(*  Title:      Pure/pure_thy.ML

    ID:         $Id$

    Author:     Markus Wenzel, TU Muenchen

Theorem storage.  The ProtoPure theory.

*)

signature BASIC_PURE_THY =

sig

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

  datatype thmref =

    Name of string |

    NameSelection of string * interval list |

    Fact of string

  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 prop_def: thm

      val term_def: thm

      val conjunction_def: thm

    end

end;

signature PURE_THY =

sig

  include BASIC_PURE_THY

  val tag_rule: Markup.property -> thm -> thm

  val untag_rule: string -> thm -> thm

  val tag: Markup.property -> attribute

  val untag: string -> attribute

  val has_name_hint: thm -> bool

  val get_name_hint: thm -> string

  val put_name_hint: string -> thm -> thm

  val get_group: thm -> string option

  val put_group: string -> thm -> thm

  val group: string -> attribute

  val has_kind: thm -> bool

  val get_kind: thm -> string

  val kind_rule: string -> thm -> thm

  val kind: string -> attribute

  val kind_internal: attribute

  val has_internal: Markup.property list -> bool

  val is_internal: thm -> bool

  val string_of_thmref: thmref -> string

  val single_thm: string -> thm list -> thm

  val name_of_thmref: thmref -> string

  val map_name_of_thmref: (string -> string) -> thmref -> thmref

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

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

  val get_thms_silent: theory -> thmref -> thm list

  val theorems_of: theory -> thm list NameSpace.table

  val all_facts_of: theory -> Facts.T

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

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

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

  val map_facts: ('a -> 'b) -> ('c * ('a list * 'd) list) list -> ('c * ('b list * 'd) list) list

  val burrow_fact: ('a list -> 'b list) -> ('a list * 'c) list -> ('b list * 'c) list

  val burrow_facts: ('a list -> 'b list) ->

    ('c * ('a list * 'd) list) list -> ('c * ('b list * 'd) list) list

  val name_multi: string -> 'a list -> (string * 'a) list

  val name_thm: bool -> bool -> string -> thm -> thm

  val name_thms: bool -> bool -> string -> thm list -> thm list

  val name_thmss: bool -> string -> (thm list * 'a) list -> (thm list * 'a) list

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

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

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

  val note: string -> string * thm -> theory -> thm * theory

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

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

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

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

  val note_thmss_grouped: string -> string -> ((bstring * attribute list) *

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

  val note_thmss_qualified: string -> string -> ((bstring * attribute list) *

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

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

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

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

    theory -> thm list list * theory

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

    theory -> thm list list * theory

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

    theory -> thm list * theory

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

    theory -> thm list * theory

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

    theory -> thm list * theory

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

    theory -> thm list * theory

  val appl_syntax: (string * typ * mixfix) list

  val applC_syntax: (string * typ * mixfix) list

end;

structure PureThy: PURE_THY =

struct

(*** theorem tags ***)

(* add / delete tags *)

fun tag_rule tg = Thm.map_tags (insert (op =) tg);

fun untag_rule s = Thm.map_tags (filter_out (fn (s', _) => s = s'));

fun tag tg x = Thm.rule_attribute (K (tag_rule tg)) x;

fun untag s x = Thm.rule_attribute (K (untag_rule s)) x;

(* unofficial theorem names *)

fun the_name_hint thm = the (AList.lookup (op =) (Thm.get_tags thm) Markup.nameN);

val has_name_hint = can the_name_hint;

val get_name_hint = the_default "??.unknown" o try the_name_hint;

fun put_name_hint name = untag_rule Markup.nameN #> tag_rule (Markup.nameN, name);

(* theorem groups *)

fun get_group thm = AList.lookup (op =) (Thm.get_tags thm) Markup.groupN;

fun put_group name =

  if name = "" then I else Thm.map_tags (AList.update (op =) (Markup.groupN, name));

fun group name = Thm.rule_attribute (K (put_group name));

(* theorem kinds *)

fun the_kind thm = the (AList.lookup (op =) (Thm.get_tags thm) Markup.kindN);

val has_kind = can the_kind;

val get_kind = the_default "" o try the_kind;

fun kind_rule k = tag_rule (Markup.kindN, k) o untag_rule Markup.kindN;

fun kind k x = if k = "" then x else Thm.rule_attribute (K (kind_rule k)) x;

fun kind_internal x = kind Thm.internalK x;

fun has_internal tags = exists (fn tg => tg = (Markup.kindN, Thm.internalK)) tags;

val is_internal = has_internal o Thm.get_tags;

(*** theorem database ***)

(** dataype theorems **)

datatype thms = Thms of

 {theorems: thm list NameSpace.table,   (* FIXME legacy *)

  all_facts: Facts.T};

fun make_thms theorems all_facts = Thms {theorems = theorems, all_facts = all_facts};

structure TheoremsData = TheoryDataFun

(

  type T = thms ref;   (* FIXME legacy *)

  val empty = ref (make_thms NameSpace.empty_table Facts.empty);

  fun copy (ref x) = ref x;

  fun extend (ref (Thms {theorems = _, all_facts})) = ref (make_thms NameSpace.empty_table all_facts);

  fun merge _

     (ref (Thms {theorems = _, all_facts = all_facts1}),

      ref (Thms {theorems = _, all_facts = all_facts2})) =

    ref (make_thms NameSpace.empty_table (Facts.merge (all_facts1, all_facts2)));

);

val get_theorems_ref = TheoremsData.get;

val get_theorems = (fn Thms args => args) o ! o get_theorems_ref;

val theorems_of = #theorems o get_theorems;

val all_facts_of = #all_facts o get_theorems;

(** 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 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;

fun interval n iv =

  let fun err () = raise Fail ("Bad interval specification " ^ string_of_interval iv) in

    (case iv of

      FromTo (i, j) => if i <= j then i upto j else err ()

    | From i => if i <= n then i upto n else err ()

    | Single i => [i])

  end;

(* datatype thmref *)

datatype thmref =

  Name of string |

  NameSelection of string * interval list |

  Fact of string;

fun name_of_thmref (Name name) = name

  | name_of_thmref (NameSelection (name, _)) = name

  | name_of_thmref (Fact _) = error "Illegal literal fact";

fun map_name_of_thmref f (Name name) = Name (f name)

  | map_name_of_thmref f (NameSelection (name, is)) = NameSelection (f name, is)

  | map_name_of_thmref _ thmref = thmref;

fun string_of_thmref (Name name) = name

  | string_of_thmref (NameSelection (name, is)) =

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

  | string_of_thmref (Fact _) = error "Illegal literal fact";

(* select_thm *)

fun select_thm (Name _) thms = thms

  | select_thm (Fact _) thms = thms

  | select_thm (NameSelection (name, ivs)) thms =

      let

        val n = length thms;

        fun err msg = error (msg ^ " for " ^ quote name ^ " (length " ^ string_of_int n ^ ")");

        fun select i =

          if i < 1 orelse i > n then err ("Bad subscript " ^ string_of_int i)

          else nth thms (i - 1);

        val is = maps (interval n) ivs handle Fail msg => err msg;

      in map select is end;

(* selections *)

fun selections (name, [thm]) = [(Name name, thm)]

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

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

(* lookup/get thms *)

local

fun lookup_thms thy xname =

  let

    val (space, thms) = #theorems (get_theorems thy);

    val name = NameSpace.intern space xname;

  in Option.map (pair name) (Symtab.lookup thms name) end;

fun lookup_fact thy xname =

  let

    val facts = all_facts_of thy;

    val name = NameSpace.intern (Facts.space_of facts) xname;

  in Option.map (pair name) (Facts.lookup facts name) end;

fun show_result NONE = "none"

  | show_result (SOME (name, _)) = quote name;

fun get_fact silent theory thmref =

  let

    val name = name_of_thmref thmref;

    val new_res = lookup_fact theory name;

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

    val is_same =

      (case (new_res, old_res) of

        (NONE, NONE) => true

      | (SOME (name1, ths1), SOME (name2, ths2)) => name1 = name2 andalso Thm.eq_thms (ths1, ths2)

      | _ => false);

    val _ =

      if is_same orelse silent then ()

      else legacy_feature ("Fact lookup differs from old-style thm database:\n" ^

        show_result new_res ^ " vs " ^ show_result old_res ^

        Position.str_of (Position.thread_data ()));

  in Option.map #2 old_res |> the_thms name |> select_thm thmref |> map (Thm.transfer theory) end;

in

val get_thms_silent = get_fact true;

val get_thms = get_fact false;

fun get_thmss thy thmrefs = maps (get_thms thy) thmrefs;

fun get_thm thy thmref = single_thm (name_of_thmref thmref) (get_thms thy thmref);

end;

(* thms_of etc. *)

fun thms_of thy =

  let val thms = #2 (theorems_of thy)

  in map (`(get_name_hint)) (maps snd (Symtab.dest thms)) end;

fun all_thms_of thy = maps thms_of (thy :: Theory.ancestors_of thy);

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

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

fun hide_thms fully names thy = CRITICAL (fn () =>

  let

    val r as ref (Thms {theorems = (space, thms), all_facts}) = get_theorems_ref thy;

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

  in r := make_thms (space', thms) all_facts; thy end);

(* fact specifications *)

fun map_facts f = map (apsnd (map (apfst (map f))));

fun burrow_fact f = split_list #>> burrow f #> op ~~;

fun burrow_facts f = split_list ##> burrow (burrow_fact f) #> op ~~;

(* naming *)

fun gen_names _ len "" = replicate len ""

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

fun name_multi name [x] = [(name, x)]

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

fun name_thm pre official name thm = thm

  |> (if Thm.get_name thm <> "" andalso pre orelse not official then I else Thm.put_name name)

  |> (if has_name_hint thm andalso pre orelse name = "" then I else put_name_hint name)

  |> Thm.map_tags (Position.default_properties (Position.thread_data ()));

fun name_thms pre official name xs =

  map (uncurry (name_thm pre official)) (name_multi name xs);

fun name_thmss official name fact =

  burrow_fact (name_thms true official name) fact;

(* 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) |> swap

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

      let

        val name = Sign.full_name thy bname;

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

        val r as ref (Thms {theorems = (space, theorems), all_facts}) = get_theorems_ref thy';

        val space' = Sign.declare_name thy' name space;

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

        val all_facts' = Facts.add_global (Sign.naming_of thy') (name, thms') all_facts;

      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 := make_thms (space', theorems') all_facts';

        (thms', thy')

      end);

(* add_thms(s) *)

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

  enter_thms pre_name (name_thms false true)

    (foldl_map (Thm.theory_attributes atts)) (bname, thms);

fun gen_add_thmss pre_name =

  fold_map (add_thms_atts pre_name);

fun gen_add_thms pre_name args =

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

val add_thmss = gen_add_thmss (name_thms true true);

val add_thms = gen_add_thms (name_thms true true);

(* note_thmss(_i) *)

local

fun gen_note_thmss get tag = fold_map (fn ((bname, more_atts), ths_atts) => fn thy =>

  let

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

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

      (name_thmss true) (name_thms false true) (apsnd flat o foldl_map app)

      (bname, map (fn (ths, atts) => (get thy ths, surround tag (atts @ more_atts))) ths_atts);

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

in

fun note_thmss k = gen_note_thmss get_thms (kind k);

fun note_thmss_i k = gen_note_thmss (K I) (kind k);

fun note_thmss_grouped k g = gen_note_thmss (K I) (kind k #> group g);

end;

fun note kind (name, thm) =

  note_thmss_i kind [((name, []), [([thm], [])])]

  #>> (fn [(_, [thm])] => thm);

fun note_thmss_qualified k path facts thy =

  thy

  |> Sign.add_path path

  |> Sign.no_base_names

  |> note_thmss_i k facts

  ||> Sign.restore_naming thy;

(* store_thm *)

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

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

  in (th', thy') end;

(* smart_store_thms(_open) *)

local

fun smart_store _ (name, []) =

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

  | smart_store official (name, [thm]) =

      fst (enter_thms (name_thms true official) (name_thms false official) I (name, [thm])

        (Thm.theory_of_thm thm))

  | smart_store official (name, thms) =

      let val thy = Theory.merge_list (map Thm.theory_of_thm thms) in

        fst (enter_thms (name_thms true official) (name_thms false official) I (name, thms) thy)

      end;

in

val smart_store_thms = smart_store true;

val smart_store_thms_open = smart_store false;

end;

(* forall_elim_var(s) -- belongs to drule.ML *)

fun forall_elim_vars_aux strip_vars i th =

  let

    val {thy, tpairs, prop, ...} = Thm.rep_thm th;

    val add_used = Term.fold_aterms

      (fn Var ((x, j), _) => if i = j then insert (op =) x else I | _ => I);

    val used = fold (fn (t, u) => add_used t o add_used u) tpairs (add_used prop []);

    val vars = strip_vars prop;

    val cvars = (Name.variant_list used (map #1 vars), vars)

      |> ListPair.map (fn (x, (_, T)) => Thm.cterm_of thy (Var ((x, i), T)));

  in fold Thm.forall_elim cvars th end;

val forall_elim_vars = forall_elim_vars_aux Term.strip_all_vars;

fun forall_elim_var i th = forall_elim_vars_aux

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

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

(* store axioms as theorems *)

local

  fun get_ax thy (name, _) = Thm.get_axiom_i thy (Sign.full_name thy name);

  fun get_axs thy named_axs = map (forall_elim_vars 0 o get_ax thy) named_axs;

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

    let

      val named_ax = [(name, ax)];

      val thy' = add named_ax thy;

      val thm = hd (get_axs thy' named_ax);

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

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

    let

      val named_axs = name_multi name axs;

      val thy' = add named_axs thy;

      val thms = get_axs thy' named_axs;

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

  fun add_singles add = fold_map (add_single add);

  fun add_multis add = fold_map (add_multi add);

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 false;

  val add_defs_i           = add_singles o Theory.add_defs_i false;

  val add_defs_unchecked   = add_singles o Theory.add_defs true;

  val add_defs_unchecked_i = add_singles o Theory.add_defs_i true;

end;

(*** the ProtoPure theory ***)

val typ = SimpleSyntax.read_typ;

val term = SimpleSyntax.read_term;

val prop = SimpleSyntax.read_prop;

val appl_syntax =

 [("_appl", typ "('b => 'a) => args => logic", Mixfix ("(1_/(1'(_')))", [1000, 0], 1000)),

  ("_appl", typ "('b => 'a) => args => aprop", Mixfix ("(1_/(1'(_')))", [1000, 0], 1000))];

val applC_syntax =

 [("",       typ "'a => cargs",                  Delimfix "_"),

  ("_cargs", typ "'a => cargs => cargs",         Mixfix ("_/ _", [1000, 1000], 1000)),

  ("_applC", typ "('b => 'a) => cargs => logic", Mixfix ("(1_/ _)", [1000, 1000], 999)),

  ("_applC", typ "('b => 'a) => cargs => aprop", Mixfix ("(1_/ _)", [1000, 1000], 999))];

val proto_pure =

  Context.pre_pure_thy

  |> Compress.init_data

  |> TheoremsData.init

  |> Sign.add_types

   [("fun", 2, NoSyn),

    ("prop", 0, NoSyn),

    ("itself", 1, NoSyn),

    ("dummy", 0, NoSyn)]

  |> Sign.add_nonterminals Syntax.basic_nonterms

  |> Sign.add_syntax_i

   [("_lambda",     typ "pttrns => 'a => logic",     Mixfix ("(3%_./ _)", [0, 3], 3)),

    ("_abs",        typ "'a",                        NoSyn),

    ("",            typ "'a => args",                Delimfix "_"),

    ("_args",       typ "'a => args => args",        Delimfix "_,/ _"),

    ("",            typ "id => idt",                 Delimfix "_"),

    ("_idtdummy",   typ "idt",                       Delimfix "'_"),

    ("_idtyp",      typ "id => type => idt",         Mixfix ("_::_", [], 0)),

    ("_idtypdummy", typ "type => idt",               Mixfix ("'_()::_", [], 0)),

    ("",            typ "idt => idt",                Delimfix "'(_')"),

    ("",            typ "idt => idts",               Delimfix "_"),

    ("_idts",       typ "idt => idts => idts",       Mixfix ("_/ _", [1, 0], 0)),

    ("",            typ "idt => pttrn",              Delimfix "_"),

    ("",            typ "pttrn => pttrns",           Delimfix "_"),

    ("_pttrns",     typ "pttrn => pttrns => pttrns", Mixfix ("_/ _", [1, 0], 0)),

    ("",            typ "id => aprop",               Delimfix "_"),

    ("",            typ "longid => aprop",           Delimfix "_"),

    ("",            typ "var => aprop",              Delimfix "_"),

    ("_DDDOT",      typ "aprop",                     Delimfix "..."),

    ("_aprop",      typ "aprop => prop",             Delimfix "PROP _"),

    ("_asm",        typ "prop => asms",              Delimfix "_"),

    ("_asms",       typ "prop => asms => asms",      Delimfix "_;/ _"),

    ("_bigimpl",    typ "asms => prop => prop",      Mixfix ("((3[| _ |])/ ==> _)", [0, 1], 1)),

    ("_ofclass",    typ "type => logic => prop",     Delimfix "(1OFCLASS/(1'(_,/ _')))"),

    ("_mk_ofclass", typ "dummy",                     NoSyn),

    ("_TYPE",       typ "type => logic",             Delimfix "(1TYPE/(1'(_')))"),

    ("",            typ "id => logic",               Delimfix "_"),

    ("",            typ "longid => logic",           Delimfix "_"),

    ("",            typ "var => logic",              Delimfix "_"),

    ("_DDDOT",      typ "logic",                     Delimfix "..."),

    ("_constify",   typ "num => num_const",          Delimfix "_"),

    ("_indexnum",   typ "num_const => index",        Delimfix "\\<^sub>_"),

    ("_index",      typ "logic => index",            Delimfix "(00\\<^bsub>_\\<^esub>)"),

    ("_indexdefault", typ "index",                   Delimfix ""),

    ("_indexvar",   typ "index",                     Delimfix "'\\<index>"),

    ("_struct",     typ "index => logic",            Mixfix ("\\<struct>_", [1000], 1000)),

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

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

  |> Sign.add_syntax_i appl_syntax

  |> Sign.add_modesyntax_i (Symbol.xsymbolsN, true)

   [("fun",      typ "type => type => type",   Mixfix ("(_/ \\<Rightarrow> _)", [1, 0], 0)),

    ("_bracket", typ "types => type => type",  Mixfix ("([_]/ \\<Rightarrow> _)", [0, 0], 0)),

    ("_ofsort",  typ "tid => sort => type",    Mixfix ("_\\<Colon>_", [1000, 0], 1000)),

    ("_constrain", typ "'a => type => 'a",     Mixfix ("_\\<Colon>_", [4, 0], 3)),

    ("_idtyp",    typ "id => type => idt",     Mixfix ("_\\<Colon>_", [], 0)),

    ("_idtypdummy", typ "type => idt",         Mixfix ("'_()\\<Colon>_", [], 0)),

    ("_type_constraint_", typ "'a",            NoSyn),

    ("_lambda",  typ "pttrns => 'a => logic",  Mixfix ("(3\\<lambda>_./ _)", [0, 3], 3)),

    ("==",       typ "'a => 'a => prop",       InfixrName ("\\<equiv>", 2)),

    ("all_binder", typ "idts => prop => prop", Mixfix ("(3\\<And>_./ _)", [0, 0], 0)),

    ("==>",      typ "prop => prop => prop",   InfixrName ("\\<Longrightarrow>", 1)),

    ("_DDDOT",   typ "aprop",                  Delimfix "\\<dots>"),

    ("_bigimpl", typ "asms => prop => prop",   Mixfix ("((1\\<lbrakk>_\\<rbrakk>)/ \\<Longrightarrow> _)", [0, 1], 1)),

    ("_DDDOT",   typ "logic",                  Delimfix "\\<dots>")]

  |> Sign.add_modesyntax_i ("", false)

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

    ("ProtoPure.term", typ "'a => prop", Delimfix "TERM _"),

    ("ProtoPure.conjunction", typ "prop => prop => prop", InfixrName ("&&", 2))]

  |> Sign.add_modesyntax_i ("HTML", false)

   [("_lambda", typ "pttrns => 'a => logic", Mixfix ("(3\\<lambda>_./ _)", [0, 3], 3))]

  |> Sign.add_consts_i

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

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

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

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

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

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

  |> Theory.add_deps "==" ("==", typ "'a => 'a => prop") []

  |> Theory.add_deps "==>" ("==>", typ "prop => prop => prop") []

  |> Theory.add_deps "all" ("all", typ "('a => prop) => prop") []

  |> Theory.add_deps "TYPE" ("TYPE", typ "'a itself") []

  |> Theory.add_deps Term.dummy_patternN (Term.dummy_patternN, typ "'a") []

  |> Sign.add_trfuns Syntax.pure_trfuns

  |> Sign.add_trfunsT Syntax.pure_trfunsT

  |> Sign.local_path

  |> Sign.add_consts_i

   [("term", typ "'a => prop", NoSyn),

    ("conjunction", typ "prop => prop => prop", NoSyn)]

  |> (add_defs_i false o map Thm.no_attributes)

   [("prop_def", prop "(CONST prop :: prop => prop) (A::prop) == A::prop"),

    ("term_def", prop "(CONST ProtoPure.term :: 'a => prop) (x::'a) == (!!A::prop. A ==> A)"),

    ("conjunction_def", prop "(A && B) == (!!C::prop. (A ==> B ==> C) ==> C)")] |> snd

  |> Sign.hide_consts false ["conjunction", "term"]

  |> add_thmss [(("nothing", []), [])] |> snd

  |> Theory.add_axioms_i Proofterm.equality_axms

  |> Theory.end_theory;

structure ProtoPure =

struct

  val thy = proto_pure;

  val prop_def = get_axiom thy "prop_def";

  val term_def = get_axiom thy "term_def";

  val conjunction_def = get_axiom thy "conjunction_def";

end;

end;

structure BasicPureThy: BASIC_PURE_THY = PureThy;

open BasicPureThy;