(* 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: tag -> thm -> thm
val untag_rule: string -> thm -> thm
val tag: tag -> 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: tag 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 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
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;
fun simple_tag name x = tag (name, []) x;
(* unofficial theorem names *)
fun the_name_hint thm =
(case AList.lookup (op =) (Thm.get_tags thm) "name" of
SOME (k :: _) => k
| _ => raise Option);
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 "name" #> tag_rule ("name", [name]);
(* theorem kinds *)
fun the_kind thm =
(case AList.lookup (op =) (Thm.get_tags thm) "kind" of
SOME (k :: _) => k
| _ => raise Option);
val has_kind = can the_kind;
val get_kind = the_default "??.unknown" o try the_kind;
fun kind_rule k = tag_rule ("kind", [k]) o untag_rule "kind";
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 ("kind", [k]) => k = Thm.internalK | _ => false) tags;
val is_internal = has_internal o Thm.get_tags;
(*** theorem database ***)
(** dataype theorems **)
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 _ _ = ();
end);
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 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;
(* 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, 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 (maps (interval n) 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 thy_ref = Theory.self_ref thy;
val (space, thms) = #theorems (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 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 =
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 =
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;
(*** the ProtoPure theory ***)
val aT = TFree ("'a", []);
val A = Free ("A", propT);
val proto_pure =
Context.pre_pure_thy
|> Compress.init_data
|> Sign.init_data
|> Theory.init_data
|> Proofterm.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
[("_lambda", "[pttrns, 'a] => logic", Mixfix ("(3%_./ _)", [0, 3], 3)),
("_abs", "'a", NoSyn),
("", "'a => args", Delimfix "_"),
("_args", "['a, args] => args", Delimfix "_,/ _"),
("", "id => idt", Delimfix "_"),
("_idtdummy", "idt", Delimfix "'_"),
("_idtyp", "[id, type] => idt", Mixfix ("_::_", [], 0)),
("_idtypdummy", "type => idt", Mixfix ("'_()::_", [], 0)),
("", "idt => idt", Delimfix "'(_')"),
("", "idt => idts", Delimfix "_"),
("_idts", "[idt, idts] => idts", Mixfix ("_/ _", [1, 0], 0)),
("", "idt => pttrn", Delimfix "_"),
("", "pttrn => pttrns", Delimfix "_"),
("_pttrns", "[pttrn, pttrns] => pttrns", Mixfix ("_/ _", [1, 0], 0)),
("", "id => aprop", Delimfix "_"),
("", "longid => aprop", Delimfix "_"),
("", "var => aprop", Delimfix "_"),
("_DDDOT", "aprop", Delimfix "..."),
("_aprop", "aprop => prop", Delimfix "PROP _"),
("_asm", "prop => asms", Delimfix "_"),
("_asms", "[prop, asms] => asms", Delimfix "_;/ _"),
("_bigimpl", "[asms, prop] => prop", Mixfix ("((3[| _ |])/ ==> _)", [0, 1], 1)),
("_ofclass", "[type, logic] => prop", Delimfix "(1OFCLASS/(1'(_,/ _')))"),
("_mk_ofclass", "_", NoSyn),
("_TYPE", "type => logic", Delimfix "(1TYPE/(1'(_')))"),
("", "id => logic", Delimfix "_"),
("", "longid => logic", Delimfix "_"),
("", "var => logic", Delimfix "_"),
("_DDDOT", "logic", Delimfix "..."),
("_constify", "num => num_const", Delimfix "_"),
("_indexnum", "num_const => index", Delimfix "\\<^sub>_"),
("_index", "logic => index", Delimfix "(00\\<^bsub>_\\<^esub>)"),
("_indexdefault", "index", Delimfix ""),
("_indexvar", "index", Delimfix "'\\<index>"),
("_struct", "index => logic", Mixfix ("\\<struct>_", [1000], 1000)),
("==>", "prop => prop => prop", Delimfix "op ==>"),
(Term.dummy_patternN, "aprop", Delimfix "'_")]
|> Sign.add_syntax Syntax.appl_syntax
|> Sign.add_modesyntax (Symbol.xsymbolsN, true)
[("fun", "[type, type] => type", Mixfix ("(_/ \\<Rightarrow> _)", [1, 0], 0)),
("_bracket", "[types, type] => type", Mixfix ("([_]/ \\<Rightarrow> _)", [0, 0], 0)),
("_ofsort", "[tid, sort] => type", Mixfix ("_\\<Colon>_", [1000, 0], 1000)),
("_constrain", "['a, type] => 'a", Mixfix ("_\\<Colon>_", [4, 0], 3)),
("_idtyp", "[id, type] => idt", Mixfix ("_\\<Colon>_", [], 0)),
("_idtypdummy", "type => idt", Mixfix ("'_()\\<Colon>_", [], 0)),
("_type_constraint_", "'a", NoSyn),
("_lambda", "[pttrns, 'a] => logic", Mixfix ("(3\\<lambda>_./ _)", [0, 3], 3)),
("==", "['a, 'a] => prop", InfixrName ("\\<equiv>", 2)),
("all_binder", "[idts, prop] => prop", Mixfix ("(3\\<And>_./ _)", [0, 0], 0)),
("==>", "[prop, prop] => prop", InfixrName ("\\<Longrightarrow>", 1)),
("_DDDOT", "aprop", Delimfix "\\<dots>"),
("_bigimpl", "[asms, prop] => prop", Mixfix ("((1\\<lbrakk>_\\<rbrakk>)/ \\<Longrightarrow> _)", [0, 1], 1)),
("_DDDOT", "logic", Delimfix "\\<dots>")]
|> Sign.add_modesyntax ("", false)
[("prop", "prop => prop", Mixfix ("_", [0], 0)),
("ProtoPure.term", "'a => prop", Delimfix "TERM _"),
("ProtoPure.conjunction", "prop => prop => prop", InfixrName ("&&", 2))]
|> Sign.add_modesyntax ("HTML", false)
[("_lambda", "[pttrns, 'a] => logic", Mixfix ("(3\\<lambda>_./ _)", [0, 3], 3))]
|> Sign.add_consts
[("==", "'a => 'a => prop", InfixrName ("==", 2)),
("==>", "prop => prop => prop", Mixfix ("(_/ ==> _)", [2, 1], 1)),
("all", "('a => prop) => prop", Binder ("!!", 0, 0)),
("prop", "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", Term.a_itselfT),
Const (Term.dummy_patternN, aT)]
|> Sign.add_trfuns Syntax.pure_trfuns
|> Sign.add_trfunsT Syntax.pure_trfunsT
|> Sign.local_path
|> Sign.add_consts
[("term", "'a => prop", NoSyn),
("conjunction", "prop => prop => prop", NoSyn)]
|> (add_defs false o map Thm.no_attributes)
[("prop_def", "prop(A) == A"),
("term_def", "term(x) == (!!A. PROP A ==> PROP A)"),
("conjunction_def",
"conjunction(A, B) == (!!C. (PROP A ==> PROP B ==> PROP C) ==> PROP 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;