src/Pure/drule.ML
author wenzelm
Sun May 18 15:04:09 2008 +0200 (2008-05-18)
changeset 26939 1035c89b4c02
parent 26653 60e0cf6bef89
child 27156 e9f2d5947887
permissions -rw-r--r--
moved global pretty/string_of functions from Sign to Syntax;
     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 OF COMP INCR_COMP COMP_INCR;
    10 
    11 signature BASIC_DRULE =
    12 sig
    13   val mk_implies: cterm * cterm -> cterm
    14   val list_implies: cterm list * cterm -> cterm
    15   val strip_imp_prems: cterm -> cterm list
    16   val strip_imp_concl: cterm -> cterm
    17   val cprems_of: thm -> cterm list
    18   val cterm_fun: (term -> term) -> (cterm -> cterm)
    19   val ctyp_fun: (typ -> typ) -> (ctyp -> ctyp)
    20   val read_insts: theory -> (indexname -> typ option) * (indexname -> sort option) ->
    21     (indexname -> typ option) * (indexname -> sort option) -> string list ->
    22     (indexname * string) list -> (ctyp * ctyp) list * (cterm * cterm) list
    23   val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
    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 gen_all: thm -> thm
    29   val lift_all: cterm -> thm -> thm
    30   val freeze_thaw: thm -> thm * (thm -> thm)
    31   val freeze_thaw_robust: thm -> thm * (int -> thm -> thm)
    32   val implies_elim_list: thm -> thm list -> thm
    33   val implies_intr_list: cterm list -> thm -> thm
    34   val instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
    35   val zero_var_indexes_list: thm list -> thm list
    36   val zero_var_indexes: thm -> thm
    37   val implies_intr_hyps: thm -> thm
    38   val standard: thm -> thm
    39   val standard': thm -> thm
    40   val rotate_prems: int -> thm -> thm
    41   val rearrange_prems: int list -> thm -> thm
    42   val RSN: thm * (int * thm) -> thm
    43   val RS: thm * thm -> thm
    44   val RLN: thm list * (int * thm list) -> thm list
    45   val RL: thm list * thm list -> thm list
    46   val MRS: thm list * thm -> thm
    47   val MRL: thm list list * thm list -> thm list
    48   val OF: thm * thm list -> thm
    49   val compose: thm * int * thm -> thm list
    50   val COMP: thm * thm -> thm
    51   val INCR_COMP: thm * thm -> thm
    52   val COMP_INCR: thm * thm -> thm
    53   val read_instantiate_sg: theory -> (string*string)list -> thm -> thm
    54   val read_instantiate: (string*string)list -> thm -> thm
    55   val cterm_instantiate: (cterm*cterm)list -> thm -> thm
    56   val size_of_thm: thm -> int
    57   val reflexive_thm: thm
    58   val symmetric_thm: thm
    59   val transitive_thm: thm
    60   val symmetric_fun: thm -> thm
    61   val extensional: thm -> thm
    62   val equals_cong: thm
    63   val imp_cong: thm
    64   val swap_prems_eq: thm
    65   val asm_rl: thm
    66   val cut_rl: thm
    67   val revcut_rl: thm
    68   val thin_rl: thm
    69   val triv_forall_equality: thm
    70   val distinct_prems_rl: thm
    71   val swap_prems_rl: thm
    72   val equal_intr_rule: thm
    73   val equal_elim_rule1: thm
    74   val equal_elim_rule2: thm
    75   val instantiate': ctyp option list -> cterm option list -> thm -> thm
    76 end;
    77 
    78 signature DRULE =
    79 sig
    80   include BASIC_DRULE
    81   val generalize: string list * string list -> thm -> thm
    82   val list_comb: cterm * cterm list -> cterm
    83   val strip_comb: cterm -> cterm * cterm list
    84   val strip_type: ctyp -> ctyp list * ctyp
    85   val beta_conv: cterm -> cterm -> cterm
    86   val add_used: thm -> string list -> string list
    87   val flexflex_unique: thm -> thm
    88   val store_thm: bstring -> thm -> thm
    89   val store_standard_thm: bstring -> thm -> thm
    90   val store_thm_open: bstring -> thm -> thm
    91   val store_standard_thm_open: bstring -> thm -> thm
    92   val compose_single: thm * int * thm -> thm
    93   val imp_cong_rule: thm -> thm -> thm
    94   val arg_cong_rule: cterm -> thm -> thm
    95   val binop_cong_rule: cterm -> thm -> thm -> thm
    96   val fun_cong_rule: thm -> cterm -> thm
    97   val beta_eta_conversion: cterm -> thm
    98   val eta_long_conversion: cterm -> thm
    99   val eta_contraction_rule: thm -> thm
   100   val norm_hhf_eq: thm
   101   val is_norm_hhf: term -> bool
   102   val norm_hhf: theory -> term -> term
   103   val norm_hhf_cterm: cterm -> cterm
   104   val protect: cterm -> cterm
   105   val protectI: thm
   106   val protectD: thm
   107   val protect_cong: thm
   108   val implies_intr_protected: cterm list -> thm -> thm
   109   val termI: thm
   110   val mk_term: cterm -> thm
   111   val dest_term: thm -> cterm
   112   val cterm_rule: (thm -> thm) -> cterm -> cterm
   113   val term_rule: theory -> (thm -> thm) -> term -> term
   114   val dummy_thm: thm
   115   val sort_triv: theory -> typ * sort -> thm list
   116   val unconstrainTs: thm -> thm
   117   val with_subgoal: int -> (thm -> thm) -> thm -> thm
   118   val rename_bvars: (string * string) list -> thm -> thm
   119   val rename_bvars': string option list -> thm -> thm
   120   val incr_type_indexes: int -> thm -> thm
   121   val incr_indexes: thm -> thm -> thm
   122   val incr_indexes2: thm -> thm -> thm -> thm
   123   val remdups_rl: thm
   124   val multi_resolve: thm list -> thm -> thm Seq.seq
   125   val multi_resolves: thm list -> thm list -> thm Seq.seq
   126   val abs_def: thm -> thm
   127   val read_instantiate_sg': theory -> (indexname * string) list -> thm -> thm
   128   val read_instantiate': (indexname * string) list -> thm -> thm
   129 end;
   130 
   131 structure Drule: DRULE =
   132 struct
   133 
   134 
   135 (** some cterm->cterm operations: faster than calling cterm_of! **)
   136 
   137 (* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
   138 fun strip_imp_prems ct =
   139   let val (cA, cB) = Thm.dest_implies ct
   140   in cA :: strip_imp_prems cB end
   141   handle TERM _ => [];
   142 
   143 (* A1==>...An==>B  goes to B, where B is not an implication *)
   144 fun strip_imp_concl ct =
   145   (case Thm.term_of ct of
   146     Const ("==>", _) $ _ $ _ => strip_imp_concl (Thm.dest_arg ct)
   147   | _ => ct);
   148 
   149 (*The premises of a theorem, as a cterm list*)
   150 val cprems_of = strip_imp_prems o cprop_of;
   151 
   152 fun cterm_fun f ct = Thm.cterm_of (Thm.theory_of_cterm ct) (f (Thm.term_of ct));
   153 fun ctyp_fun f cT = Thm.ctyp_of (Thm.theory_of_ctyp cT) (f (Thm.typ_of cT));
   154 
   155 fun certify t = Thm.cterm_of (Context.the_theory (Context.the_thread_data ())) t;
   156 
   157 val implies = certify Term.implies;
   158 fun mk_implies (A, B) = Thm.capply (Thm.capply implies A) B;
   159 
   160 (*cterm version of list_implies: [A1,...,An], B  goes to [|A1;==>;An|]==>B *)
   161 fun list_implies([], B) = B
   162   | list_implies(A::AS, B) = mk_implies (A, list_implies(AS,B));
   163 
   164 (*cterm version of list_comb: maps  (f, [t1,...,tn])  to  f(t1,...,tn) *)
   165 fun list_comb (f, []) = f
   166   | list_comb (f, t::ts) = list_comb (Thm.capply f t, ts);
   167 
   168 (*cterm version of strip_comb: maps  f(t1,...,tn)  to  (f, [t1,...,tn]) *)
   169 fun strip_comb ct =
   170   let
   171     fun stripc (p as (ct, cts)) =
   172       let val (ct1, ct2) = Thm.dest_comb ct
   173       in stripc (ct1, ct2 :: cts) end handle CTERM _ => p
   174   in stripc (ct, []) end;
   175 
   176 (* cterm version of strip_type: maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T) *)
   177 fun strip_type cT = (case Thm.typ_of cT of
   178     Type ("fun", _) =>
   179       let
   180         val [cT1, cT2] = Thm.dest_ctyp cT;
   181         val (cTs, cT') = strip_type cT2
   182       in (cT1 :: cTs, cT') end
   183   | _ => ([], cT));
   184 
   185 (*Beta-conversion for cterms, where x is an abstraction. Simply returns the rhs
   186   of the meta-equality returned by the beta_conversion rule.*)
   187 fun beta_conv x y =
   188   Thm.dest_arg (cprop_of (Thm.beta_conversion false (Thm.capply x y)));
   189 
   190 
   191 
   192 (** reading of instantiations **)
   193 
   194 fun absent ixn =
   195   error("No such variable in term: " ^ Term.string_of_vname ixn);
   196 
   197 fun inst_failure ixn =
   198   error("Instantiation of " ^ Term.string_of_vname ixn ^ " fails");
   199 
   200 fun read_insts thy (rtypes,rsorts) (types,sorts) used insts =
   201 let
   202     fun is_tv ((a, _), _) =
   203       (case Symbol.explode a of "'" :: _ => true | _ => false);
   204     val (tvs, vs) = List.partition is_tv insts;
   205     fun sort_of ixn = case rsorts ixn of SOME S => S | NONE => absent ixn;
   206     fun readT (ixn, st) =
   207         let val S = sort_of ixn;
   208             val T = Sign.read_def_typ (thy,sorts) st;
   209         in if Sign.typ_instance thy (T, TVar(ixn,S)) then (ixn,T)
   210            else inst_failure ixn
   211         end
   212     val tye = map readT tvs;
   213     fun mkty(ixn,st) = (case rtypes ixn of
   214                           SOME T => (ixn,(st,typ_subst_TVars tye T))
   215                         | NONE => absent ixn);
   216     val ixnsTs = map mkty vs;
   217     val ixns = map fst ixnsTs
   218     and sTs  = map snd ixnsTs
   219     val (cts,tye2) = Thm.read_def_cterms(thy,types,sorts) used false sTs;
   220     fun mkcVar(ixn,T) =
   221         let val U = typ_subst_TVars tye2 T
   222         in cterm_of thy (Var(ixn,U)) end
   223     val ixnTs = ListPair.zip(ixns, map snd sTs)
   224 in (map (fn (ixn, T) => (ctyp_of thy (TVar (ixn, sort_of ixn)),
   225       ctyp_of thy T)) (tye2 @ tye),
   226     ListPair.zip(map mkcVar ixnTs,cts))
   227 end;
   228 
   229 
   230 (*** Find the type (sort) associated with a (T)Var or (T)Free in a term
   231      Used for establishing default types (of variables) and sorts (of
   232      type variables) when reading another term.
   233      Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
   234 ***)
   235 
   236 fun types_sorts thm =
   237   let
   238     val vars = Thm.fold_terms Term.add_vars thm [];
   239     val frees = Thm.fold_terms Term.add_frees thm [];
   240     val tvars = Thm.fold_terms Term.add_tvars thm [];
   241     val tfrees = Thm.fold_terms Term.add_tfrees thm [];
   242     fun types (a, i) =
   243       if i < 0 then AList.lookup (op =) frees a else AList.lookup (op =) vars (a, i);
   244     fun sorts (a, i) =
   245       if i < 0 then AList.lookup (op =) tfrees a else AList.lookup (op =) tvars (a, i);
   246   in (types, sorts) end;
   247 
   248 val add_used =
   249   (Thm.fold_terms o fold_types o fold_atyps)
   250     (fn TFree (a, _) => insert (op =) a
   251       | TVar ((a, _), _) => insert (op =) a
   252       | _ => I);
   253 
   254 
   255 
   256 (** Standardization of rules **)
   257 
   258 (* type classes and sorts *)
   259 
   260 fun sort_triv thy (T, S) =
   261   let
   262     val certT = Thm.ctyp_of thy;
   263     val cT = certT T;
   264     fun class_triv c =
   265       Thm.class_triv thy c
   266       |> Thm.instantiate ([(certT (TVar ((Name.aT, 0), [c])), cT)], []);
   267   in map class_triv S end;
   268 
   269 fun unconstrainTs th =
   270   fold (Thm.unconstrainT o Thm.ctyp_of (Thm.theory_of_thm th) o TVar)
   271     (Thm.fold_terms Term.add_tvars th []) th;
   272 
   273 (*Generalization over a list of variables*)
   274 val forall_intr_list = fold_rev forall_intr;
   275 
   276 (*Generalization over all suitable Free variables*)
   277 fun forall_intr_frees th =
   278     let
   279       val thy = Thm.theory_of_thm th;
   280       val {prop, hyps, tpairs, ...} = rep_thm th;
   281       val fixed = fold Term.add_frees (Thm.terms_of_tpairs tpairs @ hyps) [];
   282       val frees = Term.fold_aterms (fn Free v =>
   283         if member (op =) fixed v then I else insert (op =) v | _ => I) prop [];
   284     in fold (forall_intr o cterm_of thy o Free) frees th end;
   285 
   286 (*Generalization over Vars -- canonical order*)
   287 fun forall_intr_vars th =
   288   fold forall_intr
   289     (map (Thm.cterm_of (Thm.theory_of_thm th) o Var) (Thm.fold_terms Term.add_vars th [])) th;
   290 
   291 fun outer_params t =
   292   let val vs = Term.strip_all_vars t
   293   in Name.variant_list [] (map (Name.clean o #1) vs) ~~ map #2 vs end;
   294 
   295 (*generalize outermost parameters*)
   296 fun gen_all th =
   297   let
   298     val thy = Thm.theory_of_thm th;
   299     val {prop, maxidx, ...} = Thm.rep_thm th;
   300     val cert = Thm.cterm_of thy;
   301     fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
   302   in fold elim (outer_params prop) th end;
   303 
   304 (*lift vars wrt. outermost goal parameters
   305   -- reverses the effect of gen_all modulo higher-order unification*)
   306 fun lift_all goal th =
   307   let
   308     val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
   309     val cert = Thm.cterm_of thy;
   310     val maxidx = Thm.maxidx_of th;
   311     val ps = outer_params (Thm.term_of goal)
   312       |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
   313     val Ts = map Term.fastype_of ps;
   314     val inst = Thm.fold_terms Term.add_vars th [] |> map (fn (xi, T) =>
   315       (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
   316   in
   317     th |> Thm.instantiate ([], inst)
   318     |> fold_rev (Thm.forall_intr o cert) ps
   319   end;
   320 
   321 (*direct generalization*)
   322 fun generalize names th = Thm.generalize names (Thm.maxidx_of th + 1) th;
   323 
   324 (*specialization over a list of cterms*)
   325 val forall_elim_list = fold forall_elim;
   326 
   327 (*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
   328 val implies_intr_list = fold_rev implies_intr;
   329 
   330 (*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
   331 fun implies_elim_list impth ths = fold Thm.elim_implies ths impth;
   332 
   333 (*Reset Var indexes to zero, renaming to preserve distinctness*)
   334 fun zero_var_indexes_list [] = []
   335   | zero_var_indexes_list ths =
   336       let
   337         val thy = Theory.merge_list (map Thm.theory_of_thm ths);
   338         val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
   339         val (instT, inst) = TermSubst.zero_var_indexes_inst (map Thm.full_prop_of ths);
   340         val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
   341         val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
   342       in map (Thm.adjust_maxidx_thm ~1 o Thm.instantiate (cinstT, cinst)) ths end;
   343 
   344 val zero_var_indexes = singleton zero_var_indexes_list;
   345 
   346 
   347 (** Standard form of object-rule: no hypotheses, flexflex constraints,
   348     Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
   349 
   350 (*Discharge all hypotheses.*)
   351 fun implies_intr_hyps th =
   352   fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
   353 
   354 (*Squash a theorem's flexflex constraints provided it can be done uniquely.
   355   This step can lose information.*)
   356 fun flexflex_unique th =
   357   if null (tpairs_of th) then th else
   358     case distinct Thm.eq_thm (Seq.list_of (flexflex_rule th)) of
   359       [th] => th
   360     | []   => raise THM("flexflex_unique: impossible constraints", 0, [th])
   361     |  _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
   362 
   363 
   364 (* legacy standard operations *)
   365 
   366 val standard' =
   367   implies_intr_hyps
   368   #> forall_intr_frees
   369   #> `Thm.maxidx_of
   370   #-> (fn maxidx =>
   371     Thm.forall_elim_vars (maxidx + 1)
   372     #> Thm.strip_shyps
   373     #> zero_var_indexes
   374     #> Thm.varifyT);
   375 
   376 val standard =
   377   flexflex_unique
   378   #> standard'
   379   #> Thm.close_derivation;
   380 
   381 
   382 (*Convert all Vars in a theorem to Frees.  Also return a function for
   383   reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
   384   Similar code in type/freeze_thaw*)
   385 
   386 fun freeze_thaw_robust th =
   387  let val fth = Thm.freezeT th
   388      val thy = Thm.theory_of_thm fth
   389      val {prop, tpairs, ...} = rep_thm fth
   390  in
   391    case List.foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
   392        [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
   393      | vars =>
   394          let fun newName (Var(ix,_)) = (ix, gensym (string_of_indexname ix))
   395              val alist = map newName vars
   396              fun mk_inst (Var(v,T)) =
   397                  (cterm_of thy (Var(v,T)),
   398                   cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
   399              val insts = map mk_inst vars
   400              fun thaw i th' = (*i is non-negative increment for Var indexes*)
   401                  th' |> forall_intr_list (map #2 insts)
   402                      |> forall_elim_list (map (Thm.incr_indexes_cterm i o #1) insts)
   403          in  (Thm.instantiate ([],insts) fth, thaw)  end
   404  end;
   405 
   406 (*Basic version of the function above. No option to rename Vars apart in thaw.
   407   The Frees created from Vars have nice names. FIXME: does not check for
   408   clashes with variables in the assumptions, so delete and use freeze_thaw_robust instead?*)
   409 fun freeze_thaw th =
   410  let val fth = Thm.freezeT th
   411      val thy = Thm.theory_of_thm fth
   412      val {prop, tpairs, ...} = rep_thm fth
   413  in
   414    case List.foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
   415        [] => (fth, fn x => x)
   416      | vars =>
   417          let fun newName (Var(ix,_), (pairs,used)) =
   418                    let val v = Name.variant used (string_of_indexname ix)
   419                    in  ((ix,v)::pairs, v::used)  end;
   420              val (alist, _) = List.foldr newName ([], Library.foldr add_term_names
   421                (prop :: Thm.terms_of_tpairs tpairs, [])) vars
   422              fun mk_inst (Var(v,T)) =
   423                  (cterm_of thy (Var(v,T)),
   424                   cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
   425              val insts = map mk_inst vars
   426              fun thaw th' =
   427                  th' |> forall_intr_list (map #2 insts)
   428                      |> forall_elim_list (map #1 insts)
   429          in  (Thm.instantiate ([],insts) fth, thaw)  end
   430  end;
   431 
   432 (*Rotates a rule's premises to the left by k*)
   433 fun rotate_prems 0 = I
   434   | rotate_prems k = permute_prems 0 k;
   435 
   436 fun with_subgoal i f = rotate_prems (i - 1) #> f #> rotate_prems (1 - i);
   437 
   438 (* permute prems, where the i-th position in the argument list (counting from 0)
   439    gives the position within the original thm to be transferred to position i.
   440    Any remaining trailing positions are left unchanged. *)
   441 val rearrange_prems = let
   442   fun rearr new []      thm = thm
   443   |   rearr new (p::ps) thm = rearr (new+1)
   444      (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
   445      (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
   446   in rearr 0 end;
   447 
   448 (*Resolution: exactly one resolvent must be produced.*)
   449 fun tha RSN (i,thb) =
   450   case Seq.chop 2 (biresolution false [(false,tha)] i thb) of
   451       ([th],_) => th
   452     | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
   453     |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
   454 
   455 (*resolution: P==>Q, Q==>R gives P==>R. *)
   456 fun tha RS thb = tha RSN (1,thb);
   457 
   458 (*For joining lists of rules*)
   459 fun thas RLN (i,thbs) =
   460   let val resolve = biresolution false (map (pair false) thas) i
   461       fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
   462   in maps resb thbs end;
   463 
   464 fun thas RL thbs = thas RLN (1,thbs);
   465 
   466 (*Resolve a list of rules against bottom_rl from right to left;
   467   makes proof trees*)
   468 fun rls MRS bottom_rl =
   469   let fun rs_aux i [] = bottom_rl
   470         | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
   471   in  rs_aux 1 rls  end;
   472 
   473 (*As above, but for rule lists*)
   474 fun rlss MRL bottom_rls =
   475   let fun rs_aux i [] = bottom_rls
   476         | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
   477   in  rs_aux 1 rlss  end;
   478 
   479 (*A version of MRS with more appropriate argument order*)
   480 fun bottom_rl OF rls = rls MRS bottom_rl;
   481 
   482 (*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
   483   with no lifting or renaming!  Q may contain ==> or meta-quants
   484   ALWAYS deletes premise i *)
   485 fun compose(tha,i,thb) =
   486     distinct Thm.eq_thm (Seq.list_of (bicompose false (false,tha,0) i thb));
   487 
   488 fun compose_single (tha,i,thb) =
   489   case compose (tha,i,thb) of
   490     [th] => th
   491   | _ => raise THM ("compose: unique result expected", i, [tha,thb]);
   492 
   493 (*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
   494 fun tha COMP thb =
   495     case compose(tha,1,thb) of
   496         [th] => th
   497       | _ =>   raise THM("COMP", 1, [tha,thb]);
   498 
   499 
   500 (** theorem equality **)
   501 
   502 (*Useful "distance" function for BEST_FIRST*)
   503 val size_of_thm = size_of_term o Thm.full_prop_of;
   504 
   505 
   506 
   507 (*** Meta-Rewriting Rules ***)
   508 
   509 val read_prop = certify o SimpleSyntax.read_prop;
   510 
   511 fun store_thm name th =
   512   Context.>>> (Context.map_theory_result (PureThy.store_thm (name, th)));
   513 
   514 fun store_thm_open name th =
   515   Context.>>> (Context.map_theory_result (PureThy.store_thm_open (name, th)));
   516 
   517 fun store_standard_thm name th = store_thm name (standard th);
   518 fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
   519 
   520 val reflexive_thm =
   521   let val cx = certify (Var(("x",0),TVar(("'a",0),[])))
   522   in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
   523 
   524 val symmetric_thm =
   525   let val xy = read_prop "x::'a == y::'a"
   526   in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
   527 
   528 val transitive_thm =
   529   let val xy = read_prop "x::'a == y::'a"
   530       val yz = read_prop "y::'a == z::'a"
   531       val xythm = Thm.assume xy and yzthm = Thm.assume yz
   532   in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
   533 
   534 fun symmetric_fun thm = thm RS symmetric_thm;
   535 
   536 fun extensional eq =
   537   let val eq' =
   538     abstract_rule "x" (Thm.dest_arg (fst (Thm.dest_equals (cprop_of eq)))) eq
   539   in equal_elim (eta_conversion (cprop_of eq')) eq' end;
   540 
   541 val equals_cong =
   542   store_standard_thm_open "equals_cong" (Thm.reflexive (read_prop "x::'a == y::'a"));
   543 
   544 val imp_cong =
   545   let
   546     val ABC = read_prop "A ==> B::prop == C::prop"
   547     val AB = read_prop "A ==> B"
   548     val AC = read_prop "A ==> C"
   549     val A = read_prop "A"
   550   in
   551     store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
   552       (implies_intr AB (implies_intr A
   553         (equal_elim (implies_elim (assume ABC) (assume A))
   554           (implies_elim (assume AB) (assume A)))))
   555       (implies_intr AC (implies_intr A
   556         (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
   557           (implies_elim (assume AC) (assume A)))))))
   558   end;
   559 
   560 val swap_prems_eq =
   561   let
   562     val ABC = read_prop "A ==> B ==> C"
   563     val BAC = read_prop "B ==> A ==> C"
   564     val A = read_prop "A"
   565     val B = read_prop "B"
   566   in
   567     store_standard_thm_open "swap_prems_eq" (equal_intr
   568       (implies_intr ABC (implies_intr B (implies_intr A
   569         (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
   570       (implies_intr BAC (implies_intr A (implies_intr B
   571         (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
   572   end;
   573 
   574 val imp_cong_rule = Thm.combination o Thm.combination (Thm.reflexive implies);
   575 
   576 fun arg_cong_rule ct th = Thm.combination (Thm.reflexive ct) th;    (*AP_TERM in LCF/HOL*)
   577 fun fun_cong_rule th ct = Thm.combination th (Thm.reflexive ct);    (*AP_THM in LCF/HOL*)
   578 fun binop_cong_rule ct th1 th2 = Thm.combination (arg_cong_rule ct th1) th2;
   579 
   580 local
   581   val dest_eq = Thm.dest_equals o cprop_of
   582   val rhs_of = snd o dest_eq
   583 in
   584 fun beta_eta_conversion t =
   585   let val thm = beta_conversion true t
   586   in transitive thm (eta_conversion (rhs_of thm)) end
   587 end;
   588 
   589 fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
   590   (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
   591 
   592 (*Contract all eta-redexes in the theorem, lest they give rise to needless abstractions*)
   593 fun eta_contraction_rule th =
   594   equal_elim (eta_conversion (cprop_of th)) th;
   595 
   596 
   597 (* abs_def *)
   598 
   599 (*
   600    f ?x1 ... ?xn == u
   601   --------------------
   602    f == %x1 ... xn. u
   603 *)
   604 
   605 local
   606 
   607 fun contract_lhs th =
   608   Thm.transitive (Thm.symmetric (beta_eta_conversion
   609     (fst (Thm.dest_equals (cprop_of th))))) th;
   610 
   611 fun var_args ct =
   612   (case try Thm.dest_comb ct of
   613     SOME (f, arg) =>
   614       (case Thm.term_of arg of
   615         Var ((x, _), _) => update (eq_snd (op aconvc)) (x, arg) (var_args f)
   616       | _ => [])
   617   | NONE => []);
   618 
   619 in
   620 
   621 fun abs_def th =
   622   let
   623     val th' = contract_lhs th;
   624     val args = var_args (Thm.lhs_of th');
   625   in contract_lhs (fold (uncurry Thm.abstract_rule) args th') end;
   626 
   627 end;
   628 
   629 
   630 
   631 (*** Some useful meta-theorems ***)
   632 
   633 (*The rule V/V, obtains assumption solving for eresolve_tac*)
   634 val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "?psi"));
   635 val _ = store_thm "_" asm_rl;
   636 
   637 (*Meta-level cut rule: [| V==>W; V |] ==> W *)
   638 val cut_rl =
   639   store_standard_thm_open "cut_rl"
   640     (Thm.trivial (read_prop "?psi ==> ?theta"));
   641 
   642 (*Generalized elim rule for one conclusion; cut_rl with reversed premises:
   643      [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
   644 val revcut_rl =
   645   let val V = read_prop "V"
   646       and VW = read_prop "V ==> W";
   647   in
   648     store_standard_thm_open "revcut_rl"
   649       (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
   650   end;
   651 
   652 (*for deleting an unwanted assumption*)
   653 val thin_rl =
   654   let val V = read_prop "V"
   655       and W = read_prop "W";
   656   in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
   657 
   658 (* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
   659 val triv_forall_equality =
   660   let val V  = read_prop "V"
   661       and QV = read_prop "!!x::'a. V"
   662       and x  = certify (Free ("x", Term.aT []));
   663   in
   664     store_standard_thm_open "triv_forall_equality"
   665       (equal_intr (implies_intr QV (forall_elim x (assume QV)))
   666         (implies_intr V  (forall_intr x (assume V))))
   667   end;
   668 
   669 (* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
   670    (PROP ?Phi ==> PROP ?Psi)
   671 *)
   672 val distinct_prems_rl =
   673   let
   674     val AAB = read_prop "Phi ==> Phi ==> Psi"
   675     val A = read_prop "Phi";
   676   in
   677     store_standard_thm_open "distinct_prems_rl"
   678       (implies_intr_list [AAB, A] (implies_elim_list (assume AAB) [assume A, assume A]))
   679   end;
   680 
   681 (* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
   682    (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
   683    `thm COMP swap_prems_rl' swaps the first two premises of `thm'
   684 *)
   685 val swap_prems_rl =
   686   let val cmajor = read_prop "PhiA ==> PhiB ==> Psi";
   687       val major = assume cmajor;
   688       val cminor1 = read_prop "PhiA";
   689       val minor1 = assume cminor1;
   690       val cminor2 = read_prop "PhiB";
   691       val minor2 = assume cminor2;
   692   in store_standard_thm_open "swap_prems_rl"
   693        (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
   694          (implies_elim (implies_elim major minor1) minor2))))
   695   end;
   696 
   697 (* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
   698    ==> PROP ?phi == PROP ?psi
   699    Introduction rule for == as a meta-theorem.
   700 *)
   701 val equal_intr_rule =
   702   let val PQ = read_prop "phi ==> psi"
   703       and QP = read_prop "psi ==> phi"
   704   in
   705     store_standard_thm_open "equal_intr_rule"
   706       (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
   707   end;
   708 
   709 (* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
   710 val equal_elim_rule1 =
   711   let val eq = read_prop "phi::prop == psi::prop"
   712       and P = read_prop "phi"
   713   in store_standard_thm_open "equal_elim_rule1"
   714     (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
   715   end;
   716 
   717 (* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
   718 val equal_elim_rule2 =
   719   store_standard_thm_open "equal_elim_rule2" (symmetric_thm RS equal_elim_rule1);
   720 
   721 (* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
   722 val remdups_rl =
   723   let val P = read_prop "phi" and Q = read_prop "psi";
   724   in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
   725 
   726 
   727 (*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
   728   Rewrite rule for HHF normalization.*)
   729 
   730 val norm_hhf_eq =
   731   let
   732     val aT = TFree ("'a", []);
   733     val all = Term.all aT;
   734     val x = Free ("x", aT);
   735     val phi = Free ("phi", propT);
   736     val psi = Free ("psi", aT --> propT);
   737 
   738     val cx = certify x;
   739     val cphi = certify phi;
   740     val lhs = certify (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
   741     val rhs = certify (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
   742   in
   743     Thm.equal_intr
   744       (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
   745         |> Thm.forall_elim cx
   746         |> Thm.implies_intr cphi
   747         |> Thm.forall_intr cx
   748         |> Thm.implies_intr lhs)
   749       (Thm.implies_elim
   750           (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
   751         |> Thm.forall_intr cx
   752         |> Thm.implies_intr cphi
   753         |> Thm.implies_intr rhs)
   754     |> store_standard_thm_open "norm_hhf_eq"
   755   end;
   756 
   757 val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
   758 
   759 fun is_norm_hhf tm =
   760   let
   761     fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
   762       | is_norm (t $ u) = is_norm t andalso is_norm u
   763       | is_norm (Abs (_, _, t)) = is_norm t
   764       | is_norm _ = true;
   765   in is_norm (Envir.beta_eta_contract tm) end;
   766 
   767 fun norm_hhf thy t =
   768   if is_norm_hhf t then t
   769   else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
   770 
   771 fun norm_hhf_cterm ct =
   772   if is_norm_hhf (Thm.term_of ct) then ct
   773   else cterm_fun (Pattern.rewrite_term (Thm.theory_of_cterm ct) [norm_hhf_prop] []) ct;
   774 
   775 
   776 (* var indexes *)
   777 
   778 (*Increment the indexes of only the type variables*)
   779 fun incr_type_indexes inc th =
   780   let val tvs = term_tvars (prop_of th)
   781       and thy = theory_of_thm th
   782       fun inc_tvar ((a,i),s) = pairself (ctyp_of thy) (TVar ((a,i),s), TVar ((a,i+inc),s))
   783   in Thm.instantiate (map inc_tvar tvs, []) th end;
   784 
   785 fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
   786 
   787 fun incr_indexes2 th1 th2 =
   788   Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
   789 
   790 fun th1 INCR_COMP th2 = incr_indexes th2 th1 COMP th2;
   791 fun th1 COMP_INCR th2 = th1 COMP incr_indexes th1 th2;
   792 
   793 
   794 (*** Instantiate theorem th, reading instantiations in theory thy ****)
   795 
   796 (*Version that normalizes the result: Thm.instantiate no longer does that*)
   797 fun instantiate instpair th =
   798   Thm.adjust_maxidx_thm ~1 (Thm.instantiate instpair th COMP_INCR asm_rl);
   799 
   800 fun read_instantiate_sg' thy sinsts th =
   801     let val ts = types_sorts th;
   802         val used = add_used th [];
   803     in  instantiate (read_insts thy ts ts used sinsts) th  end;
   804 
   805 fun read_instantiate_sg thy sinsts th =
   806   read_instantiate_sg' thy (map (apfst Syntax.read_indexname) sinsts) th;
   807 
   808 (*Instantiate theorem th, reading instantiations under theory of th*)
   809 fun read_instantiate sinsts th =
   810     read_instantiate_sg (Thm.theory_of_thm th) sinsts th;
   811 
   812 fun read_instantiate' sinsts th =
   813     read_instantiate_sg' (Thm.theory_of_thm th) sinsts th;
   814 
   815 
   816 (*Left-to-right replacements: tpairs = [...,(vi,ti),...].
   817   Instantiates distinct Vars by terms, inferring type instantiations. *)
   818 local
   819   fun add_types ((ct,cu), (thy,tye,maxidx)) =
   820     let
   821         val thyt = Thm.theory_of_cterm ct;
   822         val thyu = Thm.theory_of_cterm cu;
   823         val {t, T, maxidx = maxt, ...} = Thm.rep_cterm ct;
   824         val {t = u, T = U, maxidx = maxu, ...} = Thm.rep_cterm cu;
   825         val maxi = Int.max(maxidx, Int.max(maxt, maxu));
   826         val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
   827         val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
   828           handle Type.TUNIFY => raise TYPE ("Ill-typed instantiation:\nType\n" ^
   829             Syntax.string_of_typ_global thy' (Envir.norm_type tye T) ^
   830             "\nof variable " ^
   831             Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) t) ^
   832             "\ncannot be unified with type\n" ^
   833             Syntax.string_of_typ_global thy' (Envir.norm_type tye U) ^ "\nof term " ^
   834             Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) u),
   835             [T, U], [t, u])
   836     in  (thy', tye', maxi')  end;
   837 in
   838 fun cterm_instantiate [] th = th
   839   | cterm_instantiate ctpairs0 th =
   840   let val (thy,tye,_) = List.foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
   841       fun instT(ct,cu) =
   842         let val inst = cterm_of thy o Term.map_types (Envir.norm_type tye) o term_of
   843         in (inst ct, inst cu) end
   844       fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy (Envir.norm_type tye T))
   845   in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
   846   handle TERM _ =>
   847            raise THM("cterm_instantiate: incompatible theories",0,[th])
   848        | TYPE (msg, _, _) => raise THM(msg, 0, [th])
   849 end;
   850 
   851 
   852 (** protected propositions and embedded terms **)
   853 
   854 local
   855   val A = certify (Free ("A", propT));
   856   val get_axiom = Thm.unvarify o Thm.get_axiom (Context.the_theory (Context.the_thread_data ()));
   857   val prop_def = get_axiom "prop_def";
   858   val term_def = get_axiom "term_def";
   859 in
   860   val protect = Thm.capply (certify Logic.protectC);
   861   val protectI = store_thm "protectI" (PureThy.kind_rule Thm.internalK (standard
   862       (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
   863   val protectD = store_thm "protectD" (PureThy.kind_rule Thm.internalK (standard
   864       (Thm.equal_elim prop_def (Thm.assume (protect A)))));
   865   val protect_cong = store_standard_thm_open "protect_cong" (Thm.reflexive (protect A));
   866 
   867   val termI = store_thm "termI" (PureThy.kind_rule Thm.internalK (standard
   868       (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)))));
   869 end;
   870 
   871 fun implies_intr_protected asms th =
   872   let val asms' = map protect asms in
   873     implies_elim_list
   874       (implies_intr_list asms th)
   875       (map (fn asm' => Thm.assume asm' RS protectD) asms')
   876     |> implies_intr_list asms'
   877   end;
   878 
   879 fun mk_term ct =
   880   let
   881     val thy = Thm.theory_of_cterm ct;
   882     val cert = Thm.cterm_of thy;
   883     val certT = Thm.ctyp_of thy;
   884     val T = Thm.typ_of (Thm.ctyp_of_term ct);
   885     val a = certT (TVar (("'a", 0), []));
   886     val x = cert (Var (("x", 0), T));
   887   in Thm.instantiate ([(a, certT T)], [(x, ct)]) termI end;
   888 
   889 fun dest_term th =
   890   let val cprop = strip_imp_concl (Thm.cprop_of th) in
   891     if can Logic.dest_term (Thm.term_of cprop) then
   892       Thm.dest_arg cprop
   893     else raise THM ("dest_term", 0, [th])
   894   end;
   895 
   896 fun cterm_rule f = dest_term o f o mk_term;
   897 fun term_rule thy f t = Thm.term_of (cterm_rule f (Thm.cterm_of thy t));
   898 
   899 val dummy_thm = mk_term (certify (Term.dummy_pattern propT));
   900 
   901 
   902 
   903 (** variations on instantiate **)
   904 
   905 (* instantiate by left-to-right occurrence of variables *)
   906 
   907 fun instantiate' cTs cts thm =
   908   let
   909     fun err msg =
   910       raise TYPE ("instantiate': " ^ msg,
   911         map_filter (Option.map Thm.typ_of) cTs,
   912         map_filter (Option.map Thm.term_of) cts);
   913 
   914     fun inst_of (v, ct) =
   915       (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
   916         handle TYPE (msg, _, _) => err msg;
   917 
   918     fun tyinst_of (v, cT) =
   919       (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
   920         handle TYPE (msg, _, _) => err msg;
   921 
   922     fun zip_vars xs ys =
   923       zip_options xs ys handle Library.UnequalLengths =>
   924         err "more instantiations than variables in thm";
   925 
   926     (*instantiate types first!*)
   927     val thm' =
   928       if forall is_none cTs then thm
   929       else Thm.instantiate
   930         (map tyinst_of (zip_vars (rev (Thm.fold_terms Term.add_tvars thm [])) cTs), []) thm;
   931     val thm'' =
   932       if forall is_none cts then thm'
   933       else Thm.instantiate
   934         ([], map inst_of (zip_vars (rev (Thm.fold_terms Term.add_vars thm' [])) cts)) thm';
   935     in thm'' end;
   936 
   937 
   938 
   939 (** renaming of bound variables **)
   940 
   941 (* replace bound variables x_i in thm by y_i *)
   942 (* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
   943 
   944 fun rename_bvars [] thm = thm
   945   | rename_bvars vs thm =
   946       let
   947         val cert = Thm.cterm_of (Thm.theory_of_thm thm);
   948         fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
   949           | ren (t $ u) = ren t $ ren u
   950           | ren t = t;
   951       in equal_elim (reflexive (cert (ren (Thm.prop_of thm)))) thm end;
   952 
   953 
   954 (* renaming in left-to-right order *)
   955 
   956 fun rename_bvars' xs thm =
   957   let
   958     val cert = Thm.cterm_of (Thm.theory_of_thm thm);
   959     val prop = Thm.prop_of thm;
   960     fun rename [] t = ([], t)
   961       | rename (x' :: xs) (Abs (x, T, t)) =
   962           let val (xs', t') = rename xs t
   963           in (xs', Abs (the_default x x', T, t')) end
   964       | rename xs (t $ u) =
   965           let
   966             val (xs', t') = rename xs t;
   967             val (xs'', u') = rename xs' u
   968           in (xs'', t' $ u') end
   969       | rename xs t = (xs, t);
   970   in case rename xs prop of
   971       ([], prop') => equal_elim (reflexive (cert prop')) thm
   972     | _ => error "More names than abstractions in theorem"
   973   end;
   974 
   975 
   976 
   977 (** multi_resolve **)
   978 
   979 local
   980 
   981 fun res th i rule =
   982   Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
   983 
   984 fun multi_res _ [] rule = Seq.single rule
   985   | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
   986 
   987 in
   988 
   989 val multi_resolve = multi_res 1;
   990 fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
   991 
   992 end;
   993 
   994 end;
   995 
   996 structure BasicDrule: BASIC_DRULE = Drule;
   997 open BasicDrule;