(*  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 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 get_thm_closure: theory -> thmref -> thm

   val get_thms_closure: theory -> thmref -> thm list

   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 theorems_of: theory -> thm list NameSpace.table

   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 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_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_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 simple_def: bstring * attribute list ->

     ((bstring * typ * mixfix) * term list) * term -> theory -> (string * thm) * 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 add_defss: bool -> ((bstring * string list) * attribute list) list ->

     theory -> thm list list * theory

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

     theory -> thm list 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 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 "??.unknown" 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 **)

 structure TheoremsData = TheoryDataFun

 (

   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;

 );

 val get_theorems_ref = TheoremsData.get;

 val get_theorems = ! o get_theorems_ref;

 val theorems_of = #theorems o get_theorems;

 val fact_index_of = #index 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));

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

 (*beware of proper order of evaluation!*)

 fun lookup_thms thy =

   let

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

     val thy_ref = Theory.check_thy 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 thmref =>

       let val name = name_of_thmref thmref;

       in select_thm thmref (the_thms name (get_first (fn f => f name) closures)) end

   end;

 fun get_thm_closure thy =

   let val get = get_thms_closure thy

   in fn thmref => single_thm (name_of_thmref thmref) (get thmref) end;

 (* get_thms etc. *)

 fun get_thms theory thmref =

   let val name = name_of_thmref thmref in

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

     |> the_thms name |> select_thm thmref |> map (Thm.transfer theory)

   end;

 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);

 (* thms_containing etc. *)

 fun valid_thms thy (thmref, ths) =

   (case try (get_thms thy) thmref of

     NONE => false

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

 fun thms_containing theory spec =

   (theory :: Theory.ancestors_of theory)

   |> maps (fn thy =>

       FactIndex.find (fact_index_of thy) spec

       |> List.filter (fn (name, ths) => valid_thms theory (Name name, ths))

       |> distinct (eq_fst (op =)));

 fun thms_containing_consts thy consts =

   thms_containing thy (consts, []) |> maps #2

   |> map (`(get_name_hint));

 (* 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 {theorems = (space, thms), index} = get_theorems_ref thy;

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

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

 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 {theorems = (space, theorems), index} = get_theorems_ref thy';

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

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

         val index' = FactIndex.add_global (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'};

         (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 k = 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, atts @ more_atts @ [kind k])) ths_atts);

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

 in

 val note_thmss = gen_note_thmss get_thms;

 val note_thmss_i = gen_note_thmss (K I);

 end;

 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;

   val add_defss            = add_multis o Theory.add_defs false;

   val add_defss_i          = add_multis o Theory.add_defs_i false;

 end;

 (* simple interface for simple definitions *)

 fun simple_def (raw_name, atts) (((raw_c, ty, syn), ts), t) thy =

   let

     val c = Sign.full_name thy raw_c;

     val name = if raw_name = "" then Thm.def_name raw_c else raw_name;

     val def = Logic.mk_equals (list_comb (Const (c, ty), ts), t);

   in

     thy

     |> Sign.add_consts_authentic [] [(raw_c, ty, syn)]

     |> add_defs_i false [((name, def), atts)]

     |-> (fn [thm] => pair (c, thm))

   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_finals_i false

     [Const ("==", typ "'a => 'a => prop"),

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

      Const ("all", typ "('a => prop) => prop"),

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

      Const (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;