src/Pure/drule.ML
author wenzelm
Thu Mar 30 14:15:41 2000 +0200 (2000-03-30)
changeset 8605 625fbbe5c6b4
parent 8550 b44c185f8018
child 9288 06a55195741b
permissions -rw-r--r--
added tvars_intr_list;
     1 (*  Title:      Pure/drule.ML
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1993  University of Cambridge
     5 
     6 Derived rules and other operations on theorems.
     7 *)
     8 
     9 infix 0 RS RSN RL RLN MRS MRL COMP;
    10 
    11 signature BASIC_DRULE =
    12 sig
    13   val dest_implies      : cterm -> cterm * cterm
    14   val skip_flexpairs    : cterm -> cterm
    15   val strip_imp_prems   : cterm -> cterm list
    16   val cprems_of         : thm -> cterm list
    17   val read_insts        :
    18           Sign.sg -> (indexname -> typ option) * (indexname -> sort option)
    19                   -> (indexname -> typ option) * (indexname -> sort option)
    20                   -> string list -> (string*string)list
    21                   -> (indexname*ctyp)list * (cterm*cterm)list
    22   val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
    23   val strip_shyps_warning : thm -> thm
    24   val forall_intr_list  : cterm list -> thm -> thm
    25   val forall_intr_frees : thm -> thm
    26   val forall_intr_vars  : thm -> thm
    27   val forall_elim_list  : cterm list -> thm -> thm
    28   val forall_elim_var   : int -> thm -> thm
    29   val forall_elim_vars  : int -> thm -> thm
    30   val freeze_thaw       : thm -> thm * (thm -> thm)
    31   val implies_elim_list : thm -> thm list -> thm
    32   val implies_intr_list : cterm list -> thm -> thm
    33   val instantiate       :
    34     (indexname * ctyp) list * (cterm * cterm) list -> thm -> thm
    35   val zero_var_indexes  : thm -> thm
    36   val standard          : thm -> thm
    37   val rotate_prems      : int -> thm -> thm
    38   val assume_ax         : theory -> string -> thm
    39   val RSN               : thm * (int * thm) -> thm
    40   val RS                : thm * thm -> thm
    41   val RLN               : thm list * (int * thm list) -> thm list
    42   val RL                : thm list * thm list -> thm list
    43   val MRS               : thm list * thm -> thm
    44   val MRL               : thm list list * thm list -> thm list
    45   val compose           : thm * int * thm -> thm list
    46   val COMP              : thm * thm -> thm
    47   val read_instantiate_sg: Sign.sg -> (string*string)list -> thm -> thm
    48   val read_instantiate  : (string*string)list -> thm -> thm
    49   val cterm_instantiate : (cterm*cterm)list -> thm -> thm
    50   val weak_eq_thm       : thm * thm -> bool
    51   val eq_thm_sg         : thm * thm -> bool
    52   val size_of_thm       : thm -> int
    53   val reflexive_thm     : thm
    54   val symmetric_thm     : thm
    55   val transitive_thm    : thm
    56   val refl_implies      : thm
    57   val symmetric_fun     : thm -> thm
    58   val rewrite_rule_aux  : (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm
    59   val rewrite_thm       : bool * bool * bool
    60                           -> (meta_simpset -> thm -> thm option)
    61                           -> meta_simpset -> thm -> thm
    62   val rewrite_cterm     : bool * bool * bool
    63                           -> (meta_simpset -> thm -> thm option)
    64                           -> meta_simpset -> cterm -> thm
    65   val rewrite_goals_rule_aux: (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm
    66   val rewrite_goal_rule : bool* bool * bool
    67                           -> (meta_simpset -> thm -> thm option)
    68                           -> meta_simpset -> int -> thm -> thm
    69   val equal_abs_elim    : cterm  -> thm -> thm
    70   val equal_abs_elim_list: cterm list -> thm -> thm
    71   val flexpair_abs_elim_list: cterm list -> thm -> thm
    72   val asm_rl            : thm
    73   val cut_rl            : thm
    74   val revcut_rl         : thm
    75   val thin_rl           : thm
    76   val triv_forall_equality: thm
    77   val swap_prems_rl     : thm
    78   val equal_intr_rule   : thm
    79   val inst              : string -> string -> thm -> thm
    80   val instantiate'      : ctyp option list -> cterm option list -> thm -> thm
    81   val incr_indexes      : int -> thm -> thm
    82   val incr_indexes_wrt  : int list -> ctyp list -> cterm list -> thm list -> thm -> thm
    83 end;
    84 
    85 signature DRULE =
    86 sig
    87   include BASIC_DRULE
    88   val compose_single    : thm * int * thm -> thm
    89   val triv_goal         : thm
    90   val rev_triv_goal     : thm
    91   val freeze_all        : thm -> thm
    92   val mk_triv_goal      : cterm -> thm
    93   val mk_cgoal          : cterm -> cterm
    94   val assume_goal       : cterm -> thm
    95   val tvars_of_terms    : term list -> (indexname * sort) list
    96   val vars_of_terms     : term list -> (indexname * typ) list
    97   val tvars_of          : thm -> (indexname * sort) list
    98   val vars_of           : thm -> (indexname * typ) list
    99   val unvarifyT         : thm -> thm
   100   val unvarify          : thm -> thm
   101   val tvars_intr_list	: string list -> thm -> thm
   102   val rule_attribute    : ('a -> thm -> thm) -> 'a attribute
   103   val tag_rule          : tag -> thm -> thm
   104   val untag_rule        : string -> thm -> thm
   105   val tag               : tag -> 'a attribute
   106   val untag             : string -> 'a attribute
   107   val tag_lemma         : 'a attribute
   108   val tag_assumption    : 'a attribute
   109   val tag_internal      : 'a attribute
   110 end;
   111 
   112 structure Drule: DRULE =
   113 struct
   114 
   115 
   116 (** some cterm->cterm operations: much faster than calling cterm_of! **)
   117 
   118 (** SAME NAMES as in structure Logic: use compound identifiers! **)
   119 
   120 (*dest_implies for cterms. Note T=prop below*)
   121 fun dest_implies ct =
   122     case term_of ct of
   123         (Const("==>", _) $ _ $ _) =>
   124             let val (ct1,ct2) = dest_comb ct
   125             in  (#2 (dest_comb ct1), ct2)  end
   126       | _ => raise TERM ("dest_implies", [term_of ct]) ;
   127 
   128 
   129 (*Discard flexflex pairs; return a cterm*)
   130 fun skip_flexpairs ct =
   131     case term_of ct of
   132         (Const("==>", _) $ (Const("=?=",_)$_$_) $ _) =>
   133             skip_flexpairs (#2 (dest_implies ct))
   134       | _ => ct;
   135 
   136 (* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
   137 fun strip_imp_prems ct =
   138     let val (cA,cB) = dest_implies ct
   139     in  cA :: strip_imp_prems cB  end
   140     handle TERM _ => [];
   141 
   142 (* A1==>...An==>B  goes to B, where B is not an implication *)
   143 fun strip_imp_concl ct =
   144     case term_of ct of (Const("==>", _) $ _ $ _) =>
   145         strip_imp_concl (#2 (dest_comb ct))
   146   | _ => ct;
   147 
   148 (*The premises of a theorem, as a cterm list*)
   149 val cprems_of = strip_imp_prems o skip_flexpairs o cprop_of;
   150 
   151 
   152 (** reading of instantiations **)
   153 
   154 fun absent ixn =
   155   error("No such variable in term: " ^ Syntax.string_of_vname ixn);
   156 
   157 fun inst_failure ixn =
   158   error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails");
   159 
   160 fun read_insts sign (rtypes,rsorts) (types,sorts) used insts =
   161 let val {tsig,...} = Sign.rep_sg sign
   162     fun split([],tvs,vs) = (tvs,vs)
   163       | split((sv,st)::l,tvs,vs) = (case Symbol.explode sv of
   164                   "'"::cs => split(l,(Syntax.indexname cs,st)::tvs,vs)
   165                 | cs => split(l,tvs,(Syntax.indexname cs,st)::vs));
   166     val (tvs,vs) = split(insts,[],[]);
   167     fun readT((a,i),st) =
   168         let val ixn = ("'" ^ a,i);
   169             val S = case rsorts ixn of Some S => S | None => absent ixn;
   170             val T = Sign.read_typ (sign,sorts) st;
   171         in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T)
   172            else inst_failure ixn
   173         end
   174     val tye = map readT tvs;
   175     fun mkty(ixn,st) = (case rtypes ixn of
   176                           Some T => (ixn,(st,typ_subst_TVars tye T))
   177                         | None => absent ixn);
   178     val ixnsTs = map mkty vs;
   179     val ixns = map fst ixnsTs
   180     and sTs  = map snd ixnsTs
   181     val (cts,tye2) = read_def_cterms(sign,types,sorts) used false sTs;
   182     fun mkcVar(ixn,T) =
   183         let val U = typ_subst_TVars tye2 T
   184         in cterm_of sign (Var(ixn,U)) end
   185     val ixnTs = ListPair.zip(ixns, map snd sTs)
   186 in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) (tye2 @ tye),
   187     ListPair.zip(map mkcVar ixnTs,cts))
   188 end;
   189 
   190 
   191 (*** Find the type (sort) associated with a (T)Var or (T)Free in a term
   192      Used for establishing default types (of variables) and sorts (of
   193      type variables) when reading another term.
   194      Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
   195 ***)
   196 
   197 fun types_sorts thm =
   198     let val {prop,hyps,...} = rep_thm thm;
   199         val big = list_comb(prop,hyps); (* bogus term! *)
   200         val vars = map dest_Var (term_vars big);
   201         val frees = map dest_Free (term_frees big);
   202         val tvars = term_tvars big;
   203         val tfrees = term_tfrees big;
   204         fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i));
   205         fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
   206     in (typ,sort) end;
   207 
   208 
   209 (** Standardization of rules **)
   210 
   211 (*Strip extraneous shyps as far as possible*)
   212 fun strip_shyps_warning thm =
   213   let
   214     val str_of_sort = Sign.str_of_sort (Thm.sign_of_thm thm);
   215     val thm' = Thm.strip_shyps thm;
   216     val xshyps = Thm.extra_shyps thm';
   217   in
   218     if null xshyps then ()
   219     else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
   220     thm'
   221   end;
   222 
   223 (*Generalization over a list of variables, IGNORING bad ones*)
   224 fun forall_intr_list [] th = th
   225   | forall_intr_list (y::ys) th =
   226         let val gth = forall_intr_list ys th
   227         in  forall_intr y gth   handle THM _ =>  gth  end;
   228 
   229 (*Generalization over all suitable Free variables*)
   230 fun forall_intr_frees th =
   231     let val {prop,sign,...} = rep_thm th
   232     in  forall_intr_list
   233          (map (cterm_of sign) (sort (make_ord atless) (term_frees prop)))
   234          th
   235     end;
   236 
   237 val forall_elim_var = PureThy.forall_elim_var;
   238 val forall_elim_vars = PureThy.forall_elim_vars;
   239 
   240 (*Specialization over a list of cterms*)
   241 fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
   242 
   243 (* maps [A1,...,An], B   to   [| A1;...;An |] ==> B  *)
   244 fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
   245 
   246 (* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
   247 fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
   248 
   249 (*Reset Var indexes to zero, renaming to preserve distinctness*)
   250 fun zero_var_indexes th =
   251     let val {prop,sign,...} = rep_thm th;
   252         val vars = term_vars prop
   253         val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
   254         val inrs = add_term_tvars(prop,[]);
   255         val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
   256         val tye = ListPair.map (fn ((v,rs),a) => (v, TVar((a,0),rs)))
   257                      (inrs, nms')
   258         val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
   259         fun varpairs([],[]) = []
   260           | varpairs((var as Var(v,T)) :: vars, b::bs) =
   261                 let val T' = typ_subst_TVars tye T
   262                 in (cterm_of sign (Var(v,T')),
   263                     cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
   264                 end
   265           | varpairs _ = raise TERM("varpairs", []);
   266     in Thm.instantiate (ctye, varpairs(vars,rev bs)) th end;
   267 
   268 
   269 (*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
   270     all generality expressed by Vars having index 0.*)
   271 fun standard th =
   272   let val {maxidx,...} = rep_thm th
   273   in
   274     th |> implies_intr_hyps
   275        |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
   276        |> strip_shyps_warning
   277        |> zero_var_indexes |> Thm.varifyT |> Thm.compress
   278   end;
   279 
   280 
   281 (*Convert all Vars in a theorem to Frees.  Also return a function for
   282   reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
   283   Similar code in type/freeze_thaw*)
   284 fun freeze_thaw th =
   285  let val fth = freezeT th
   286      val {prop,sign,...} = rep_thm fth
   287  in
   288    case term_vars prop of
   289        [] => (fth, fn x => x)
   290      | vars =>
   291          let fun newName (Var(ix,_), (pairs,used)) =
   292                    let val v = variant used (string_of_indexname ix)
   293                    in  ((ix,v)::pairs, v::used)  end;
   294              val (alist, _) = foldr newName
   295                                 (vars, ([], add_term_names (prop, [])))
   296              fun mk_inst (Var(v,T)) =
   297                  (cterm_of sign (Var(v,T)),
   298                   cterm_of sign (Free(the (assoc(alist,v)), T)))
   299              val insts = map mk_inst vars
   300              fun thaw th' =
   301                  th' |> forall_intr_list (map #2 insts)
   302                      |> forall_elim_list (map #1 insts)
   303          in  (Thm.instantiate ([],insts) fth, thaw)  end
   304  end;
   305 
   306 
   307 (*Rotates a rule's premises to the left by k*)
   308 val rotate_prems = permute_prems 0;
   309 
   310 
   311 (*Assume a new formula, read following the same conventions as axioms.
   312   Generalizes over Free variables,
   313   creates the assumption, and then strips quantifiers.
   314   Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
   315              [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
   316 fun assume_ax thy sP =
   317     let val sign = Theory.sign_of thy
   318         val prop = Logic.close_form (term_of (read_cterm sign (sP, propT)))
   319     in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
   320 
   321 (*Resolution: exactly one resolvent must be produced.*)
   322 fun tha RSN (i,thb) =
   323   case Seq.chop (2, biresolution false [(false,tha)] i thb) of
   324       ([th],_) => th
   325     | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
   326     |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
   327 
   328 (*resolution: P==>Q, Q==>R gives P==>R. *)
   329 fun tha RS thb = tha RSN (1,thb);
   330 
   331 (*For joining lists of rules*)
   332 fun thas RLN (i,thbs) =
   333   let val resolve = biresolution false (map (pair false) thas) i
   334       fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
   335   in  List.concat (map resb thbs)  end;
   336 
   337 fun thas RL thbs = thas RLN (1,thbs);
   338 
   339 (*Resolve a list of rules against bottom_rl from right to left;
   340   makes proof trees*)
   341 fun rls MRS bottom_rl =
   342   let fun rs_aux i [] = bottom_rl
   343         | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
   344   in  rs_aux 1 rls  end;
   345 
   346 (*As above, but for rule lists*)
   347 fun rlss MRL bottom_rls =
   348   let fun rs_aux i [] = bottom_rls
   349         | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
   350   in  rs_aux 1 rlss  end;
   351 
   352 (*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
   353   with no lifting or renaming!  Q may contain ==> or meta-quants
   354   ALWAYS deletes premise i *)
   355 fun compose(tha,i,thb) =
   356     Seq.list_of (bicompose false (false,tha,0) i thb);
   357 
   358 fun compose_single (tha,i,thb) =
   359   (case compose (tha,i,thb) of
   360     [th] => th
   361   | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
   362 
   363 (*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
   364 fun tha COMP thb =
   365     case compose(tha,1,thb) of
   366         [th] => th
   367       | _ =>   raise THM("COMP", 1, [tha,thb]);
   368 
   369 (** theorem equality **)
   370 
   371 (*Do the two theorems have the same signature?*)
   372 fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
   373 
   374 (*Useful "distance" function for BEST_FIRST*)
   375 val size_of_thm = size_of_term o #prop o rep_thm;
   376 
   377 
   378 (** Mark Staples's weaker version of eq_thm: ignores variable renaming and
   379     (some) type variable renaming **)
   380 
   381  (* Can't use term_vars, because it sorts the resulting list of variable names.
   382     We instead need the unique list noramlised by the order of appearance
   383     in the term. *)
   384 fun term_vars' (t as Var(v,T)) = [t]
   385   | term_vars' (Abs(_,_,b)) = term_vars' b
   386   | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
   387   | term_vars' _ = [];
   388 
   389 fun forall_intr_vars th =
   390   let val {prop,sign,...} = rep_thm th;
   391       val vars = distinct (term_vars' prop);
   392   in forall_intr_list (map (cterm_of sign) vars) th end;
   393 
   394 fun weak_eq_thm (tha,thb) =
   395     eq_thm(forall_intr_vars (freezeT tha), forall_intr_vars (freezeT thb));
   396 
   397 
   398 
   399 (*** Meta-Rewriting Rules ***)
   400 
   401 val proto_sign = Theory.sign_of ProtoPure.thy;
   402 
   403 fun read_prop s = read_cterm proto_sign (s, propT);
   404 
   405 fun store_thm name thm = hd (PureThy.smart_store_thms (name, [standard thm]));
   406 
   407 val reflexive_thm =
   408   let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),logicS)))
   409   in store_thm "reflexive" (Thm.reflexive cx) end;
   410 
   411 val symmetric_thm =
   412   let val xy = read_prop "x::'a::logic == y"
   413   in store_thm "symmetric"
   414       (Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy)))
   415    end;
   416 
   417 val transitive_thm =
   418   let val xy = read_prop "x::'a::logic == y"
   419       val yz = read_prop "y::'a::logic == z"
   420       val xythm = Thm.assume xy and yzthm = Thm.assume yz
   421   in store_thm "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm))
   422   end;
   423 
   424 fun symmetric_fun thm = thm RS symmetric_thm;
   425 
   426 (** Below, a "conversion" has type cterm -> thm **)
   427 
   428 val refl_implies = reflexive (cterm_of proto_sign implies);
   429 
   430 (*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
   431 (*Do not rewrite flex-flex pairs*)
   432 fun goals_conv pred cv =
   433   let fun gconv i ct =
   434         let val (A,B) = dest_implies ct
   435             val (thA,j) = case term_of A of
   436                   Const("=?=",_)$_$_ => (reflexive A, i)
   437                 | _ => (if pred i then cv A else reflexive A, i+1)
   438         in  combination (combination refl_implies thA) (gconv j B) end
   439         handle TERM _ => reflexive ct
   440   in gconv 1 end;
   441 
   442 (*Use a conversion to transform a theorem*)
   443 fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
   444 
   445 (*rewriting conversion*)
   446 fun rew_conv mode prover mss = rewrite_cterm mode mss prover;
   447 
   448 (*Rewrite a theorem*)
   449 fun rewrite_rule_aux _ []   th = th
   450   | rewrite_rule_aux prover thms th =
   451       fconv_rule (rew_conv (true,false,false) prover (Thm.mss_of thms)) th;
   452 
   453 fun rewrite_thm mode prover mss = fconv_rule (rew_conv mode prover mss);
   454 fun rewrite_cterm mode prover mss = Thm.rewrite_cterm mode mss prover;
   455 
   456 (*Rewrite the subgoals of a proof state (represented by a theorem) *)
   457 fun rewrite_goals_rule_aux _ []   th = th
   458   | rewrite_goals_rule_aux prover thms th =
   459       fconv_rule (goals_conv (K true) (rew_conv (true, true, false) prover
   460         (Thm.mss_of thms))) th;
   461 
   462 (*Rewrite the subgoal of a proof state (represented by a theorem) *)
   463 fun rewrite_goal_rule mode prover mss i thm =
   464   if 0 < i  andalso  i <= nprems_of thm
   465   then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm
   466   else raise THM("rewrite_goal_rule",i,[thm]);
   467 
   468 
   469 (*** Some useful meta-theorems ***)
   470 
   471 (*The rule V/V, obtains assumption solving for eresolve_tac*)
   472 val asm_rl = store_thm "asm_rl" (trivial(read_prop "PROP ?psi"));
   473 val _ = store_thm "_" asm_rl;
   474 
   475 (*Meta-level cut rule: [| V==>W; V |] ==> W *)
   476 val cut_rl =
   477   store_thm "cut_rl"
   478     (trivial(read_prop "PROP ?psi ==> PROP ?theta"));
   479 
   480 (*Generalized elim rule for one conclusion; cut_rl with reversed premises:
   481      [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
   482 val revcut_rl =
   483   let val V = read_prop "PROP V"
   484       and VW = read_prop "PROP V ==> PROP W";
   485   in
   486     store_thm "revcut_rl"
   487       (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
   488   end;
   489 
   490 (*for deleting an unwanted assumption*)
   491 val thin_rl =
   492   let val V = read_prop "PROP V"
   493       and W = read_prop "PROP W";
   494   in  store_thm "thin_rl" (implies_intr V (implies_intr W (assume W)))
   495   end;
   496 
   497 (* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
   498 val triv_forall_equality =
   499   let val V  = read_prop "PROP V"
   500       and QV = read_prop "!!x::'a. PROP V"
   501       and x  = read_cterm proto_sign ("x", TypeInfer.logicT);
   502   in
   503     store_thm "triv_forall_equality"
   504       (equal_intr (implies_intr QV (forall_elim x (assume QV)))
   505         (implies_intr V  (forall_intr x (assume V))))
   506   end;
   507 
   508 (* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
   509    (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
   510    `thm COMP swap_prems_rl' swaps the first two premises of `thm'
   511 *)
   512 val swap_prems_rl =
   513   let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
   514       val major = assume cmajor;
   515       val cminor1 = read_prop "PROP PhiA";
   516       val minor1 = assume cminor1;
   517       val cminor2 = read_prop "PROP PhiB";
   518       val minor2 = assume cminor2;
   519   in store_thm "swap_prems_rl"
   520        (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
   521          (implies_elim (implies_elim major minor1) minor2))))
   522   end;
   523 
   524 (* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
   525    ==> PROP ?phi == PROP ?psi
   526    Introduction rule for == as a meta-theorem.
   527 *)
   528 val equal_intr_rule =
   529   let val PQ = read_prop "PROP phi ==> PROP psi"
   530       and QP = read_prop "PROP psi ==> PROP phi"
   531   in
   532     store_thm "equal_intr_rule"
   533       (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
   534   end;
   535 
   536 
   537 (*** Instantiate theorem th, reading instantiations under signature sg ****)
   538 
   539 (*Version that normalizes the result: Thm.instantiate no longer does that*)
   540 fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
   541 
   542 fun read_instantiate_sg sg sinsts th =
   543     let val ts = types_sorts th;
   544         val used = add_term_tvarnames(#prop(rep_thm th),[]);
   545     in  instantiate (read_insts sg ts ts used sinsts) th  end;
   546 
   547 (*Instantiate theorem th, reading instantiations under theory of th*)
   548 fun read_instantiate sinsts th =
   549     read_instantiate_sg (#sign (rep_thm th)) sinsts th;
   550 
   551 
   552 (*Left-to-right replacements: tpairs = [...,(vi,ti),...].
   553   Instantiates distinct Vars by terms, inferring type instantiations. *)
   554 local
   555   fun add_types ((ct,cu), (sign,tye,maxidx)) =
   556     let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
   557         and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
   558         val maxi = Int.max(maxidx, Int.max(maxt, maxu));
   559         val sign' = Sign.merge(sign, Sign.merge(signt, signu))
   560         val (tye',maxi') = Type.unify (#tsig(Sign.rep_sg sign')) maxi tye (T,U)
   561           handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u])
   562     in  (sign', tye', maxi')  end;
   563 in
   564 fun cterm_instantiate ctpairs0 th =
   565   let val (sign,tye,_) = foldr add_types (ctpairs0, (#sign(rep_thm th), Vartab.empty, 0))
   566       val tsig = #tsig(Sign.rep_sg sign);
   567       fun instT(ct,cu) = let val inst = subst_TVars_Vartab tye
   568                          in (cterm_fun inst ct, cterm_fun inst cu) end
   569       fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
   570   in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
   571   handle TERM _ =>
   572            raise THM("cterm_instantiate: incompatible signatures",0,[th])
   573        | TYPE (msg, _, _) => raise THM(msg, 0, [th])
   574 end;
   575 
   576 
   577 (** Derived rules mainly for METAHYPS **)
   578 
   579 (*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
   580 fun equal_abs_elim ca eqth =
   581   let val {sign=signa, t=a, ...} = rep_cterm ca
   582       and combth = combination eqth (reflexive ca)
   583       val {sign,prop,...} = rep_thm eqth
   584       val (abst,absu) = Logic.dest_equals prop
   585       val cterm = cterm_of (Sign.merge (sign,signa))
   586   in  transitive (symmetric (beta_conversion (cterm (abst$a))))
   587            (transitive combth (beta_conversion (cterm (absu$a))))
   588   end
   589   handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
   590 
   591 (*Calling equal_abs_elim with multiple terms*)
   592 fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
   593 
   594 local
   595   val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
   596   fun err th = raise THM("flexpair_inst: ", 0, [th])
   597   fun flexpair_inst def th =
   598     let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
   599         val cterm = cterm_of sign
   600         fun cvar a = cterm(Var((a,0),alpha))
   601         val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)]
   602                    def
   603     in  equal_elim def' th
   604     end
   605     handle THM _ => err th | Bind => err th
   606 in
   607 val flexpair_intr = flexpair_inst (symmetric ProtoPure.flexpair_def)
   608 and flexpair_elim = flexpair_inst ProtoPure.flexpair_def
   609 end;
   610 
   611 (*Version for flexflex pairs -- this supports lifting.*)
   612 fun flexpair_abs_elim_list cts =
   613     flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
   614 
   615 
   616 (*** GOAL (PROP A) <==> PROP A ***)
   617 
   618 local
   619   val A = read_prop "PROP A";
   620   val G = read_prop "GOAL (PROP A)";
   621   val (G_def, _) = freeze_thaw ProtoPure.Goal_def;
   622 in
   623   val triv_goal = store_thm "triv_goal" (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume A));
   624   val rev_triv_goal = store_thm "rev_triv_goal" (Thm.equal_elim G_def (Thm.assume G));
   625 end;
   626 
   627 val mk_cgoal = Thm.capply (Thm.cterm_of proto_sign (Const ("Goal", propT --> propT)));
   628 fun assume_goal ct = Thm.assume (mk_cgoal ct) RS rev_triv_goal;
   629 
   630 
   631 
   632 (** variations on instantiate **)
   633 
   634 (*shorthand for instantiating just one variable in the current theory*)
   635 fun inst x t = read_instantiate_sg (sign_of (the_context())) [(x,t)];
   636 
   637 
   638 (* collect vars *)
   639 
   640 val add_tvarsT = foldl_atyps (fn (vs, TVar v) => v ins vs | (vs, _) => vs);
   641 val add_tvars = foldl_types add_tvarsT;
   642 val add_vars = foldl_aterms (fn (vs, Var v) => v ins vs | (vs, _) => vs);
   643 
   644 fun tvars_of_terms ts = rev (foldl add_tvars ([], ts));
   645 fun vars_of_terms ts = rev (foldl add_vars ([], ts));
   646 
   647 fun tvars_of thm = tvars_of_terms [#prop (Thm.rep_thm thm)];
   648 fun vars_of thm = vars_of_terms [#prop (Thm.rep_thm thm)];
   649 
   650 
   651 (* instantiate by left-to-right occurrence of variables *)
   652 
   653 fun instantiate' cTs cts thm =
   654   let
   655     fun err msg =
   656       raise TYPE ("instantiate': " ^ msg,
   657         mapfilter (apsome Thm.typ_of) cTs,
   658         mapfilter (apsome Thm.term_of) cts);
   659 
   660     fun inst_of (v, ct) =
   661       (Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct)
   662         handle TYPE (msg, _, _) => err msg;
   663 
   664     fun zip_vars _ [] = []
   665       | zip_vars (_ :: vs) (None :: opt_ts) = zip_vars vs opt_ts
   666       | zip_vars (v :: vs) (Some t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
   667       | zip_vars [] _ = err "more instantiations than variables in thm";
   668 
   669     (*instantiate types first!*)
   670     val thm' =
   671       if forall is_none cTs then thm
   672       else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm;
   673     in
   674       if forall is_none cts then thm'
   675       else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
   676     end;
   677 
   678 
   679 (* unvarify(T) *)
   680 
   681 (*assume thm in standard form, i.e. no frees, 0 var indexes*)
   682 
   683 fun unvarifyT thm =
   684   let
   685     val cT = Thm.ctyp_of (Thm.sign_of_thm thm);
   686     val tfrees = map (fn ((x, _), S) => Some (cT (TFree (x, S)))) (tvars_of thm);
   687   in instantiate' tfrees [] thm end;
   688 
   689 fun unvarify raw_thm =
   690   let
   691     val thm = unvarifyT raw_thm;
   692     val ct = Thm.cterm_of (Thm.sign_of_thm thm);
   693     val frees = map (fn ((x, _), T) => Some (ct (Free (x, T)))) (vars_of thm);
   694   in instantiate' [] frees thm end;
   695 
   696 
   697 (* tvars_intr_list *)
   698 
   699 fun tfrees_of thm =
   700   let val {hyps, prop, ...} = Thm.rep_thm thm
   701   in foldr Term.add_term_tfree_names (prop :: hyps, []) end;
   702 
   703 fun tvars_intr_list tfrees thm =
   704   Thm.varifyT' (tfrees_of thm \\ tfrees) thm;
   705 
   706 
   707 (* increment var indexes *)
   708 
   709 fun incr_indexes 0 thm = thm
   710   | incr_indexes inc thm =
   711       let
   712         val sign = Thm.sign_of_thm thm;
   713 
   714         fun inc_tvar ((x, i), S) = Some (Thm.ctyp_of sign (TVar ((x, i + inc), S)));
   715         fun inc_var ((x, i), T) = Some (Thm.cterm_of sign (Var ((x, i + inc), T)));
   716         val thm' = instantiate' (map inc_tvar (tvars_of thm)) [] thm;
   717         val thm'' = instantiate' [] (map inc_var (vars_of thm')) thm';
   718       in thm'' end;
   719 
   720 fun incr_indexes_wrt is cTs cts thms =
   721   let
   722     val maxidx =
   723       foldl Int.max (~1, is @
   724         map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
   725         map (#maxidx o Thm.rep_cterm) cts @
   726         map (#maxidx o Thm.rep_thm) thms);
   727   in incr_indexes (maxidx + 1) end;
   728 
   729 
   730 (* freeze_all *)
   731 
   732 (*freeze all (T)Vars; assumes thm in standard form*)
   733 
   734 fun freeze_all_TVars thm =
   735   (case tvars_of thm of
   736     [] => thm
   737   | tvars =>
   738       let val cert = Thm.ctyp_of (Thm.sign_of_thm thm)
   739       in instantiate' (map (fn ((x, _), S) => Some (cert (TFree (x, S)))) tvars) [] thm end);
   740 
   741 fun freeze_all_Vars thm =
   742   (case vars_of thm of
   743     [] => thm
   744   | vars =>
   745       let val cert = Thm.cterm_of (Thm.sign_of_thm thm)
   746       in instantiate' [] (map (fn ((x, _), T) => Some (cert (Free (x, T)))) vars) thm end);
   747 
   748 val freeze_all = freeze_all_Vars o freeze_all_TVars;
   749 
   750 
   751 (* mk_triv_goal *)
   752 
   753 (*make an initial proof state, "PROP A ==> (PROP A)" *)
   754 fun mk_triv_goal ct = instantiate' [] [Some ct] triv_goal;
   755 
   756 
   757 
   758 (** basic attributes **)
   759 
   760 (* dependent rules *)
   761 
   762 fun rule_attribute f (x, thm) = (x, (f x thm));
   763 
   764 
   765 (* add / delete tags *)
   766 
   767 fun map_tags f thm =
   768   Thm.put_name_tags (Thm.name_of_thm thm, f (#2 (Thm.get_name_tags thm))) thm;
   769 
   770 fun tag_rule tg = map_tags (fn tgs => if tg mem tgs then tgs else tgs @ [tg]);
   771 fun untag_rule s = map_tags (filter_out (equal s o #1));
   772 
   773 fun tag tg x = rule_attribute (K (tag_rule tg)) x;
   774 fun untag s x = rule_attribute (K (untag_rule s)) x;
   775 
   776 fun simple_tag name x = tag (name, []) x;
   777 
   778 fun tag_lemma x = simple_tag "lemma" x;
   779 fun tag_assumption x = simple_tag "assumption" x;
   780 fun tag_internal x = simple_tag "internal" x;
   781 
   782 
   783 end;
   784 
   785 
   786 structure BasicDrule: BASIC_DRULE = Drule;
   787 open BasicDrule;