src/Pure/drule.ML
author skalberg
Wed Jun 23 14:44:22 2004 +0200 (2004-06-23)
changeset 15001 fb2141a9f8c0
parent 14854 61bdf2ae4dc5
child 15262 49f70168f4c0
permissions -rw-r--r--
Moved conversion rules from MetaSimplifier to Drule. refl_implies removed
from Drule, instead imp_cong' exported from there.
wenzelm@252
     1
(*  Title:      Pure/drule.ML
clasohm@0
     2
    ID:         $Id$
wenzelm@252
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0
     4
    Copyright   1993  University of Cambridge
clasohm@0
     5
wenzelm@3766
     6
Derived rules and other operations on theorems.
clasohm@0
     7
*)
clasohm@0
     8
berghofe@13606
     9
infix 0 RS RSN RL RLN MRS MRL OF COMP;
clasohm@0
    10
wenzelm@5903
    11
signature BASIC_DRULE =
wenzelm@3766
    12
sig
paulson@9547
    13
  val mk_implies        : cterm * cterm -> cterm
paulson@9547
    14
  val list_implies      : cterm list * cterm -> cterm
wenzelm@4285
    15
  val dest_implies      : cterm -> cterm * cterm
berghofe@10414
    16
  val dest_equals       : cterm -> cterm * cterm
wenzelm@8328
    17
  val strip_imp_prems   : cterm -> cterm list
berghofe@10414
    18
  val strip_imp_concl   : cterm -> cterm
wenzelm@8328
    19
  val cprems_of         : thm -> cterm list
wenzelm@8328
    20
  val read_insts        :
wenzelm@4285
    21
          Sign.sg -> (indexname -> typ option) * (indexname -> sort option)
wenzelm@4285
    22
                  -> (indexname -> typ option) * (indexname -> sort option)
wenzelm@4285
    23
                  -> string list -> (string*string)list
wenzelm@4285
    24
                  -> (indexname*ctyp)list * (cterm*cterm)list
wenzelm@4285
    25
  val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
wenzelm@7636
    26
  val strip_shyps_warning : thm -> thm
wenzelm@8328
    27
  val forall_intr_list  : cterm list -> thm -> thm
wenzelm@8328
    28
  val forall_intr_frees : thm -> thm
wenzelm@8328
    29
  val forall_intr_vars  : thm -> thm
wenzelm@8328
    30
  val forall_elim_list  : cterm list -> thm -> thm
wenzelm@8328
    31
  val forall_elim_var   : int -> thm -> thm
wenzelm@8328
    32
  val forall_elim_vars  : int -> thm -> thm
wenzelm@12725
    33
  val gen_all           : thm -> thm
wenzelm@8328
    34
  val freeze_thaw       : thm -> thm * (thm -> thm)
wenzelm@8328
    35
  val implies_elim_list : thm -> thm list -> thm
wenzelm@8328
    36
  val implies_intr_list : cterm list -> thm -> thm
paulson@8129
    37
  val instantiate       :
paulson@8129
    38
    (indexname * ctyp) list * (cterm * cterm) list -> thm -> thm
wenzelm@8328
    39
  val zero_var_indexes  : thm -> thm
wenzelm@8328
    40
  val standard          : thm -> thm
berghofe@11512
    41
  val standard'         : thm -> thm
paulson@4610
    42
  val rotate_prems      : int -> thm -> thm
oheimb@11163
    43
  val rearrange_prems   : int list -> thm -> thm
wenzelm@8328
    44
  val assume_ax         : theory -> string -> thm
wenzelm@8328
    45
  val RSN               : thm * (int * thm) -> thm
wenzelm@8328
    46
  val RS                : thm * thm -> thm
wenzelm@8328
    47
  val RLN               : thm list * (int * thm list) -> thm list
wenzelm@8328
    48
  val RL                : thm list * thm list -> thm list
wenzelm@8328
    49
  val MRS               : thm list * thm -> thm
wenzelm@8328
    50
  val MRL               : thm list list * thm list -> thm list
wenzelm@9288
    51
  val OF                : thm * thm list -> thm
wenzelm@8328
    52
  val compose           : thm * int * thm -> thm list
wenzelm@8328
    53
  val COMP              : thm * thm -> thm
clasohm@0
    54
  val read_instantiate_sg: Sign.sg -> (string*string)list -> thm -> thm
wenzelm@8328
    55
  val read_instantiate  : (string*string)list -> thm -> thm
wenzelm@8328
    56
  val cterm_instantiate : (cterm*cterm)list -> thm -> thm
wenzelm@13105
    57
  val eq_thm_sg         : thm * thm -> bool
wenzelm@13105
    58
  val eq_thm_prop	: thm * thm -> bool
wenzelm@8328
    59
  val weak_eq_thm       : thm * thm -> bool
wenzelm@8328
    60
  val size_of_thm       : thm -> int
wenzelm@8328
    61
  val reflexive_thm     : thm
wenzelm@8328
    62
  val symmetric_thm     : thm
wenzelm@8328
    63
  val transitive_thm    : thm
nipkow@4679
    64
  val symmetric_fun     : thm -> thm
berghofe@11512
    65
  val extensional       : thm -> thm
berghofe@10414
    66
  val imp_cong          : thm
berghofe@10414
    67
  val swap_prems_eq     : thm
wenzelm@8328
    68
  val equal_abs_elim    : cterm  -> thm -> thm
wenzelm@4285
    69
  val equal_abs_elim_list: cterm list -> thm -> thm
wenzelm@8328
    70
  val asm_rl            : thm
wenzelm@8328
    71
  val cut_rl            : thm
wenzelm@8328
    72
  val revcut_rl         : thm
wenzelm@8328
    73
  val thin_rl           : thm
wenzelm@4285
    74
  val triv_forall_equality: thm
nipkow@1756
    75
  val swap_prems_rl     : thm
wenzelm@4285
    76
  val equal_intr_rule   : thm
wenzelm@13368
    77
  val equal_elim_rule1  : thm
paulson@8550
    78
  val inst              : string -> string -> thm -> thm
wenzelm@8328
    79
  val instantiate'      : ctyp option list -> cterm option list -> thm -> thm
wenzelm@8328
    80
  val incr_indexes_wrt  : int list -> ctyp list -> cterm list -> thm list -> thm -> thm
wenzelm@5903
    81
end;
wenzelm@5903
    82
wenzelm@5903
    83
signature DRULE =
wenzelm@5903
    84
sig
wenzelm@5903
    85
  include BASIC_DRULE
berghofe@12908
    86
  val strip_comb: cterm -> cterm * cterm list
wenzelm@11975
    87
  val rule_attribute: ('a -> thm -> thm) -> 'a attribute
wenzelm@11975
    88
  val tag_rule: tag -> thm -> thm
wenzelm@11975
    89
  val untag_rule: string -> thm -> thm
wenzelm@11975
    90
  val tag: tag -> 'a attribute
wenzelm@11975
    91
  val untag: string -> 'a attribute
wenzelm@11975
    92
  val get_kind: thm -> string
wenzelm@11975
    93
  val kind: string -> 'a attribute
wenzelm@11975
    94
  val theoremK: string
wenzelm@11975
    95
  val lemmaK: string
wenzelm@11975
    96
  val corollaryK: string
wenzelm@11975
    97
  val internalK: string
wenzelm@11975
    98
  val kind_internal: 'a attribute
wenzelm@11975
    99
  val has_internal: tag list -> bool
wenzelm@11975
   100
  val impose_hyps: cterm list -> thm -> thm
wenzelm@13389
   101
  val satisfy_hyps: thm list -> thm -> thm
wenzelm@11975
   102
  val close_derivation: thm -> thm
wenzelm@12005
   103
  val local_standard: thm -> thm
wenzelm@11975
   104
  val compose_single: thm * int * thm -> thm
wenzelm@12373
   105
  val add_rule: thm -> thm list -> thm list
wenzelm@12373
   106
  val del_rule: thm -> thm list -> thm list
wenzelm@11975
   107
  val add_rules: thm list -> thm list -> thm list
wenzelm@11975
   108
  val del_rules: thm list -> thm list -> thm list
wenzelm@11975
   109
  val merge_rules: thm list * thm list -> thm list
skalberg@15001
   110
  val imp_cong'         : thm -> thm -> thm
skalberg@15001
   111
  val beta_eta_conversion: cterm -> thm
skalberg@15001
   112
  val goals_conv        : (int -> bool) -> (cterm -> thm) -> cterm -> thm
skalberg@15001
   113
  val forall_conv       : (cterm -> thm) -> cterm -> thm
skalberg@15001
   114
  val fconv_rule        : (cterm -> thm) -> thm -> thm
wenzelm@11975
   115
  val norm_hhf_eq: thm
wenzelm@12800
   116
  val is_norm_hhf: term -> bool
wenzelm@12800
   117
  val norm_hhf: Sign.sg -> term -> term
wenzelm@11975
   118
  val triv_goal: thm
wenzelm@11975
   119
  val rev_triv_goal: thm
wenzelm@11815
   120
  val implies_intr_goals: cterm list -> thm -> thm
wenzelm@11975
   121
  val freeze_all: thm -> thm
wenzelm@11975
   122
  val mk_triv_goal: cterm -> thm
wenzelm@11975
   123
  val tvars_of_terms: term list -> (indexname * sort) list
wenzelm@11975
   124
  val vars_of_terms: term list -> (indexname * typ) list
wenzelm@11975
   125
  val tvars_of: thm -> (indexname * sort) list
wenzelm@11975
   126
  val vars_of: thm -> (indexname * typ) list
berghofe@14081
   127
  val rename_bvars: (string * string) list -> thm -> thm
berghofe@14081
   128
  val rename_bvars': string option list -> thm -> thm
wenzelm@11975
   129
  val unvarifyT: thm -> thm
wenzelm@11975
   130
  val unvarify: thm -> thm
wenzelm@12495
   131
  val tvars_intr_list: string list -> thm -> thm * (string * indexname) list
wenzelm@12297
   132
  val remdups_rl: thm
wenzelm@11975
   133
  val conj_intr: thm -> thm -> thm
wenzelm@11975
   134
  val conj_intr_list: thm list -> thm
wenzelm@11975
   135
  val conj_elim: thm -> thm * thm
wenzelm@11975
   136
  val conj_elim_list: thm -> thm list
wenzelm@12135
   137
  val conj_elim_precise: int -> thm -> thm list
wenzelm@12135
   138
  val conj_intr_thm: thm
berghofe@13325
   139
  val abs_def: thm -> thm
wenzelm@3766
   140
end;
clasohm@0
   141
wenzelm@5903
   142
structure Drule: DRULE =
clasohm@0
   143
struct
clasohm@0
   144
wenzelm@3991
   145
lcp@708
   146
(** some cterm->cterm operations: much faster than calling cterm_of! **)
lcp@708
   147
paulson@2004
   148
(** SAME NAMES as in structure Logic: use compound identifiers! **)
paulson@2004
   149
clasohm@1703
   150
(*dest_implies for cterms. Note T=prop below*)
paulson@2004
   151
fun dest_implies ct =
wenzelm@8328
   152
    case term_of ct of
wenzelm@8328
   153
        (Const("==>", _) $ _ $ _) =>
wenzelm@10767
   154
            let val (ct1,ct2) = Thm.dest_comb ct
wenzelm@10767
   155
            in  (#2 (Thm.dest_comb ct1), ct2)  end
paulson@2004
   156
      | _ => raise TERM ("dest_implies", [term_of ct]) ;
clasohm@1703
   157
berghofe@10414
   158
fun dest_equals ct =
berghofe@10414
   159
    case term_of ct of
berghofe@10414
   160
        (Const("==", _) $ _ $ _) =>
wenzelm@10767
   161
            let val (ct1,ct2) = Thm.dest_comb ct
wenzelm@10767
   162
            in  (#2 (Thm.dest_comb ct1), ct2)  end
berghofe@10414
   163
      | _ => raise TERM ("dest_equals", [term_of ct]) ;
berghofe@10414
   164
clasohm@1703
   165
lcp@708
   166
(* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
paulson@2004
   167
fun strip_imp_prems ct =
paulson@2004
   168
    let val (cA,cB) = dest_implies ct
paulson@2004
   169
    in  cA :: strip_imp_prems cB  end
lcp@708
   170
    handle TERM _ => [];
lcp@708
   171
paulson@2004
   172
(* A1==>...An==>B  goes to B, where B is not an implication *)
paulson@2004
   173
fun strip_imp_concl ct =
wenzelm@8328
   174
    case term_of ct of (Const("==>", _) $ _ $ _) =>
wenzelm@10767
   175
        strip_imp_concl (#2 (Thm.dest_comb ct))
paulson@2004
   176
  | _ => ct;
paulson@2004
   177
lcp@708
   178
(*The premises of a theorem, as a cterm list*)
berghofe@13659
   179
val cprems_of = strip_imp_prems o cprop_of;
lcp@708
   180
paulson@9547
   181
val proto_sign = Theory.sign_of ProtoPure.thy;
paulson@9547
   182
paulson@9547
   183
val implies = cterm_of proto_sign Term.implies;
paulson@9547
   184
paulson@9547
   185
(*cterm version of mk_implies*)
wenzelm@10767
   186
fun mk_implies(A,B) = Thm.capply (Thm.capply implies A) B;
paulson@9547
   187
paulson@9547
   188
(*cterm version of list_implies: [A1,...,An], B  goes to [|A1;==>;An|]==>B *)
paulson@9547
   189
fun list_implies([], B) = B
paulson@9547
   190
  | list_implies(A::AS, B) = mk_implies (A, list_implies(AS,B));
paulson@9547
   191
berghofe@12908
   192
(*cterm version of strip_comb: maps  f(t1,...,tn)  to  (f, [t1,...,tn]) *)
berghofe@12908
   193
fun strip_comb ct = 
berghofe@12908
   194
  let
berghofe@12908
   195
    fun stripc (p as (ct, cts)) =
berghofe@12908
   196
      let val (ct1, ct2) = Thm.dest_comb ct
berghofe@12908
   197
      in stripc (ct1, ct2 :: cts) end handle CTERM _ => p
berghofe@12908
   198
  in stripc (ct, []) end;
berghofe@12908
   199
lcp@708
   200
lcp@229
   201
(** reading of instantiations **)
lcp@229
   202
lcp@229
   203
fun absent ixn =
lcp@229
   204
  error("No such variable in term: " ^ Syntax.string_of_vname ixn);
lcp@229
   205
lcp@229
   206
fun inst_failure ixn =
lcp@229
   207
  error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails");
lcp@229
   208
nipkow@4281
   209
fun read_insts sign (rtypes,rsorts) (types,sorts) used insts =
wenzelm@10403
   210
let
nipkow@4281
   211
    fun split([],tvs,vs) = (tvs,vs)
wenzelm@4691
   212
      | split((sv,st)::l,tvs,vs) = (case Symbol.explode sv of
wenzelm@4691
   213
                  "'"::cs => split(l,(Syntax.indexname cs,st)::tvs,vs)
wenzelm@4691
   214
                | cs => split(l,tvs,(Syntax.indexname cs,st)::vs));
nipkow@4281
   215
    val (tvs,vs) = split(insts,[],[]);
nipkow@4281
   216
    fun readT((a,i),st) =
nipkow@4281
   217
        let val ixn = ("'" ^ a,i);
nipkow@4281
   218
            val S = case rsorts ixn of Some S => S | None => absent ixn;
nipkow@4281
   219
            val T = Sign.read_typ (sign,sorts) st;
wenzelm@10403
   220
        in if Sign.typ_instance sign (T, TVar(ixn,S)) then (ixn,T)
nipkow@4281
   221
           else inst_failure ixn
nipkow@4281
   222
        end
nipkow@4281
   223
    val tye = map readT tvs;
nipkow@4281
   224
    fun mkty(ixn,st) = (case rtypes ixn of
nipkow@4281
   225
                          Some T => (ixn,(st,typ_subst_TVars tye T))
nipkow@4281
   226
                        | None => absent ixn);
nipkow@4281
   227
    val ixnsTs = map mkty vs;
nipkow@4281
   228
    val ixns = map fst ixnsTs
nipkow@4281
   229
    and sTs  = map snd ixnsTs
nipkow@4281
   230
    val (cts,tye2) = read_def_cterms(sign,types,sorts) used false sTs;
nipkow@4281
   231
    fun mkcVar(ixn,T) =
nipkow@4281
   232
        let val U = typ_subst_TVars tye2 T
nipkow@4281
   233
        in cterm_of sign (Var(ixn,U)) end
nipkow@4281
   234
    val ixnTs = ListPair.zip(ixns, map snd sTs)
nipkow@4281
   235
in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) (tye2 @ tye),
nipkow@4281
   236
    ListPair.zip(map mkcVar ixnTs,cts))
nipkow@4281
   237
end;
lcp@229
   238
lcp@229
   239
wenzelm@252
   240
(*** Find the type (sort) associated with a (T)Var or (T)Free in a term
clasohm@0
   241
     Used for establishing default types (of variables) and sorts (of
clasohm@0
   242
     type variables) when reading another term.
clasohm@0
   243
     Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
clasohm@0
   244
***)
clasohm@0
   245
clasohm@0
   246
fun types_sorts thm =
clasohm@0
   247
    let val {prop,hyps,...} = rep_thm thm;
wenzelm@252
   248
        val big = list_comb(prop,hyps); (* bogus term! *)
wenzelm@252
   249
        val vars = map dest_Var (term_vars big);
wenzelm@252
   250
        val frees = map dest_Free (term_frees big);
wenzelm@252
   251
        val tvars = term_tvars big;
wenzelm@252
   252
        val tfrees = term_tfrees big;
wenzelm@252
   253
        fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i));
wenzelm@252
   254
        fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
clasohm@0
   255
    in (typ,sort) end;
clasohm@0
   256
wenzelm@7636
   257
wenzelm@9455
   258
wenzelm@9455
   259
(** basic attributes **)
wenzelm@9455
   260
wenzelm@9455
   261
(* dependent rules *)
wenzelm@9455
   262
wenzelm@9455
   263
fun rule_attribute f (x, thm) = (x, (f x thm));
wenzelm@9455
   264
wenzelm@9455
   265
wenzelm@9455
   266
(* add / delete tags *)
wenzelm@9455
   267
wenzelm@9455
   268
fun map_tags f thm =
wenzelm@9455
   269
  Thm.put_name_tags (Thm.name_of_thm thm, f (#2 (Thm.get_name_tags thm))) thm;
wenzelm@9455
   270
wenzelm@9455
   271
fun tag_rule tg = map_tags (fn tgs => if tg mem tgs then tgs else tgs @ [tg]);
wenzelm@9455
   272
fun untag_rule s = map_tags (filter_out (equal s o #1));
wenzelm@9455
   273
wenzelm@9455
   274
fun tag tg x = rule_attribute (K (tag_rule tg)) x;
wenzelm@9455
   275
fun untag s x = rule_attribute (K (untag_rule s)) x;
wenzelm@9455
   276
wenzelm@9455
   277
fun simple_tag name x = tag (name, []) x;
wenzelm@9455
   278
wenzelm@11741
   279
wenzelm@11741
   280
(* theorem kinds *)
wenzelm@11741
   281
wenzelm@11741
   282
val theoremK = "theorem";
wenzelm@11741
   283
val lemmaK = "lemma";
wenzelm@11741
   284
val corollaryK = "corollary";
wenzelm@11741
   285
val internalK = "internal";
wenzelm@9455
   286
wenzelm@11741
   287
fun get_kind thm =
wenzelm@11741
   288
  (case Library.assoc (#2 (Thm.get_name_tags thm), "kind") of
wenzelm@11741
   289
    Some (k :: _) => k
wenzelm@11741
   290
  | _ => "unknown");
wenzelm@11741
   291
wenzelm@11741
   292
fun kind_rule k = tag_rule ("kind", [k]) o untag_rule "kind";
wenzelm@12710
   293
fun kind k x = if k = "" then x else rule_attribute (K (kind_rule k)) x;
wenzelm@11741
   294
fun kind_internal x = kind internalK x;
wenzelm@11741
   295
fun has_internal tags = exists (equal internalK o fst) tags;
wenzelm@9455
   296
wenzelm@9455
   297
wenzelm@9455
   298
clasohm@0
   299
(** Standardization of rules **)
clasohm@0
   300
wenzelm@7636
   301
(*Strip extraneous shyps as far as possible*)
wenzelm@7636
   302
fun strip_shyps_warning thm =
wenzelm@7636
   303
  let
wenzelm@14824
   304
    val str_of_sort = Pretty.str_of o Sign.pretty_sort (Thm.sign_of_thm thm);
wenzelm@7636
   305
    val thm' = Thm.strip_shyps thm;
wenzelm@7636
   306
    val xshyps = Thm.extra_shyps thm';
wenzelm@7636
   307
  in
wenzelm@7636
   308
    if null xshyps then ()
wenzelm@7636
   309
    else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
wenzelm@7636
   310
    thm'
wenzelm@7636
   311
  end;
wenzelm@7636
   312
clasohm@0
   313
(*Generalization over a list of variables, IGNORING bad ones*)
clasohm@0
   314
fun forall_intr_list [] th = th
clasohm@0
   315
  | forall_intr_list (y::ys) th =
wenzelm@252
   316
        let val gth = forall_intr_list ys th
wenzelm@252
   317
        in  forall_intr y gth   handle THM _ =>  gth  end;
clasohm@0
   318
clasohm@0
   319
(*Generalization over all suitable Free variables*)
clasohm@0
   320
fun forall_intr_frees th =
clasohm@0
   321
    let val {prop,sign,...} = rep_thm th
clasohm@0
   322
    in  forall_intr_list
wenzelm@4440
   323
         (map (cterm_of sign) (sort (make_ord atless) (term_frees prop)))
clasohm@0
   324
         th
clasohm@0
   325
    end;
clasohm@0
   326
wenzelm@7898
   327
val forall_elim_var = PureThy.forall_elim_var;
wenzelm@7898
   328
val forall_elim_vars = PureThy.forall_elim_vars;
clasohm@0
   329
wenzelm@12725
   330
fun gen_all thm =
wenzelm@12719
   331
  let
wenzelm@12719
   332
    val {sign, prop, maxidx, ...} = Thm.rep_thm thm;
wenzelm@12719
   333
    fun elim (th, (x, T)) = Thm.forall_elim (Thm.cterm_of sign (Var ((x, maxidx + 1), T))) th;
wenzelm@12719
   334
    val vs = Term.strip_all_vars prop;
wenzelm@12719
   335
  in foldl elim (thm, Term.variantlist (map #1 vs, []) ~~ map #2 vs) end;
wenzelm@9554
   336
clasohm@0
   337
(*Specialization over a list of cterms*)
clasohm@0
   338
fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
clasohm@0
   339
wenzelm@11815
   340
(* maps A1,...,An |- B   to   [| A1;...;An |] ==> B  *)
clasohm@0
   341
fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
clasohm@0
   342
clasohm@0
   343
(* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
clasohm@0
   344
fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   345
wenzelm@11960
   346
(* maps |- B to A1,...,An |- B *)
wenzelm@11960
   347
fun impose_hyps chyps th =
wenzelm@12092
   348
  let val chyps' = gen_rems (op aconv o apfst Thm.term_of) (chyps, #hyps (Thm.rep_thm th))
wenzelm@12092
   349
  in implies_elim_list (implies_intr_list chyps' th) (map Thm.assume chyps') end;
wenzelm@11960
   350
wenzelm@13389
   351
(* maps A1,...,An and A1,...,An |- B to |- B *)
wenzelm@13389
   352
fun satisfy_hyps ths th =
wenzelm@13389
   353
  implies_elim_list (implies_intr_list (map (#prop o Thm.crep_thm) ths) th) ths;
wenzelm@13389
   354
clasohm@0
   355
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   356
fun zero_var_indexes th =
clasohm@0
   357
    let val {prop,sign,...} = rep_thm th;
clasohm@0
   358
        val vars = term_vars prop
clasohm@0
   359
        val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
wenzelm@252
   360
        val inrs = add_term_tvars(prop,[]);
wenzelm@252
   361
        val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
paulson@2266
   362
        val tye = ListPair.map (fn ((v,rs),a) => (v, TVar((a,0),rs)))
wenzelm@8328
   363
                     (inrs, nms')
wenzelm@252
   364
        val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
wenzelm@252
   365
        fun varpairs([],[]) = []
wenzelm@252
   366
          | varpairs((var as Var(v,T)) :: vars, b::bs) =
wenzelm@252
   367
                let val T' = typ_subst_TVars tye T
wenzelm@252
   368
                in (cterm_of sign (Var(v,T')),
wenzelm@252
   369
                    cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
wenzelm@252
   370
                end
wenzelm@252
   371
          | varpairs _ = raise TERM("varpairs", []);
paulson@8129
   372
    in Thm.instantiate (ctye, varpairs(vars,rev bs)) th end;
clasohm@0
   373
clasohm@0
   374
paulson@14394
   375
(** Standard form of object-rule: no hypotheses, flexflex constraints,
paulson@14394
   376
    Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
wenzelm@10515
   377
paulson@14394
   378
(*Squash a theorem's flexflex constraints provided it can be done uniquely.
paulson@14394
   379
  This step can lose information.*)
paulson@14387
   380
fun flexflex_unique th =
paulson@14387
   381
    case Seq.chop (2, flexflex_rule th) of
paulson@14387
   382
      ([th],_) => th
paulson@14387
   383
    | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
paulson@14387
   384
    |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
paulson@14387
   385
wenzelm@10515
   386
fun close_derivation thm =
wenzelm@10515
   387
  if Thm.get_name_tags thm = ("", []) then Thm.name_thm ("", thm)
wenzelm@10515
   388
  else thm;
wenzelm@10515
   389
berghofe@11512
   390
fun standard' th =
wenzelm@10515
   391
  let val {maxidx,...} = rep_thm th in
wenzelm@10515
   392
    th
berghofe@14391
   393
    |> implies_intr_hyps
wenzelm@10515
   394
    |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
wenzelm@10515
   395
    |> strip_shyps_warning
berghofe@11512
   396
    |> zero_var_indexes |> Thm.varifyT |> Thm.compress
wenzelm@1218
   397
  end;
wenzelm@1218
   398
berghofe@14391
   399
val standard = close_derivation o standard' o flexflex_unique;
berghofe@11512
   400
wenzelm@12005
   401
fun local_standard th =
wenzelm@12221
   402
  th |> strip_shyps |> zero_var_indexes
wenzelm@12005
   403
  |> Thm.compress |> close_derivation;
wenzelm@12005
   404
clasohm@0
   405
wenzelm@8328
   406
(*Convert all Vars in a theorem to Frees.  Also return a function for
paulson@4610
   407
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   408
  Similar code in type/freeze_thaw*)
paulson@4610
   409
fun freeze_thaw th =
paulson@7248
   410
 let val fth = freezeT th
berghofe@13659
   411
     val {prop, tpairs, sign, ...} = rep_thm fth
paulson@7248
   412
 in
berghofe@13659
   413
   case foldr add_term_vars (prop :: Thm.terms_of_tpairs tpairs, []) of
paulson@7248
   414
       [] => (fth, fn x => x)
paulson@7248
   415
     | vars =>
wenzelm@8328
   416
         let fun newName (Var(ix,_), (pairs,used)) =
wenzelm@8328
   417
                   let val v = variant used (string_of_indexname ix)
wenzelm@8328
   418
                   in  ((ix,v)::pairs, v::used)  end;
berghofe@13659
   419
             val (alist, _) = foldr newName (vars, ([], foldr add_term_names
berghofe@13659
   420
               (prop :: Thm.terms_of_tpairs tpairs, [])))
wenzelm@8328
   421
             fun mk_inst (Var(v,T)) =
wenzelm@8328
   422
                 (cterm_of sign (Var(v,T)),
wenzelm@8328
   423
                  cterm_of sign (Free(the (assoc(alist,v)), T)))
wenzelm@8328
   424
             val insts = map mk_inst vars
wenzelm@8328
   425
             fun thaw th' =
wenzelm@8328
   426
                 th' |> forall_intr_list (map #2 insts)
wenzelm@8328
   427
                     |> forall_elim_list (map #1 insts)
wenzelm@8328
   428
         in  (Thm.instantiate ([],insts) fth, thaw)  end
paulson@7248
   429
 end;
paulson@4610
   430
paulson@4610
   431
paulson@7248
   432
(*Rotates a rule's premises to the left by k*)
paulson@7248
   433
val rotate_prems = permute_prems 0;
paulson@4610
   434
oheimb@11163
   435
(* permute prems, where the i-th position in the argument list (counting from 0)
oheimb@11163
   436
   gives the position within the original thm to be transferred to position i.
oheimb@11163
   437
   Any remaining trailing positions are left unchanged. *)
oheimb@11163
   438
val rearrange_prems = let
oheimb@11163
   439
  fun rearr new []      thm = thm
wenzelm@11815
   440
  |   rearr new (p::ps) thm = rearr (new+1)
oheimb@11163
   441
     (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
oheimb@11163
   442
     (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
oheimb@11163
   443
  in rearr 0 end;
paulson@4610
   444
wenzelm@252
   445
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   446
  Generalizes over Free variables,
clasohm@0
   447
  creates the assumption, and then strips quantifiers.
clasohm@0
   448
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   449
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   450
fun assume_ax thy sP =
wenzelm@6390
   451
    let val sign = Theory.sign_of thy
paulson@4610
   452
        val prop = Logic.close_form (term_of (read_cterm sign (sP, propT)))
lcp@229
   453
    in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
clasohm@0
   454
wenzelm@252
   455
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   456
fun tha RSN (i,thb) =
wenzelm@4270
   457
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   458
      ([th],_) => th
clasohm@0
   459
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   460
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   461
clasohm@0
   462
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   463
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   464
clasohm@0
   465
(*For joining lists of rules*)
wenzelm@252
   466
fun thas RLN (i,thbs) =
clasohm@0
   467
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   468
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
paulson@2672
   469
  in  List.concat (map resb thbs)  end;
clasohm@0
   470
clasohm@0
   471
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   472
lcp@11
   473
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   474
  makes proof trees*)
wenzelm@252
   475
fun rls MRS bottom_rl =
lcp@11
   476
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   477
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   478
  in  rs_aux 1 rls  end;
lcp@11
   479
lcp@11
   480
(*As above, but for rule lists*)
wenzelm@252
   481
fun rlss MRL bottom_rls =
lcp@11
   482
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   483
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   484
  in  rs_aux 1 rlss  end;
lcp@11
   485
wenzelm@9288
   486
(*A version of MRS with more appropriate argument order*)
wenzelm@9288
   487
fun bottom_rl OF rls = rls MRS bottom_rl;
wenzelm@9288
   488
wenzelm@252
   489
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   490
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   491
  ALWAYS deletes premise i *)
wenzelm@252
   492
fun compose(tha,i,thb) =
wenzelm@4270
   493
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   494
wenzelm@6946
   495
fun compose_single (tha,i,thb) =
wenzelm@6946
   496
  (case compose (tha,i,thb) of
wenzelm@6946
   497
    [th] => th
wenzelm@6946
   498
  | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
wenzelm@6946
   499
clasohm@0
   500
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   501
fun tha COMP thb =
clasohm@0
   502
    case compose(tha,1,thb) of
wenzelm@252
   503
        [th] => th
clasohm@0
   504
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   505
wenzelm@13105
   506
wenzelm@4016
   507
(** theorem equality **)
clasohm@0
   508
paulson@13650
   509
(*True if the two theorems have the same signature.*)
wenzelm@13105
   510
val eq_thm_sg = Sign.eq_sg o pairself Thm.sign_of_thm;
paulson@13650
   511
paulson@13650
   512
(*True if the two theorems have the same prop field, ignoring hyps, der, etc.*)
wenzelm@13105
   513
val eq_thm_prop = op aconv o pairself Thm.prop_of;
clasohm@0
   514
clasohm@0
   515
(*Useful "distance" function for BEST_FIRST*)
wenzelm@12800
   516
val size_of_thm = size_of_term o prop_of;
clasohm@0
   517
wenzelm@9829
   518
(*maintain lists of theorems --- preserving canonical order*)
wenzelm@13105
   519
fun del_rules rs rules = Library.gen_rems eq_thm_prop (rules, rs);
wenzelm@9862
   520
fun add_rules rs rules = rs @ del_rules rs rules;
wenzelm@12373
   521
val del_rule = del_rules o single;
wenzelm@12373
   522
val add_rule = add_rules o single;
wenzelm@13105
   523
fun merge_rules (rules1, rules2) = gen_merge_lists' eq_thm_prop rules1 rules2;
wenzelm@9829
   524
lcp@1194
   525
(** Mark Staples's weaker version of eq_thm: ignores variable renaming and
lcp@1194
   526
    (some) type variable renaming **)
lcp@1194
   527
lcp@1194
   528
 (* Can't use term_vars, because it sorts the resulting list of variable names.
lcp@1194
   529
    We instead need the unique list noramlised by the order of appearance
lcp@1194
   530
    in the term. *)
lcp@1194
   531
fun term_vars' (t as Var(v,T)) = [t]
lcp@1194
   532
  | term_vars' (Abs(_,_,b)) = term_vars' b
lcp@1194
   533
  | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
lcp@1194
   534
  | term_vars' _ = [];
lcp@1194
   535
lcp@1194
   536
fun forall_intr_vars th =
lcp@1194
   537
  let val {prop,sign,...} = rep_thm th;
lcp@1194
   538
      val vars = distinct (term_vars' prop);
lcp@1194
   539
  in forall_intr_list (map (cterm_of sign) vars) th end;
lcp@1194
   540
wenzelm@13105
   541
val weak_eq_thm = Thm.eq_thm o pairself (forall_intr_vars o freezeT);
lcp@1194
   542
lcp@1194
   543
clasohm@0
   544
(*** Meta-Rewriting Rules ***)
clasohm@0
   545
paulson@4610
   546
fun read_prop s = read_cterm proto_sign (s, propT);
paulson@4610
   547
wenzelm@9455
   548
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
wenzelm@9455
   549
fun store_standard_thm name thm = store_thm name (standard thm);
wenzelm@12135
   550
fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
wenzelm@12135
   551
fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
wenzelm@4016
   552
clasohm@0
   553
val reflexive_thm =
wenzelm@14854
   554
  let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),[])))
wenzelm@12135
   555
  in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
clasohm@0
   556
clasohm@0
   557
val symmetric_thm =
wenzelm@14854
   558
  let val xy = read_prop "x == y"
wenzelm@12135
   559
  in store_standard_thm_open "symmetric" (Thm.implies_intr_hyps (Thm.symmetric (Thm.assume xy))) end;
clasohm@0
   560
clasohm@0
   561
val transitive_thm =
wenzelm@14854
   562
  let val xy = read_prop "x == y"
wenzelm@14854
   563
      val yz = read_prop "y == z"
clasohm@0
   564
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
wenzelm@12135
   565
  in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   566
nipkow@4679
   567
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   568
berghofe@11512
   569
fun extensional eq =
berghofe@11512
   570
  let val eq' =
berghofe@11512
   571
    abstract_rule "x" (snd (Thm.dest_comb (fst (dest_equals (cprop_of eq))))) eq
berghofe@11512
   572
  in equal_elim (eta_conversion (cprop_of eq')) eq' end;
berghofe@11512
   573
berghofe@10414
   574
val imp_cong =
berghofe@10414
   575
  let
berghofe@10414
   576
    val ABC = read_prop "PROP A ==> PROP B == PROP C"
berghofe@10414
   577
    val AB = read_prop "PROP A ==> PROP B"
berghofe@10414
   578
    val AC = read_prop "PROP A ==> PROP C"
berghofe@10414
   579
    val A = read_prop "PROP A"
berghofe@10414
   580
  in
wenzelm@12135
   581
    store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
berghofe@10414
   582
      (implies_intr AB (implies_intr A
berghofe@10414
   583
        (equal_elim (implies_elim (assume ABC) (assume A))
berghofe@10414
   584
          (implies_elim (assume AB) (assume A)))))
berghofe@10414
   585
      (implies_intr AC (implies_intr A
berghofe@10414
   586
        (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
berghofe@10414
   587
          (implies_elim (assume AC) (assume A)))))))
berghofe@10414
   588
  end;
berghofe@10414
   589
berghofe@10414
   590
val swap_prems_eq =
berghofe@10414
   591
  let
berghofe@10414
   592
    val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
berghofe@10414
   593
    val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
berghofe@10414
   594
    val A = read_prop "PROP A"
berghofe@10414
   595
    val B = read_prop "PROP B"
berghofe@10414
   596
  in
wenzelm@12135
   597
    store_standard_thm_open "swap_prems_eq" (equal_intr
berghofe@10414
   598
      (implies_intr ABC (implies_intr B (implies_intr A
berghofe@10414
   599
        (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
berghofe@10414
   600
      (implies_intr BAC (implies_intr A (implies_intr B
berghofe@10414
   601
        (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
berghofe@10414
   602
  end;
lcp@229
   603
skalberg@15001
   604
val imp_cong' = combination o combination (reflexive implies)
clasohm@0
   605
berghofe@13325
   606
fun abs_def thm =
berghofe@13325
   607
  let
berghofe@13325
   608
    val (_, cvs) = strip_comb (fst (dest_equals (cprop_of thm)));
berghofe@13325
   609
    val thm' = foldr (fn (ct, thm) => Thm.abstract_rule
berghofe@13325
   610
      (case term_of ct of Var ((a, _), _) => a | Free (a, _) => a | _ => "x")
berghofe@13325
   611
        ct thm) (cvs, thm)
berghofe@13325
   612
  in transitive
berghofe@13325
   613
    (symmetric (eta_conversion (fst (dest_equals (cprop_of thm'))))) thm'
berghofe@13325
   614
  end;
berghofe@13325
   615
clasohm@0
   616
skalberg@15001
   617
local
skalberg@15001
   618
  val dest_eq = dest_equals o cprop_of
skalberg@15001
   619
  val rhs_of = snd o dest_eq
skalberg@15001
   620
in
skalberg@15001
   621
fun beta_eta_conversion t =
skalberg@15001
   622
  let val thm = beta_conversion true t
skalberg@15001
   623
  in transitive thm (eta_conversion (rhs_of thm)) end
skalberg@15001
   624
end;
skalberg@15001
   625
skalberg@15001
   626
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
skalberg@15001
   627
fun goals_conv pred cv =
skalberg@15001
   628
  let fun gconv i ct =
skalberg@15001
   629
        let val (A,B) = dest_implies ct
skalberg@15001
   630
        in imp_cong' (if pred i then cv A else reflexive A) (gconv (i+1) B) end
skalberg@15001
   631
        handle TERM _ => reflexive ct
skalberg@15001
   632
  in gconv 1 end
skalberg@15001
   633
skalberg@15001
   634
(* Rewrite A in !!x1,...,xn. A *)
skalberg@15001
   635
fun forall_conv cv ct =
skalberg@15001
   636
  let val p as (ct1, ct2) = Thm.dest_comb ct
skalberg@15001
   637
  in (case pairself term_of p of
skalberg@15001
   638
      (Const ("all", _), Abs (s, _, _)) =>
skalberg@15001
   639
         let val (v, ct') = Thm.dest_abs (Some "@") ct2;
skalberg@15001
   640
         in Thm.combination (Thm.reflexive ct1)
skalberg@15001
   641
           (Thm.abstract_rule s v (forall_conv cv ct'))
skalberg@15001
   642
         end
skalberg@15001
   643
    | _ => cv ct)
skalberg@15001
   644
  end handle TERM _ => cv ct;
skalberg@15001
   645
skalberg@15001
   646
(*Use a conversion to transform a theorem*)
skalberg@15001
   647
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
skalberg@15001
   648
clasohm@0
   649
(*** Some useful meta-theorems ***)
clasohm@0
   650
clasohm@0
   651
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@12135
   652
val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
wenzelm@7380
   653
val _ = store_thm "_" asm_rl;
clasohm@0
   654
clasohm@0
   655
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   656
val cut_rl =
wenzelm@12135
   657
  store_standard_thm_open "cut_rl"
wenzelm@9455
   658
    (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   659
wenzelm@252
   660
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   661
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   662
val revcut_rl =
paulson@4610
   663
  let val V = read_prop "PROP V"
paulson@4610
   664
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   665
  in
wenzelm@12135
   666
    store_standard_thm_open "revcut_rl"
wenzelm@4016
   667
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   668
  end;
clasohm@0
   669
lcp@668
   670
(*for deleting an unwanted assumption*)
lcp@668
   671
val thin_rl =
paulson@4610
   672
  let val V = read_prop "PROP V"
paulson@4610
   673
      and W = read_prop "PROP W";
wenzelm@12135
   674
  in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
lcp@668
   675
clasohm@0
   676
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   677
val triv_forall_equality =
paulson@4610
   678
  let val V  = read_prop "PROP V"
paulson@4610
   679
      and QV = read_prop "!!x::'a. PROP V"
wenzelm@8086
   680
      and x  = read_cterm proto_sign ("x", TypeInfer.logicT);
wenzelm@4016
   681
  in
wenzelm@12135
   682
    store_standard_thm_open "triv_forall_equality"
berghofe@11512
   683
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
berghofe@11512
   684
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   685
  end;
clasohm@0
   686
nipkow@1756
   687
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   688
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   689
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   690
*)
nipkow@1756
   691
val swap_prems_rl =
paulson@4610
   692
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   693
      val major = assume cmajor;
paulson@4610
   694
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   695
      val minor1 = assume cminor1;
paulson@4610
   696
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   697
      val minor2 = assume cminor2;
wenzelm@12135
   698
  in store_standard_thm_open "swap_prems_rl"
nipkow@1756
   699
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   700
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   701
  end;
nipkow@1756
   702
nipkow@3653
   703
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   704
   ==> PROP ?phi == PROP ?psi
wenzelm@8328
   705
   Introduction rule for == as a meta-theorem.
nipkow@3653
   706
*)
nipkow@3653
   707
val equal_intr_rule =
paulson@4610
   708
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   709
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   710
  in
wenzelm@12135
   711
    store_standard_thm_open "equal_intr_rule"
wenzelm@4016
   712
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   713
  end;
nipkow@3653
   714
wenzelm@13368
   715
(* [| PROP ?phi == PROP ?psi; PROP ?phi |] ==> PROP ?psi *)
wenzelm@13368
   716
val equal_elim_rule1 =
wenzelm@13368
   717
  let val eq = read_prop "PROP phi == PROP psi"
wenzelm@13368
   718
      and P = read_prop "PROP phi"
wenzelm@13368
   719
  in store_standard_thm_open "equal_elim_rule1"
wenzelm@13368
   720
    (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
wenzelm@13368
   721
  end;
wenzelm@4285
   722
wenzelm@12297
   723
(* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
wenzelm@12297
   724
wenzelm@12297
   725
val remdups_rl =
wenzelm@12297
   726
  let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
wenzelm@12297
   727
  in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
wenzelm@12297
   728
wenzelm@12297
   729
wenzelm@9554
   730
(*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
wenzelm@12297
   731
  Rewrite rule for HHF normalization.*)
wenzelm@9554
   732
wenzelm@9554
   733
val norm_hhf_eq =
wenzelm@9554
   734
  let
wenzelm@9554
   735
    val cert = Thm.cterm_of proto_sign;
wenzelm@14854
   736
    val aT = TFree ("'a", []);
wenzelm@9554
   737
    val all = Term.all aT;
wenzelm@9554
   738
    val x = Free ("x", aT);
wenzelm@9554
   739
    val phi = Free ("phi", propT);
wenzelm@9554
   740
    val psi = Free ("psi", aT --> propT);
wenzelm@9554
   741
wenzelm@9554
   742
    val cx = cert x;
wenzelm@9554
   743
    val cphi = cert phi;
wenzelm@9554
   744
    val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
wenzelm@9554
   745
    val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
wenzelm@9554
   746
  in
wenzelm@9554
   747
    Thm.equal_intr
wenzelm@9554
   748
      (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
wenzelm@9554
   749
        |> Thm.forall_elim cx
wenzelm@9554
   750
        |> Thm.implies_intr cphi
wenzelm@9554
   751
        |> Thm.forall_intr cx
wenzelm@9554
   752
        |> Thm.implies_intr lhs)
wenzelm@9554
   753
      (Thm.implies_elim
wenzelm@9554
   754
          (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
wenzelm@9554
   755
        |> Thm.forall_intr cx
wenzelm@9554
   756
        |> Thm.implies_intr cphi
wenzelm@9554
   757
        |> Thm.implies_intr rhs)
wenzelm@12135
   758
    |> store_standard_thm_open "norm_hhf_eq"
wenzelm@9554
   759
  end;
wenzelm@9554
   760
wenzelm@12800
   761
fun is_norm_hhf tm =
wenzelm@12800
   762
  let
wenzelm@12800
   763
    fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
wenzelm@12800
   764
      | is_norm (t $ u) = is_norm t andalso is_norm u
wenzelm@12800
   765
      | is_norm (Abs (_, _, t)) = is_norm t
wenzelm@12800
   766
      | is_norm _ = true;
wenzelm@12800
   767
  in is_norm (Pattern.beta_eta_contract tm) end;
wenzelm@12800
   768
wenzelm@12800
   769
fun norm_hhf sg t =
wenzelm@12800
   770
  if is_norm_hhf t then t
berghofe@13198
   771
  else Pattern.rewrite_term (Sign.tsig_of sg) [Logic.dest_equals (prop_of norm_hhf_eq)] [] t;
wenzelm@12800
   772
wenzelm@9554
   773
paulson@8129
   774
(*** Instantiate theorem th, reading instantiations under signature sg ****)
paulson@8129
   775
paulson@8129
   776
(*Version that normalizes the result: Thm.instantiate no longer does that*)
paulson@8129
   777
fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
paulson@8129
   778
paulson@8129
   779
fun read_instantiate_sg sg sinsts th =
paulson@8129
   780
    let val ts = types_sorts th;
wenzelm@12800
   781
        val used = add_term_tvarnames (prop_of th, []);
paulson@8129
   782
    in  instantiate (read_insts sg ts ts used sinsts) th  end;
paulson@8129
   783
paulson@8129
   784
(*Instantiate theorem th, reading instantiations under theory of th*)
paulson@8129
   785
fun read_instantiate sinsts th =
wenzelm@14643
   786
    read_instantiate_sg (Thm.sign_of_thm th) sinsts th;
paulson@8129
   787
paulson@8129
   788
paulson@8129
   789
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
paulson@8129
   790
  Instantiates distinct Vars by terms, inferring type instantiations. *)
paulson@8129
   791
local
paulson@8129
   792
  fun add_types ((ct,cu), (sign,tye,maxidx)) =
paulson@8129
   793
    let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
paulson@8129
   794
        and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@8129
   795
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
paulson@8129
   796
        val sign' = Sign.merge(sign, Sign.merge(signt, signu))
wenzelm@14643
   797
        val (tye',maxi') = Type.unify (Sign.tsig_of sign') (tye, maxi) (T, U)
wenzelm@10403
   798
          handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
paulson@8129
   799
    in  (sign', tye', maxi')  end;
paulson@8129
   800
in
paulson@8129
   801
fun cterm_instantiate ctpairs0 th =
wenzelm@14643
   802
  let val (sign,tye,_) = foldr add_types (ctpairs0, (Thm.sign_of_thm th, Vartab.empty, 0))
paulson@14340
   803
      fun instT(ct,cu) = 
paulson@14340
   804
        let val inst = cterm_of sign o subst_TVars_Vartab tye o term_of
paulson@14340
   805
        in (inst ct, inst cu) end
paulson@8129
   806
      fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
berghofe@8406
   807
  in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
paulson@8129
   808
  handle TERM _ =>
paulson@8129
   809
           raise THM("cterm_instantiate: incompatible signatures",0,[th])
paulson@8129
   810
       | TYPE (msg, _, _) => raise THM(msg, 0, [th])
paulson@8129
   811
end;
paulson@8129
   812
paulson@8129
   813
paulson@8129
   814
(** Derived rules mainly for METAHYPS **)
paulson@8129
   815
paulson@8129
   816
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
paulson@8129
   817
fun equal_abs_elim ca eqth =
paulson@8129
   818
  let val {sign=signa, t=a, ...} = rep_cterm ca
paulson@8129
   819
      and combth = combination eqth (reflexive ca)
paulson@8129
   820
      val {sign,prop,...} = rep_thm eqth
paulson@8129
   821
      val (abst,absu) = Logic.dest_equals prop
paulson@8129
   822
      val cterm = cterm_of (Sign.merge (sign,signa))
berghofe@10414
   823
  in  transitive (symmetric (beta_conversion false (cterm (abst$a))))
berghofe@10414
   824
           (transitive combth (beta_conversion false (cterm (absu$a))))
paulson@8129
   825
  end
paulson@8129
   826
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
paulson@8129
   827
paulson@8129
   828
(*Calling equal_abs_elim with multiple terms*)
paulson@8129
   829
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
paulson@8129
   830
paulson@8129
   831
wenzelm@10667
   832
(*** Goal (PROP A) <==> PROP A ***)
wenzelm@4789
   833
wenzelm@4789
   834
local
wenzelm@10667
   835
  val cert = Thm.cterm_of proto_sign;
wenzelm@10667
   836
  val A = Free ("A", propT);
wenzelm@10667
   837
  val G = Logic.mk_goal A;
wenzelm@4789
   838
  val (G_def, _) = freeze_thaw ProtoPure.Goal_def;
wenzelm@4789
   839
in
wenzelm@11741
   840
  val triv_goal = store_thm "triv_goal" (kind_rule internalK (standard
wenzelm@10667
   841
      (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume (cert A)))));
wenzelm@11741
   842
  val rev_triv_goal = store_thm "rev_triv_goal" (kind_rule internalK (standard
wenzelm@10667
   843
      (Thm.equal_elim G_def (Thm.assume (cert G)))));
wenzelm@4789
   844
end;
wenzelm@4789
   845
wenzelm@9460
   846
val mk_cgoal = Thm.capply (Thm.cterm_of proto_sign Logic.goal_const);
wenzelm@6995
   847
fun assume_goal ct = Thm.assume (mk_cgoal ct) RS rev_triv_goal;
wenzelm@6995
   848
wenzelm@11815
   849
fun implies_intr_goals cprops thm =
wenzelm@11815
   850
  implies_elim_list (implies_intr_list cprops thm) (map assume_goal cprops)
wenzelm@11815
   851
  |> implies_intr_list (map mk_cgoal cprops);
wenzelm@11815
   852
wenzelm@4789
   853
wenzelm@4285
   854
wenzelm@5688
   855
(** variations on instantiate **)
wenzelm@4285
   856
paulson@8550
   857
(*shorthand for instantiating just one variable in the current theory*)
paulson@8550
   858
fun inst x t = read_instantiate_sg (sign_of (the_context())) [(x,t)];
paulson@8550
   859
paulson@8550
   860
wenzelm@12495
   861
(* collect vars in left-to-right order *)
wenzelm@4285
   862
wenzelm@12495
   863
fun tvars_of_terms ts = rev (foldl Term.add_tvars ([], ts));
wenzelm@12495
   864
fun vars_of_terms ts = rev (foldl Term.add_vars ([], ts));
wenzelm@5903
   865
wenzelm@12800
   866
fun tvars_of thm = tvars_of_terms [prop_of thm];
wenzelm@12800
   867
fun vars_of thm = vars_of_terms [prop_of thm];
wenzelm@4285
   868
wenzelm@4285
   869
wenzelm@4285
   870
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   871
wenzelm@4285
   872
fun instantiate' cTs cts thm =
wenzelm@4285
   873
  let
wenzelm@4285
   874
    fun err msg =
wenzelm@4285
   875
      raise TYPE ("instantiate': " ^ msg,
wenzelm@4285
   876
        mapfilter (apsome Thm.typ_of) cTs,
wenzelm@4285
   877
        mapfilter (apsome Thm.term_of) cts);
wenzelm@4285
   878
wenzelm@4285
   879
    fun inst_of (v, ct) =
wenzelm@4285
   880
      (Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct)
wenzelm@4285
   881
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   882
wenzelm@4285
   883
    fun zip_vars _ [] = []
wenzelm@4285
   884
      | zip_vars (_ :: vs) (None :: opt_ts) = zip_vars vs opt_ts
wenzelm@4285
   885
      | zip_vars (v :: vs) (Some t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
   886
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
   887
wenzelm@4285
   888
    (*instantiate types first!*)
wenzelm@4285
   889
    val thm' =
wenzelm@4285
   890
      if forall is_none cTs then thm
wenzelm@4285
   891
      else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm;
wenzelm@4285
   892
    in
wenzelm@4285
   893
      if forall is_none cts then thm'
wenzelm@4285
   894
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
   895
    end;
wenzelm@4285
   896
wenzelm@4285
   897
berghofe@14081
   898
berghofe@14081
   899
(** renaming of bound variables **)
berghofe@14081
   900
berghofe@14081
   901
(* replace bound variables x_i in thm by y_i *)
berghofe@14081
   902
(* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
berghofe@14081
   903
berghofe@14081
   904
fun rename_bvars [] thm = thm
berghofe@14081
   905
  | rename_bvars vs thm =
berghofe@14081
   906
    let
berghofe@14081
   907
      val {sign, prop, ...} = rep_thm thm;
berghofe@14081
   908
      fun ren (Abs (x, T, t)) = Abs (if_none (assoc (vs, x)) x, T, ren t)
berghofe@14081
   909
        | ren (t $ u) = ren t $ ren u
berghofe@14081
   910
        | ren t = t;
berghofe@14081
   911
    in equal_elim (reflexive (cterm_of sign (ren prop))) thm end;
berghofe@14081
   912
berghofe@14081
   913
berghofe@14081
   914
(* renaming in left-to-right order *)
berghofe@14081
   915
berghofe@14081
   916
fun rename_bvars' xs thm =
berghofe@14081
   917
  let
berghofe@14081
   918
    val {sign, prop, ...} = rep_thm thm;
berghofe@14081
   919
    fun rename [] t = ([], t)
berghofe@14081
   920
      | rename (x' :: xs) (Abs (x, T, t)) =
berghofe@14081
   921
          let val (xs', t') = rename xs t
berghofe@14081
   922
          in (xs', Abs (if_none x' x, T, t')) end
berghofe@14081
   923
      | rename xs (t $ u) =
berghofe@14081
   924
          let
berghofe@14081
   925
            val (xs', t') = rename xs t;
berghofe@14081
   926
            val (xs'', u') = rename xs' u
berghofe@14081
   927
          in (xs'', t' $ u') end
berghofe@14081
   928
      | rename xs t = (xs, t);
berghofe@14081
   929
  in case rename xs prop of
berghofe@14081
   930
      ([], prop') => equal_elim (reflexive (cterm_of sign prop')) thm
berghofe@14081
   931
    | _ => error "More names than abstractions in theorem"
berghofe@14081
   932
  end;
berghofe@14081
   933
berghofe@14081
   934
berghofe@14081
   935
wenzelm@5688
   936
(* unvarify(T) *)
wenzelm@5688
   937
wenzelm@5688
   938
(*assume thm in standard form, i.e. no frees, 0 var indexes*)
wenzelm@5688
   939
wenzelm@5688
   940
fun unvarifyT thm =
wenzelm@5688
   941
  let
wenzelm@5688
   942
    val cT = Thm.ctyp_of (Thm.sign_of_thm thm);
wenzelm@5688
   943
    val tfrees = map (fn ((x, _), S) => Some (cT (TFree (x, S)))) (tvars_of thm);
wenzelm@5688
   944
  in instantiate' tfrees [] thm end;
wenzelm@5688
   945
wenzelm@5688
   946
fun unvarify raw_thm =
wenzelm@5688
   947
  let
wenzelm@5688
   948
    val thm = unvarifyT raw_thm;
wenzelm@5688
   949
    val ct = Thm.cterm_of (Thm.sign_of_thm thm);
wenzelm@5688
   950
    val frees = map (fn ((x, _), T) => Some (ct (Free (x, T)))) (vars_of thm);
wenzelm@5688
   951
  in instantiate' [] frees thm end;
wenzelm@5688
   952
wenzelm@5688
   953
wenzelm@8605
   954
(* tvars_intr_list *)
wenzelm@8605
   955
wenzelm@8605
   956
fun tfrees_of thm =
wenzelm@8605
   957
  let val {hyps, prop, ...} = Thm.rep_thm thm
wenzelm@8605
   958
  in foldr Term.add_term_tfree_names (prop :: hyps, []) end;
wenzelm@8605
   959
wenzelm@8605
   960
fun tvars_intr_list tfrees thm =
wenzelm@8605
   961
  Thm.varifyT' (tfrees_of thm \\ tfrees) thm;
wenzelm@8605
   962
wenzelm@8605
   963
wenzelm@6435
   964
(* increment var indexes *)
wenzelm@6435
   965
wenzelm@6435
   966
fun incr_indexes_wrt is cTs cts thms =
wenzelm@6435
   967
  let
wenzelm@6435
   968
    val maxidx =
wenzelm@6435
   969
      foldl Int.max (~1, is @
wenzelm@6435
   970
        map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
wenzelm@6435
   971
        map (#maxidx o Thm.rep_cterm) cts @
wenzelm@6435
   972
        map (#maxidx o Thm.rep_thm) thms);
berghofe@10414
   973
  in Thm.incr_indexes (maxidx + 1) end;
wenzelm@6435
   974
wenzelm@6435
   975
wenzelm@8328
   976
(* freeze_all *)
wenzelm@8328
   977
wenzelm@8328
   978
(*freeze all (T)Vars; assumes thm in standard form*)
wenzelm@8328
   979
wenzelm@8328
   980
fun freeze_all_TVars thm =
wenzelm@8328
   981
  (case tvars_of thm of
wenzelm@8328
   982
    [] => thm
wenzelm@8328
   983
  | tvars =>
wenzelm@8328
   984
      let val cert = Thm.ctyp_of (Thm.sign_of_thm thm)
wenzelm@8328
   985
      in instantiate' (map (fn ((x, _), S) => Some (cert (TFree (x, S)))) tvars) [] thm end);
wenzelm@8328
   986
wenzelm@8328
   987
fun freeze_all_Vars thm =
wenzelm@8328
   988
  (case vars_of thm of
wenzelm@8328
   989
    [] => thm
wenzelm@8328
   990
  | vars =>
wenzelm@8328
   991
      let val cert = Thm.cterm_of (Thm.sign_of_thm thm)
wenzelm@8328
   992
      in instantiate' [] (map (fn ((x, _), T) => Some (cert (Free (x, T)))) vars) thm end);
wenzelm@8328
   993
wenzelm@8328
   994
val freeze_all = freeze_all_Vars o freeze_all_TVars;
wenzelm@8328
   995
wenzelm@8328
   996
wenzelm@5688
   997
(* mk_triv_goal *)
wenzelm@5688
   998
wenzelm@5688
   999
(*make an initial proof state, "PROP A ==> (PROP A)" *)
paulson@5311
  1000
fun mk_triv_goal ct = instantiate' [] [Some ct] triv_goal;
paulson@5311
  1001
wenzelm@11975
  1002
wenzelm@11975
  1003
wenzelm@11975
  1004
(** meta-level conjunction **)
wenzelm@11975
  1005
wenzelm@11975
  1006
local
wenzelm@11975
  1007
  val A = read_prop "PROP A";
wenzelm@11975
  1008
  val B = read_prop "PROP B";
wenzelm@11975
  1009
  val C = read_prop "PROP C";
wenzelm@11975
  1010
  val ABC = read_prop "PROP A ==> PROP B ==> PROP C";
wenzelm@11975
  1011
wenzelm@11975
  1012
  val proj1 =
wenzelm@11975
  1013
    forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume A))
wenzelm@11975
  1014
    |> forall_elim_vars 0;
wenzelm@11975
  1015
wenzelm@11975
  1016
  val proj2 =
wenzelm@11975
  1017
    forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume B))
wenzelm@11975
  1018
    |> forall_elim_vars 0;
wenzelm@11975
  1019
wenzelm@11975
  1020
  val conj_intr_rule =
wenzelm@11975
  1021
    forall_intr_list [A, B] (implies_intr_list [A, B]
wenzelm@11975
  1022
      (Thm.forall_intr C (Thm.implies_intr ABC
wenzelm@11975
  1023
        (implies_elim_list (Thm.assume ABC) [Thm.assume A, Thm.assume B]))))
wenzelm@11975
  1024
    |> forall_elim_vars 0;
wenzelm@11975
  1025
wenzelm@11975
  1026
  val incr = incr_indexes_wrt [] [] [];
wenzelm@11975
  1027
in
wenzelm@11975
  1028
wenzelm@11975
  1029
fun conj_intr tha thb = thb COMP (tha COMP incr [tha, thb] conj_intr_rule);
wenzelm@12756
  1030
wenzelm@12756
  1031
fun conj_intr_list [] = asm_rl
wenzelm@12756
  1032
  | conj_intr_list ths = foldr1 (uncurry conj_intr) ths;
wenzelm@11975
  1033
wenzelm@11975
  1034
fun conj_elim th =
wenzelm@11975
  1035
  let val th' = forall_elim_var (#maxidx (Thm.rep_thm th) + 1) th
wenzelm@11975
  1036
  in (incr [th'] proj1 COMP th', incr [th'] proj2 COMP th') end;
wenzelm@11975
  1037
wenzelm@11975
  1038
fun conj_elim_list th =
wenzelm@11975
  1039
  let val (th1, th2) = conj_elim th
wenzelm@11975
  1040
  in conj_elim_list th1 @ conj_elim_list th2 end handle THM _ => [th];
wenzelm@11975
  1041
wenzelm@12756
  1042
fun conj_elim_precise 0 _ = []
wenzelm@12756
  1043
  | conj_elim_precise 1 th = [th]
wenzelm@12135
  1044
  | conj_elim_precise n th =
wenzelm@12135
  1045
      let val (th1, th2) = conj_elim th
wenzelm@12135
  1046
      in th1 :: conj_elim_precise (n - 1) th2 end;
wenzelm@12135
  1047
wenzelm@12135
  1048
val conj_intr_thm = store_standard_thm_open "conjunctionI"
wenzelm@12135
  1049
  (implies_intr_list [A, B] (conj_intr (Thm.assume A) (Thm.assume B)));
wenzelm@12135
  1050
clasohm@0
  1051
end;
wenzelm@252
  1052
wenzelm@11975
  1053
end;
wenzelm@5903
  1054
wenzelm@5903
  1055
structure BasicDrule: BASIC_DRULE = Drule;
wenzelm@5903
  1056
open BasicDrule;