(*  Title:      Pure/pure_thy.ML

    Author:     Markus Wenzel, TU Muenchen

Theorem storage.  Pure theory syntax and logical content.

*)

signature PURE_THY =

sig

  val facts_of: theory -> Facts.T

  val intern_fact: theory -> xstring -> string

  val defined_fact: theory -> string -> bool

  val hide_fact: bool -> string -> theory -> theory

  val join_proofs: theory -> exn list

  val cancel_proofs: theory -> unit

  val get_fact: Context.generic -> theory -> Facts.ref -> thm list

  val get_thms: theory -> xstring -> thm list

  val get_thm: theory -> xstring -> thm

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

  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 -> Position.T -> string -> thm -> thm

  val name_thms: bool -> bool -> Position.T -> string -> thm list -> thm list

  val name_thmss: bool -> Position.T -> string -> (thm list * 'a) list -> (thm list * 'a) list

  val store_thms: binding * thm list -> theory -> thm list * theory

  val store_thm: binding * thm -> theory -> thm * theory

  val store_thm_open: binding * thm -> theory -> thm * theory

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

  val add_thm: (binding * thm) * attribute list -> theory -> thm * theory

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

  val add_thms_dynamic: binding * (Context.generic -> thm list) -> theory -> theory

  val note_thmss: string -> (Thm.binding *

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

  val note_thmss_grouped: string -> string -> (Thm.binding *

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

  val add_axioms: ((binding * term) * attribute list) list -> theory -> thm list * theory

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

  val add_defs: bool -> ((binding * term) * attribute list) list ->

    theory -> thm list * theory

  val add_defs_unchecked: bool -> ((binding * term) * attribute list) list ->

    theory -> thm list * theory

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

    theory -> thm list * theory

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

    theory -> thm list * theory

  val old_appl_syntax: theory -> bool

  val old_appl_syntax_setup: theory -> theory

end;

structure PureThy: PURE_THY =

struct

(*** stored facts ***)

(** theory data **)

structure FactsData = TheoryDataFun

(

  type T = Facts.T * (unit lazy list * Task_Queue.group list);

  val empty = (Facts.empty, ([], []));

  val copy = I;

  fun extend (facts, _) = (facts, ([], []));

  fun merge _ ((facts1, _), (facts2, _)) = (Facts.merge (facts1, facts2), ([], []));

);

(* facts *)

val facts_of = #1 o FactsData.get;

val intern_fact = Facts.intern o facts_of;

val defined_fact = Facts.defined o facts_of;

fun hide_fact fully name = FactsData.map (apfst (Facts.hide fully name));

(* proofs *)

fun lazy_proof thm = Lazy.lazy (fn () => Thm.join_proof thm);

fun join_proofs thy =

  map_filter (Exn.get_exn o Lazy.force_result) (rev (#1 (#2 (FactsData.get thy))));

fun cancel_proofs thy = List.app Future.cancel_group (#2 (#2 (FactsData.get thy)));

(** retrieve theorems **)

fun get_fact context thy xthmref =

  let

    val xname = Facts.name_of_ref xthmref;

    val pos = Facts.pos_of_ref xthmref;

    val name = intern_fact thy xname;

    val res = Facts.lookup context (facts_of thy) name;

    val _ = Theory.check_thy thy;

  in

    (case res of

      NONE => error ("Unknown fact " ^ quote name ^ Position.str_of pos)

    | SOME (static, ths) =>

        (Position.report ((if static then Markup.fact else Markup.dynamic_fact) name) pos;

         Facts.select xthmref (map (Thm.transfer thy) ths)))

  end;

fun get_thms thy = get_fact (Context.Theory thy) thy o Facts.named;

fun get_thm thy name = Facts.the_single name (get_thms thy name);

fun all_thms_of thy =

  Facts.fold_static (fn (_, ths) => append (map (`(Thm.get_name_hint)) ths)) (facts_of thy) [];

(** store theorems **)

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

  | name_multi "" xs = map (pair "") xs

  | name_multi name xs = map_index (fn (i, x) => (name ^ "_" ^ string_of_int (i + 1), x)) xs;

fun name_thm pre official pos name thm = thm

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

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

  |> Thm.default_position pos

  |> Thm.default_position (Position.thread_data ());

fun name_thms pre official pos name xs =

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

fun name_thmss official pos name fact =

  burrow_fact (name_thms true official pos name) fact;

(* enter_thms *)

fun enter_proofs (thy, thms) =

  (FactsData.map (apsnd (fn (proofs, groups) =>

    (fold (cons o lazy_proof) thms proofs, fold Thm.pending_groups thms groups))) thy, thms);

fun enter_thms pre_name post_name app_att (b, thms) thy =

  if Binding.is_empty b

  then swap (enter_proofs (app_att (thy, thms)))

  else

    let

      val naming = Sign.naming_of thy;

      val name = NameSpace.full_name naming b;

      val (thy', thms') =

        enter_proofs (apsnd (post_name name) (app_att (thy, pre_name name thms)));

      val thms'' = map (Thm.transfer thy') thms';

      val thy'' = thy' |> (FactsData.map o apfst) (Facts.add_global naming (b, thms'') #> snd);

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

(* store_thm(s) *)

fun store_thms (b, thms) = enter_thms (name_thms true true Position.none)

  (name_thms false true Position.none) I (b, thms);

fun store_thm (b, th) = store_thms (b, [th]) #>> the_single;

fun store_thm_open (b, th) =

  enter_thms (name_thms true false Position.none) (name_thms false false Position.none) I

    (b, [th]) #>> the_single;

(* add_thms(s) *)

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

  enter_thms pre_name (name_thms false true Position.none)

    (Library.foldl_map (Thm.theory_attributes atts)) (b, 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 Position.none);

val add_thms = gen_add_thms (name_thms true true Position.none);

val add_thm = yield_singleton add_thms;

(* add_thms_dynamic *)

fun add_thms_dynamic (b, f) thy = thy

  |> (FactsData.map o apfst)

      (Facts.add_dynamic (Sign.naming_of thy) (b, f) #> snd);

(* note_thmss *)

local

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

  let

    val pos = Binding.pos_of b;

    val name = Sign.full_name thy b;

    val _ = Position.report (Markup.fact_decl name) pos;

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

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

      (name_thmss true pos) (name_thms false true pos) (apsnd flat o Library.foldl_map app)

      (b, map (fn (ths, atts) => (ths, surround tag (atts @ more_atts))) ths_atts);

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

in

fun note_thmss k = gen_note_thmss (Thm.kind k);

fun note_thmss_grouped k g = gen_note_thmss (Thm.kind k #> Thm.group g);

end;

(* store axioms as theorems *)

local

  fun get_ax thy (b, _) = Thm.axiom thy (Sign.full_name thy b);

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

  fun add_axm prep_b add = fold_map (fn ((b, ax), atts) => fn thy =>

    let

      val named_ax = [(b, ax)];

      val thy' = add named_ax thy;

      val thm = hd (get_axs thy' ((map o apfst) prep_b named_ax));

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

in

  val add_defs               = add_axm I o Theory.add_defs_i false;

  val add_defs_unchecked     = add_axm I o Theory.add_defs_i true;

  val add_axioms             = add_axm I Theory.add_axioms_i;

  val add_defs_cmd           = add_axm Binding.name o Theory.add_defs false;

  val add_defs_unchecked_cmd = add_axm Binding.name o Theory.add_defs true;

  val add_axioms_cmd         = add_axm Binding.name Theory.add_axioms;

end;

(*** Pure theory syntax and logical content ***)

val typ = SimpleSyntax.read_typ;

val term = SimpleSyntax.read_term;

val prop = SimpleSyntax.read_prop;

val typeT = Syntax.typeT;

val spropT = Syntax.spropT;

(* application syntax variants *)

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))];

structure OldApplSyntax = TheoryDataFun

(

  type T = bool;

  val empty = false;

  val copy = I;

  val extend = I;

  fun merge _ (b1, b2) : T =

    if b1 = b2 then b1

    else error "Cannot merge theories with different application syntax";

);

val old_appl_syntax = OldApplSyntax.get;

val old_appl_syntax_setup =

  OldApplSyntax.put true #>

  Sign.del_modesyntax_i Syntax.mode_default applC_syntax #>

  Sign.add_syntax_i appl_syntax;

(* main content *)

val _ = Context.>> (Context.map_theory

  (OldApplSyntax.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 "aprop => aprop",              Delimfix "'(_')"),

    ("",            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 "_"),

    ("_constify",   typ "float_token => float_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 "'_"),

    ("_sort_constraint", typ "type => prop",           Delimfix "(1SORT'_CONSTRAINT/(1'(_')))"),

    ("Pure.term",   typ "logic => prop",               Delimfix "TERM _"),

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

  #> Sign.add_syntax_i applC_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 "logic => type => logic", Mixfix ("_\\<Colon>_", [4, 0], 3)),

    ("_constrain", [spropT, typeT] ---> spropT, 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))]

  #> 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),

    ("sort_constraint", typ "'a itself => prop", NoSyn),

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

  #> (add_defs false o map Thm.no_attributes)

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

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

    (Binding.name "sort_constraint_def",

      prop "(CONST Pure.sort_constraint :: 'a itself => prop) (CONST TYPE :: 'a itself) ==\

      \ (CONST Pure.term :: 'a itself => prop) (CONST TYPE :: 'a itself)"),

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

  #> Sign.hide_const false "Pure.term"

  #> Sign.hide_const false "Pure.sort_constraint"

  #> Sign.hide_const false "Pure.conjunction"

  #> add_thmss [((Binding.name "nothing", []), [])] #> snd

  #> Theory.add_axioms_i ((map o apfst) Binding.name Proofterm.equality_axms)));

end;