(*  Title:      Pure/pure_thy.ML

    ID:         $Id$

    Author:     Markus Wenzel, TU Muenchen

    License:    GPL (GNU GENERAL PUBLIC LICENSE)

Theorem database, derived theory operations, and the ProtoPure theory.

*)

signature BASIC_PURE_THY =

sig

  val print_theorems: theory -> unit

  val print_theory: theory -> unit

  val get_thm: theory -> xstring -> thm

  val get_thms: theory -> xstring -> thm list

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

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

  structure ProtoPure:

    sig

      val thy: theory

      val flexpair_def: thm

      val Goal_def: thm

    end

end;

signature PURE_THY =

sig

  include BASIC_PURE_THY

  val get_thm_closure: theory -> xstring -> thm

  val get_thms_closure: theory -> xstring -> thm list

  val single_thm: string -> thm list -> thm

  val cond_extern_thm_sg: Sign.sg -> string -> xstring

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

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

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

  val open_smart_store_thms: (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 have_thmss: theory attribute list -> ((bstring * theory attribute list) *

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

  val get_name: theory -> string

  val put_name: string -> theory -> theory

  val global_path: theory -> theory

  val local_path: theory -> theory

  val begin_theory: string -> theory list -> theory

  val end_theory: theory -> theory

  val checkpoint: theory -> theory

  val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory

end;

structure PureThy: PURE_THY =

struct

(*** theorem database ***)

(** data kind 'Pure/theorems' **)

structure TheoremsDataArgs =

struct

  val name = "Pure/theorems";

  type T =

    {space: NameSpace.T,

      thms_tab: thm list Symtab.table,

      const_idx: int * (int * thm) list Symtab.table} ref;

  fun mk_empty _ =

    ref {space = NameSpace.empty, thms_tab = Symtab.empty, const_idx = (0, Symtab.empty)} : T;

  val empty = mk_empty ();

  fun copy (ref x) = ref x;

  val prep_ext = mk_empty;

  val merge = mk_empty;

  fun pretty sg (ref {space, thms_tab, const_idx = _}) =

    let

      val prt_thm = Display.pretty_thm_sg sg;

      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.cond_extern_table space thms_tab;

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

  fun print sg data = Pretty.writeln (pretty sg data);

end;

structure TheoremsData = TheoryDataFun(TheoremsDataArgs);

val get_theorems_sg = TheoremsData.get_sg;

val get_theorems = TheoremsData.get;

val cond_extern_thm_sg = NameSpace.cond_extern o #space o ! o get_theorems_sg;

(* print theory *)

val print_theorems = TheoremsData.print;

fun print_theory thy =

  Display.pretty_full_theory thy @

  [TheoremsDataArgs.pretty (Theory.sign_of thy) (get_theorems thy)]

  |> Pretty.chunks |> Pretty.writeln;

(** retrieve theorems **)

(* selections *)

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);

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

(*beware of proper order of evaluation!*)

fun lookup_thms thy =

  let

    val sg_ref = Sign.self_ref (Theory.sign_of thy);

    val ref {space, thms_tab, ...} = get_theorems thy;

  in

    fn name =>

      apsome (map (Thm.transfer_sg (Sign.deref sg_ref)))        (*semi-dynamic identity*)

      (Symtab.lookup (thms_tab, 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 => 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 => single_thm name (get name) end;

(* get_thm etc. *)

fun get_thms theory name =

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

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

fun get_thmss thy names = flat (map (get_thms thy) names);

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

(* thms_of *)

fun attach_name thm = (Thm.name_of_thm thm, thm);

fun thms_of thy =

  let val ref {thms_tab, ...} = get_theorems thy in

    map attach_name (flat (map snd (Symtab.dest thms_tab)))

  end;

(** theorems indexed by constants **)

(* make index *)

fun add_const_idx ((next, table), thm) =

  let

    val {hyps, prop, ...} = Thm.rep_thm thm;

    val consts =

      foldr add_term_consts (hyps, add_term_consts (prop, []));

    fun add (tab, c) =

      Symtab.update ((c, (next, thm) :: Symtab.lookup_multi (tab, c)), tab);

  in (next + 1, foldl add (table, consts)) end;

fun make_const_idx thm_tab =

  Symtab.foldl (fn (x, (_, ths)) => foldl add_const_idx (x, ths)) ((0, Symtab.empty), thm_tab);

(* lookup index *)

(*search locally*)

fun containing [] thy = thms_of thy

  | containing consts thy =

      let

        fun int ([], _) = []

          | int (_, []) = []

          | int (xxs as ((x as (i:int, _)) :: xs), yys as ((y as (j, _)) :: ys)) =

              if i = j then x :: int (xs, ys)

              else if i > j then int (xs, yys)

              else int (xxs, ys);

        fun ints [xs] = xs

          | ints xss = if exists null xss then [] else foldl int (hd xss, tl xss);

        val ref {const_idx = (_, ctab), ...} = get_theorems thy;

        val ithmss = map (fn c => Symtab.lookup_multi (ctab, c)) consts;

      in map (attach_name o snd) (ints ithmss) end;

(*search globally*)

fun thms_containing thy consts =

  (case filter (is_none o Sign.const_type (Theory.sign_of thy)) consts of

    [] => flat (map (containing consts) (thy :: Theory.ancestors_of thy))

  | cs => raise THEORY ("thms_containing: undeclared consts " ^ commas_quote cs, [thy]))

  |> map (apsnd (Thm.transfer thy));

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

(* naming *)

fun gen_names j len name =

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

fun name_thm name [x] = [Thm.name_thm (name, x)];

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

fun name_thms name xs = map Thm.name_thm (name_multi name xs);

fun name_thmss name = snd o foldl_map (fn (i, (ys, z)) => (i + length ys,

  (map Thm.name_thm (gen_names i (length ys) name ~~ ys), z))) o pair 0;

(* 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 thy ("", thms) = app_att (thy, thms)

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

      let

        val name = Sign.full_name sg bname;

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

        val named_thms = post_name name thms';

        val r as ref {space, thms_tab, const_idx} = get_theorems_sg sg;

        val overwrite =

          (case Symtab.lookup (thms_tab, name) of

            None => false

          | Some thms' =>

              if Library.equal_lists Thm.eq_thm (thms', named_thms) then (warn_same name; false)

              else (warn_overwrite name; true));

        val space' = NameSpace.extend (space, [name]);

        val thms_tab' = Symtab.update ((name, named_thms), thms_tab);

        val const_idx' =

          if overwrite then make_const_idx thms_tab'

          else foldl add_const_idx (const_idx, named_thms);

      in r := {space = space', thms_tab = thms_tab', const_idx = const_idx'};

        (thy', named_thms)

      end;

(* add_thms(s) *)

fun add_thms' app_name ((bname, thms), atts) thy =

  enter_thms (Theory.sign_of thy) app_name app_name

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

fun add_thms args theory =

  (theory, args)

  |> foldl_map (fn (thy, ((bname, thm), atts)) => add_thms' name_thm

       ((bname, [thm]), atts) thy)

  |> apsnd (map hd);

fun add_thmss args theory =

  (theory, args)

  |> foldl_map (fn (thy, arg) => add_thms' name_thms arg thy);

(* have_thmss *)

local

  fun have_thss kind_atts (thy, ((bname, more_atts), ths_atts)) =

    let

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

      val (thy', thms) = enter_thms (Theory.sign_of thy)

        name_thmss name_thms (apsnd flat o foldl_map app) thy

        (bname, map (fn (ths, atts) =>

          (ths, atts @ more_atts @ kind_atts)) ths_atts);

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

in

  fun have_thmss kind_atts args thy = foldl_map (have_thss kind_atts) (thy, args);

end;

(* store_thm *)

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

  let val (thy', [th']) = add_thms' name_thm ((bname, [thm]), atts) thy

  in (thy', th') end;

(* smart_store_thms *)

fun gen_smart_store_thms _ _ (name, []) =

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

  | gen_smart_store_thms name_thm _ (name, [thm]) =

      snd (enter_thms (Thm.sign_of_thm thm) name_thm name_thm I () (name, [thm]))

  | gen_smart_store_thms _ name_thm (name, thms) =

      let

        val merge_sg = Sign.merge_refs o apsnd (Sign.self_ref o Thm.sign_of_thm);

        val sg_ref = foldl merge_sg (Sign.self_ref (Thm.sign_of_thm (hd thms)), tl thms);

      in snd (enter_thms (Sign.deref sg_ref) name_thm name_thm I () (name, thms)) end;

val smart_store_thms = gen_smart_store_thms name_thm name_thms;

val open_smart_store_thms = gen_smart_store_thms (K I) (K I);

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

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

    Could clash with Vars already present.*)

fun forall_elim_var i th =

    let val {prop,sign,...} = rep_thm th

    in case prop of

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

              forall_elim (cterm_of sign (Var((a,i), T)))  th

        | _ => 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 (add_thms [((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 (add_thmss [((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;

(*** derived theory operations ***)

(** theory management **)

(* data kind 'Pure/theory_management' *)

structure TheoryManagementDataArgs =

struct

  val name = "Pure/theory_management";

  type T = {name: string, version: int};

  val empty = {name = "", version = 0};

  val copy = I;

  val prep_ext  = I;

  fun merge _ = empty;

  fun print _ _ = ();

end;

structure TheoryManagementData = TheoryDataFun(TheoryManagementDataArgs);

val get_info = TheoryManagementData.get;

val put_info = TheoryManagementData.put;

(* get / put name *)

val get_name = #name o get_info;

fun put_name name = put_info {name = name, version = 0};

(* control prefixing of theory name *)

val global_path = Theory.root_path;

fun local_path thy =

  thy |> Theory.root_path |> Theory.add_path (get_name thy);

(* begin / end theory *)

fun begin_theory name thys =

  Theory.prep_ext_merge thys

  |> put_name name

  |> local_path;

fun end_theory thy = Theory.add_name (get_name thy) thy;

fun checkpoint thy =

  if is_draft thy then

    let val {name, version} = get_info thy in

      thy

      |> Theory.add_name (name ^ ":" ^ string_of_int version)

      |> put_info {name = name, version = version + 1}

    end

  else thy;

(** add logical types **)

fun add_typedecls decls thy =

  let

    val full = Sign.full_name (Theory.sign_of thy);

    fun type_of (raw_name, vs, mx) =

      if null (duplicates vs) then (raw_name, length vs, mx)

      else error ("Duplicate parameters in type declaration: " ^ quote raw_name);

    fun arity_of (raw_name, len, mx) =

      (full (Syntax.type_name raw_name mx), replicate len logicS, logicS);

    val types = map type_of decls;

    val arities = map arity_of types;

  in

    thy

    |> Theory.add_types types

    |> Theory.add_arities_i arities

  end;

(*** the ProtoPure theory ***)

val proto_pure =

  Theory.pre_pure

  |> Library.apply [TheoremsData.init, TheoryManagementData.init, Proofterm.init]

  |> put_name "ProtoPure"

  |> global_path

  |> Theory.add_types

   [("fun", 2, NoSyn),

    ("prop", 0, NoSyn),

    ("itself", 1, NoSyn),

    ("dummy", 0, NoSyn)]

  |> Theory.add_classes_i [(logicC, [])]

  |> Theory.add_defsort_i logicS

  |> Theory.add_arities_i

   [("fun", [logicS, logicS], logicS),

    ("prop", [], logicS),

    ("itself", [logicS], logicS)]

  |> Theory.add_nonterminals Syntax.pure_nonterms

  |> Theory.add_syntax Syntax.pure_syntax

  |> Theory.add_modesyntax (Symbol.symbolsN, true) Syntax.pure_sym_syntax

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

  |> Theory.add_trfuns Syntax.pure_trfuns

  |> Theory.add_trfunsT Syntax.pure_trfunsT

  |> Theory.add_syntax

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

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

  |> Theory.add_consts

   [("==", "['a::{}, 'a] => prop", InfixrName ("==", 2)),

    ("=?=", "['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_modesyntax ("", false)

    (("Goal", "prop => prop", Mixfix ("_", [0], 0))

      :: Syntax.pure_appl_syntax)

  |> local_path

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

   [("flexpair_def", "(t =?= u) == (t == u::'a::{})")]

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

   [("Goal_def", let val A = Free ("A", propT) in Logic.mk_equals (Logic.mk_goal A, A) end)]

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

  |> Theory.add_axioms_i Proofterm.equality_axms

  |> end_theory;

structure ProtoPure =

struct

  val thy = proto_pure;

  val flexpair_def = get_axiom thy "flexpair_def";

  val Goal_def = get_axiom thy "Goal_def";

end;

end;

structure BasicPureThy: BASIC_PURE_THY = PureThy;

open BasicPureThy;