src/Pure/drule.ML
author paulson
Wed Mar 22 12:33:34 2000 +0100 (2000-03-22)
changeset 8550 b44c185f8018
parent 8496 7e4a466b18d5
child 8605 625fbbe5c6b4
permissions -rw-r--r--
new meta-rule "inst", a shorthand for read_instantiate_sg
     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 rule_attribute    : ('a -> thm -> thm) -> 'a attribute
   102   val tag_rule          : tag -> thm -> thm
   103   val untag_rule        : string -> thm -> thm
   104   val tag               : tag -> 'a attribute
   105   val untag             : string -> 'a attribute
   106   val tag_lemma         : 'a attribute
   107   val tag_assumption    : 'a attribute
   108   val tag_internal      : 'a attribute
   109 end;
   110 
   111 structure Drule: DRULE =
   112 struct
   113 
   114 
   115 (** some cterm->cterm operations: much faster than calling cterm_of! **)
   116 
   117 (** SAME NAMES as in structure Logic: use compound identifiers! **)
   118 
   119 (*dest_implies for cterms. Note T=prop below*)
   120 fun dest_implies ct =
   121     case term_of ct of
   122         (Const("==>", _) $ _ $ _) =>
   123             let val (ct1,ct2) = dest_comb ct
   124             in  (#2 (dest_comb ct1), ct2)  end
   125       | _ => raise TERM ("dest_implies", [term_of ct]) ;
   126 
   127 
   128 (*Discard flexflex pairs; return a cterm*)
   129 fun skip_flexpairs ct =
   130     case term_of ct of
   131         (Const("==>", _) $ (Const("=?=",_)$_$_) $ _) =>
   132             skip_flexpairs (#2 (dest_implies ct))
   133       | _ => ct;
   134 
   135 (* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
   136 fun strip_imp_prems ct =
   137     let val (cA,cB) = dest_implies ct
   138     in  cA :: strip_imp_prems cB  end
   139     handle TERM _ => [];
   140 
   141 (* A1==>...An==>B  goes to B, where B is not an implication *)
   142 fun strip_imp_concl ct =
   143     case term_of ct of (Const("==>", _) $ _ $ _) =>
   144         strip_imp_concl (#2 (dest_comb ct))
   145   | _ => ct;
   146 
   147 (*The premises of a theorem, as a cterm list*)
   148 val cprems_of = strip_imp_prems o skip_flexpairs o cprop_of;
   149 
   150 
   151 (** reading of instantiations **)
   152 
   153 fun absent ixn =
   154   error("No such variable in term: " ^ Syntax.string_of_vname ixn);
   155 
   156 fun inst_failure ixn =
   157   error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails");
   158 
   159 fun read_insts sign (rtypes,rsorts) (types,sorts) used insts =
   160 let val {tsig,...} = Sign.rep_sg sign
   161     fun split([],tvs,vs) = (tvs,vs)
   162       | split((sv,st)::l,tvs,vs) = (case Symbol.explode sv of
   163                   "'"::cs => split(l,(Syntax.indexname cs,st)::tvs,vs)
   164                 | cs => split(l,tvs,(Syntax.indexname cs,st)::vs));
   165     val (tvs,vs) = split(insts,[],[]);
   166     fun readT((a,i),st) =
   167         let val ixn = ("'" ^ a,i);
   168             val S = case rsorts ixn of Some S => S | None => absent ixn;
   169             val T = Sign.read_typ (sign,sorts) st;
   170         in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T)
   171            else inst_failure ixn
   172         end
   173     val tye = map readT tvs;
   174     fun mkty(ixn,st) = (case rtypes ixn of
   175                           Some T => (ixn,(st,typ_subst_TVars tye T))
   176                         | None => absent ixn);
   177     val ixnsTs = map mkty vs;
   178     val ixns = map fst ixnsTs
   179     and sTs  = map snd ixnsTs
   180     val (cts,tye2) = read_def_cterms(sign,types,sorts) used false sTs;
   181     fun mkcVar(ixn,T) =
   182         let val U = typ_subst_TVars tye2 T
   183         in cterm_of sign (Var(ixn,U)) end
   184     val ixnTs = ListPair.zip(ixns, map snd sTs)
   185 in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) (tye2 @ tye),
   186     ListPair.zip(map mkcVar ixnTs,cts))
   187 end;
   188 
   189 
   190 (*** Find the type (sort) associated with a (T)Var or (T)Free in a term
   191      Used for establishing default types (of variables) and sorts (of
   192      type variables) when reading another term.
   193      Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
   194 ***)
   195 
   196 fun types_sorts thm =
   197     let val {prop,hyps,...} = rep_thm thm;
   198         val big = list_comb(prop,hyps); (* bogus term! *)
   199         val vars = map dest_Var (term_vars big);
   200         val frees = map dest_Free (term_frees big);
   201         val tvars = term_tvars big;
   202         val tfrees = term_tfrees big;
   203         fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i));
   204         fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
   205     in (typ,sort) end;
   206 
   207 
   208 (** Standardization of rules **)
   209 
   210 (*Strip extraneous shyps as far as possible*)
   211 fun strip_shyps_warning thm =
   212   let
   213     val str_of_sort = Sign.str_of_sort (Thm.sign_of_thm thm);
   214     val thm' = Thm.strip_shyps thm;
   215     val xshyps = Thm.extra_shyps thm';
   216   in
   217     if null xshyps then ()
   218     else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
   219     thm'
   220   end;
   221 
   222 (*Generalization over a list of variables, IGNORING bad ones*)
   223 fun forall_intr_list [] th = th
   224   | forall_intr_list (y::ys) th =
   225         let val gth = forall_intr_list ys th
   226         in  forall_intr y gth   handle THM _ =>  gth  end;
   227 
   228 (*Generalization over all suitable Free variables*)
   229 fun forall_intr_frees th =
   230     let val {prop,sign,...} = rep_thm th
   231     in  forall_intr_list
   232          (map (cterm_of sign) (sort (make_ord atless) (term_frees prop)))
   233          th
   234     end;
   235 
   236 val forall_elim_var = PureThy.forall_elim_var;
   237 val forall_elim_vars = PureThy.forall_elim_vars;
   238 
   239 (*Specialization over a list of cterms*)
   240 fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
   241 
   242 (* maps [A1,...,An], B   to   [| A1;...;An |] ==> B  *)
   243 fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
   244 
   245 (* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
   246 fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
   247 
   248 (*Reset Var indexes to zero, renaming to preserve distinctness*)
   249 fun zero_var_indexes th =
   250     let val {prop,sign,...} = rep_thm th;
   251         val vars = term_vars prop
   252         val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
   253         val inrs = add_term_tvars(prop,[]);
   254         val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
   255         val tye = ListPair.map (fn ((v,rs),a) => (v, TVar((a,0),rs)))
   256                      (inrs, nms')
   257         val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
   258         fun varpairs([],[]) = []
   259           | varpairs((var as Var(v,T)) :: vars, b::bs) =
   260                 let val T' = typ_subst_TVars tye T
   261                 in (cterm_of sign (Var(v,T')),
   262                     cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
   263                 end
   264           | varpairs _ = raise TERM("varpairs", []);
   265     in Thm.instantiate (ctye, varpairs(vars,rev bs)) th end;
   266 
   267 
   268 (*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
   269     all generality expressed by Vars having index 0.*)
   270 fun standard th =
   271   let val {maxidx,...} = rep_thm th
   272   in
   273     th |> implies_intr_hyps
   274        |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
   275        |> strip_shyps_warning
   276        |> zero_var_indexes |> Thm.varifyT |> Thm.compress
   277   end;
   278 
   279 
   280 (*Convert all Vars in a theorem to Frees.  Also return a function for
   281   reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
   282   Similar code in type/freeze_thaw*)
   283 fun freeze_thaw th =
   284  let val fth = freezeT th
   285      val {prop,sign,...} = rep_thm fth
   286  in
   287    case term_vars prop of
   288        [] => (fth, fn x => x)
   289      | vars =>
   290          let fun newName (Var(ix,_), (pairs,used)) =
   291                    let val v = variant used (string_of_indexname ix)
   292                    in  ((ix,v)::pairs, v::used)  end;
   293              val (alist, _) = foldr newName
   294                                 (vars, ([], add_term_names (prop, [])))
   295              fun mk_inst (Var(v,T)) =
   296                  (cterm_of sign (Var(v,T)),
   297                   cterm_of sign (Free(the (assoc(alist,v)), T)))
   298              val insts = map mk_inst vars
   299              fun thaw th' =
   300                  th' |> forall_intr_list (map #2 insts)
   301                      |> forall_elim_list (map #1 insts)
   302          in  (Thm.instantiate ([],insts) fth, thaw)  end
   303  end;
   304 
   305 
   306 (*Rotates a rule's premises to the left by k*)
   307 val rotate_prems = permute_prems 0;
   308 
   309 
   310 (*Assume a new formula, read following the same conventions as axioms.
   311   Generalizes over Free variables,
   312   creates the assumption, and then strips quantifiers.
   313   Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
   314              [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
   315 fun assume_ax thy sP =
   316     let val sign = Theory.sign_of thy
   317         val prop = Logic.close_form (term_of (read_cterm sign (sP, propT)))
   318     in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
   319 
   320 (*Resolution: exactly one resolvent must be produced.*)
   321 fun tha RSN (i,thb) =
   322   case Seq.chop (2, biresolution false [(false,tha)] i thb) of
   323       ([th],_) => th
   324     | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
   325     |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
   326 
   327 (*resolution: P==>Q, Q==>R gives P==>R. *)
   328 fun tha RS thb = tha RSN (1,thb);
   329 
   330 (*For joining lists of rules*)
   331 fun thas RLN (i,thbs) =
   332   let val resolve = biresolution false (map (pair false) thas) i
   333       fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
   334   in  List.concat (map resb thbs)  end;
   335 
   336 fun thas RL thbs = thas RLN (1,thbs);
   337 
   338 (*Resolve a list of rules against bottom_rl from right to left;
   339   makes proof trees*)
   340 fun rls MRS bottom_rl =
   341   let fun rs_aux i [] = bottom_rl
   342         | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
   343   in  rs_aux 1 rls  end;
   344 
   345 (*As above, but for rule lists*)
   346 fun rlss MRL bottom_rls =
   347   let fun rs_aux i [] = bottom_rls
   348         | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
   349   in  rs_aux 1 rlss  end;
   350 
   351 (*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
   352   with no lifting or renaming!  Q may contain ==> or meta-quants
   353   ALWAYS deletes premise i *)
   354 fun compose(tha,i,thb) =
   355     Seq.list_of (bicompose false (false,tha,0) i thb);
   356 
   357 fun compose_single (tha,i,thb) =
   358   (case compose (tha,i,thb) of
   359     [th] => th
   360   | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
   361 
   362 (*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
   363 fun tha COMP thb =
   364     case compose(tha,1,thb) of
   365         [th] => th
   366       | _ =>   raise THM("COMP", 1, [tha,thb]);
   367 
   368 (** theorem equality **)
   369 
   370 (*Do the two theorems have the same signature?*)
   371 fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
   372 
   373 (*Useful "distance" function for BEST_FIRST*)
   374 val size_of_thm = size_of_term o #prop o rep_thm;
   375 
   376 
   377 (** Mark Staples's weaker version of eq_thm: ignores variable renaming and
   378     (some) type variable renaming **)
   379 
   380  (* Can't use term_vars, because it sorts the resulting list of variable names.
   381     We instead need the unique list noramlised by the order of appearance
   382     in the term. *)
   383 fun term_vars' (t as Var(v,T)) = [t]
   384   | term_vars' (Abs(_,_,b)) = term_vars' b
   385   | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
   386   | term_vars' _ = [];
   387 
   388 fun forall_intr_vars th =
   389   let val {prop,sign,...} = rep_thm th;
   390       val vars = distinct (term_vars' prop);
   391   in forall_intr_list (map (cterm_of sign) vars) th end;
   392 
   393 fun weak_eq_thm (tha,thb) =
   394     eq_thm(forall_intr_vars (freezeT tha), forall_intr_vars (freezeT thb));
   395 
   396 
   397 
   398 (*** Meta-Rewriting Rules ***)
   399 
   400 val proto_sign = Theory.sign_of ProtoPure.thy;
   401 
   402 fun read_prop s = read_cterm proto_sign (s, propT);
   403 
   404 fun store_thm name thm = hd (PureThy.smart_store_thms (name, [standard thm]));
   405 
   406 val reflexive_thm =
   407   let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),logicS)))
   408   in store_thm "reflexive" (Thm.reflexive cx) end;
   409 
   410 val symmetric_thm =
   411   let val xy = read_prop "x::'a::logic == y"
   412   in store_thm "symmetric"
   413       (Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy)))
   414    end;
   415 
   416 val transitive_thm =
   417   let val xy = read_prop "x::'a::logic == y"
   418       val yz = read_prop "y::'a::logic == z"
   419       val xythm = Thm.assume xy and yzthm = Thm.assume yz
   420   in store_thm "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm))
   421   end;
   422 
   423 fun symmetric_fun thm = thm RS symmetric_thm;
   424 
   425 (** Below, a "conversion" has type cterm -> thm **)
   426 
   427 val refl_implies = reflexive (cterm_of proto_sign implies);
   428 
   429 (*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
   430 (*Do not rewrite flex-flex pairs*)
   431 fun goals_conv pred cv =
   432   let fun gconv i ct =
   433         let val (A,B) = dest_implies ct
   434             val (thA,j) = case term_of A of
   435                   Const("=?=",_)$_$_ => (reflexive A, i)
   436                 | _ => (if pred i then cv A else reflexive A, i+1)
   437         in  combination (combination refl_implies thA) (gconv j B) end
   438         handle TERM _ => reflexive ct
   439   in gconv 1 end;
   440 
   441 (*Use a conversion to transform a theorem*)
   442 fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
   443 
   444 (*rewriting conversion*)
   445 fun rew_conv mode prover mss = rewrite_cterm mode mss prover;
   446 
   447 (*Rewrite a theorem*)
   448 fun rewrite_rule_aux _ []   th = th
   449   | rewrite_rule_aux prover thms th =
   450       fconv_rule (rew_conv (true,false,false) prover (Thm.mss_of thms)) th;
   451 
   452 fun rewrite_thm mode prover mss = fconv_rule (rew_conv mode prover mss);
   453 fun rewrite_cterm mode prover mss = Thm.rewrite_cterm mode mss prover;
   454 
   455 (*Rewrite the subgoals of a proof state (represented by a theorem) *)
   456 fun rewrite_goals_rule_aux _ []   th = th
   457   | rewrite_goals_rule_aux prover thms th =
   458       fconv_rule (goals_conv (K true) (rew_conv (true, true, false) prover
   459         (Thm.mss_of thms))) th;
   460 
   461 (*Rewrite the subgoal of a proof state (represented by a theorem) *)
   462 fun rewrite_goal_rule mode prover mss i thm =
   463   if 0 < i  andalso  i <= nprems_of thm
   464   then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm
   465   else raise THM("rewrite_goal_rule",i,[thm]);
   466 
   467 
   468 (*** Some useful meta-theorems ***)
   469 
   470 (*The rule V/V, obtains assumption solving for eresolve_tac*)
   471 val asm_rl = store_thm "asm_rl" (trivial(read_prop "PROP ?psi"));
   472 val _ = store_thm "_" asm_rl;
   473 
   474 (*Meta-level cut rule: [| V==>W; V |] ==> W *)
   475 val cut_rl =
   476   store_thm "cut_rl"
   477     (trivial(read_prop "PROP ?psi ==> PROP ?theta"));
   478 
   479 (*Generalized elim rule for one conclusion; cut_rl with reversed premises:
   480      [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
   481 val revcut_rl =
   482   let val V = read_prop "PROP V"
   483       and VW = read_prop "PROP V ==> PROP W";
   484   in
   485     store_thm "revcut_rl"
   486       (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
   487   end;
   488 
   489 (*for deleting an unwanted assumption*)
   490 val thin_rl =
   491   let val V = read_prop "PROP V"
   492       and W = read_prop "PROP W";
   493   in  store_thm "thin_rl" (implies_intr V (implies_intr W (assume W)))
   494   end;
   495 
   496 (* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
   497 val triv_forall_equality =
   498   let val V  = read_prop "PROP V"
   499       and QV = read_prop "!!x::'a. PROP V"
   500       and x  = read_cterm proto_sign ("x", TypeInfer.logicT);
   501   in
   502     store_thm "triv_forall_equality"
   503       (equal_intr (implies_intr QV (forall_elim x (assume QV)))
   504         (implies_intr V  (forall_intr x (assume V))))
   505   end;
   506 
   507 (* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
   508    (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
   509    `thm COMP swap_prems_rl' swaps the first two premises of `thm'
   510 *)
   511 val swap_prems_rl =
   512   let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
   513       val major = assume cmajor;
   514       val cminor1 = read_prop "PROP PhiA";
   515       val minor1 = assume cminor1;
   516       val cminor2 = read_prop "PROP PhiB";
   517       val minor2 = assume cminor2;
   518   in store_thm "swap_prems_rl"
   519        (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
   520          (implies_elim (implies_elim major minor1) minor2))))
   521   end;
   522 
   523 (* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
   524    ==> PROP ?phi == PROP ?psi
   525    Introduction rule for == as a meta-theorem.
   526 *)
   527 val equal_intr_rule =
   528   let val PQ = read_prop "PROP phi ==> PROP psi"
   529       and QP = read_prop "PROP psi ==> PROP phi"
   530   in
   531     store_thm "equal_intr_rule"
   532       (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
   533   end;
   534 
   535 
   536 (*** Instantiate theorem th, reading instantiations under signature sg ****)
   537 
   538 (*Version that normalizes the result: Thm.instantiate no longer does that*)
   539 fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
   540 
   541 fun read_instantiate_sg sg sinsts th =
   542     let val ts = types_sorts th;
   543         val used = add_term_tvarnames(#prop(rep_thm th),[]);
   544     in  instantiate (read_insts sg ts ts used sinsts) th  end;
   545 
   546 (*Instantiate theorem th, reading instantiations under theory of th*)
   547 fun read_instantiate sinsts th =
   548     read_instantiate_sg (#sign (rep_thm th)) sinsts th;
   549 
   550 
   551 (*Left-to-right replacements: tpairs = [...,(vi,ti),...].
   552   Instantiates distinct Vars by terms, inferring type instantiations. *)
   553 local
   554   fun add_types ((ct,cu), (sign,tye,maxidx)) =
   555     let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
   556         and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
   557         val maxi = Int.max(maxidx, Int.max(maxt, maxu));
   558         val sign' = Sign.merge(sign, Sign.merge(signt, signu))
   559         val (tye',maxi') = Type.unify (#tsig(Sign.rep_sg sign')) maxi tye (T,U)
   560           handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u])
   561     in  (sign', tye', maxi')  end;
   562 in
   563 fun cterm_instantiate ctpairs0 th =
   564   let val (sign,tye,_) = foldr add_types (ctpairs0, (#sign(rep_thm th), Vartab.empty, 0))
   565       val tsig = #tsig(Sign.rep_sg sign);
   566       fun instT(ct,cu) = let val inst = subst_TVars_Vartab tye
   567                          in (cterm_fun inst ct, cterm_fun inst cu) end
   568       fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
   569   in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
   570   handle TERM _ =>
   571            raise THM("cterm_instantiate: incompatible signatures",0,[th])
   572        | TYPE (msg, _, _) => raise THM(msg, 0, [th])
   573 end;
   574 
   575 
   576 (** Derived rules mainly for METAHYPS **)
   577 
   578 (*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
   579 fun equal_abs_elim ca eqth =
   580   let val {sign=signa, t=a, ...} = rep_cterm ca
   581       and combth = combination eqth (reflexive ca)
   582       val {sign,prop,...} = rep_thm eqth
   583       val (abst,absu) = Logic.dest_equals prop
   584       val cterm = cterm_of (Sign.merge (sign,signa))
   585   in  transitive (symmetric (beta_conversion (cterm (abst$a))))
   586            (transitive combth (beta_conversion (cterm (absu$a))))
   587   end
   588   handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
   589 
   590 (*Calling equal_abs_elim with multiple terms*)
   591 fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
   592 
   593 local
   594   val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
   595   fun err th = raise THM("flexpair_inst: ", 0, [th])
   596   fun flexpair_inst def th =
   597     let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
   598         val cterm = cterm_of sign
   599         fun cvar a = cterm(Var((a,0),alpha))
   600         val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)]
   601                    def
   602     in  equal_elim def' th
   603     end
   604     handle THM _ => err th | Bind => err th
   605 in
   606 val flexpair_intr = flexpair_inst (symmetric ProtoPure.flexpair_def)
   607 and flexpair_elim = flexpair_inst ProtoPure.flexpair_def
   608 end;
   609 
   610 (*Version for flexflex pairs -- this supports lifting.*)
   611 fun flexpair_abs_elim_list cts =
   612     flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
   613 
   614 
   615 (*** GOAL (PROP A) <==> PROP A ***)
   616 
   617 local
   618   val A = read_prop "PROP A";
   619   val G = read_prop "GOAL (PROP A)";
   620   val (G_def, _) = freeze_thaw ProtoPure.Goal_def;
   621 in
   622   val triv_goal = store_thm "triv_goal" (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume A));
   623   val rev_triv_goal = store_thm "rev_triv_goal" (Thm.equal_elim G_def (Thm.assume G));
   624 end;
   625 
   626 val mk_cgoal = Thm.capply (Thm.cterm_of proto_sign (Const ("Goal", propT --> propT)));
   627 fun assume_goal ct = Thm.assume (mk_cgoal ct) RS rev_triv_goal;
   628 
   629 
   630 
   631 (** variations on instantiate **)
   632 
   633 (*shorthand for instantiating just one variable in the current theory*)
   634 fun inst x t = read_instantiate_sg (sign_of (the_context())) [(x,t)];
   635 
   636 
   637 (* collect vars *)
   638 
   639 val add_tvarsT = foldl_atyps (fn (vs, TVar v) => v ins vs | (vs, _) => vs);
   640 val add_tvars = foldl_types add_tvarsT;
   641 val add_vars = foldl_aterms (fn (vs, Var v) => v ins vs | (vs, _) => vs);
   642 
   643 fun tvars_of_terms ts = rev (foldl add_tvars ([], ts));
   644 fun vars_of_terms ts = rev (foldl add_vars ([], ts));
   645 
   646 fun tvars_of thm = tvars_of_terms [#prop (Thm.rep_thm thm)];
   647 fun vars_of thm = vars_of_terms [#prop (Thm.rep_thm thm)];
   648 
   649 
   650 (* instantiate by left-to-right occurrence of variables *)
   651 
   652 fun instantiate' cTs cts thm =
   653   let
   654     fun err msg =
   655       raise TYPE ("instantiate': " ^ msg,
   656         mapfilter (apsome Thm.typ_of) cTs,
   657         mapfilter (apsome Thm.term_of) cts);
   658 
   659     fun inst_of (v, ct) =
   660       (Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct)
   661         handle TYPE (msg, _, _) => err msg;
   662 
   663     fun zip_vars _ [] = []
   664       | zip_vars (_ :: vs) (None :: opt_ts) = zip_vars vs opt_ts
   665       | zip_vars (v :: vs) (Some t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
   666       | zip_vars [] _ = err "more instantiations than variables in thm";
   667 
   668     (*instantiate types first!*)
   669     val thm' =
   670       if forall is_none cTs then thm
   671       else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm;
   672     in
   673       if forall is_none cts then thm'
   674       else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
   675     end;
   676 
   677 
   678 (* unvarify(T) *)
   679 
   680 (*assume thm in standard form, i.e. no frees, 0 var indexes*)
   681 
   682 fun unvarifyT thm =
   683   let
   684     val cT = Thm.ctyp_of (Thm.sign_of_thm thm);
   685     val tfrees = map (fn ((x, _), S) => Some (cT (TFree (x, S)))) (tvars_of thm);
   686   in instantiate' tfrees [] thm end;
   687 
   688 fun unvarify raw_thm =
   689   let
   690     val thm = unvarifyT raw_thm;
   691     val ct = Thm.cterm_of (Thm.sign_of_thm thm);
   692     val frees = map (fn ((x, _), T) => Some (ct (Free (x, T)))) (vars_of thm);
   693   in instantiate' [] frees thm end;
   694 
   695 
   696 (* increment var indexes *)
   697 
   698 fun incr_indexes 0 thm = thm
   699   | incr_indexes inc thm =
   700       let
   701         val sign = Thm.sign_of_thm thm;
   702 
   703         fun inc_tvar ((x, i), S) = Some (Thm.ctyp_of sign (TVar ((x, i + inc), S)));
   704         fun inc_var ((x, i), T) = Some (Thm.cterm_of sign (Var ((x, i + inc), T)));
   705         val thm' = instantiate' (map inc_tvar (tvars_of thm)) [] thm;
   706         val thm'' = instantiate' [] (map inc_var (vars_of thm')) thm';
   707       in thm'' end;
   708 
   709 fun incr_indexes_wrt is cTs cts thms =
   710   let
   711     val maxidx =
   712       foldl Int.max (~1, is @
   713         map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
   714         map (#maxidx o Thm.rep_cterm) cts @
   715         map (#maxidx o Thm.rep_thm) thms);
   716   in incr_indexes (maxidx + 1) end;
   717 
   718 
   719 (* freeze_all *)
   720 
   721 (*freeze all (T)Vars; assumes thm in standard form*)
   722 
   723 fun freeze_all_TVars thm =
   724   (case tvars_of thm of
   725     [] => thm
   726   | tvars =>
   727       let val cert = Thm.ctyp_of (Thm.sign_of_thm thm)
   728       in instantiate' (map (fn ((x, _), S) => Some (cert (TFree (x, S)))) tvars) [] thm end);
   729 
   730 fun freeze_all_Vars thm =
   731   (case vars_of thm of
   732     [] => thm
   733   | vars =>
   734       let val cert = Thm.cterm_of (Thm.sign_of_thm thm)
   735       in instantiate' [] (map (fn ((x, _), T) => Some (cert (Free (x, T)))) vars) thm end);
   736 
   737 val freeze_all = freeze_all_Vars o freeze_all_TVars;
   738 
   739 
   740 (* mk_triv_goal *)
   741 
   742 (*make an initial proof state, "PROP A ==> (PROP A)" *)
   743 fun mk_triv_goal ct = instantiate' [] [Some ct] triv_goal;
   744 
   745 
   746 
   747 (** basic attributes **)
   748 
   749 (* dependent rules *)
   750 
   751 fun rule_attribute f (x, thm) = (x, (f x thm));
   752 
   753 
   754 (* add / delete tags *)
   755 
   756 fun map_tags f thm =
   757   Thm.put_name_tags (Thm.name_of_thm thm, f (#2 (Thm.get_name_tags thm))) thm;
   758 
   759 fun tag_rule tg = map_tags (fn tgs => if tg mem tgs then tgs else tgs @ [tg]);
   760 fun untag_rule s = map_tags (filter_out (equal s o #1));
   761 
   762 fun tag tg x = rule_attribute (K (tag_rule tg)) x;
   763 fun untag s x = rule_attribute (K (untag_rule s)) x;
   764 
   765 fun simple_tag name x = tag (name, []) x;
   766 
   767 fun tag_lemma x = simple_tag "lemma" x;
   768 fun tag_assumption x = simple_tag "assumption" x;
   769 fun tag_internal x = simple_tag "internal" x;
   770 
   771 
   772 end;
   773 
   774 
   775 structure BasicDrule: BASIC_DRULE = Drule;
   776 open BasicDrule;