src/Pure/drule.ML
author paulson
Thu Aug 13 17:43:00 1998 +0200 (1998-08-13)
changeset 5311 f3f71669878e
parent 5079 2a8ed71f791f
child 5688 7f582495967c
permissions -rw-r--r--
Rule mk_triv_goal for making instances of triv_goal
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
lcp@11
     9
infix 0 RS RSN RL RLN MRS MRL COMP;
clasohm@0
    10
clasohm@0
    11
signature DRULE =
wenzelm@3766
    12
sig
wenzelm@4285
    13
  val dest_implies      : cterm -> cterm * cterm
wenzelm@4285
    14
  val skip_flexpairs	: cterm -> cterm
wenzelm@4285
    15
  val strip_imp_prems	: cterm -> cterm list
clasohm@1460
    16
  val cprems_of		: thm -> cterm list
wenzelm@4285
    17
  val read_insts	:
wenzelm@4285
    18
          Sign.sg -> (indexname -> typ option) * (indexname -> sort option)
wenzelm@4285
    19
                  -> (indexname -> typ option) * (indexname -> sort option)
wenzelm@4285
    20
                  -> string list -> (string*string)list
wenzelm@4285
    21
                  -> (indexname*ctyp)list * (cterm*cterm)list
wenzelm@4285
    22
  val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
clasohm@1460
    23
  val forall_intr_list	: cterm list -> thm -> thm
clasohm@1460
    24
  val forall_intr_frees	: thm -> thm
clasohm@1460
    25
  val forall_intr_vars	: thm -> thm
clasohm@1460
    26
  val forall_elim_list	: cterm list -> thm -> thm
clasohm@1460
    27
  val forall_elim_var	: int -> thm -> thm
clasohm@1460
    28
  val forall_elim_vars	: int -> thm -> thm
paulson@4610
    29
  val freeze_thaw	: thm -> thm * (thm -> thm)
clasohm@1460
    30
  val implies_elim_list	: thm -> thm list -> thm
clasohm@1460
    31
  val implies_intr_list	: cterm list -> thm -> thm
wenzelm@4285
    32
  val zero_var_indexes	: thm -> thm
wenzelm@4285
    33
  val standard		: thm -> thm
paulson@4610
    34
  val rotate_prems      : int -> thm -> thm
wenzelm@4285
    35
  val assume_ax		: theory -> string -> thm
wenzelm@4285
    36
  val RSN		: thm * (int * thm) -> thm
wenzelm@4285
    37
  val RS		: thm * thm -> thm
wenzelm@4285
    38
  val RLN		: thm list * (int * thm list) -> thm list
wenzelm@4285
    39
  val RL		: thm list * thm list -> thm list
wenzelm@4285
    40
  val MRS		: thm list * thm -> thm
clasohm@1460
    41
  val MRL		: thm list list * thm list -> thm list
wenzelm@4285
    42
  val compose		: thm * int * thm -> thm list
wenzelm@4285
    43
  val COMP		: thm * thm -> thm
clasohm@0
    44
  val read_instantiate_sg: Sign.sg -> (string*string)list -> thm -> thm
wenzelm@4285
    45
  val read_instantiate	: (string*string)list -> thm -> thm
wenzelm@4285
    46
  val cterm_instantiate	: (cterm*cterm)list -> thm -> thm
wenzelm@4285
    47
  val weak_eq_thm	: thm * thm -> bool
wenzelm@4285
    48
  val eq_thm_sg		: thm * thm -> bool
wenzelm@4285
    49
  val size_of_thm	: thm -> int
clasohm@1460
    50
  val reflexive_thm	: thm
wenzelm@4285
    51
  val symmetric_thm	: thm
wenzelm@4285
    52
  val transitive_thm	: thm
paulson@2004
    53
  val refl_implies      : thm
nipkow@4679
    54
  val symmetric_fun     : thm -> thm
wenzelm@3575
    55
  val rewrite_rule_aux	: (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm
nipkow@4713
    56
  val rewrite_thm	: bool * bool * bool
nipkow@4713
    57
                          -> (meta_simpset -> thm -> thm option)
nipkow@4713
    58
                          -> meta_simpset -> thm -> thm
wenzelm@5079
    59
  val rewrite_cterm	: bool * bool * bool
wenzelm@5079
    60
                          -> (meta_simpset -> thm -> thm option)
wenzelm@5079
    61
                          -> meta_simpset -> cterm -> thm
wenzelm@4285
    62
  val rewrite_goals_rule_aux: (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm
nipkow@4713
    63
  val rewrite_goal_rule	: bool* bool * bool
nipkow@4713
    64
                          -> (meta_simpset -> thm -> thm option)
nipkow@4713
    65
                          -> meta_simpset -> int -> thm -> thm
wenzelm@4285
    66
  val equal_abs_elim	: cterm  -> thm -> thm
wenzelm@4285
    67
  val equal_abs_elim_list: cterm list -> thm -> thm
wenzelm@4285
    68
  val flexpair_abs_elim_list: cterm list -> thm -> thm
wenzelm@4285
    69
  val asm_rl		: thm
wenzelm@4285
    70
  val cut_rl		: thm
wenzelm@4285
    71
  val revcut_rl		: thm
wenzelm@4285
    72
  val thin_rl		: thm
wenzelm@4285
    73
  val triv_forall_equality: thm
nipkow@1756
    74
  val swap_prems_rl     : thm
wenzelm@4285
    75
  val equal_intr_rule   : thm
paulson@5311
    76
  val triv_goal		: thm
paulson@5311
    77
  val rev_triv_goal	: thm
paulson@5311
    78
  val mk_triv_goal      : cterm -> thm
paulson@5311
    79
  val instantiate'	: ctyp option list -> cterm option list -> thm -> thm
wenzelm@3766
    80
end;
clasohm@0
    81
paulson@1499
    82
structure Drule : DRULE =
clasohm@0
    83
struct
clasohm@0
    84
wenzelm@3991
    85
lcp@708
    86
(** some cterm->cterm operations: much faster than calling cterm_of! **)
lcp@708
    87
paulson@2004
    88
(** SAME NAMES as in structure Logic: use compound identifiers! **)
paulson@2004
    89
clasohm@1703
    90
(*dest_implies for cterms. Note T=prop below*)
paulson@2004
    91
fun dest_implies ct =
paulson@2004
    92
    case term_of ct of 
paulson@2004
    93
	(Const("==>", _) $ _ $ _) => 
paulson@2004
    94
	    let val (ct1,ct2) = dest_comb ct
paulson@2004
    95
	    in  (#2 (dest_comb ct1), ct2)  end	     
paulson@2004
    96
      | _ => raise TERM ("dest_implies", [term_of ct]) ;
clasohm@1703
    97
clasohm@1703
    98
lcp@708
    99
(*Discard flexflex pairs; return a cterm*)
paulson@2004
   100
fun skip_flexpairs ct =
lcp@708
   101
    case term_of ct of
clasohm@1460
   102
	(Const("==>", _) $ (Const("=?=",_)$_$_) $ _) =>
paulson@2004
   103
	    skip_flexpairs (#2 (dest_implies ct))
lcp@708
   104
      | _ => ct;
lcp@708
   105
lcp@708
   106
(* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
paulson@2004
   107
fun strip_imp_prems ct =
paulson@2004
   108
    let val (cA,cB) = dest_implies ct
paulson@2004
   109
    in  cA :: strip_imp_prems cB  end
lcp@708
   110
    handle TERM _ => [];
lcp@708
   111
paulson@2004
   112
(* A1==>...An==>B  goes to B, where B is not an implication *)
paulson@2004
   113
fun strip_imp_concl ct =
paulson@2004
   114
    case term_of ct of (Const("==>", _) $ _ $ _) => 
paulson@2004
   115
	strip_imp_concl (#2 (dest_comb ct))
paulson@2004
   116
  | _ => ct;
paulson@2004
   117
lcp@708
   118
(*The premises of a theorem, as a cterm list*)
paulson@2004
   119
val cprems_of = strip_imp_prems o skip_flexpairs o cprop_of;
lcp@708
   120
lcp@708
   121
lcp@229
   122
(** reading of instantiations **)
lcp@229
   123
lcp@229
   124
fun absent ixn =
lcp@229
   125
  error("No such variable in term: " ^ Syntax.string_of_vname ixn);
lcp@229
   126
lcp@229
   127
fun inst_failure ixn =
lcp@229
   128
  error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails");
lcp@229
   129
nipkow@4281
   130
fun read_insts sign (rtypes,rsorts) (types,sorts) used insts =
nipkow@4281
   131
let val {tsig,...} = Sign.rep_sg sign
nipkow@4281
   132
    fun split([],tvs,vs) = (tvs,vs)
wenzelm@4691
   133
      | split((sv,st)::l,tvs,vs) = (case Symbol.explode sv of
wenzelm@4691
   134
                  "'"::cs => split(l,(Syntax.indexname cs,st)::tvs,vs)
wenzelm@4691
   135
                | cs => split(l,tvs,(Syntax.indexname cs,st)::vs));
nipkow@4281
   136
    val (tvs,vs) = split(insts,[],[]);
nipkow@4281
   137
    fun readT((a,i),st) =
nipkow@4281
   138
        let val ixn = ("'" ^ a,i);
nipkow@4281
   139
            val S = case rsorts ixn of Some S => S | None => absent ixn;
nipkow@4281
   140
            val T = Sign.read_typ (sign,sorts) st;
nipkow@4281
   141
        in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T)
nipkow@4281
   142
           else inst_failure ixn
nipkow@4281
   143
        end
nipkow@4281
   144
    val tye = map readT tvs;
nipkow@4281
   145
    fun mkty(ixn,st) = (case rtypes ixn of
nipkow@4281
   146
                          Some T => (ixn,(st,typ_subst_TVars tye T))
nipkow@4281
   147
                        | None => absent ixn);
nipkow@4281
   148
    val ixnsTs = map mkty vs;
nipkow@4281
   149
    val ixns = map fst ixnsTs
nipkow@4281
   150
    and sTs  = map snd ixnsTs
nipkow@4281
   151
    val (cts,tye2) = read_def_cterms(sign,types,sorts) used false sTs;
nipkow@4281
   152
    fun mkcVar(ixn,T) =
nipkow@4281
   153
        let val U = typ_subst_TVars tye2 T
nipkow@4281
   154
        in cterm_of sign (Var(ixn,U)) end
nipkow@4281
   155
    val ixnTs = ListPair.zip(ixns, map snd sTs)
nipkow@4281
   156
in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) (tye2 @ tye),
nipkow@4281
   157
    ListPair.zip(map mkcVar ixnTs,cts))
nipkow@4281
   158
end;
lcp@229
   159
lcp@229
   160
wenzelm@252
   161
(*** Find the type (sort) associated with a (T)Var or (T)Free in a term
clasohm@0
   162
     Used for establishing default types (of variables) and sorts (of
clasohm@0
   163
     type variables) when reading another term.
clasohm@0
   164
     Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
clasohm@0
   165
***)
clasohm@0
   166
clasohm@0
   167
fun types_sorts thm =
clasohm@0
   168
    let val {prop,hyps,...} = rep_thm thm;
wenzelm@252
   169
        val big = list_comb(prop,hyps); (* bogus term! *)
wenzelm@252
   170
        val vars = map dest_Var (term_vars big);
wenzelm@252
   171
        val frees = map dest_Free (term_frees big);
wenzelm@252
   172
        val tvars = term_tvars big;
wenzelm@252
   173
        val tfrees = term_tfrees big;
wenzelm@252
   174
        fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i));
wenzelm@252
   175
        fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
clasohm@0
   176
    in (typ,sort) end;
clasohm@0
   177
clasohm@0
   178
(** Standardization of rules **)
clasohm@0
   179
clasohm@0
   180
(*Generalization over a list of variables, IGNORING bad ones*)
clasohm@0
   181
fun forall_intr_list [] th = th
clasohm@0
   182
  | forall_intr_list (y::ys) th =
wenzelm@252
   183
        let val gth = forall_intr_list ys th
wenzelm@252
   184
        in  forall_intr y gth   handle THM _ =>  gth  end;
clasohm@0
   185
clasohm@0
   186
(*Generalization over all suitable Free variables*)
clasohm@0
   187
fun forall_intr_frees th =
clasohm@0
   188
    let val {prop,sign,...} = rep_thm th
clasohm@0
   189
    in  forall_intr_list
wenzelm@4440
   190
         (map (cterm_of sign) (sort (make_ord atless) (term_frees prop)))
clasohm@0
   191
         th
clasohm@0
   192
    end;
clasohm@0
   193
clasohm@0
   194
(*Replace outermost quantified variable by Var of given index.
clasohm@0
   195
    Could clash with Vars already present.*)
wenzelm@252
   196
fun forall_elim_var i th =
clasohm@0
   197
    let val {prop,sign,...} = rep_thm th
clasohm@0
   198
    in case prop of
wenzelm@252
   199
          Const("all",_) $ Abs(a,T,_) =>
wenzelm@252
   200
              forall_elim (cterm_of sign (Var((a,i), T)))  th
wenzelm@252
   201
        | _ => raise THM("forall_elim_var", i, [th])
clasohm@0
   202
    end;
clasohm@0
   203
clasohm@0
   204
(*Repeat forall_elim_var until all outer quantifiers are removed*)
wenzelm@252
   205
fun forall_elim_vars i th =
clasohm@0
   206
    forall_elim_vars i (forall_elim_var i th)
wenzelm@252
   207
        handle THM _ => th;
clasohm@0
   208
clasohm@0
   209
(*Specialization over a list of cterms*)
clasohm@0
   210
fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
clasohm@0
   211
clasohm@0
   212
(* maps [A1,...,An], B   to   [| A1;...;An |] ==> B  *)
clasohm@0
   213
fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
clasohm@0
   214
clasohm@0
   215
(* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
clasohm@0
   216
fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   217
clasohm@0
   218
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   219
fun zero_var_indexes th =
clasohm@0
   220
    let val {prop,sign,...} = rep_thm th;
clasohm@0
   221
        val vars = term_vars prop
clasohm@0
   222
        val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
wenzelm@252
   223
        val inrs = add_term_tvars(prop,[]);
wenzelm@252
   224
        val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
paulson@2266
   225
        val tye = ListPair.map (fn ((v,rs),a) => (v, TVar((a,0),rs)))
paulson@2266
   226
	             (inrs, nms')
wenzelm@252
   227
        val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
wenzelm@252
   228
        fun varpairs([],[]) = []
wenzelm@252
   229
          | varpairs((var as Var(v,T)) :: vars, b::bs) =
wenzelm@252
   230
                let val T' = typ_subst_TVars tye T
wenzelm@252
   231
                in (cterm_of sign (Var(v,T')),
wenzelm@252
   232
                    cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
wenzelm@252
   233
                end
wenzelm@252
   234
          | varpairs _ = raise TERM("varpairs", []);
clasohm@0
   235
    in instantiate (ctye, varpairs(vars,rev bs)) th end;
clasohm@0
   236
clasohm@0
   237
clasohm@0
   238
(*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
clasohm@0
   239
    all generality expressed by Vars having index 0.*)
clasohm@0
   240
fun standard th =
wenzelm@1218
   241
  let val {maxidx,...} = rep_thm th
wenzelm@1237
   242
  in
wenzelm@1218
   243
    th |> implies_intr_hyps
paulson@1412
   244
       |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
wenzelm@1439
   245
       |> Thm.strip_shyps |> Thm.implies_intr_shyps
paulson@1412
   246
       |> zero_var_indexes |> Thm.varifyT |> Thm.compress
wenzelm@1218
   247
  end;
wenzelm@1218
   248
clasohm@0
   249
paulson@4610
   250
(*Convert all Vars in a theorem to Frees.  Also return a function for 
paulson@4610
   251
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@4610
   252
  Similar code in type/freeze_thaw*)
paulson@4610
   253
fun freeze_thaw th =
paulson@4610
   254
  let val fth = freezeT th
paulson@4610
   255
      val {prop,sign,...} = rep_thm fth
paulson@4610
   256
      val used = add_term_names (prop, [])
paulson@4610
   257
      and vars = term_vars prop
paulson@4610
   258
      fun newName (Var(ix,_), (pairs,used)) = 
paulson@4610
   259
	    let val v = variant used (string_of_indexname ix)
paulson@4610
   260
	    in  ((ix,v)::pairs, v::used)  end;
paulson@4610
   261
      val (alist, _) = foldr newName (vars, ([], used))
paulson@4610
   262
      fun mk_inst (Var(v,T)) = 
paulson@4610
   263
	  (cterm_of sign (Var(v,T)),
paulson@4610
   264
	   cterm_of sign (Free(the (assoc(alist,v)), T)))
paulson@4610
   265
      val insts = map mk_inst vars
paulson@4610
   266
      fun thaw th' = 
paulson@4610
   267
	  th' |> forall_intr_list (map #2 insts)
paulson@4610
   268
	      |> forall_elim_list (map #1 insts)
paulson@4610
   269
  in  (instantiate ([],insts) fth, thaw)  end;
paulson@4610
   270
paulson@4610
   271
paulson@4610
   272
(*Rotates a rule's premises to the left by k.  Does nothing if k=0 or
paulson@4610
   273
  if k equals the number of premises.  Useful, for instance, with etac.
paulson@4610
   274
  Similar to tactic/defer_tac*)
paulson@4610
   275
fun rotate_prems k rl = 
paulson@4610
   276
    let val (rl',thaw) = freeze_thaw rl
paulson@4610
   277
	val hyps = strip_imp_prems (adjust_maxidx (cprop_of rl'))
paulson@4610
   278
	val hyps' = List.drop(hyps, k)
paulson@4610
   279
    in  implies_elim_list rl' (map assume hyps)
paulson@4610
   280
        |> implies_intr_list (hyps' @ List.take(hyps, k))
paulson@4610
   281
        |> thaw |> varifyT
paulson@4610
   282
    end;
paulson@4610
   283
paulson@4610
   284
wenzelm@252
   285
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   286
  Generalizes over Free variables,
clasohm@0
   287
  creates the assumption, and then strips quantifiers.
clasohm@0
   288
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   289
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   290
fun assume_ax thy sP =
clasohm@0
   291
    let val sign = sign_of thy
paulson@4610
   292
        val prop = Logic.close_form (term_of (read_cterm sign (sP, propT)))
lcp@229
   293
    in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
clasohm@0
   294
wenzelm@252
   295
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   296
fun tha RSN (i,thb) =
wenzelm@4270
   297
  case Seq.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   298
      ([th],_) => th
clasohm@0
   299
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   300
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   301
clasohm@0
   302
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   303
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   304
clasohm@0
   305
(*For joining lists of rules*)
wenzelm@252
   306
fun thas RLN (i,thbs) =
clasohm@0
   307
  let val resolve = biresolution false (map (pair false) thas) i
wenzelm@4270
   308
      fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
paulson@2672
   309
  in  List.concat (map resb thbs)  end;
clasohm@0
   310
clasohm@0
   311
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   312
lcp@11
   313
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   314
  makes proof trees*)
wenzelm@252
   315
fun rls MRS bottom_rl =
lcp@11
   316
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   317
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   318
  in  rs_aux 1 rls  end;
lcp@11
   319
lcp@11
   320
(*As above, but for rule lists*)
wenzelm@252
   321
fun rlss MRL bottom_rls =
lcp@11
   322
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   323
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   324
  in  rs_aux 1 rlss  end;
lcp@11
   325
wenzelm@252
   326
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   327
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   328
  ALWAYS deletes premise i *)
wenzelm@252
   329
fun compose(tha,i,thb) =
wenzelm@4270
   330
    Seq.list_of (bicompose false (false,tha,0) i thb);
clasohm@0
   331
clasohm@0
   332
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   333
fun tha COMP thb =
clasohm@0
   334
    case compose(tha,1,thb) of
wenzelm@252
   335
        [th] => th
clasohm@0
   336
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   337
clasohm@0
   338
(*Instantiate theorem th, reading instantiations under signature sg*)
clasohm@0
   339
fun read_instantiate_sg sg sinsts th =
clasohm@0
   340
    let val ts = types_sorts th;
nipkow@952
   341
        val used = add_term_tvarnames(#prop(rep_thm th),[]);
nipkow@952
   342
    in  instantiate (read_insts sg ts ts used sinsts) th  end;
clasohm@0
   343
clasohm@0
   344
(*Instantiate theorem th, reading instantiations under theory of th*)
clasohm@0
   345
fun read_instantiate sinsts th =
clasohm@0
   346
    read_instantiate_sg (#sign (rep_thm th)) sinsts th;
clasohm@0
   347
clasohm@0
   348
clasohm@0
   349
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
clasohm@0
   350
  Instantiates distinct Vars by terms, inferring type instantiations. *)
clasohm@0
   351
local
nipkow@1435
   352
  fun add_types ((ct,cu), (sign,tye,maxidx)) =
paulson@2152
   353
    let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
paulson@2152
   354
        and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
paulson@2152
   355
        val maxi = Int.max(maxidx, Int.max(maxt, maxu));
clasohm@0
   356
        val sign' = Sign.merge(sign, Sign.merge(signt, signu))
nipkow@1435
   357
        val (tye',maxi') = Type.unify (#tsig(Sign.rep_sg sign')) maxi tye (T,U)
wenzelm@252
   358
          handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u])
nipkow@1435
   359
    in  (sign', tye', maxi')  end;
clasohm@0
   360
in
wenzelm@252
   361
fun cterm_instantiate ctpairs0 th =
nipkow@1435
   362
  let val (sign,tye,_) = foldr add_types (ctpairs0, (#sign(rep_thm th),[],0))
clasohm@0
   363
      val tsig = #tsig(Sign.rep_sg sign);
clasohm@0
   364
      fun instT(ct,cu) = let val inst = subst_TVars tye
wenzelm@252
   365
                         in (cterm_fun inst ct, cterm_fun inst cu) end
lcp@229
   366
      fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
clasohm@0
   367
  in  instantiate (map ctyp2 tye, map instT ctpairs0) th  end
wenzelm@252
   368
  handle TERM _ =>
clasohm@0
   369
           raise THM("cterm_instantiate: incompatible signatures",0,[th])
wenzelm@4057
   370
       | TYPE (msg, _, _) => raise THM("cterm_instantiate: " ^ msg, 0, [th])
clasohm@0
   371
end;
clasohm@0
   372
clasohm@0
   373
wenzelm@4016
   374
(** theorem equality **)
clasohm@0
   375
clasohm@0
   376
(*Do the two theorems have the same signature?*)
wenzelm@252
   377
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
clasohm@0
   378
clasohm@0
   379
(*Useful "distance" function for BEST_FIRST*)
clasohm@0
   380
val size_of_thm = size_of_term o #prop o rep_thm;
clasohm@0
   381
clasohm@0
   382
lcp@1194
   383
(** Mark Staples's weaker version of eq_thm: ignores variable renaming and
lcp@1194
   384
    (some) type variable renaming **)
lcp@1194
   385
lcp@1194
   386
 (* Can't use term_vars, because it sorts the resulting list of variable names.
lcp@1194
   387
    We instead need the unique list noramlised by the order of appearance
lcp@1194
   388
    in the term. *)
lcp@1194
   389
fun term_vars' (t as Var(v,T)) = [t]
lcp@1194
   390
  | term_vars' (Abs(_,_,b)) = term_vars' b
lcp@1194
   391
  | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
lcp@1194
   392
  | term_vars' _ = [];
lcp@1194
   393
lcp@1194
   394
fun forall_intr_vars th =
lcp@1194
   395
  let val {prop,sign,...} = rep_thm th;
lcp@1194
   396
      val vars = distinct (term_vars' prop);
lcp@1194
   397
  in forall_intr_list (map (cterm_of sign) vars) th end;
lcp@1194
   398
wenzelm@1237
   399
fun weak_eq_thm (tha,thb) =
lcp@1194
   400
    eq_thm(forall_intr_vars (freezeT tha), forall_intr_vars (freezeT thb));
lcp@1194
   401
lcp@1194
   402
lcp@1194
   403
clasohm@0
   404
(*** Meta-Rewriting Rules ***)
clasohm@0
   405
paulson@4610
   406
val proto_sign = sign_of ProtoPure.thy;
paulson@4610
   407
paulson@4610
   408
fun read_prop s = read_cterm proto_sign (s, propT);
paulson@4610
   409
wenzelm@4016
   410
fun store_thm name thm = PureThy.smart_store_thm (name, standard thm);
wenzelm@4016
   411
clasohm@0
   412
val reflexive_thm =
paulson@4610
   413
  let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),logicS)))
wenzelm@4016
   414
  in store_thm "reflexive" (Thm.reflexive cx) end;
clasohm@0
   415
clasohm@0
   416
val symmetric_thm =
paulson@4610
   417
  let val xy = read_prop "x::'a::logic == y"
paulson@4610
   418
  in store_thm "symmetric" 
paulson@4610
   419
      (Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy)))
paulson@4610
   420
   end;
clasohm@0
   421
clasohm@0
   422
val transitive_thm =
paulson@4610
   423
  let val xy = read_prop "x::'a::logic == y"
paulson@4610
   424
      val yz = read_prop "y::'a::logic == z"
clasohm@0
   425
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
paulson@4610
   426
  in store_thm "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm))
paulson@4610
   427
  end;
clasohm@0
   428
nipkow@4679
   429
fun symmetric_fun thm = thm RS symmetric_thm;
nipkow@4679
   430
lcp@229
   431
(** Below, a "conversion" has type cterm -> thm **)
lcp@229
   432
paulson@4610
   433
val refl_implies = reflexive (cterm_of proto_sign implies);
clasohm@0
   434
clasohm@0
   435
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
nipkow@214
   436
(*Do not rewrite flex-flex pairs*)
wenzelm@252
   437
fun goals_conv pred cv =
lcp@229
   438
  let fun gconv i ct =
paulson@2004
   439
        let val (A,B) = dest_implies ct
lcp@229
   440
            val (thA,j) = case term_of A of
lcp@229
   441
                  Const("=?=",_)$_$_ => (reflexive A, i)
lcp@229
   442
                | _ => (if pred i then cv A else reflexive A, i+1)
paulson@2004
   443
        in  combination (combination refl_implies thA) (gconv j B) end
lcp@229
   444
        handle TERM _ => reflexive ct
clasohm@0
   445
  in gconv 1 end;
clasohm@0
   446
clasohm@0
   447
(*Use a conversion to transform a theorem*)
lcp@229
   448
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
clasohm@0
   449
clasohm@0
   450
(*rewriting conversion*)
lcp@229
   451
fun rew_conv mode prover mss = rewrite_cterm mode mss prover;
clasohm@0
   452
clasohm@0
   453
(*Rewrite a theorem*)
wenzelm@3575
   454
fun rewrite_rule_aux _ []   th = th
wenzelm@3575
   455
  | rewrite_rule_aux prover thms th =
nipkow@4713
   456
      fconv_rule (rew_conv (true,false,false) prover (Thm.mss_of thms)) th;
clasohm@0
   457
wenzelm@3555
   458
fun rewrite_thm mode prover mss = fconv_rule (rew_conv mode prover mss);
wenzelm@5079
   459
fun rewrite_cterm mode prover mss = Thm.rewrite_cterm mode mss prover;
wenzelm@3555
   460
clasohm@0
   461
(*Rewrite the subgoals of a proof state (represented by a theorem) *)
wenzelm@3575
   462
fun rewrite_goals_rule_aux _ []   th = th
wenzelm@3575
   463
  | rewrite_goals_rule_aux prover thms th =
nipkow@4713
   464
      fconv_rule (goals_conv (K true) (rew_conv (true, true, false) prover
wenzelm@3575
   465
        (Thm.mss_of thms))) th;
clasohm@0
   466
clasohm@0
   467
(*Rewrite the subgoal of a proof state (represented by a theorem) *)
nipkow@214
   468
fun rewrite_goal_rule mode prover mss i thm =
nipkow@214
   469
  if 0 < i  andalso  i <= nprems_of thm
nipkow@214
   470
  then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm
nipkow@214
   471
  else raise THM("rewrite_goal_rule",i,[thm]);
clasohm@0
   472
clasohm@0
   473
clasohm@0
   474
(** Derived rules mainly for METAHYPS **)
clasohm@0
   475
clasohm@0
   476
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
clasohm@0
   477
fun equal_abs_elim ca eqth =
lcp@229
   478
  let val {sign=signa, t=a, ...} = rep_cterm ca
clasohm@0
   479
      and combth = combination eqth (reflexive ca)
clasohm@0
   480
      val {sign,prop,...} = rep_thm eqth
clasohm@0
   481
      val (abst,absu) = Logic.dest_equals prop
lcp@229
   482
      val cterm = cterm_of (Sign.merge (sign,signa))
clasohm@0
   483
  in  transitive (symmetric (beta_conversion (cterm (abst$a))))
clasohm@0
   484
           (transitive combth (beta_conversion (cterm (absu$a))))
clasohm@0
   485
  end
clasohm@0
   486
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
clasohm@0
   487
clasohm@0
   488
(*Calling equal_abs_elim with multiple terms*)
clasohm@0
   489
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
clasohm@0
   490
clasohm@0
   491
local
clasohm@0
   492
  val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
clasohm@0
   493
  fun err th = raise THM("flexpair_inst: ", 0, [th])
clasohm@0
   494
  fun flexpair_inst def th =
clasohm@0
   495
    let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
wenzelm@252
   496
        val cterm = cterm_of sign
wenzelm@252
   497
        fun cvar a = cterm(Var((a,0),alpha))
wenzelm@252
   498
        val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)]
wenzelm@252
   499
                   def
clasohm@0
   500
    in  equal_elim def' th
clasohm@0
   501
    end
clasohm@0
   502
    handle THM _ => err th | bind => err th
clasohm@0
   503
in
wenzelm@3991
   504
val flexpair_intr = flexpair_inst (symmetric ProtoPure.flexpair_def)
wenzelm@3991
   505
and flexpair_elim = flexpair_inst ProtoPure.flexpair_def
clasohm@0
   506
end;
clasohm@0
   507
clasohm@0
   508
(*Version for flexflex pairs -- this supports lifting.*)
wenzelm@252
   509
fun flexpair_abs_elim_list cts =
clasohm@0
   510
    flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
clasohm@0
   511
clasohm@0
   512
clasohm@0
   513
(*** Some useful meta-theorems ***)
clasohm@0
   514
clasohm@0
   515
(*The rule V/V, obtains assumption solving for eresolve_tac*)
wenzelm@4016
   516
val asm_rl =
paulson@4610
   517
  store_thm "asm_rl" (trivial(read_prop "PROP ?psi"));
clasohm@0
   518
clasohm@0
   519
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@4016
   520
val cut_rl =
wenzelm@4016
   521
  store_thm "cut_rl"
paulson@4610
   522
    (trivial(read_prop "PROP ?psi ==> PROP ?theta"));
clasohm@0
   523
wenzelm@252
   524
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   525
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   526
val revcut_rl =
paulson@4610
   527
  let val V = read_prop "PROP V"
paulson@4610
   528
      and VW = read_prop "PROP V ==> PROP W";
wenzelm@4016
   529
  in
wenzelm@4016
   530
    store_thm "revcut_rl"
wenzelm@4016
   531
      (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
clasohm@0
   532
  end;
clasohm@0
   533
lcp@668
   534
(*for deleting an unwanted assumption*)
lcp@668
   535
val thin_rl =
paulson@4610
   536
  let val V = read_prop "PROP V"
paulson@4610
   537
      and W = read_prop "PROP W";
wenzelm@4016
   538
  in  store_thm "thin_rl" (implies_intr V (implies_intr W (assume W)))
lcp@668
   539
  end;
lcp@668
   540
clasohm@0
   541
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   542
val triv_forall_equality =
paulson@4610
   543
  let val V  = read_prop "PROP V"
paulson@4610
   544
      and QV = read_prop "!!x::'a. PROP V"
paulson@4610
   545
      and x  = read_cterm proto_sign ("x", TFree("'a",logicS));
wenzelm@4016
   546
  in
wenzelm@4016
   547
    store_thm "triv_forall_equality"
wenzelm@4016
   548
      (equal_intr (implies_intr QV (forall_elim x (assume QV)))
wenzelm@4016
   549
        (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   550
  end;
clasohm@0
   551
nipkow@1756
   552
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
nipkow@1756
   553
   (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
nipkow@1756
   554
   `thm COMP swap_prems_rl' swaps the first two premises of `thm'
nipkow@1756
   555
*)
nipkow@1756
   556
val swap_prems_rl =
paulson@4610
   557
  let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
nipkow@1756
   558
      val major = assume cmajor;
paulson@4610
   559
      val cminor1 = read_prop "PROP PhiA";
nipkow@1756
   560
      val minor1 = assume cminor1;
paulson@4610
   561
      val cminor2 = read_prop "PROP PhiB";
nipkow@1756
   562
      val minor2 = assume cminor2;
wenzelm@4016
   563
  in store_thm "swap_prems_rl"
nipkow@1756
   564
       (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
nipkow@1756
   565
         (implies_elim (implies_elim major minor1) minor2))))
nipkow@1756
   566
  end;
nipkow@1756
   567
nipkow@3653
   568
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
nipkow@3653
   569
   ==> PROP ?phi == PROP ?psi
paulson@4610
   570
   Introduction rule for == as a meta-theorem.  
nipkow@3653
   571
*)
nipkow@3653
   572
val equal_intr_rule =
paulson@4610
   573
  let val PQ = read_prop "PROP phi ==> PROP psi"
paulson@4610
   574
      and QP = read_prop "PROP psi ==> PROP phi"
wenzelm@4016
   575
  in
wenzelm@4016
   576
    store_thm "equal_intr_rule"
wenzelm@4016
   577
      (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
nipkow@3653
   578
  end;
nipkow@3653
   579
wenzelm@4285
   580
wenzelm@4789
   581
(* GOAL (PROP A) <==> PROP A *)
wenzelm@4789
   582
wenzelm@4789
   583
local
wenzelm@4789
   584
  val A = read_prop "PROP A";
wenzelm@4789
   585
  val G = read_prop "GOAL (PROP A)";
wenzelm@4789
   586
  val (G_def, _) = freeze_thaw ProtoPure.Goal_def;
wenzelm@4789
   587
in
wenzelm@4789
   588
  val triv_goal = store_thm "triv_goal" (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume A));
wenzelm@4789
   589
  val rev_triv_goal = store_thm "rev_triv_goal" (Thm.equal_elim G_def (Thm.assume G));
wenzelm@4789
   590
end;
wenzelm@4789
   591
wenzelm@4789
   592
wenzelm@4285
   593
wenzelm@4285
   594
(** instantiate' rule **)
wenzelm@4285
   595
wenzelm@4285
   596
(* collect vars *)
wenzelm@4285
   597
wenzelm@4285
   598
val add_tvarsT = foldl_atyps (fn (vs, TVar v) => v ins vs | (vs, _) => vs);
wenzelm@4285
   599
val add_tvars = foldl_types add_tvarsT;
wenzelm@4285
   600
val add_vars = foldl_aterms (fn (vs, Var v) => v ins vs | (vs, _) => vs);
wenzelm@4285
   601
wenzelm@4285
   602
fun tvars_of thm = rev (add_tvars ([], #prop (Thm.rep_thm thm)));
wenzelm@4285
   603
fun vars_of thm = rev (add_vars ([], #prop (Thm.rep_thm thm)));
wenzelm@4285
   604
wenzelm@4285
   605
wenzelm@4285
   606
(* instantiate by left-to-right occurrence of variables *)
wenzelm@4285
   607
wenzelm@4285
   608
fun instantiate' cTs cts thm =
wenzelm@4285
   609
  let
wenzelm@4285
   610
    fun err msg =
wenzelm@4285
   611
      raise TYPE ("instantiate': " ^ msg,
wenzelm@4285
   612
        mapfilter (apsome Thm.typ_of) cTs,
wenzelm@4285
   613
        mapfilter (apsome Thm.term_of) cts);
wenzelm@4285
   614
wenzelm@4285
   615
    fun inst_of (v, ct) =
wenzelm@4285
   616
      (Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct)
wenzelm@4285
   617
        handle TYPE (msg, _, _) => err msg;
wenzelm@4285
   618
wenzelm@4285
   619
    fun zip_vars _ [] = []
wenzelm@4285
   620
      | zip_vars (_ :: vs) (None :: opt_ts) = zip_vars vs opt_ts
wenzelm@4285
   621
      | zip_vars (v :: vs) (Some t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
wenzelm@4285
   622
      | zip_vars [] _ = err "more instantiations than variables in thm";
wenzelm@4285
   623
wenzelm@4285
   624
    (*instantiate types first!*)
wenzelm@4285
   625
    val thm' =
wenzelm@4285
   626
      if forall is_none cTs then thm
wenzelm@4285
   627
      else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm;
wenzelm@4285
   628
    in
wenzelm@4285
   629
      if forall is_none cts then thm'
wenzelm@4285
   630
      else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
wenzelm@4285
   631
    end;
wenzelm@4285
   632
wenzelm@4285
   633
paulson@5311
   634
(*Make an initial proof state, "PROP A ==> (PROP A)" *)
paulson@5311
   635
fun mk_triv_goal ct = instantiate' [] [Some ct] triv_goal;
paulson@5311
   636
clasohm@0
   637
end;
wenzelm@252
   638
paulson@1499
   639
open Drule;