src/Pure/drule.ML
author wenzelm
Thu Mar 02 18:18:10 2000 +0100 (2000-03-02)
changeset 8328 efbcec3eb02f
parent 8129 29e239c7b8c2
child 8365 affb2989d238
permissions -rw-r--r--
added freeze_all;
tuned spacing;
     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 instantiate'      : ctyp option list -> cterm option list -> thm -> thm
    80   val incr_indexes      : int -> thm -> thm
    81   val incr_indexes_wrt  : int list -> ctyp list -> cterm list -> thm list -> thm -> thm
    82 end;
    83 
    84 signature DRULE =
    85 sig
    86   include BASIC_DRULE
    87   val compose_single    : thm * int * thm -> thm
    88   val triv_goal         : thm
    89   val rev_triv_goal     : thm
    90   val freeze_all        : thm -> thm
    91   val mk_triv_goal      : cterm -> thm
    92   val mk_cgoal          : cterm -> cterm
    93   val assume_goal       : cterm -> thm
    94   val tvars_of_terms    : term list -> (indexname * sort) list
    95   val vars_of_terms     : term list -> (indexname * typ) list
    96   val tvars_of          : thm -> (indexname * sort) list
    97   val vars_of           : thm -> (indexname * typ) list
    98   val unvarifyT         : thm -> thm
    99   val unvarify          : thm -> thm
   100   val rule_attribute    : ('a -> thm -> thm) -> 'a attribute
   101   val tag               : tag -> 'a attribute
   102   val untag             : tag -> 'a attribute
   103   val tag_lemma         : 'a attribute
   104   val tag_assumption    : 'a attribute
   105   val tag_internal      : 'a attribute
   106 end;
   107 
   108 structure Drule: DRULE =
   109 struct
   110 
   111 
   112 (** some cterm->cterm operations: much faster than calling cterm_of! **)
   113 
   114 (** SAME NAMES as in structure Logic: use compound identifiers! **)
   115 
   116 (*dest_implies for cterms. Note T=prop below*)
   117 fun dest_implies ct =
   118     case term_of ct of
   119         (Const("==>", _) $ _ $ _) =>
   120             let val (ct1,ct2) = dest_comb ct
   121             in  (#2 (dest_comb ct1), ct2)  end
   122       | _ => raise TERM ("dest_implies", [term_of ct]) ;
   123 
   124 
   125 (*Discard flexflex pairs; return a cterm*)
   126 fun skip_flexpairs ct =
   127     case term_of ct of
   128         (Const("==>", _) $ (Const("=?=",_)$_$_) $ _) =>
   129             skip_flexpairs (#2 (dest_implies ct))
   130       | _ => ct;
   131 
   132 (* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
   133 fun strip_imp_prems ct =
   134     let val (cA,cB) = dest_implies ct
   135     in  cA :: strip_imp_prems cB  end
   136     handle TERM _ => [];
   137 
   138 (* A1==>...An==>B  goes to B, where B is not an implication *)
   139 fun strip_imp_concl ct =
   140     case term_of ct of (Const("==>", _) $ _ $ _) =>
   141         strip_imp_concl (#2 (dest_comb ct))
   142   | _ => ct;
   143 
   144 (*The premises of a theorem, as a cterm list*)
   145 val cprems_of = strip_imp_prems o skip_flexpairs o cprop_of;
   146 
   147 
   148 (** reading of instantiations **)
   149 
   150 fun absent ixn =
   151   error("No such variable in term: " ^ Syntax.string_of_vname ixn);
   152 
   153 fun inst_failure ixn =
   154   error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails");
   155 
   156 fun read_insts sign (rtypes,rsorts) (types,sorts) used insts =
   157 let val {tsig,...} = Sign.rep_sg sign
   158     fun split([],tvs,vs) = (tvs,vs)
   159       | split((sv,st)::l,tvs,vs) = (case Symbol.explode sv of
   160                   "'"::cs => split(l,(Syntax.indexname cs,st)::tvs,vs)
   161                 | cs => split(l,tvs,(Syntax.indexname cs,st)::vs));
   162     val (tvs,vs) = split(insts,[],[]);
   163     fun readT((a,i),st) =
   164         let val ixn = ("'" ^ a,i);
   165             val S = case rsorts ixn of Some S => S | None => absent ixn;
   166             val T = Sign.read_typ (sign,sorts) st;
   167         in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T)
   168            else inst_failure ixn
   169         end
   170     val tye = map readT tvs;
   171     fun mkty(ixn,st) = (case rtypes ixn of
   172                           Some T => (ixn,(st,typ_subst_TVars tye T))
   173                         | None => absent ixn);
   174     val ixnsTs = map mkty vs;
   175     val ixns = map fst ixnsTs
   176     and sTs  = map snd ixnsTs
   177     val (cts,tye2) = read_def_cterms(sign,types,sorts) used false sTs;
   178     fun mkcVar(ixn,T) =
   179         let val U = typ_subst_TVars tye2 T
   180         in cterm_of sign (Var(ixn,U)) end
   181     val ixnTs = ListPair.zip(ixns, map snd sTs)
   182 in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) (tye2 @ tye),
   183     ListPair.zip(map mkcVar ixnTs,cts))
   184 end;
   185 
   186 
   187 (*** Find the type (sort) associated with a (T)Var or (T)Free in a term
   188      Used for establishing default types (of variables) and sorts (of
   189      type variables) when reading another term.
   190      Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
   191 ***)
   192 
   193 fun types_sorts thm =
   194     let val {prop,hyps,...} = rep_thm thm;
   195         val big = list_comb(prop,hyps); (* bogus term! *)
   196         val vars = map dest_Var (term_vars big);
   197         val frees = map dest_Free (term_frees big);
   198         val tvars = term_tvars big;
   199         val tfrees = term_tfrees big;
   200         fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i));
   201         fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
   202     in (typ,sort) end;
   203 
   204 
   205 (** Standardization of rules **)
   206 
   207 (*Strip extraneous shyps as far as possible*)
   208 fun strip_shyps_warning thm =
   209   let
   210     val str_of_sort = Sign.str_of_sort (Thm.sign_of_thm thm);
   211     val thm' = Thm.strip_shyps thm;
   212     val xshyps = Thm.extra_shyps thm';
   213   in
   214     if null xshyps then ()
   215     else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
   216     thm'
   217   end;
   218 
   219 (*Generalization over a list of variables, IGNORING bad ones*)
   220 fun forall_intr_list [] th = th
   221   | forall_intr_list (y::ys) th =
   222         let val gth = forall_intr_list ys th
   223         in  forall_intr y gth   handle THM _ =>  gth  end;
   224 
   225 (*Generalization over all suitable Free variables*)
   226 fun forall_intr_frees th =
   227     let val {prop,sign,...} = rep_thm th
   228     in  forall_intr_list
   229          (map (cterm_of sign) (sort (make_ord atless) (term_frees prop)))
   230          th
   231     end;
   232 
   233 val forall_elim_var = PureThy.forall_elim_var;
   234 val forall_elim_vars = PureThy.forall_elim_vars;
   235 
   236 (*Specialization over a list of cterms*)
   237 fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
   238 
   239 (* maps [A1,...,An], B   to   [| A1;...;An |] ==> B  *)
   240 fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
   241 
   242 (* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
   243 fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
   244 
   245 (*Reset Var indexes to zero, renaming to preserve distinctness*)
   246 fun zero_var_indexes th =
   247     let val {prop,sign,...} = rep_thm th;
   248         val vars = term_vars prop
   249         val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
   250         val inrs = add_term_tvars(prop,[]);
   251         val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
   252         val tye = ListPair.map (fn ((v,rs),a) => (v, TVar((a,0),rs)))
   253                      (inrs, nms')
   254         val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
   255         fun varpairs([],[]) = []
   256           | varpairs((var as Var(v,T)) :: vars, b::bs) =
   257                 let val T' = typ_subst_TVars tye T
   258                 in (cterm_of sign (Var(v,T')),
   259                     cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
   260                 end
   261           | varpairs _ = raise TERM("varpairs", []);
   262     in Thm.instantiate (ctye, varpairs(vars,rev bs)) th end;
   263 
   264 
   265 (*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
   266     all generality expressed by Vars having index 0.*)
   267 fun standard th =
   268   let val {maxidx,...} = rep_thm th
   269   in
   270     th |> implies_intr_hyps
   271        |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
   272        |> strip_shyps_warning
   273        |> zero_var_indexes |> Thm.varifyT |> Thm.compress
   274   end;
   275 
   276 
   277 (*Convert all Vars in a theorem to Frees.  Also return a function for
   278   reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
   279   Similar code in type/freeze_thaw*)
   280 fun freeze_thaw th =
   281  let val fth = freezeT th
   282      val {prop,sign,...} = rep_thm fth
   283  in
   284    case term_vars prop of
   285        [] => (fth, fn x => x)
   286      | vars =>
   287          let fun newName (Var(ix,_), (pairs,used)) =
   288                    let val v = variant used (string_of_indexname ix)
   289                    in  ((ix,v)::pairs, v::used)  end;
   290              val (alist, _) = foldr newName
   291                                 (vars, ([], add_term_names (prop, [])))
   292              fun mk_inst (Var(v,T)) =
   293                  (cterm_of sign (Var(v,T)),
   294                   cterm_of sign (Free(the (assoc(alist,v)), T)))
   295              val insts = map mk_inst vars
   296              fun thaw th' =
   297                  th' |> forall_intr_list (map #2 insts)
   298                      |> forall_elim_list (map #1 insts)
   299          in  (Thm.instantiate ([],insts) fth, thaw)  end
   300  end;
   301 
   302 
   303 (*Rotates a rule's premises to the left by k*)
   304 val rotate_prems = permute_prems 0;
   305 
   306 
   307 (*Assume a new formula, read following the same conventions as axioms.
   308   Generalizes over Free variables,
   309   creates the assumption, and then strips quantifiers.
   310   Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
   311              [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
   312 fun assume_ax thy sP =
   313     let val sign = Theory.sign_of thy
   314         val prop = Logic.close_form (term_of (read_cterm sign (sP, propT)))
   315     in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
   316 
   317 (*Resolution: exactly one resolvent must be produced.*)
   318 fun tha RSN (i,thb) =
   319   case Seq.chop (2, biresolution false [(false,tha)] i thb) of
   320       ([th],_) => th
   321     | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
   322     |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
   323 
   324 (*resolution: P==>Q, Q==>R gives P==>R. *)
   325 fun tha RS thb = tha RSN (1,thb);
   326 
   327 (*For joining lists of rules*)
   328 fun thas RLN (i,thbs) =
   329   let val resolve = biresolution false (map (pair false) thas) i
   330       fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
   331   in  List.concat (map resb thbs)  end;
   332 
   333 fun thas RL thbs = thas RLN (1,thbs);
   334 
   335 (*Resolve a list of rules against bottom_rl from right to left;
   336   makes proof trees*)
   337 fun rls MRS bottom_rl =
   338   let fun rs_aux i [] = bottom_rl
   339         | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
   340   in  rs_aux 1 rls  end;
   341 
   342 (*As above, but for rule lists*)
   343 fun rlss MRL bottom_rls =
   344   let fun rs_aux i [] = bottom_rls
   345         | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
   346   in  rs_aux 1 rlss  end;
   347 
   348 (*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
   349   with no lifting or renaming!  Q may contain ==> or meta-quants
   350   ALWAYS deletes premise i *)
   351 fun compose(tha,i,thb) =
   352     Seq.list_of (bicompose false (false,tha,0) i thb);
   353 
   354 fun compose_single (tha,i,thb) =
   355   (case compose (tha,i,thb) of
   356     [th] => th
   357   | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
   358 
   359 (*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
   360 fun tha COMP thb =
   361     case compose(tha,1,thb) of
   362         [th] => th
   363       | _ =>   raise THM("COMP", 1, [tha,thb]);
   364 
   365 (** theorem equality **)
   366 
   367 (*Do the two theorems have the same signature?*)
   368 fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
   369 
   370 (*Useful "distance" function for BEST_FIRST*)
   371 val size_of_thm = size_of_term o #prop o rep_thm;
   372 
   373 
   374 (** Mark Staples's weaker version of eq_thm: ignores variable renaming and
   375     (some) type variable renaming **)
   376 
   377  (* Can't use term_vars, because it sorts the resulting list of variable names.
   378     We instead need the unique list noramlised by the order of appearance
   379     in the term. *)
   380 fun term_vars' (t as Var(v,T)) = [t]
   381   | term_vars' (Abs(_,_,b)) = term_vars' b
   382   | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
   383   | term_vars' _ = [];
   384 
   385 fun forall_intr_vars th =
   386   let val {prop,sign,...} = rep_thm th;
   387       val vars = distinct (term_vars' prop);
   388   in forall_intr_list (map (cterm_of sign) vars) th end;
   389 
   390 fun weak_eq_thm (tha,thb) =
   391     eq_thm(forall_intr_vars (freezeT tha), forall_intr_vars (freezeT thb));
   392 
   393 
   394 
   395 (*** Meta-Rewriting Rules ***)
   396 
   397 val proto_sign = Theory.sign_of ProtoPure.thy;
   398 
   399 fun read_prop s = read_cterm proto_sign (s, propT);
   400 
   401 fun store_thm name thm = hd (PureThy.smart_store_thms (name, [standard thm]));
   402 
   403 val reflexive_thm =
   404   let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),logicS)))
   405   in store_thm "reflexive" (Thm.reflexive cx) end;
   406 
   407 val symmetric_thm =
   408   let val xy = read_prop "x::'a::logic == y"
   409   in store_thm "symmetric"
   410       (Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy)))
   411    end;
   412 
   413 val transitive_thm =
   414   let val xy = read_prop "x::'a::logic == y"
   415       val yz = read_prop "y::'a::logic == z"
   416       val xythm = Thm.assume xy and yzthm = Thm.assume yz
   417   in store_thm "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm))
   418   end;
   419 
   420 fun symmetric_fun thm = thm RS symmetric_thm;
   421 
   422 (** Below, a "conversion" has type cterm -> thm **)
   423 
   424 val refl_implies = reflexive (cterm_of proto_sign implies);
   425 
   426 (*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
   427 (*Do not rewrite flex-flex pairs*)
   428 fun goals_conv pred cv =
   429   let fun gconv i ct =
   430         let val (A,B) = dest_implies ct
   431             val (thA,j) = case term_of A of
   432                   Const("=?=",_)$_$_ => (reflexive A, i)
   433                 | _ => (if pred i then cv A else reflexive A, i+1)
   434         in  combination (combination refl_implies thA) (gconv j B) end
   435         handle TERM _ => reflexive ct
   436   in gconv 1 end;
   437 
   438 (*Use a conversion to transform a theorem*)
   439 fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
   440 
   441 (*rewriting conversion*)
   442 fun rew_conv mode prover mss = rewrite_cterm mode mss prover;
   443 
   444 (*Rewrite a theorem*)
   445 fun rewrite_rule_aux _ []   th = th
   446   | rewrite_rule_aux prover thms th =
   447       fconv_rule (rew_conv (true,false,false) prover (Thm.mss_of thms)) th;
   448 
   449 fun rewrite_thm mode prover mss = fconv_rule (rew_conv mode prover mss);
   450 fun rewrite_cterm mode prover mss = Thm.rewrite_cterm mode mss prover;
   451 
   452 (*Rewrite the subgoals of a proof state (represented by a theorem) *)
   453 fun rewrite_goals_rule_aux _ []   th = th
   454   | rewrite_goals_rule_aux prover thms th =
   455       fconv_rule (goals_conv (K true) (rew_conv (true, true, false) prover
   456         (Thm.mss_of thms))) th;
   457 
   458 (*Rewrite the subgoal of a proof state (represented by a theorem) *)
   459 fun rewrite_goal_rule mode prover mss i thm =
   460   if 0 < i  andalso  i <= nprems_of thm
   461   then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm
   462   else raise THM("rewrite_goal_rule",i,[thm]);
   463 
   464 
   465 (*** Some useful meta-theorems ***)
   466 
   467 (*The rule V/V, obtains assumption solving for eresolve_tac*)
   468 val asm_rl = store_thm "asm_rl" (trivial(read_prop "PROP ?psi"));
   469 val _ = store_thm "_" asm_rl;
   470 
   471 (*Meta-level cut rule: [| V==>W; V |] ==> W *)
   472 val cut_rl =
   473   store_thm "cut_rl"
   474     (trivial(read_prop "PROP ?psi ==> PROP ?theta"));
   475 
   476 (*Generalized elim rule for one conclusion; cut_rl with reversed premises:
   477      [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
   478 val revcut_rl =
   479   let val V = read_prop "PROP V"
   480       and VW = read_prop "PROP V ==> PROP W";
   481   in
   482     store_thm "revcut_rl"
   483       (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
   484   end;
   485 
   486 (*for deleting an unwanted assumption*)
   487 val thin_rl =
   488   let val V = read_prop "PROP V"
   489       and W = read_prop "PROP W";
   490   in  store_thm "thin_rl" (implies_intr V (implies_intr W (assume W)))
   491   end;
   492 
   493 (* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
   494 val triv_forall_equality =
   495   let val V  = read_prop "PROP V"
   496       and QV = read_prop "!!x::'a. PROP V"
   497       and x  = read_cterm proto_sign ("x", TypeInfer.logicT);
   498   in
   499     store_thm "triv_forall_equality"
   500       (equal_intr (implies_intr QV (forall_elim x (assume QV)))
   501         (implies_intr V  (forall_intr x (assume V))))
   502   end;
   503 
   504 (* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
   505    (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
   506    `thm COMP swap_prems_rl' swaps the first two premises of `thm'
   507 *)
   508 val swap_prems_rl =
   509   let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
   510       val major = assume cmajor;
   511       val cminor1 = read_prop "PROP PhiA";
   512       val minor1 = assume cminor1;
   513       val cminor2 = read_prop "PROP PhiB";
   514       val minor2 = assume cminor2;
   515   in store_thm "swap_prems_rl"
   516        (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
   517          (implies_elim (implies_elim major minor1) minor2))))
   518   end;
   519 
   520 (* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
   521    ==> PROP ?phi == PROP ?psi
   522    Introduction rule for == as a meta-theorem.
   523 *)
   524 val equal_intr_rule =
   525   let val PQ = read_prop "PROP phi ==> PROP psi"
   526       and QP = read_prop "PROP psi ==> PROP phi"
   527   in
   528     store_thm "equal_intr_rule"
   529       (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
   530   end;
   531 
   532 
   533 (*** Instantiate theorem th, reading instantiations under signature sg ****)
   534 
   535 (*Version that normalizes the result: Thm.instantiate no longer does that*)
   536 fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
   537 
   538 fun read_instantiate_sg sg sinsts th =
   539     let val ts = types_sorts th;
   540         val used = add_term_tvarnames(#prop(rep_thm th),[]);
   541     in  instantiate (read_insts sg ts ts used sinsts) th  end;
   542 
   543 (*Instantiate theorem th, reading instantiations under theory of th*)
   544 fun read_instantiate sinsts th =
   545     read_instantiate_sg (#sign (rep_thm th)) sinsts th;
   546 
   547 
   548 (*Left-to-right replacements: tpairs = [...,(vi,ti),...].
   549   Instantiates distinct Vars by terms, inferring type instantiations. *)
   550 local
   551   fun add_types ((ct,cu), (sign,tye,maxidx)) =
   552     let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
   553         and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
   554         val maxi = Int.max(maxidx, Int.max(maxt, maxu));
   555         val sign' = Sign.merge(sign, Sign.merge(signt, signu))
   556         val (tye',maxi') = Type.unify (#tsig(Sign.rep_sg sign')) maxi tye (T,U)
   557           handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u])
   558     in  (sign', tye', maxi')  end;
   559 in
   560 fun cterm_instantiate ctpairs0 th =
   561   let val (sign,tye,_) = foldr add_types (ctpairs0, (#sign(rep_thm th),[],0))
   562       val tsig = #tsig(Sign.rep_sg sign);
   563       fun instT(ct,cu) = let val inst = subst_TVars tye
   564                          in (cterm_fun inst ct, cterm_fun inst cu) end
   565       fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
   566   in  instantiate (map ctyp2 tye, map instT ctpairs0) th  end
   567   handle TERM _ =>
   568            raise THM("cterm_instantiate: incompatible signatures",0,[th])
   569        | TYPE (msg, _, _) => raise THM(msg, 0, [th])
   570 end;
   571 
   572 
   573 (** Derived rules mainly for METAHYPS **)
   574 
   575 (*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
   576 fun equal_abs_elim ca eqth =
   577   let val {sign=signa, t=a, ...} = rep_cterm ca
   578       and combth = combination eqth (reflexive ca)
   579       val {sign,prop,...} = rep_thm eqth
   580       val (abst,absu) = Logic.dest_equals prop
   581       val cterm = cterm_of (Sign.merge (sign,signa))
   582   in  transitive (symmetric (beta_conversion (cterm (abst$a))))
   583            (transitive combth (beta_conversion (cterm (absu$a))))
   584   end
   585   handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
   586 
   587 (*Calling equal_abs_elim with multiple terms*)
   588 fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
   589 
   590 local
   591   val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
   592   fun err th = raise THM("flexpair_inst: ", 0, [th])
   593   fun flexpair_inst def th =
   594     let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
   595         val cterm = cterm_of sign
   596         fun cvar a = cterm(Var((a,0),alpha))
   597         val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)]
   598                    def
   599     in  equal_elim def' th
   600     end
   601     handle THM _ => err th | Bind => err th
   602 in
   603 val flexpair_intr = flexpair_inst (symmetric ProtoPure.flexpair_def)
   604 and flexpair_elim = flexpair_inst ProtoPure.flexpair_def
   605 end;
   606 
   607 (*Version for flexflex pairs -- this supports lifting.*)
   608 fun flexpair_abs_elim_list cts =
   609     flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
   610 
   611 
   612 (*** GOAL (PROP A) <==> PROP A ***)
   613 
   614 local
   615   val A = read_prop "PROP A";
   616   val G = read_prop "GOAL (PROP A)";
   617   val (G_def, _) = freeze_thaw ProtoPure.Goal_def;
   618 in
   619   val triv_goal = store_thm "triv_goal" (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume A));
   620   val rev_triv_goal = store_thm "rev_triv_goal" (Thm.equal_elim G_def (Thm.assume G));
   621 end;
   622 
   623 val mk_cgoal = Thm.capply (Thm.cterm_of proto_sign (Const ("Goal", propT --> propT)));
   624 fun assume_goal ct = Thm.assume (mk_cgoal ct) RS rev_triv_goal;
   625 
   626 
   627 
   628 (** variations on instantiate **)
   629 
   630 (* collect vars *)
   631 
   632 val add_tvarsT = foldl_atyps (fn (vs, TVar v) => v ins vs | (vs, _) => vs);
   633 val add_tvars = foldl_types add_tvarsT;
   634 val add_vars = foldl_aterms (fn (vs, Var v) => v ins vs | (vs, _) => vs);
   635 
   636 fun tvars_of_terms ts = rev (foldl add_tvars ([], ts));
   637 fun vars_of_terms ts = rev (foldl add_vars ([], ts));
   638 
   639 fun tvars_of thm = tvars_of_terms [#prop (Thm.rep_thm thm)];
   640 fun vars_of thm = vars_of_terms [#prop (Thm.rep_thm thm)];
   641 
   642 
   643 (* instantiate by left-to-right occurrence of variables *)
   644 
   645 fun instantiate' cTs cts thm =
   646   let
   647     fun err msg =
   648       raise TYPE ("instantiate': " ^ msg,
   649         mapfilter (apsome Thm.typ_of) cTs,
   650         mapfilter (apsome Thm.term_of) cts);
   651 
   652     fun inst_of (v, ct) =
   653       (Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct)
   654         handle TYPE (msg, _, _) => err msg;
   655 
   656     fun zip_vars _ [] = []
   657       | zip_vars (_ :: vs) (None :: opt_ts) = zip_vars vs opt_ts
   658       | zip_vars (v :: vs) (Some t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
   659       | zip_vars [] _ = err "more instantiations than variables in thm";
   660 
   661     (*instantiate types first!*)
   662     val thm' =
   663       if forall is_none cTs then thm
   664       else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm;
   665     in
   666       if forall is_none cts then thm'
   667       else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
   668     end;
   669 
   670 
   671 (* unvarify(T) *)
   672 
   673 (*assume thm in standard form, i.e. no frees, 0 var indexes*)
   674 
   675 fun unvarifyT thm =
   676   let
   677     val cT = Thm.ctyp_of (Thm.sign_of_thm thm);
   678     val tfrees = map (fn ((x, _), S) => Some (cT (TFree (x, S)))) (tvars_of thm);
   679   in instantiate' tfrees [] thm end;
   680 
   681 fun unvarify raw_thm =
   682   let
   683     val thm = unvarifyT raw_thm;
   684     val ct = Thm.cterm_of (Thm.sign_of_thm thm);
   685     val frees = map (fn ((x, _), T) => Some (ct (Free (x, T)))) (vars_of thm);
   686   in instantiate' [] frees thm end;
   687 
   688 
   689 (* increment var indexes *)
   690 
   691 fun incr_indexes 0 thm = thm
   692   | incr_indexes inc thm =
   693       let
   694         val sign = Thm.sign_of_thm thm;
   695 
   696         fun inc_tvar ((x, i), S) = Some (Thm.ctyp_of sign (TVar ((x, i + inc), S)));
   697         fun inc_var ((x, i), T) = Some (Thm.cterm_of sign (Var ((x, i + inc), T)));
   698         val thm' = instantiate' (map inc_tvar (tvars_of thm)) [] thm;
   699         val thm'' = instantiate' [] (map inc_var (vars_of thm')) thm';
   700       in thm'' end;
   701 
   702 fun incr_indexes_wrt is cTs cts thms =
   703   let
   704     val maxidx =
   705       foldl Int.max (~1, is @
   706         map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
   707         map (#maxidx o Thm.rep_cterm) cts @
   708         map (#maxidx o Thm.rep_thm) thms);
   709   in incr_indexes (maxidx + 1) end;
   710 
   711 
   712 (* freeze_all *)
   713 
   714 (*freeze all (T)Vars; assumes thm in standard form*)
   715 
   716 fun freeze_all_TVars thm =
   717   (case tvars_of thm of
   718     [] => thm
   719   | tvars =>
   720       let val cert = Thm.ctyp_of (Thm.sign_of_thm thm)
   721       in instantiate' (map (fn ((x, _), S) => Some (cert (TFree (x, S)))) tvars) [] thm end);
   722 
   723 fun freeze_all_Vars thm =
   724   (case vars_of thm of
   725     [] => thm
   726   | vars =>
   727       let val cert = Thm.cterm_of (Thm.sign_of_thm thm)
   728       in instantiate' [] (map (fn ((x, _), T) => Some (cert (Free (x, T)))) vars) thm end);
   729 
   730 val freeze_all = freeze_all_Vars o freeze_all_TVars;
   731 
   732 
   733 (* mk_triv_goal *)
   734 
   735 (*make an initial proof state, "PROP A ==> (PROP A)" *)
   736 fun mk_triv_goal ct = instantiate' [] [Some ct] triv_goal;
   737 
   738 
   739 
   740 (** basic attributes **)
   741 
   742 (* dependent rules *)
   743 
   744 fun rule_attribute f (x, thm) = (x, (f x thm));
   745 
   746 
   747 (* add / delete tags *)
   748 
   749 fun map_tags f thm =
   750   Thm.put_name_tags (Thm.name_of_thm thm, f (#2 (Thm.get_name_tags thm))) thm;
   751 
   752 fun tag tg x = rule_attribute (K (map_tags (fn tgs => if tg mem tgs then tgs else tgs @ [tg]))) x;
   753 fun untag tg x = rule_attribute (K (map_tags (fn tgs => tgs \ tg))) x;
   754 
   755 fun simple_tag name x = tag (name, []) x;
   756 
   757 fun tag_lemma x = simple_tag "lemma" x;
   758 fun tag_assumption x = simple_tag "assumption" x;
   759 fun tag_internal x = simple_tag "internal" x;
   760 
   761 
   762 end;
   763 
   764 
   765 structure BasicDrule: BASIC_DRULE = Drule;
   766 open BasicDrule;