src/HOL/Import/shuffler.ML
author wenzelm
Wed Nov 29 15:44:51 2006 +0100 (2006-11-29)
changeset 21588 cd0dc678a205
parent 21078 101aefd61aac
child 22578 b0eb5652f210
permissions -rw-r--r--
simplified method setup;
     1 (*  Title:      HOL/Import/shuffler.ML
     2     ID:         $Id$
     3     Author:     Sebastian Skalberg, TU Muenchen
     4 
     5 Package for proving two terms equal by normalizing (hence the
     6 "shuffler" name).  Uses the simplifier for the normalization.
     7 *)
     8 
     9 signature Shuffler =
    10 sig
    11     val debug      : bool ref
    12 
    13     val norm_term  : theory -> term -> thm
    14     val make_equal : theory -> term -> term -> thm option
    15     val set_prop   : theory -> term -> (string * thm) list -> (string * thm) option
    16 
    17     val find_potential: theory -> term -> (string * thm) list
    18 
    19     val gen_shuffle_tac: theory -> bool -> (string * thm) list -> int -> tactic
    20 
    21     val shuffle_tac: (string * thm) list -> int -> tactic
    22     val search_tac : (string * thm) list -> int -> tactic
    23 
    24     val print_shuffles: theory -> unit
    25 
    26     val add_shuffle_rule: thm -> theory -> theory
    27     val shuffle_attr: attribute
    28 
    29     val setup      : theory -> theory
    30 end
    31 
    32 structure Shuffler :> Shuffler =
    33 struct
    34 
    35 val debug = ref false
    36 
    37 fun if_debug f x = if !debug then f x else ()
    38 val message = if_debug writeln
    39 
    40 (*Prints exceptions readably to users*)
    41 fun print_sign_exn_unit sign e =
    42   case e of
    43      THM (msg,i,thms) =>
    44          (writeln ("Exception THM " ^ string_of_int i ^ " raised:\n" ^ msg);
    45           List.app print_thm thms)
    46    | THEORY (msg,thys) =>
    47          (writeln ("Exception THEORY raised:\n" ^ msg);
    48           List.app (writeln o Context.str_of_thy) thys)
    49    | TERM (msg,ts) =>
    50          (writeln ("Exception TERM raised:\n" ^ msg);
    51           List.app (writeln o Sign.string_of_term sign) ts)
    52    | TYPE (msg,Ts,ts) =>
    53          (writeln ("Exception TYPE raised:\n" ^ msg);
    54           List.app (writeln o Sign.string_of_typ sign) Ts;
    55           List.app (writeln o Sign.string_of_term sign) ts)
    56    | e => raise e
    57 
    58 (*Prints an exception, then fails*)
    59 fun print_sign_exn sign e = (print_sign_exn_unit sign e; raise e)
    60 
    61 val string_of_thm = Library.setmp print_mode [] string_of_thm;
    62 val string_of_cterm = Library.setmp print_mode [] string_of_cterm;
    63 
    64 fun mk_meta_eq th =
    65     (case concl_of th of
    66          Const("Trueprop",_) $ (Const("op =",_) $ _ $ _) => th RS eq_reflection
    67        | Const("==",_) $ _ $ _ => th
    68        | _ => raise THM("Not an equality",0,[th]))
    69     handle _ => raise THM("Couldn't make meta equality",0,[th])
    70 
    71 fun mk_obj_eq th =
    72     (case concl_of th of
    73          Const("Trueprop",_) $ (Const("op =",_) $ _ $ _) => th
    74        | Const("==",_) $ _ $ _ => th RS meta_eq_to_obj_eq
    75        | _ => raise THM("Not an equality",0,[th]))
    76     handle _ => raise THM("Couldn't make object equality",0,[th])
    77 
    78 structure ShuffleDataArgs: THEORY_DATA_ARGS =
    79 struct
    80 val name = "HOL/shuffles"
    81 type T = thm list
    82 val empty = []
    83 val copy = I
    84 val extend = I
    85 fun merge _ = Library.gen_union Thm.eq_thm
    86 fun print _ thms =
    87     Pretty.writeln (Pretty.big_list "Shuffle theorems:"
    88                                     (map Display.pretty_thm thms))
    89 end
    90 
    91 structure ShuffleData = TheoryDataFun(ShuffleDataArgs)
    92 
    93 val weaken =
    94     let
    95         val cert = cterm_of ProtoPure.thy
    96         val P = Free("P",propT)
    97         val Q = Free("Q",propT)
    98         val PQ = Logic.mk_implies(P,Q)
    99         val PPQ = Logic.mk_implies(P,PQ)
   100         val cP = cert P
   101         val cQ = cert Q
   102         val cPQ = cert PQ
   103         val cPPQ = cert PPQ
   104         val th1 = assume cPQ |> implies_intr_list [cPQ,cP]
   105         val th3 = assume cP
   106         val th4 = implies_elim_list (assume cPPQ) [th3,th3]
   107                                     |> implies_intr_list [cPPQ,cP]
   108     in
   109         equal_intr th4 th1 |> standard
   110     end
   111 
   112 val imp_comm =
   113     let
   114         val cert = cterm_of ProtoPure.thy
   115         val P = Free("P",propT)
   116         val Q = Free("Q",propT)
   117         val R = Free("R",propT)
   118         val PQR = Logic.mk_implies(P,Logic.mk_implies(Q,R))
   119         val QPR = Logic.mk_implies(Q,Logic.mk_implies(P,R))
   120         val cP = cert P
   121         val cQ = cert Q
   122         val cPQR = cert PQR
   123         val cQPR = cert QPR
   124         val th1 = implies_elim_list (assume cPQR) [assume cP,assume cQ]
   125                                     |> implies_intr_list [cPQR,cQ,cP]
   126         val th2 = implies_elim_list (assume cQPR) [assume cQ,assume cP]
   127                                     |> implies_intr_list [cQPR,cP,cQ]
   128     in
   129         equal_intr th1 th2 |> standard
   130     end
   131 
   132 val def_norm =
   133     let
   134         val cert = cterm_of ProtoPure.thy
   135         val aT = TFree("'a",[])
   136         val bT = TFree("'b",[])
   137         val v = Free("v",aT)
   138         val P = Free("P",aT-->bT)
   139         val Q = Free("Q",aT-->bT)
   140         val cvPQ = cert (list_all ([("v",aT)],Logic.mk_equals(P $ Bound 0,Q $ Bound 0)))
   141         val cPQ = cert (Logic.mk_equals(P,Q))
   142         val cv = cert v
   143         val rew = assume cvPQ
   144                          |> forall_elim cv
   145                          |> abstract_rule "v" cv
   146         val (lhs,rhs) = Logic.dest_equals(concl_of rew)
   147         val th1 = transitive (transitive
   148                                   (eta_conversion (cert lhs) |> symmetric)
   149                                   rew)
   150                              (eta_conversion (cert rhs))
   151                              |> implies_intr cvPQ
   152         val th2 = combination (assume cPQ) (reflexive cv)
   153                               |> forall_intr cv
   154                               |> implies_intr cPQ
   155     in
   156         equal_intr th1 th2 |> standard
   157     end
   158 
   159 val all_comm =
   160     let
   161         val cert = cterm_of ProtoPure.thy
   162         val xT = TFree("'a",[])
   163         val yT = TFree("'b",[])
   164         val P = Free("P",xT-->yT-->propT)
   165         val lhs = all xT $ (Abs("x",xT,all yT $ (Abs("y",yT,P $ Bound 1 $ Bound 0))))
   166         val rhs = all yT $ (Abs("y",yT,all xT $ (Abs("x",xT,P $ Bound 0 $ Bound 1))))
   167         val cl = cert lhs
   168         val cr = cert rhs
   169         val cx = cert (Free("x",xT))
   170         val cy = cert (Free("y",yT))
   171         val th1 = assume cr
   172                          |> forall_elim_list [cy,cx]
   173                          |> forall_intr_list [cx,cy]
   174                          |> implies_intr cr
   175         val th2 = assume cl
   176                          |> forall_elim_list [cx,cy]
   177                          |> forall_intr_list [cy,cx]
   178                          |> implies_intr cl
   179     in
   180         equal_intr th1 th2 |> standard
   181     end
   182 
   183 val equiv_comm =
   184     let
   185         val cert = cterm_of ProtoPure.thy
   186         val T    = TFree("'a",[])
   187         val t    = Free("t",T)
   188         val u    = Free("u",T)
   189         val ctu  = cert (Logic.mk_equals(t,u))
   190         val cut  = cert (Logic.mk_equals(u,t))
   191         val th1  = assume ctu |> symmetric |> implies_intr ctu
   192         val th2  = assume cut |> symmetric |> implies_intr cut
   193     in
   194         equal_intr th1 th2 |> standard
   195     end
   196 
   197 (* This simplification procedure rewrites !!x y. P x y
   198 deterministicly, in order for the normalization function, defined
   199 below, to handle nested quantifiers robustly *)
   200 
   201 local
   202 
   203 exception RESULT of int
   204 
   205 fun find_bound n (Bound i) = if i = n then raise RESULT 0
   206                              else if i = n+1 then raise RESULT 1
   207                              else ()
   208   | find_bound n (t $ u) = (find_bound n t; find_bound n u)
   209   | find_bound n (Abs(_,_,t)) = find_bound (n+1) t
   210   | find_bound _ _ = ()
   211 
   212 fun swap_bound n (Bound i) = if i = n then Bound (n+1)
   213                              else if i = n+1 then Bound n
   214                              else Bound i
   215   | swap_bound n (t $ u) = (swap_bound n t $ swap_bound n u)
   216   | swap_bound n (Abs(x,xT,t)) = Abs(x,xT,swap_bound (n+1) t)
   217   | swap_bound n t = t
   218 
   219 fun rew_th thy (xv as (x,xT)) (yv as (y,yT)) t =
   220     let
   221         val lhs = list_all ([xv,yv],t)
   222         val rhs = list_all ([yv,xv],swap_bound 0 t)
   223         val rew = Logic.mk_equals (lhs,rhs)
   224         val init = trivial (cterm_of thy rew)
   225     in
   226         (all_comm RS init handle e => (message "rew_th"; OldGoals.print_exn e))
   227     end
   228 
   229 fun quant_rewrite thy assumes (t as Const("all",T1) $ (Abs(x,xT,Const("all",T2) $ Abs(y,yT,body)))) =
   230     let
   231         val res = (find_bound 0 body;2) handle RESULT i => i
   232     in
   233         case res of
   234             0 => SOME (rew_th thy (x,xT) (y,yT) body)
   235           | 1 => if string_ord(y,x) = LESS
   236                  then
   237                      let
   238                          val newt = Const("all",T1) $ (Abs(y,xT,Const("all",T2) $ Abs(x,yT,body)))
   239                          val t_th    = reflexive (cterm_of thy t)
   240                          val newt_th = reflexive (cterm_of thy newt)
   241                      in
   242                          SOME (transitive t_th newt_th)
   243                      end
   244                  else NONE
   245           | _ => error "norm_term (quant_rewrite) internal error"
   246      end
   247   | quant_rewrite _ _ _ = (warning "quant_rewrite: Unknown lhs"; NONE)
   248 
   249 fun freeze_thaw_term t =
   250     let
   251         val tvars = term_tvars t
   252         val tfree_names = add_term_tfree_names(t,[])
   253         val (type_inst,_) =
   254             Library.foldl (fn ((inst,used),(w as (v,_),S)) =>
   255                       let
   256                           val v' = Name.variant used v
   257                       in
   258                           ((w,TFree(v',S))::inst,v'::used)
   259                       end)
   260                   (([],tfree_names),tvars)
   261         val t' = subst_TVars type_inst t
   262     in
   263         (t',map (fn (w,TFree(v,S)) => (v,TVar(w,S))
   264                   | _ => error "Internal error in Shuffler.freeze_thaw") type_inst)
   265     end
   266 
   267 fun inst_tfrees thy [] thm = thm
   268   | inst_tfrees thy ((name,U)::rest) thm =
   269     let
   270         val cU = ctyp_of thy U
   271         val tfrees = add_term_tfrees (prop_of thm,[])
   272         val (rens, thm') = Thm.varifyT'
   273     (remove (op = o apsnd fst) name tfrees) thm
   274         val mid =
   275             case rens of
   276                 [] => thm'
   277               | [((_, S), idx)] => instantiate
   278             ([(ctyp_of thy (TVar (idx, S)), cU)], []) thm'
   279               | _ => error "Shuffler.inst_tfrees internal error"
   280     in
   281         inst_tfrees thy rest mid
   282     end
   283 
   284 fun is_Abs (Abs _) = true
   285   | is_Abs _ = false
   286 
   287 fun eta_redex (t $ Bound 0) =
   288     let
   289         fun free n (Bound i) = i = n
   290           | free n (t $ u) = free n t orelse free n u
   291           | free n (Abs(_,_,t)) = free (n+1) t
   292           | free n _ = false
   293     in
   294         not (free 0 t)
   295     end
   296   | eta_redex _ = false
   297 
   298 fun eta_contract thy assumes origt =
   299     let
   300         val (typet,Tinst) = freeze_thaw_term origt
   301         val (init,thaw) = freeze_thaw (reflexive (cterm_of thy typet))
   302         val final = inst_tfrees thy Tinst o thaw
   303         val t = #1 (Logic.dest_equals (prop_of init))
   304         val _ =
   305             let
   306                 val lhs = #1 (Logic.dest_equals (prop_of (final init)))
   307             in
   308                 if not (lhs aconv origt)
   309                 then (writeln "Something is utterly wrong: (orig,lhs,frozen type,t,tinst)";
   310                       writeln (string_of_cterm (cterm_of thy origt));
   311                       writeln (string_of_cterm (cterm_of thy lhs));
   312                       writeln (string_of_cterm (cterm_of thy typet));
   313                       writeln (string_of_cterm (cterm_of thy t));
   314                       app (fn (n,T) => writeln (n ^ ": " ^ (string_of_ctyp (ctyp_of thy T)))) Tinst;
   315                       writeln "done")
   316                 else ()
   317             end
   318     in
   319         case t of
   320             Const("all",_) $ (Abs(x,xT,Const("==",eqT) $ P $ Q)) =>
   321             ((if eta_redex P andalso eta_redex Q
   322               then
   323                   let
   324                       val cert = cterm_of thy
   325                       val v = Free(Name.variant (add_term_free_names(t,[])) "v",xT)
   326                       val cv = cert v
   327                       val ct = cert t
   328                       val th = (assume ct)
   329                                    |> forall_elim cv
   330                                    |> abstract_rule x cv
   331                       val ext_th = eta_conversion (cert (Abs(x,xT,P)))
   332                       val th' = transitive (symmetric ext_th) th
   333                       val cu = cert (prop_of th')
   334                       val uth = combination (assume cu) (reflexive cv)
   335                       val uth' = (beta_conversion false (cert (Abs(x,xT,Q) $ v)))
   336                                      |> transitive uth
   337                                      |> forall_intr cv
   338                                      |> implies_intr cu
   339                       val rew_th = equal_intr (th' |> implies_intr ct) uth'
   340                       val res = final rew_th
   341                       val lhs = (#1 (Logic.dest_equals (prop_of res)))
   342                   in
   343                        SOME res
   344                   end
   345               else NONE)
   346              handle e => OldGoals.print_exn e)
   347           | _ => NONE
   348        end
   349 
   350 fun beta_fun thy assume t =
   351     SOME (beta_conversion true (cterm_of thy t))
   352 
   353 val meta_sym_rew = thm "refl"
   354 
   355 fun equals_fun thy assume t =
   356     case t of
   357         Const("op ==",_) $ u $ v => if Term.term_ord (u,v) = LESS then SOME (meta_sym_rew) else NONE
   358       | _ => NONE
   359 
   360 fun eta_expand thy assumes origt =
   361     let
   362         val (typet,Tinst) = freeze_thaw_term origt
   363         val (init,thaw) = freeze_thaw (reflexive (cterm_of thy typet))
   364         val final = inst_tfrees thy Tinst o thaw
   365         val t = #1 (Logic.dest_equals (prop_of init))
   366         val _ =
   367             let
   368                 val lhs = #1 (Logic.dest_equals (prop_of (final init)))
   369             in
   370                 if not (lhs aconv origt)
   371                 then (writeln "Something is utterly wrong: (orig,lhs,frozen type,t,tinst)";
   372                       writeln (string_of_cterm (cterm_of thy origt));
   373                       writeln (string_of_cterm (cterm_of thy lhs));
   374                       writeln (string_of_cterm (cterm_of thy typet));
   375                       writeln (string_of_cterm (cterm_of thy t));
   376                       app (fn (n,T) => writeln (n ^ ": " ^ (string_of_ctyp (ctyp_of thy T)))) Tinst;
   377                       writeln "done")
   378                 else ()
   379             end
   380     in
   381         case t of
   382             Const("==",T) $ P $ Q =>
   383             if is_Abs P orelse is_Abs Q
   384             then (case domain_type T of
   385                       Type("fun",[aT,bT]) =>
   386                       let
   387                           val cert = cterm_of thy
   388                           val vname = Name.variant (add_term_free_names(t,[])) "v"
   389                           val v = Free(vname,aT)
   390                           val cv = cert v
   391                           val ct = cert t
   392                           val th1 = (combination (assume ct) (reflexive cv))
   393                                         |> forall_intr cv
   394                                         |> implies_intr ct
   395                           val concl = cert (concl_of th1)
   396                           val th2 = (assume concl)
   397                                         |> forall_elim cv
   398                                         |> abstract_rule vname cv
   399                           val (lhs,rhs) = Logic.dest_equals (prop_of th2)
   400                           val elhs = eta_conversion (cert lhs)
   401                           val erhs = eta_conversion (cert rhs)
   402                           val th2' = transitive
   403                                          (transitive (symmetric elhs) th2)
   404                                          erhs
   405                           val res = equal_intr th1 (th2' |> implies_intr concl)
   406                           val res' = final res
   407                       in
   408                           SOME res'
   409                       end
   410                     | _ => NONE)
   411             else NONE
   412           | _ => (error ("Bad eta_expand argument" ^ (string_of_cterm (cterm_of thy t))); NONE)
   413     end
   414     handle e => (writeln "eta_expand internal error"; OldGoals.print_exn e)
   415 
   416 fun mk_tfree s = TFree("'"^s,[])
   417 fun mk_free s t = Free (s,t)
   418 val xT = mk_tfree "a"
   419 val yT = mk_tfree "b"
   420 val P  = mk_free "P" (xT-->yT-->propT)
   421 val Q  = mk_free "Q" (xT-->yT)
   422 val R  = mk_free "R" (xT-->yT)
   423 val S  = mk_free "S" xT
   424 val S'  = mk_free "S'" xT
   425 in
   426 fun beta_simproc thy = Simplifier.simproc_i
   427                       thy
   428                       "Beta-contraction"
   429                       [Abs("x",xT,Q) $ S]
   430                       beta_fun
   431 
   432 fun equals_simproc thy = Simplifier.simproc_i
   433                       thy
   434                       "Ordered rewriting of meta equalities"
   435                       [Const("op ==",xT) $ S $ S']
   436                       equals_fun
   437 
   438 fun quant_simproc thy = Simplifier.simproc_i
   439                            thy
   440                            "Ordered rewriting of nested quantifiers"
   441                            [all xT $ (Abs("x",xT,all yT $ (Abs("y",yT,P $ Bound 1 $ Bound 0))))]
   442                            quant_rewrite
   443 fun eta_expand_simproc thy = Simplifier.simproc_i
   444                          thy
   445                          "Smart eta-expansion by equivalences"
   446                          [Logic.mk_equals(Q,R)]
   447                          eta_expand
   448 fun eta_contract_simproc thy = Simplifier.simproc_i
   449                          thy
   450                          "Smart handling of eta-contractions"
   451                          [all xT $ (Abs("x",xT,Logic.mk_equals(Q $ Bound 0,R $ Bound 0)))]
   452                          eta_contract
   453 end
   454 
   455 (* Disambiguates the names of bound variables in a term, returning t
   456 == t' where all the names of bound variables in t' are unique *)
   457 
   458 fun disamb_bound thy t =
   459     let
   460 
   461         fun F (t $ u,idx) =
   462             let
   463                 val (t',idx') = F (t,idx)
   464                 val (u',idx'') = F (u,idx')
   465             in
   466                 (t' $ u',idx'')
   467             end
   468           | F (Abs(x,xT,t),idx) =
   469             let
   470                 val x' = "x" ^ (LargeInt.toString idx) (* amazing *)
   471                 val (t',idx') = F (t,idx+1)
   472             in
   473                 (Abs(x',xT,t'),idx')
   474             end
   475           | F arg = arg
   476         val (t',_) = F (t,0)
   477         val ct = cterm_of thy t
   478         val ct' = cterm_of thy t'
   479         val res = transitive (reflexive ct) (reflexive ct')
   480         val _ = message ("disamb_term: " ^ (string_of_thm res))
   481     in
   482         res
   483     end
   484 
   485 (* Transforms a term t to some normal form t', returning the theorem t
   486 == t'.  This is originally a help function for make_equal, but might
   487 be handy in its own right, for example for indexing terms. *)
   488 
   489 fun norm_term thy t =
   490     let
   491         val norms = ShuffleData.get thy
   492         val ss = Simplifier.theory_context thy empty_ss
   493           setmksimps single
   494           addsimps (map (Thm.transfer thy) norms)
   495           addsimprocs [quant_simproc thy, eta_expand_simproc thy,eta_contract_simproc thy]
   496         fun chain f th =
   497             let
   498                 val rhs = snd (dest_equals (cprop_of th))
   499             in
   500                 transitive th (f rhs)
   501             end
   502         val th =
   503             t |> disamb_bound thy
   504               |> chain (Simplifier.full_rewrite ss)
   505               |> chain eta_conversion
   506               |> strip_shyps
   507         val _ = message ("norm_term: " ^ (string_of_thm th))
   508     in
   509         th
   510     end
   511     handle e => (writeln "norm_term internal error"; print_sign_exn thy e)
   512 
   513 
   514 (* Closes a theorem with respect to free and schematic variables (does
   515 not touch type variables, though). *)
   516 
   517 fun close_thm th =
   518     let
   519         val thy = sign_of_thm th
   520         val c = prop_of th
   521         val vars = add_term_frees (c,add_term_vars(c,[]))
   522     in
   523         Drule.forall_intr_list (map (cterm_of thy) vars) th
   524     end
   525     handle e => (writeln "close_thm internal error"; OldGoals.print_exn e)
   526 
   527 (* Normalizes a theorem's conclusion using norm_term. *)
   528 
   529 fun norm_thm thy th =
   530     let
   531         val c = prop_of th
   532     in
   533         equal_elim (norm_term thy c) th
   534     end
   535 
   536 (* make_equal thy t u tries to construct the theorem t == u under the
   537 signature thy.  If it succeeds, SOME (t == u) is returned, otherwise
   538 NONE is returned. *)
   539 
   540 fun make_equal thy t u =
   541     let
   542         val t_is_t' = norm_term thy t
   543         val u_is_u' = norm_term thy u
   544         val th = transitive t_is_t' (symmetric u_is_u')
   545         val _ = message ("make_equal: SOME " ^ (string_of_thm th))
   546     in
   547         SOME th
   548     end
   549     handle e as THM _ => (message "make_equal: NONE";NONE)
   550 
   551 fun match_consts ignore t (* th *) =
   552     let
   553         fun add_consts (Const (c, _), cs) =
   554             if c mem_string ignore
   555             then cs
   556             else insert (op =) c cs
   557           | add_consts (t $ u, cs) = add_consts (t, add_consts (u, cs))
   558           | add_consts (Abs (_, _, t), cs) = add_consts (t, cs)
   559           | add_consts (_, cs) = cs
   560         val t_consts = add_consts(t,[])
   561     in
   562      fn (name,th) =>
   563         let
   564             val th_consts = add_consts(prop_of th,[])
   565         in
   566             eq_set(t_consts,th_consts)
   567         end
   568     end
   569 
   570 val collect_ignored =
   571     fold_rev (fn thm => fn cs =>
   572               let
   573                   val (lhs,rhs) = Logic.dest_equals (prop_of thm)
   574                   val ignore_lhs = term_consts lhs \\ term_consts rhs
   575                   val ignore_rhs = term_consts rhs \\ term_consts lhs
   576               in
   577                   fold_rev (insert (op =)) cs (ignore_lhs @ ignore_rhs)
   578               end)
   579 
   580 (* set_prop t thms tries to make a theorem with the proposition t from
   581 one of the theorems thms, by shuffling the propositions around.  If it
   582 succeeds, SOME theorem is returned, otherwise NONE.  *)
   583 
   584 fun set_prop thy t =
   585     let
   586         val vars = add_term_frees (t,add_term_vars (t,[]))
   587         val closed_t = Library.foldr (fn (v, body) =>
   588       let val vT = type_of v in all vT $ (Abs ("x", vT, abstract_over (v, body))) end) (vars, t)
   589         val rew_th = norm_term thy closed_t
   590         val rhs = snd (dest_equals (cprop_of rew_th))
   591 
   592         val shuffles = ShuffleData.get thy
   593         fun process [] = NONE
   594           | process ((name,th)::thms) =
   595             let
   596                 val norm_th = Thm.varifyT (norm_thm thy (close_thm (Thm.transfer thy th)))
   597                 val triv_th = trivial rhs
   598                 val _ = message ("Shuffler.set_prop: Gluing together " ^ (string_of_thm norm_th) ^ " and " ^ (string_of_thm triv_th))
   599                 val mod_th = case Seq.pull (bicompose false (*true*) (false,norm_th,0) 1 triv_th) of
   600                                  SOME(th,_) => SOME th
   601                                | NONE => NONE
   602             in
   603                 case mod_th of
   604                     SOME mod_th =>
   605                     let
   606                         val closed_th = equal_elim (symmetric rew_th) mod_th
   607                     in
   608                         message ("Shuffler.set_prop succeeded by " ^ name);
   609                         SOME (name,forall_elim_list (map (cterm_of thy) vars) closed_th)
   610                     end
   611                   | NONE => process thms
   612             end
   613             handle e as THM _ => process thms
   614     in
   615         fn thms =>
   616            case process thms of
   617                res as SOME (name,th) => if (prop_of th) aconv t
   618                                         then res
   619                                         else error "Internal error in set_prop"
   620              | NONE => NONE
   621     end
   622     handle e => (writeln "set_prop internal error"; OldGoals.print_exn e)
   623 
   624 fun find_potential thy t =
   625     let
   626         val shuffles = ShuffleData.get thy
   627         val ignored = collect_ignored shuffles []
   628         val rel_consts = term_consts t \\ ignored
   629         val pot_thms = PureThy.thms_containing_consts thy rel_consts
   630     in
   631         List.filter (match_consts ignored t) pot_thms
   632     end
   633 
   634 fun gen_shuffle_tac thy search thms i st =
   635     let
   636         val _ = message ("Shuffling " ^ (string_of_thm st))
   637         val t = List.nth(prems_of st,i-1)
   638         val set = set_prop thy t
   639         fun process_tac thms st =
   640             case set thms of
   641                 SOME (_,th) => Seq.of_list (compose (th,i,st))
   642               | NONE => Seq.empty
   643     in
   644         (process_tac thms APPEND (if search
   645                                   then process_tac (find_potential thy t)
   646                                   else no_tac)) st
   647     end
   648 
   649 fun shuffle_tac thms i st =
   650     gen_shuffle_tac (the_context()) false thms i st
   651 
   652 fun search_tac thms i st =
   653     gen_shuffle_tac (the_context()) true thms i st
   654 
   655 fun shuffle_meth (thms:thm list) ctxt =
   656     let
   657         val thy = ProofContext.theory_of ctxt
   658     in
   659         Method.SIMPLE_METHOD' (gen_shuffle_tac thy false (map (pair "") thms))
   660     end
   661 
   662 fun search_meth ctxt =
   663     let
   664         val thy = ProofContext.theory_of ctxt
   665         val prems = Assumption.prems_of ctxt
   666     in
   667         Method.SIMPLE_METHOD' (gen_shuffle_tac thy true (map (pair "premise") prems))
   668     end
   669 
   670 val print_shuffles = ShuffleData.print
   671 
   672 fun add_shuffle_rule thm thy =
   673     let
   674         val shuffles = ShuffleData.get thy
   675     in
   676         if exists (curry Thm.eq_thm thm) shuffles
   677         then (warning ((string_of_thm thm) ^ " already known to the shuffler");
   678               thy)
   679         else ShuffleData.put (thm::shuffles) thy
   680     end
   681 
   682 val shuffle_attr = Thm.declaration_attribute (fn th => Context.mapping (add_shuffle_rule th) I);
   683 
   684 val setup =
   685   Method.add_method ("shuffle_tac",Method.thms_ctxt_args shuffle_meth,"solve goal by shuffling terms around") #>
   686   Method.add_method ("search_tac",Method.ctxt_args search_meth,"search for suitable theorems") #>
   687   ShuffleData.init #>
   688   add_shuffle_rule weaken #>
   689   add_shuffle_rule equiv_comm #>
   690   add_shuffle_rule imp_comm #>
   691   add_shuffle_rule Drule.norm_hhf_eq #>
   692   add_shuffle_rule Drule.triv_forall_equality #>
   693   Attrib.add_attributes [("shuffle_rule", Attrib.no_args shuffle_attr, "declare rule for shuffler")]
   694 
   695 end