_dir@["Wf"]
]

let prelude_module_name = init_dir@["Prelude"]
let prelude_module = make_dir prelude_module_name

let logic_module_name = init_dir@["Logic"]
let logic_module = make_dir logic_module_name

let logic_type_module_name = init_dir@["Logic_Type"]
let logic_type_module = make_dir logic_type_module_name

let datatypes_module_name = init_dir@["Datatypes"]
let datatypes_module = make_dir datatypes_module_name

let jmeq_module_name = [coq;"Logic";"JMeq"]
let jmeq_module = make_dir jmeq_module_name

(* TODO: temporary hack. Works only if the module isn't an alias *)
let make_ind dir id = Globnames.encode_mind dir (Id.of_string id)
let make_con dir id = Globnames.encode_con dir (Id.of_string id)

(** Identity *)

let id = make_con datatypes_module "idProp"
let type_of_id = make_con datatypes_module "IDProp"

(** Natural numbers *)
let nat_kn = make_ind datatypes_module "nat"
let nat_path = Libnames.make_path datatypes_module (Id.of_string "nat")

let glob_nat = IndRef (nat_kn,0)

let path_of_O = ((nat_kn,0),1)
let path_of_S = ((nat_kn,0),2)
let glob_O = ConstructRef path_of_O
let glob_S = ConstructRef path_of_S

(** Booleans *)
let bool_kn = make_ind datatypes_module "bool"

let glob_bool = IndRef (bool_kn,0)

let path_of_true = ((bool_kn,0),1)
let path_of_false = ((bool_kn,0),2)
let glob_true  = ConstructRef path_of_true
let glob_false  = ConstructRef path_of_false

(** Equality *)
let eq_kn = make_ind logic_module "eq"
let glob_eq = IndRef (eq_kn,0)

let identity_kn = make_ind datatypes_module "identity"
let glob_identity = IndRef (identity_kn,0)

let jmeq_kn = make_ind jmeq_module "JMeq"
let glob_jmeq = IndRef (jmeq_kn,0)

type coq_sigma_data = {
  proj1 : GlobRef.t;
  proj2 : GlobRef.t;
  elim  : GlobRef.t;
  intro : GlobRef.t;
  typ   : GlobRef.t }

type coq_bool_data  = {
  andb : GlobRef.t;
  andb_prop : GlobRef.t;
  andb_true_intro : GlobRef.t}

let build_bool_type () =
  { andb =  init_reference ["Datatypes"] "andb";
    andb_prop =  init_reference ["Datatypes"] "andb_prop";
    andb_true_intro =  init_reference ["Datatypes"] "andb_true_intro" }

let build_sigma_set () = anomaly (Pp.str "Use build_sigma_type.")

let build_sigma_type () =
  { proj1 = init_reference ["Specif"] "projT1";
    proj2 = init_reference ["Specif"] "projT2";
    elim = init_reference ["Specif"] "sigT_rect";
    intro = init_reference ["Specif"] "existT";
    typ = init_reference ["Specif"] "sigT" }

let build_sigma () =
  { proj1 = init_reference ["Specif"] "proj1_sig";
    proj2 = init_reference ["Specif"] "proj2_sig";
    elim = init_reference ["Specif"] "sig_rect";
    intro = init_reference ["Specif"] "exist";
    typ = init_reference ["Specif"] "sig" }


let build_prod () =
  { proj1 = init_reference ["Datatypes"] "fst";
    proj2 = init_reference ["Datatypes"] "snd";
    elim = init_reference ["Datatypes"] "prod_rec";
    intro = init_reference ["Datatypes"] "pair";
    typ = init_reference ["Datatypes"] "prod" }

(* Equalities *)
type coq_eq_data = {
  eq   : GlobRef.t;
  ind  : GlobRef.t;
  refl : GlobRef.t;
  sym  : GlobRef.t;
  trans: GlobRef.t;
  congr: GlobRef.t }

(* Data needed for discriminate and injection *)
type coq_inversion_data = {
  inv_eq   : GlobRef.t; (* : forall params, t -> Prop *)
  inv_ind  : GlobRef.t; (* : forall params P y, eq params y -> P y *)
  inv_congr: GlobRef.t  (* : forall params B (f:t->B) y, eq params y -> f c=f y *)
}

let lazy_init_reference dir id = lazy (init_reference dir id)
let lazy_logic_reference dir id = lazy (logic_reference dir id)

(* Leibniz equality on Type *)

let coq_eq_eq = lazy_init_reference ["Logic"] "eq"
let coq_eq_refl = lazy_init_reference ["Logic"] "eq_refl"
let coq_eq_ind = lazy_init_reference ["Logic"] "eq_ind"
let coq_eq_congr = lazy_init_reference ["Logic"] "f_equal"
let coq_eq_sym  = lazy_init_reference ["Logic"] "eq_sym"
let coq_eq_trans  = lazy_init_reference ["Logic"] "eq_trans"
let coq_f_equal2 = lazy_init_reference ["Logic"] "f_equal2"
let coq_eq_congr_canonical =
  lazy_init_reference ["Logic"] "f_equal_canonical_form"

let build_coq_eq_data () =
  let _ = check_required_library logic_module_name in {
  eq = Lazy.force coq_eq_eq;
  ind = Lazy.force coq_eq_ind;
  refl = Lazy.force coq_eq_refl;
  sym = Lazy.force coq_eq_sym;
  trans = Lazy.force coq_eq_trans;
  congr = Lazy.force coq_eq_congr }

let build_coq_eq () = Lazy.force coq_eq_eq
let build_coq_eq_refl () = Lazy.force coq_eq_refl
let build_coq_eq_sym () = Lazy.force coq_eq_sym
let build_coq_f_equal2 () = Lazy.force coq_f_equal2

let build_coq_inversion_eq_data () =
  let _ = check_required_library logic_module_name in {
  inv_eq = Lazy.force coq_eq_eq;
  inv_ind = Lazy.force coq_eq_ind;
  inv_congr = Lazy.force coq_eq_congr_canonical }

(* Heterogenous equality on Type *)

let coq_jmeq_eq = lazy_logic_reference ["JMeq"] "JMeq"
let coq_jmeq_hom = lazy_logic_reference ["JMeq"] "JMeq_hom"
let coq_jmeq_refl = lazy_logic_reference ["JMeq"] "JMeq_refl"
let coq_jmeq_ind = lazy_logic_reference ["JMeq"] "JMeq_ind"
let coq_jmeq_sym  = lazy_logic_reference ["JMeq"] "JMeq_sym"
let coq_jmeq_congr  = lazy_logic_reference ["JMeq"] "JMeq_congr"
let coq_jmeq_trans  = lazy_logic_reference ["JMeq"] "JMeq_trans"
let coq_jmeq_congr_canonical =
  lazy_logic_reference ["JMeq"] "JMeq_congr_canonical_form"

let build_coq_jmeq_data () =
  let _ = check_required_library jmeq_module_name in {
  eq = Lazy.force coq_jmeq_eq;
  ind = Lazy.force coq_jmeq_ind;
  refl = Lazy.force coq_jmeq_refl;
  sym = Lazy.force coq_jmeq_sym;
  trans = Lazy.force coq_jmeq_trans;
  congr = Lazy.force coq_jmeq_congr }

let build_coq_inversion_jmeq_data () =
  let _ = check_required_library logic_module_name in {
  inv_eq = Lazy.force coq_jmeq_hom;
  inv_ind = Lazy.force coq_jmeq_ind;
  inv_congr = Lazy.force coq_jmeq_congr_canonical }

(* Specif *)
let coq_sumbool  = lazy_init_reference ["Specif"] "sumbool"

let build_coq_sumbool () = Lazy.force coq_sumbool

(* Equality on Type as a Type *)
let coq_identity_eq = lazy_init_reference ["Datatypes"] "identity"
let coq_identity_refl = lazy_init_reference ["Datatypes"] "identity_refl"
let coq_identity_ind = lazy_init_reference ["Datatypes"] "identity_ind"
let coq_identity_congr = lazy_init_reference ["Logic_Type"] "identity_congr"
let coq_identity_sym = lazy_init_reference ["Logic_Type"] "identity_sym"
let coq_identity_trans = lazy_init_reference ["Logic_Type"] "identity_trans"
let coq_identity_congr_canonical = lazy_init_reference ["Logic_Type"] "identity_congr_canonical_form"

let build_coq_identity_data () =
  let _ = check_required_library datatypes_module_name in {
  eq = Lazy.force coq_identity_eq;
  ind = Lazy.force coq_identity_ind;
  refl = Lazy.force coq_identity_refl;
  sym = Lazy.force coq_identity_sym;
  trans = Lazy.force coq_identity_trans;
  congr = Lazy.force coq_identity_congr }

let build_coq_inversion_identity_data () =
  let _ = check_required_library datatypes_module_name in
  let _ = check_required_library logic_type_module_name in {
  inv_eq = Lazy.force coq_identity_eq;
  inv_ind = Lazy.force coq_identity_ind;
  inv_congr = Lazy.force coq_identity_congr_canonical }

(* Equality to true *)
let coq_eq_true_eq = lazy_init_reference ["Datatypes"] "eq_true"
let coq_eq_true_ind = lazy_init_reference ["Datatypes"] "eq_true_ind"
let coq_eq_true_congr = lazy_init_reference ["Logic"] "eq_true_congr"

let build_coq_inversion_eq_true_data () =
  let _ = check_required_library datatypes_module_name in
  let _ = check_required_library logic_module_name in {
  inv_eq = Lazy.force coq_eq_true_eq;
  inv_ind = Lazy.force coq_eq_true_ind;
  inv_congr = Lazy.force coq_eq_true_congr }

(* The False proposition *)
let coq_False  = lazy_init_reference ["Logic"] "False"

(* The True proposition and its unique proof *)
let coq_True   = lazy_init_reference ["Logic"] "True"
let coq_I      = lazy_init_reference ["Logic"] "I"

(* Connectives *)
let coq_not = lazy_init_reference ["Logic"] "not"
let coq_and = lazy_init_reference ["Logic"] "and"
let coq_conj = lazy_init_reference ["Logic"] "conj"
let coq_or = lazy_init_reference ["Logic"] "or"
let coq_ex = lazy_init_reference ["Logic"] "ex"
let coq_iff = lazy_init_reference ["Logic"] "iff"

let coq_iff_left_proj  = lazy_init_reference ["Logic"] "proj1"
let coq_iff_right_proj = lazy_init_reference ["Logic"] "proj2"

(* Runtime part *)
let build_coq_True ()  = Lazy.force coq_True
let build_coq_I ()     = Lazy.force coq_I

let build_coq_False () = Lazy.force coq_False
let build_coq_not ()   = Lazy.force coq_not
let build_coq_and ()   = Lazy.force coq_and
let build_coq_conj ()  = Lazy.force coq_conj
let build_coq_or ()    = Lazy.force coq_or
let build_coq_ex ()    = Lazy.force coq_ex
let build_coq_iff ()   = Lazy.force coq_iff

let build_coq_iff_left_proj ()  = Lazy.force coq_iff_left_proj
let build_coq_iff_right_proj () = Lazy.force coq_iff_right_proj


(* The following is less readable but does not depend on parsing *)
let coq_eq_ref      = lazy (init_reference ["Logic"] "eq")
let coq_identity_ref = lazy (init_reference ["Datatypes"] "identity")
let coq_jmeq_ref     = lazy (find_reference "Coqlib" [coq;"Logic";"JMeq"] "JMeq")
let coq_eq_true_ref = lazy (find_reference "Coqlib" [coq;"Init";"Datatypes"] "eq_true")
let coq_existS_ref  = lazy (anomaly (Pp.str "use coq_existT_ref."))
let coq_existT_ref  = lazy (init_reference ["Specif"] "existT")
let coq_exist_ref  = lazy (init_reference ["Specif"] "exist")
let coq_not_ref     = lazy (init_reference ["Logic"] "not")
let coq_False_ref   = lazy (init_reference ["Logic"] "False")
let coq_sumbool_ref = lazy (init_reference ["Specif"] "sumbool")
let coq_sig_ref = lazy (init_reference ["Specif"] "sig")
let coq_or_ref     = lazy (init_reference ["Logic"] "or")
let coq_iff_ref    = lazy (init_reference ["Logic"] "iff")