(*  Title:      Pure/pure_thy.ML

    ID:         $Id$

    Author:     Markus Wenzel, TU Muenchen

Theorem storage.  The ProtoPure theory.

*)

signature BASIC_PURE_THY =

sig

  type thmref

  val print_theorems: theory -> unit

  val print_theory: theory -> unit

  val get_thm: theory -> thmref -> thm

  val get_thms: theory -> thmref -> thm list

  val get_thmss: theory -> thmref list -> thm list

  structure ProtoPure:

    sig

      val thy: theory

      val Goal_def: thm

    end

end;

signature PURE_THY =

sig

  include BASIC_PURE_THY

  datatype interval = FromTo of int * int | From of int | Single of int

  val string_of_thmref: thmref -> string

  val theorem_space: theory -> NameSpace.T

  val get_thm_closure: theory -> thmref -> thm

  val get_thms_closure: theory -> thmref -> thm list

  val single_thm: string -> thm list -> thm

  val select_thm: thmref -> thm list -> thm list

  val selections: string * thm list -> (thmref * thm) list

  val fact_index_of: theory -> FactIndex.T

  val valid_thms: theory -> thmref * thm list -> bool

  val thms_containing: theory -> FactIndex.spec -> (string * thm list) list

  val thms_containing_consts: theory -> string list -> (string * thm) list

  val thms_of: theory -> (string * thm) list

  val all_thms_of: theory -> (string * thm) list

  val hide_thms: bool -> string list -> theory -> theory

  val store_thm: (bstring * thm) * theory attribute list -> theory -> theory * thm

  val smart_store_thms: (bstring * thm list) -> thm list

  val smart_store_thms_open: (bstring * thm list) -> thm list

  val forall_elim_var: int -> thm -> thm

  val forall_elim_vars: int -> thm -> thm

  val add_thms: ((bstring * thm) * theory attribute list) list -> theory -> theory * thm list

  val add_thmss: ((bstring * thm list) * theory attribute list) list -> theory

    -> theory * thm list list

  val note_thmss: theory attribute -> ((bstring * theory attribute list) *

    (thmref * theory attribute list) list) list ->

    theory -> theory * (bstring * thm list) list

  val note_thmss_i: theory attribute -> ((bstring * theory attribute list) *

    (thm list * theory attribute list) list) list ->

    theory -> theory * (bstring * thm list) list

  val add_axioms: ((bstring * string) * theory attribute list) list ->

    theory -> theory * thm list

  val add_axioms_i: ((bstring * term) * theory attribute list) list ->

    theory -> theory * thm list

  val add_axiomss: ((bstring * string list) * theory attribute list) list ->

    theory -> theory * thm list list

  val add_axiomss_i: ((bstring * term list) * theory attribute list) list ->

    theory -> theory * thm list list

  val add_defs: bool -> ((bstring * string) * theory attribute list) list ->

    theory -> theory * thm list

  val add_defs_i: bool -> ((bstring * term) * theory attribute list) list ->

    theory -> theory * thm list

  val add_defss: bool -> ((bstring * string list) * theory attribute list) list ->

    theory -> theory * thm list list

  val add_defss_i: bool -> ((bstring * term list) * theory attribute list) list ->

    theory -> theory * thm list list

end;

structure PureThy: PURE_THY =

struct

(*** theorem database ***)

(** dataype theorems **)

fun pretty_theorems thy theorems =

  let

    val prt_thm = Display.pretty_thm_sg thy;

    fun prt_thms (name, [th]) =

          Pretty.block [Pretty.str (name ^ ":"), Pretty.brk 1, prt_thm th]

      | prt_thms (name, ths) = Pretty.big_list (name ^ ":") (map prt_thm ths);

    val thmss = NameSpace.extern_table theorems;

  in Pretty.big_list "theorems:" (map prt_thms thmss) end;

structure TheoremsData = TheoryDataFun

(struct

  val name = "Pure/theorems";

  type T =

   {theorems: thm list NameSpace.table,

    index: FactIndex.T} ref;

  fun mk_empty _ =

    ref {theorems = NameSpace.empty_table, index = FactIndex.empty}: T;

  val empty = mk_empty ();

  fun copy (ref x) = ref x;

  val extend = mk_empty;

  fun merge _ = mk_empty;

  fun print thy (ref {theorems, index}) = Pretty.writeln (pretty_theorems thy theorems);

end);

val get_theorems = TheoremsData.get;

val theorem_space = #1 o #theorems o ! o get_theorems;

val fact_index_of = #index o ! o get_theorems;

(* print theory *)

val print_theorems = TheoremsData.print;

fun print_theory thy =

  Display.pretty_full_theory thy @

    [pretty_theorems thy (#theorems (! (get_theorems thy)))]

  |> Pretty.chunks |> Pretty.writeln;

(** retrieve theorems **)

fun the_thms _ (SOME thms) = thms

  | the_thms name NONE = error ("Unknown theorem(s) " ^ quote name);

fun single_thm _ [thm] = thm

  | single_thm name _ = error ("Single theorem expected " ^ quote name);

(* datatype interval *)

datatype interval =

  FromTo of int * int |

  From of int |

  Single of int;

fun interval _ (FromTo (i, j)) = i upto j

  | interval n (From i) = i upto n

  | interval _ (Single i) = [i];

fun string_of_interval (FromTo (i, j)) = string_of_int i ^ "-" ^ string_of_int j

  | string_of_interval (From i) = string_of_int i ^ "-"

  | string_of_interval (Single i) = string_of_int i;

(* type thmref *)

type thmref = xstring * interval list option;

fun string_of_thmref (name, NONE) = name

  | string_of_thmref (name, SOME is) =

      name ^ enclose "(" ")" (commas (map string_of_interval is));

(* select_thm *)

fun select_thm (_, NONE) thms = thms

  | select_thm (name, SOME is) thms =

      let

        val n = length thms;

        fun select i =

          if i < 1 orelse i > n then

            error ("Bad subscript " ^ string_of_int i ^ " for " ^

              quote name ^ " (length " ^ string_of_int n ^ ")")

          else List.nth (thms, i - 1);

      in map select (List.concat (map (interval n) is)) end;

(* selections *)

fun selections (name, [thm]) = [((name, NONE), thm)]

  | selections (name, thms) = (1 upto length thms, thms) |> ListPair.map (fn (i, thm) =>

      ((name, SOME [Single i]), thm));

(* get_thm(s)_closure -- statically scoped versions *)

(*beware of proper order of evaluation!*)

fun lookup_thms thy =

  let

    val thy_ref = Theory.self_ref thy;

    val ref {theorems = (space, thms), ...} = get_theorems thy;

  in

    fn name =>

      Option.map (map (Thm.transfer (Theory.deref thy_ref)))    (*dynamic identity*)

      (Symtab.lookup (thms, NameSpace.intern space name))       (*static content*)

  end;

fun get_thms_closure thy =

  let val closures = map lookup_thms (thy :: Theory.ancestors_of thy) in

    fn (name, i) => select_thm (name, i) (the_thms name (get_first (fn f => f name) closures))

  end;

fun get_thm_closure thy =

  let val get = get_thms_closure thy

  in fn (name, i) => single_thm name (get (name, i)) end;

(* get_thms etc. *)

fun get_thms theory (name, i) =

  get_first (fn thy => lookup_thms thy name) (theory :: Theory.ancestors_of theory)

  |> the_thms name |> select_thm (name, i) |> map (Thm.transfer theory);

fun get_thmss thy names = List.concat (map (get_thms thy) names);

fun get_thm thy (name, i) = single_thm name (get_thms thy (name, i));

(* thms_containing etc. *)

fun valid_thms thy (thmref, ths) =

  (case try (transform_error (get_thms thy)) thmref of

    NONE => false

  | SOME ths' => Thm.eq_thms (ths, ths'));

fun thms_containing theory spec =

  (theory :: Theory.ancestors_of theory)

  |> map (fn thy =>

      FactIndex.find (fact_index_of thy) spec

      |> List.filter (fn (name, ths) => valid_thms theory ((name, NONE), ths))

      |> gen_distinct eq_fst)

  |> List.concat;

fun thms_containing_consts thy consts =

  thms_containing thy (consts, []) |> map #2 |> List.concat

  |> map (fn th => (Thm.name_of_thm th, th));

(* thms_of etc. *)

fun thms_of thy =

  let val ref {theorems = (_, thms), ...} = get_theorems thy in

    map (fn th => (Thm.name_of_thm th, th)) (List.concat (map snd (Symtab.dest thms)))

  end;

fun all_thms_of thy = List.concat (map thms_of (thy :: Theory.ancestors_of thy));

(** store theorems **)                    (*DESTRUCTIVE*)

(* hiding -- affects current theory node only *)

fun hide_thms fully names thy =

  let

    val r as ref {theorems = (space, thms), index} = get_theorems thy;

    val space' = fold (NameSpace.hide fully) names space;

  in r := {theorems = (space', thms), index = index}; thy end;

(* naming *)

fun gen_names j len name =

  map (fn i => name ^ "_" ^ string_of_int i) (j + 1 upto j + len);

fun name_multi name xs = gen_names 0 (length xs) name ~~ xs;

fun name_thm pre (name, thm) =

  if Thm.name_of_thm thm <> "" andalso pre then thm else Thm.name_thm (name, thm);

fun name_thms pre name [x] = [name_thm pre (name, x)]

  | name_thms pre name xs = map (name_thm pre) (name_multi name xs);

fun name_thmss name xs =

  (case filter_out (null o fst) xs of

    [([x], z)] => [([name_thm true (name, x)], z)]

  | _ => snd (foldl_map (fn (i, (ys, z)) =>

    (i + length ys, (map (name_thm true) (gen_names i (length ys) name ~~ ys), z))) (0, xs)));

(* enter_thms *)

fun warn_overwrite name = warning ("Replaced old copy of theorems " ^ quote name);

fun warn_same name = warning ("Theorem database already contains a copy of " ^ quote name);

fun enter_thms _ _ app_att ("", thms) thy = app_att (thy, thms)

  | enter_thms pre_name post_name app_att (bname, thms) thy =

      let

        val name = Sign.full_name thy bname;

        val r as ref {theorems = (space, theorems), index} = get_theorems thy;

        val space' = Sign.declare_name thy name space;

        val (thy', thms') = apsnd (post_name name) (app_att (thy, pre_name name thms));

        val theorems' = Symtab.update ((name, thms'), theorems);

        val index' = FactIndex.add (K false) (name, thms') index;

      in

        (case Symtab.lookup (theorems, name) of

          NONE => ()

        | SOME thms'' =>

            if Thm.eq_thms (thms', thms'') then warn_same name

            else warn_overwrite name);

        r := {theorems = (space', theorems'), index = index'};

        (thy', thms')

      end;

(* add_thms(s) *)

fun add_thms_atts pre_name ((bname, thms), atts) =

  enter_thms pre_name (name_thms false)

    (Thm.applys_attributes o rpair atts) (bname, thms);

fun gen_add_thmss pre_name args theory =

  foldl_map (fn (thy, arg) => add_thms_atts pre_name arg thy) (theory, args);

fun gen_add_thms pre_name args =

  apsnd (map hd) o gen_add_thmss pre_name (map (apfst (apsnd single)) args);

val add_thmss = gen_add_thmss (name_thms true);

val add_thms = gen_add_thms (name_thms true);

(* note_thmss(_i) *)

local

fun gen_note_thss get kind_att (thy, ((bname, more_atts), ths_atts)) =

  let

    fun app (x, (ths, atts)) = Thm.applys_attributes ((x, ths), atts);

    val (thy', thms) = thy |> enter_thms

      name_thmss (name_thms false) (apsnd List.concat o foldl_map app)

      (bname, map (fn (ths, atts) => (get thy ths, atts @ more_atts @ [kind_att])) ths_atts);

  in (thy', (bname, thms)) end;

fun gen_note_thmss get kind_att args thy =

  foldl_map (gen_note_thss get kind_att) (thy, args);

in

val note_thmss = gen_note_thmss get_thms;

val note_thmss_i = gen_note_thmss (K I);

end;

(* store_thm *)

fun store_thm ((bname, thm), atts) thy =

  let val (thy', [th']) = add_thms_atts (name_thms true) ((bname, [thm]), atts) thy

  in (thy', th') end;

(* smart_store_thms(_open) *)

local

fun smart_store _ (name, []) =

      error ("Cannot store empty list of theorems: " ^ quote name)

  | smart_store name_thm (name, [thm]) =

      #2 (enter_thms (name_thm true) (name_thm false) I (name, [thm]) (Thm.theory_of_thm thm))

  | smart_store name_thm (name, thms) =

      let

        fun merge (thy, th) = Theory.merge (thy, Thm.theory_of_thm th);

        val thy = Library.foldl merge (Thm.theory_of_thm (hd thms), tl thms);

      in #2 (enter_thms (name_thm true) (name_thm false) I (name, thms) thy) end;

in

val smart_store_thms = smart_store name_thms;

val smart_store_thms_open = smart_store (K (K I));

end;

(* forall_elim_vars (belongs to drule.ML) *)

(*Replace outermost quantified variable by Var of given index.*)

fun forall_elim_var i th =

  let val {prop, thy, ...} = Thm.rep_thm th

  in case prop of

        Const ("all", _) $ Abs (a, T, _) =>

          let val used = map (fst o fst)

            (List.filter (equal i o snd o fst) (Term.add_vars ([], prop)))

          in Thm.forall_elim (Thm.cterm_of thy (Var ((variant used a, i), T))) th end

     | _ => raise THM ("forall_elim_var", i, [th])

  end;

(*Repeat forall_elim_var until all outer quantifiers are removed*)

fun forall_elim_vars i th =

  forall_elim_vars i (forall_elim_var i th) handle THM _ => th;

(* store axioms as theorems *)

local

  fun get_axs thy named_axs =

    map (forall_elim_vars 0 o Thm.get_axiom thy o fst) named_axs;

  fun add_single add (thy, ((name, ax), atts)) =

    let

      val named_ax = [(name, ax)];

      val thy' = add named_ax thy;

      val thm = hd (get_axs thy' named_ax);

    in apsnd hd (gen_add_thms (K I) [((name, thm), atts)] thy') end;

  fun add_multi add (thy, ((name, axs), atts)) =

    let

      val named_axs = name_multi name axs;

      val thy' = add named_axs thy;

      val thms = get_axs thy' named_axs;

    in apsnd hd (gen_add_thmss (K I) [((name, thms), atts)] thy') end;

  fun add_singles add args thy = foldl_map (add_single add) (thy, args);

  fun add_multis add args thy = foldl_map (add_multi add) (thy, args);

in

  val add_axioms    = add_singles Theory.add_axioms;

  val add_axioms_i  = add_singles Theory.add_axioms_i;

  val add_axiomss   = add_multis Theory.add_axioms;

  val add_axiomss_i = add_multis Theory.add_axioms_i;

  val add_defs      = add_singles o Theory.add_defs;

  val add_defs_i    = add_singles o Theory.add_defs_i;

  val add_defss     = add_multis o Theory.add_defs;

  val add_defss_i   = add_multis o Theory.add_defs_i;

end;

(*** the ProtoPure theory ***)

val aT = TFree ("'a", []);

val A = Free ("A", propT);

val proto_pure =

  Context.pre_pure

  |> Sign.init

  |> Theory.init

  |> Proofterm.init

  |> TheoremsData.init

  |> Theory.add_types

   [("fun", 2, NoSyn),

    ("prop", 0, NoSyn),

    ("itself", 1, NoSyn),

    ("dummy", 0, NoSyn)]

  |> Theory.add_nonterminals Syntax.pure_nonterms

  |> Theory.add_syntax Syntax.pure_syntax

  |> Theory.add_syntax Syntax.pure_appl_syntax

  |> Theory.add_modesyntax (Symbol.xsymbolsN, true) Syntax.pure_xsym_syntax

  |> Theory.add_syntax

   [("==>", "prop => prop => prop", Delimfix "op ==>"),

    (Term.dummy_patternN, "aprop", Delimfix "'_")]

  |> Theory.add_consts

   [("==", "'a => 'a => prop", InfixrName ("==", 2)),

    ("==>", "prop => prop => prop", Mixfix ("(_/ ==> _)", [2, 1], 1)),

    ("all", "('a => prop) => prop", Binder ("!!", 0, 0)),

    ("Goal", "prop => prop", NoSyn),

    ("TYPE", "'a itself", NoSyn),

    (Term.dummy_patternN, "'a", Delimfix "'_")]

  |> Theory.add_finals_i false

    [Const ("==", [aT, aT] ---> propT),

     Const ("==>", [propT, propT] ---> propT),

     Const ("all", (aT --> propT) --> propT),

     Const ("TYPE", a_itselfT)]

  |> Theory.add_modesyntax ("", false)

    (Syntax.pure_syntax_output @ Syntax.pure_appl_syntax)

  |> Theory.add_trfuns Syntax.pure_trfuns

  |> Theory.add_trfunsT Syntax.pure_trfunsT

  |> Sign.local_path

  |> (#1 oo (add_defs_i false o map Thm.no_attributes))

   [("Goal_def", Logic.mk_equals (Logic.mk_goal A, A))]

  |> (#1 o add_thmss [(("nothing", []), [])])

  |> Theory.add_axioms_i Proofterm.equality_axms

  |> Context.end_theory;

structure ProtoPure =

struct

  val thy = proto_pure;

  val Goal_def = get_axiom thy "Goal_def";

end;

end;

structure BasicPureThy: BASIC_PURE_THY = PureThy;

open BasicPureThy;