src/Pure/pure_thy.ML

improved forall_elim_vars_safe (no longer invents new indexes);

(*  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 hide_thms: bool -> string list -> theory -> theory
  val store_thm: (bstring * thm) * theory attribute list -> theory -> theory * thm
  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) * 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 -> ((bstring * theory attribute list) *
    (xstring * theory attribute list) list) list -> theory -> theory * (bstring * thm list) list
  val have_thmss_i: theory attribute -> ((bstring * theory attribute list) *
    (thm list * theory attribute list) list) list -> theory -> theory * (bstring * 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*)

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

fun hide_thms b names thy =
  let
    val r as ref {space, thms_tab, const_idx} = get_theorems thy;
    val space' = NameSpace.hide b (space, names);
  in r := {space = space', thms_tab = thms_tab, const_idx = const_idx}; thy end;


(* naming *)

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

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

fun name_thms name [x] = [Thm.name_thm (name, x)]
  | name_thms name xs = map Thm.name_thm (name_multi name xs);

fun name_thmss name xs = (case filter_out (null o fst) xs of
    [([x], z)] => [([Thm.name_thm (name, x)], z)]
  | _ => snd (foldl_map (fn (i, (ys, z)) => (i + length ys,
  (map Thm.name_thm (gen_names i (length ys) name ~~ ys), z))) (0, xs)));


(* 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_atts pre_name ((bname, thms), atts) thy =
  enter_thms (Theory.sign_of thy) pre_name name_thms
    (Thm.applys_attributes o rpair atts) thy (bname, thms);

fun gen_add_thmss pre_name args theory =
  foldl_map (fn (thy, arg) => add_thms_atts pre_name arg thy) (theory, args);

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

val add_thmss = gen_add_thmss name_thms;
val add_thms = gen_add_thms name_thms;


(* have_thmss(_i) *)

local

fun gen_have_thss get kind_att (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) => (get thy ths, atts @ more_atts @ [kind_att])) ths_atts);
  in (thy', (bname, thms)) end;

fun gen_have_thmss get kind_att args thy =
  foldl_map (gen_have_thss get kind_att) (thy, args);

in

val have_thmss = gen_have_thmss get_thms;
val have_thmss_i = gen_have_thmss (K I);

end;


(* store_thm *)

fun store_thm ((bname, thm), atts) thy =
  let val (thy', [th']) = add_thms_atts name_thms ((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_thms;
val smart_store_thms_open = gen_smart_store_thms (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 (gen_add_thms (K I) [((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 (gen_add_thmss (K I) [((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 =
  thy
  |> Theory.add_name (get_name 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.xsymbolsN, true) Syntax.pure_xsym_syntax
  |> 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)
    (Syntax.pure_syntax_output @ Syntax.pure_appl_syntax)
  |> Theory.add_trfuns Syntax.pure_trfuns
  |> Theory.add_trfunsT Syntax.pure_trfunsT
  |> 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;