src/Pure/drule.ML
author wenzelm
Thu Sep 02 00:48:07 2010 +0200 (2010-09-02)
changeset 38980 af73cf0dc31f
parent 38709 04414091f3b5
child 39557 fe5722fce758
permissions -rw-r--r--
turned show_question_marks into proper configuration option;
show_question_marks only affects regular type/term pretty printing, not raw Term.string_of_vname;
tuned;
     1 (*  Title:      Pure/drule.ML
     2     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     3 
     4 Derived rules and other operations on theorems.
     5 *)
     6 
     7 infix 0 RS RSN RL RLN MRS MRL OF COMP INCR_COMP COMP_INCR;
     8 
     9 signature BASIC_DRULE =
    10 sig
    11   val mk_implies: cterm * cterm -> cterm
    12   val list_implies: cterm list * cterm -> cterm
    13   val strip_imp_prems: cterm -> cterm list
    14   val strip_imp_concl: cterm -> cterm
    15   val cprems_of: thm -> cterm list
    16   val cterm_fun: (term -> term) -> (cterm -> cterm)
    17   val ctyp_fun: (typ -> typ) -> (ctyp -> ctyp)
    18   val forall_intr_list: cterm list -> thm -> thm
    19   val forall_intr_vars: thm -> thm
    20   val forall_elim_list: cterm list -> thm -> thm
    21   val gen_all: thm -> thm
    22   val lift_all: cterm -> thm -> thm
    23   val legacy_freeze_thaw: thm -> thm * (thm -> thm)
    24   val legacy_freeze_thaw_robust: thm -> thm * (int -> thm -> thm)
    25   val implies_elim_list: thm -> thm list -> thm
    26   val implies_intr_list: cterm list -> thm -> thm
    27   val instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
    28   val zero_var_indexes_list: thm list -> thm list
    29   val zero_var_indexes: thm -> thm
    30   val implies_intr_hyps: thm -> thm
    31   val rotate_prems: int -> thm -> thm
    32   val rearrange_prems: int list -> thm -> thm
    33   val RSN: thm * (int * thm) -> thm
    34   val RS: thm * thm -> thm
    35   val RLN: thm list * (int * thm list) -> thm list
    36   val RL: thm list * thm list -> thm list
    37   val MRS: thm list * thm -> thm
    38   val MRL: thm list list * thm list -> thm list
    39   val OF: thm * thm list -> thm
    40   val compose: thm * int * thm -> thm list
    41   val COMP: thm * thm -> thm
    42   val INCR_COMP: thm * thm -> thm
    43   val COMP_INCR: thm * thm -> thm
    44   val cterm_instantiate: (cterm*cterm)list -> thm -> thm
    45   val size_of_thm: thm -> int
    46   val reflexive_thm: thm
    47   val symmetric_thm: thm
    48   val transitive_thm: thm
    49   val symmetric_fun: thm -> thm
    50   val extensional: thm -> thm
    51   val equals_cong: thm
    52   val imp_cong: thm
    53   val swap_prems_eq: thm
    54   val asm_rl: thm
    55   val cut_rl: thm
    56   val revcut_rl: thm
    57   val thin_rl: thm
    58   val triv_forall_equality: thm
    59   val distinct_prems_rl: thm
    60   val swap_prems_rl: thm
    61   val equal_intr_rule: thm
    62   val equal_elim_rule1: thm
    63   val equal_elim_rule2: thm
    64   val instantiate': ctyp option list -> cterm option list -> thm -> thm
    65 end;
    66 
    67 signature DRULE =
    68 sig
    69   include BASIC_DRULE
    70   val generalize: string list * string list -> thm -> thm
    71   val list_comb: cterm * cterm list -> cterm
    72   val strip_comb: cterm -> cterm * cterm list
    73   val strip_type: ctyp -> ctyp list * ctyp
    74   val beta_conv: cterm -> cterm -> cterm
    75   val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
    76   val flexflex_unique: thm -> thm
    77   val export_without_context: thm -> thm
    78   val export_without_context_open: thm -> thm
    79   val store_thm: binding -> thm -> thm
    80   val store_standard_thm: binding -> thm -> thm
    81   val store_thm_open: binding -> thm -> thm
    82   val store_standard_thm_open: binding -> thm -> thm
    83   val compose_single: thm * int * thm -> thm
    84   val imp_cong_rule: thm -> thm -> thm
    85   val arg_cong_rule: cterm -> thm -> thm
    86   val binop_cong_rule: cterm -> thm -> thm -> thm
    87   val fun_cong_rule: thm -> cterm -> thm
    88   val beta_eta_conversion: cterm -> thm
    89   val eta_long_conversion: cterm -> thm
    90   val eta_contraction_rule: thm -> thm
    91   val norm_hhf_eq: thm
    92   val norm_hhf_eqs: thm list
    93   val is_norm_hhf: term -> bool
    94   val norm_hhf: theory -> term -> term
    95   val norm_hhf_cterm: cterm -> cterm
    96   val protect: cterm -> cterm
    97   val protectI: thm
    98   val protectD: thm
    99   val protect_cong: thm
   100   val implies_intr_protected: cterm list -> thm -> thm
   101   val termI: thm
   102   val mk_term: cterm -> thm
   103   val dest_term: thm -> cterm
   104   val cterm_rule: (thm -> thm) -> cterm -> cterm
   105   val term_rule: theory -> (thm -> thm) -> term -> term
   106   val dummy_thm: thm
   107   val sort_constraintI: thm
   108   val sort_constraint_eq: thm
   109   val with_subgoal: int -> (thm -> thm) -> thm -> thm
   110   val comp_no_flatten: thm * int -> int -> thm -> thm
   111   val rename_bvars: (string * string) list -> thm -> thm
   112   val rename_bvars': string option list -> thm -> thm
   113   val incr_type_indexes: int -> thm -> thm
   114   val incr_indexes: thm -> thm -> thm
   115   val incr_indexes2: thm -> thm -> thm -> thm
   116   val remdups_rl: thm
   117   val multi_resolve: thm list -> thm -> thm Seq.seq
   118   val multi_resolves: thm list -> thm list -> thm Seq.seq
   119   val abs_def: thm -> thm
   120 end;
   121 
   122 structure Drule: DRULE =
   123 struct
   124 
   125 
   126 (** some cterm->cterm operations: faster than calling cterm_of! **)
   127 
   128 (* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
   129 fun strip_imp_prems ct =
   130   let val (cA, cB) = Thm.dest_implies ct
   131   in cA :: strip_imp_prems cB end
   132   handle TERM _ => [];
   133 
   134 (* A1==>...An==>B  goes to B, where B is not an implication *)
   135 fun strip_imp_concl ct =
   136   (case Thm.term_of ct of
   137     Const ("==>", _) $ _ $ _ => strip_imp_concl (Thm.dest_arg ct)
   138   | _ => ct);
   139 
   140 (*The premises of a theorem, as a cterm list*)
   141 val cprems_of = strip_imp_prems o cprop_of;
   142 
   143 fun cterm_fun f ct = Thm.cterm_of (Thm.theory_of_cterm ct) (f (Thm.term_of ct));
   144 fun ctyp_fun f cT = Thm.ctyp_of (Thm.theory_of_ctyp cT) (f (Thm.typ_of cT));
   145 
   146 fun certify t = Thm.cterm_of (Context.the_theory (Context.the_thread_data ())) t;
   147 
   148 val implies = certify Logic.implies;
   149 fun mk_implies (A, B) = Thm.capply (Thm.capply implies A) B;
   150 
   151 (*cterm version of list_implies: [A1,...,An], B  goes to [|A1;==>;An|]==>B *)
   152 fun list_implies([], B) = B
   153   | list_implies(A::AS, B) = mk_implies (A, list_implies(AS,B));
   154 
   155 (*cterm version of list_comb: maps  (f, [t1,...,tn])  to  f(t1,...,tn) *)
   156 fun list_comb (f, []) = f
   157   | list_comb (f, t::ts) = list_comb (Thm.capply f t, ts);
   158 
   159 (*cterm version of strip_comb: maps  f(t1,...,tn)  to  (f, [t1,...,tn]) *)
   160 fun strip_comb ct =
   161   let
   162     fun stripc (p as (ct, cts)) =
   163       let val (ct1, ct2) = Thm.dest_comb ct
   164       in stripc (ct1, ct2 :: cts) end handle CTERM _ => p
   165   in stripc (ct, []) end;
   166 
   167 (* cterm version of strip_type: maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T) *)
   168 fun strip_type cT = (case Thm.typ_of cT of
   169     Type ("fun", _) =>
   170       let
   171         val [cT1, cT2] = Thm.dest_ctyp cT;
   172         val (cTs, cT') = strip_type cT2
   173       in (cT1 :: cTs, cT') end
   174   | _ => ([], cT));
   175 
   176 (*Beta-conversion for cterms, where x is an abstraction. Simply returns the rhs
   177   of the meta-equality returned by the beta_conversion rule.*)
   178 fun beta_conv x y =
   179   Thm.dest_arg (cprop_of (Thm.beta_conversion false (Thm.capply x y)));
   180 
   181 
   182 
   183 (*** Find the type (sort) associated with a (T)Var or (T)Free in a term
   184      Used for establishing default types (of variables) and sorts (of
   185      type variables) when reading another term.
   186      Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
   187 ***)
   188 
   189 fun types_sorts thm =
   190   let
   191     val vars = Thm.fold_terms Term.add_vars thm [];
   192     val frees = Thm.fold_terms Term.add_frees thm [];
   193     val tvars = Thm.fold_terms Term.add_tvars thm [];
   194     val tfrees = Thm.fold_terms Term.add_tfrees thm [];
   195     fun types (a, i) =
   196       if i < 0 then AList.lookup (op =) frees a else AList.lookup (op =) vars (a, i);
   197     fun sorts (a, i) =
   198       if i < 0 then AList.lookup (op =) tfrees a else AList.lookup (op =) tvars (a, i);
   199   in (types, sorts) end;
   200 
   201 
   202 
   203 
   204 (** Standardization of rules **)
   205 
   206 (*Generalization over a list of variables*)
   207 val forall_intr_list = fold_rev Thm.forall_intr;
   208 
   209 (*Generalization over Vars -- canonical order*)
   210 fun forall_intr_vars th =
   211   fold Thm.forall_intr
   212     (map (Thm.cterm_of (Thm.theory_of_thm th) o Var) (Thm.fold_terms Term.add_vars th [])) th;
   213 
   214 fun outer_params t =
   215   let val vs = Term.strip_all_vars t
   216   in Name.variant_list [] (map (Name.clean o #1) vs) ~~ map #2 vs end;
   217 
   218 (*generalize outermost parameters*)
   219 fun gen_all th =
   220   let
   221     val thy = Thm.theory_of_thm th;
   222     val {prop, maxidx, ...} = Thm.rep_thm th;
   223     val cert = Thm.cterm_of thy;
   224     fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
   225   in fold elim (outer_params prop) th end;
   226 
   227 (*lift vars wrt. outermost goal parameters
   228   -- reverses the effect of gen_all modulo higher-order unification*)
   229 fun lift_all goal th =
   230   let
   231     val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
   232     val cert = Thm.cterm_of thy;
   233     val maxidx = Thm.maxidx_of th;
   234     val ps = outer_params (Thm.term_of goal)
   235       |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
   236     val Ts = map Term.fastype_of ps;
   237     val inst = Thm.fold_terms Term.add_vars th [] |> map (fn (xi, T) =>
   238       (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
   239   in
   240     th |> Thm.instantiate ([], inst)
   241     |> fold_rev (Thm.forall_intr o cert) ps
   242   end;
   243 
   244 (*direct generalization*)
   245 fun generalize names th = Thm.generalize names (Thm.maxidx_of th + 1) th;
   246 
   247 (*specialization over a list of cterms*)
   248 val forall_elim_list = fold Thm.forall_elim;
   249 
   250 (*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
   251 val implies_intr_list = fold_rev Thm.implies_intr;
   252 
   253 (*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
   254 fun implies_elim_list impth ths = fold Thm.elim_implies ths impth;
   255 
   256 (*Reset Var indexes to zero, renaming to preserve distinctness*)
   257 fun zero_var_indexes_list [] = []
   258   | zero_var_indexes_list ths =
   259       let
   260         val thy = Theory.merge_list (map Thm.theory_of_thm ths);
   261         val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
   262         val (instT, inst) = Term_Subst.zero_var_indexes_inst (map Thm.full_prop_of ths);
   263         val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
   264         val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
   265       in map (Thm.adjust_maxidx_thm ~1 o Thm.instantiate (cinstT, cinst)) ths end;
   266 
   267 val zero_var_indexes = singleton zero_var_indexes_list;
   268 
   269 
   270 (** Standard form of object-rule: no hypotheses, flexflex constraints,
   271     Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
   272 
   273 (*Discharge all hypotheses.*)
   274 fun implies_intr_hyps th =
   275   fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
   276 
   277 (*Squash a theorem's flexflex constraints provided it can be done uniquely.
   278   This step can lose information.*)
   279 fun flexflex_unique th =
   280   if null (Thm.tpairs_of th) then th else
   281     case distinct Thm.eq_thm (Seq.list_of (Thm.flexflex_rule th)) of
   282       [th] => th
   283     | []   => raise THM("flexflex_unique: impossible constraints", 0, [th])
   284     |  _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
   285 
   286 
   287 (* old-style export without context *)
   288 
   289 val export_without_context_open =
   290   implies_intr_hyps
   291   #> Thm.forall_intr_frees
   292   #> `Thm.maxidx_of
   293   #-> (fn maxidx =>
   294     Thm.forall_elim_vars (maxidx + 1)
   295     #> Thm.strip_shyps
   296     #> zero_var_indexes
   297     #> Thm.varifyT_global);
   298 
   299 val export_without_context =
   300   flexflex_unique
   301   #> export_without_context_open
   302   #> Thm.close_derivation;
   303 
   304 
   305 (*Convert all Vars in a theorem to Frees.  Also return a function for
   306   reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
   307   Similar code in type/freeze_thaw*)
   308 
   309 fun legacy_freeze_thaw_robust th =
   310  let val fth = Thm.legacy_freezeT th
   311      val thy = Thm.theory_of_thm fth
   312      val {prop, tpairs, ...} = rep_thm fth
   313  in
   314    case List.foldr OldTerm.add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
   315        [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
   316      | vars =>
   317          let fun newName (Var(ix,_)) = (ix, gensym (string_of_indexname ix))
   318              val alist = map newName vars
   319              fun mk_inst (Var(v,T)) =
   320                  (cterm_of thy (Var(v,T)),
   321                   cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
   322              val insts = map mk_inst vars
   323              fun thaw i th' = (*i is non-negative increment for Var indexes*)
   324                  th' |> forall_intr_list (map #2 insts)
   325                      |> forall_elim_list (map (Thm.incr_indexes_cterm i o #1) insts)
   326          in  (Thm.instantiate ([],insts) fth, thaw)  end
   327  end;
   328 
   329 (*Basic version of the function above. No option to rename Vars apart in thaw.
   330   The Frees created from Vars have nice names.*)
   331 fun legacy_freeze_thaw th =
   332  let val fth = Thm.legacy_freezeT th
   333      val thy = Thm.theory_of_thm fth
   334      val {prop, tpairs, ...} = rep_thm fth
   335  in
   336    case List.foldr OldTerm.add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
   337        [] => (fth, fn x => x)
   338      | vars =>
   339          let fun newName (Var(ix,_), (pairs,used)) =
   340                    let val v = Name.variant used (string_of_indexname ix)
   341                    in  ((ix,v)::pairs, v::used)  end;
   342              val (alist, _) = List.foldr newName ([], Library.foldr OldTerm.add_term_names
   343                (prop :: Thm.terms_of_tpairs tpairs, [])) vars
   344              fun mk_inst (Var(v,T)) =
   345                  (cterm_of thy (Var(v,T)),
   346                   cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
   347              val insts = map mk_inst vars
   348              fun thaw th' =
   349                  th' |> forall_intr_list (map #2 insts)
   350                      |> forall_elim_list (map #1 insts)
   351          in  (Thm.instantiate ([],insts) fth, thaw)  end
   352  end;
   353 
   354 (*Rotates a rule's premises to the left by k*)
   355 fun rotate_prems 0 = I
   356   | rotate_prems k = Thm.permute_prems 0 k;
   357 
   358 fun with_subgoal i f = rotate_prems (i - 1) #> f #> rotate_prems (1 - i);
   359 
   360 (*Permute prems, where the i-th position in the argument list (counting from 0)
   361   gives the position within the original thm to be transferred to position i.
   362   Any remaining trailing positions are left unchanged.*)
   363 val rearrange_prems =
   364   let
   365     fun rearr new [] thm = thm
   366       | rearr new (p :: ps) thm =
   367           rearr (new + 1)
   368             (map (fn q => if new <= q andalso q < p then q + 1 else q) ps)
   369             (Thm.permute_prems (new + 1) (new - p) (Thm.permute_prems new (p - new) thm))
   370   in rearr 0 end;
   371 
   372 (*Resolution: exactly one resolvent must be produced.*)
   373 fun tha RSN (i,thb) =
   374   case Seq.chop 2 (Thm.biresolution false [(false,tha)] i thb) of
   375       ([th],_) => th
   376     | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
   377     |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
   378 
   379 (*resolution: P==>Q, Q==>R gives P==>R. *)
   380 fun tha RS thb = tha RSN (1,thb);
   381 
   382 (*For joining lists of rules*)
   383 fun thas RLN (i,thbs) =
   384   let val resolve = Thm.biresolution false (map (pair false) thas) i
   385       fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
   386   in maps resb thbs end;
   387 
   388 fun thas RL thbs = thas RLN (1,thbs);
   389 
   390 (*Resolve a list of rules against bottom_rl from right to left;
   391   makes proof trees*)
   392 fun rls MRS bottom_rl =
   393   let fun rs_aux i [] = bottom_rl
   394         | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
   395   in  rs_aux 1 rls  end;
   396 
   397 (*As above, but for rule lists*)
   398 fun rlss MRL bottom_rls =
   399   let fun rs_aux i [] = bottom_rls
   400         | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
   401   in  rs_aux 1 rlss  end;
   402 
   403 (*A version of MRS with more appropriate argument order*)
   404 fun bottom_rl OF rls = rls MRS bottom_rl;
   405 
   406 (*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
   407   with no lifting or renaming!  Q may contain ==> or meta-quants
   408   ALWAYS deletes premise i *)
   409 fun compose(tha,i,thb) =
   410     distinct Thm.eq_thm (Seq.list_of (Thm.bicompose false (false,tha,0) i thb));
   411 
   412 fun compose_single (tha,i,thb) =
   413   case compose (tha,i,thb) of
   414     [th] => th
   415   | _ => raise THM ("compose: unique result expected", i, [tha,thb]);
   416 
   417 (*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
   418 fun tha COMP thb =
   419     case compose(tha,1,thb) of
   420         [th] => th
   421       | _ =>   raise THM("COMP", 1, [tha,thb]);
   422 
   423 
   424 (** theorem equality **)
   425 
   426 (*Useful "distance" function for BEST_FIRST*)
   427 val size_of_thm = size_of_term o Thm.full_prop_of;
   428 
   429 
   430 
   431 (*** Meta-Rewriting Rules ***)
   432 
   433 val read_prop = certify o Simple_Syntax.read_prop;
   434 
   435 fun store_thm name th =
   436   Context.>>> (Context.map_theory_result (PureThy.store_thm (name, th)));
   437 
   438 fun store_thm_open name th =
   439   Context.>>> (Context.map_theory_result (PureThy.store_thm_open (name, th)));
   440 
   441 fun store_standard_thm name th = store_thm name (export_without_context th);
   442 fun store_standard_thm_open name thm = store_thm_open name (export_without_context_open thm);
   443 
   444 val reflexive_thm =
   445   let val cx = certify (Var(("x",0),TVar(("'a",0),[])))
   446   in store_standard_thm_open (Binding.name "reflexive") (Thm.reflexive cx) end;
   447 
   448 val symmetric_thm =
   449   let
   450     val xy = read_prop "x::'a == y::'a";
   451     val thm = Thm.implies_intr xy (Thm.symmetric (Thm.assume xy));
   452   in store_standard_thm_open (Binding.name "symmetric") thm end;
   453 
   454 val transitive_thm =
   455   let
   456     val xy = read_prop "x::'a == y::'a";
   457     val yz = read_prop "y::'a == z::'a";
   458     val xythm = Thm.assume xy;
   459     val yzthm = Thm.assume yz;
   460     val thm = Thm.implies_intr yz (Thm.transitive xythm yzthm);
   461   in store_standard_thm_open (Binding.name "transitive") thm end;
   462 
   463 fun symmetric_fun thm = thm RS symmetric_thm;
   464 
   465 fun extensional eq =
   466   let val eq' =
   467     Thm.abstract_rule "x" (Thm.dest_arg (fst (Thm.dest_equals (cprop_of eq)))) eq
   468   in Thm.equal_elim (Thm.eta_conversion (cprop_of eq')) eq' end;
   469 
   470 val equals_cong =
   471   store_standard_thm_open (Binding.name "equals_cong")
   472     (Thm.reflexive (read_prop "x::'a == y::'a"));
   473 
   474 val imp_cong =
   475   let
   476     val ABC = read_prop "A ==> B::prop == C::prop"
   477     val AB = read_prop "A ==> B"
   478     val AC = read_prop "A ==> C"
   479     val A = read_prop "A"
   480   in
   481     store_standard_thm_open (Binding.name "imp_cong") (Thm.implies_intr ABC (Thm.equal_intr
   482       (Thm.implies_intr AB (Thm.implies_intr A
   483         (Thm.equal_elim (Thm.implies_elim (Thm.assume ABC) (Thm.assume A))
   484           (Thm.implies_elim (Thm.assume AB) (Thm.assume A)))))
   485       (Thm.implies_intr AC (Thm.implies_intr A
   486         (Thm.equal_elim (Thm.symmetric (Thm.implies_elim (Thm.assume ABC) (Thm.assume A)))
   487           (Thm.implies_elim (Thm.assume AC) (Thm.assume A)))))))
   488   end;
   489 
   490 val swap_prems_eq =
   491   let
   492     val ABC = read_prop "A ==> B ==> C"
   493     val BAC = read_prop "B ==> A ==> C"
   494     val A = read_prop "A"
   495     val B = read_prop "B"
   496   in
   497     store_standard_thm_open (Binding.name "swap_prems_eq")
   498       (Thm.equal_intr
   499         (Thm.implies_intr ABC (Thm.implies_intr B (Thm.implies_intr A
   500           (Thm.implies_elim (Thm.implies_elim (Thm.assume ABC) (Thm.assume A)) (Thm.assume B)))))
   501         (Thm.implies_intr BAC (Thm.implies_intr A (Thm.implies_intr B
   502           (Thm.implies_elim (Thm.implies_elim (Thm.assume BAC) (Thm.assume B)) (Thm.assume A))))))
   503   end;
   504 
   505 val imp_cong_rule = Thm.combination o Thm.combination (Thm.reflexive implies);
   506 
   507 fun arg_cong_rule ct th = Thm.combination (Thm.reflexive ct) th;    (*AP_TERM in LCF/HOL*)
   508 fun fun_cong_rule th ct = Thm.combination th (Thm.reflexive ct);    (*AP_THM in LCF/HOL*)
   509 fun binop_cong_rule ct th1 th2 = Thm.combination (arg_cong_rule ct th1) th2;
   510 
   511 local
   512   val dest_eq = Thm.dest_equals o cprop_of
   513   val rhs_of = snd o dest_eq
   514 in
   515 fun beta_eta_conversion t =
   516   let val thm = Thm.beta_conversion true t
   517   in Thm.transitive thm (Thm.eta_conversion (rhs_of thm)) end
   518 end;
   519 
   520 fun eta_long_conversion ct =
   521   Thm.transitive
   522     (beta_eta_conversion ct)
   523     (Thm.symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
   524 
   525 (*Contract all eta-redexes in the theorem, lest they give rise to needless abstractions*)
   526 fun eta_contraction_rule th =
   527   Thm.equal_elim (Thm.eta_conversion (cprop_of th)) th;
   528 
   529 
   530 (* abs_def *)
   531 
   532 (*
   533    f ?x1 ... ?xn == u
   534   --------------------
   535    f == %x1 ... xn. u
   536 *)
   537 
   538 local
   539 
   540 fun contract_lhs th =
   541   Thm.transitive (Thm.symmetric (beta_eta_conversion
   542     (fst (Thm.dest_equals (cprop_of th))))) th;
   543 
   544 fun var_args ct =
   545   (case try Thm.dest_comb ct of
   546     SOME (f, arg) =>
   547       (case Thm.term_of arg of
   548         Var ((x, _), _) => update (eq_snd (op aconvc)) (x, arg) (var_args f)
   549       | _ => [])
   550   | NONE => []);
   551 
   552 in
   553 
   554 fun abs_def th =
   555   let
   556     val th' = contract_lhs th;
   557     val args = var_args (Thm.lhs_of th');
   558   in contract_lhs (fold (uncurry Thm.abstract_rule) args th') end;
   559 
   560 end;
   561 
   562 
   563 
   564 (*** Some useful meta-theorems ***)
   565 
   566 (*The rule V/V, obtains assumption solving for eresolve_tac*)
   567 val asm_rl = store_standard_thm_open (Binding.name "asm_rl") (Thm.trivial (read_prop "?psi"));
   568 val _ = store_thm_open (Binding.name "_") asm_rl;
   569 
   570 (*Meta-level cut rule: [| V==>W; V |] ==> W *)
   571 val cut_rl =
   572   store_standard_thm_open (Binding.name "cut_rl")
   573     (Thm.trivial (read_prop "?psi ==> ?theta"));
   574 
   575 (*Generalized elim rule for one conclusion; cut_rl with reversed premises:
   576      [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
   577 val revcut_rl =
   578   let
   579     val V = read_prop "V";
   580     val VW = read_prop "V ==> W";
   581   in
   582     store_standard_thm_open (Binding.name "revcut_rl")
   583       (Thm.implies_intr V (Thm.implies_intr VW (Thm.implies_elim (Thm.assume VW) (Thm.assume V))))
   584   end;
   585 
   586 (*for deleting an unwanted assumption*)
   587 val thin_rl =
   588   let
   589     val V = read_prop "V";
   590     val W = read_prop "W";
   591     val thm = Thm.implies_intr V (Thm.implies_intr W (Thm.assume W));
   592   in store_standard_thm_open (Binding.name "thin_rl") thm end;
   593 
   594 (* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
   595 val triv_forall_equality =
   596   let
   597     val V = read_prop "V";
   598     val QV = read_prop "!!x::'a. V";
   599     val x = certify (Free ("x", Term.aT []));
   600   in
   601     store_standard_thm_open (Binding.name "triv_forall_equality")
   602       (Thm.equal_intr (Thm.implies_intr QV (Thm.forall_elim x (Thm.assume QV)))
   603         (Thm.implies_intr V (Thm.forall_intr x (Thm.assume V))))
   604   end;
   605 
   606 (* (PROP ?Phi ==> PROP ?Phi ==> PROP ?Psi) ==>
   607    (PROP ?Phi ==> PROP ?Psi)
   608 *)
   609 val distinct_prems_rl =
   610   let
   611     val AAB = read_prop "Phi ==> Phi ==> Psi";
   612     val A = read_prop "Phi";
   613   in
   614     store_standard_thm_open (Binding.name "distinct_prems_rl")
   615       (implies_intr_list [AAB, A] (implies_elim_list (Thm.assume AAB) [Thm.assume A, Thm.assume A]))
   616   end;
   617 
   618 (* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
   619    (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
   620    `thm COMP swap_prems_rl' swaps the first two premises of `thm'
   621 *)
   622 val swap_prems_rl =
   623   let
   624     val cmajor = read_prop "PhiA ==> PhiB ==> Psi";
   625     val major = Thm.assume cmajor;
   626     val cminor1 = read_prop "PhiA";
   627     val minor1 = Thm.assume cminor1;
   628     val cminor2 = read_prop "PhiB";
   629     val minor2 = Thm.assume cminor2;
   630   in
   631     store_standard_thm_open (Binding.name "swap_prems_rl")
   632       (Thm.implies_intr cmajor (Thm.implies_intr cminor2 (Thm.implies_intr cminor1
   633         (Thm.implies_elim (Thm.implies_elim major minor1) minor2))))
   634   end;
   635 
   636 (* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
   637    ==> PROP ?phi == PROP ?psi
   638    Introduction rule for == as a meta-theorem.
   639 *)
   640 val equal_intr_rule =
   641   let
   642     val PQ = read_prop "phi ==> psi";
   643     val QP = read_prop "psi ==> phi";
   644   in
   645     store_standard_thm_open (Binding.name "equal_intr_rule")
   646       (Thm.implies_intr PQ (Thm.implies_intr QP (Thm.equal_intr (Thm.assume PQ) (Thm.assume QP))))
   647   end;
   648 
   649 (* PROP ?phi == PROP ?psi ==> PROP ?phi ==> PROP ?psi *)
   650 val equal_elim_rule1 =
   651   let
   652     val eq = read_prop "phi::prop == psi::prop";
   653     val P = read_prop "phi";
   654   in
   655     store_standard_thm_open (Binding.name "equal_elim_rule1")
   656       (Thm.equal_elim (Thm.assume eq) (Thm.assume P) |> implies_intr_list [eq, P])
   657   end;
   658 
   659 (* PROP ?psi == PROP ?phi ==> PROP ?phi ==> PROP ?psi *)
   660 val equal_elim_rule2 =
   661   store_standard_thm_open (Binding.name "equal_elim_rule2")
   662     (symmetric_thm RS equal_elim_rule1);
   663 
   664 (* PROP ?phi ==> PROP ?phi ==> PROP ?psi ==> PROP ?psi *)
   665 val remdups_rl =
   666   let
   667     val P = read_prop "phi";
   668     val Q = read_prop "psi";
   669     val thm = implies_intr_list [P, P, Q] (Thm.assume Q);
   670   in store_standard_thm_open (Binding.name "remdups_rl") thm end;
   671 
   672 
   673 
   674 (** embedded terms and types **)
   675 
   676 local
   677   val A = certify (Free ("A", propT));
   678   val axiom = Thm.unvarify_global o Thm.axiom (Context.the_theory (Context.the_thread_data ()));
   679   val prop_def = axiom "Pure.prop_def";
   680   val term_def = axiom "Pure.term_def";
   681   val sort_constraint_def = axiom "Pure.sort_constraint_def";
   682   val C = Thm.lhs_of sort_constraint_def;
   683   val T = Thm.dest_arg C;
   684   val CA = mk_implies (C, A);
   685 in
   686 
   687 (* protect *)
   688 
   689 val protect = Thm.capply (certify Logic.protectC);
   690 
   691 val protectI =
   692   store_standard_thm (Binding.conceal (Binding.name "protectI"))
   693     (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A));
   694 
   695 val protectD =
   696   store_standard_thm (Binding.conceal (Binding.name "protectD"))
   697     (Thm.equal_elim prop_def (Thm.assume (protect A)));
   698 
   699 val protect_cong =
   700   store_standard_thm_open (Binding.name "protect_cong") (Thm.reflexive (protect A));
   701 
   702 fun implies_intr_protected asms th =
   703   let val asms' = map protect asms in
   704     implies_elim_list
   705       (implies_intr_list asms th)
   706       (map (fn asm' => Thm.assume asm' RS protectD) asms')
   707     |> implies_intr_list asms'
   708   end;
   709 
   710 
   711 (* term *)
   712 
   713 val termI =
   714   store_standard_thm (Binding.conceal (Binding.name "termI"))
   715     (Thm.equal_elim (Thm.symmetric term_def) (Thm.forall_intr A (Thm.trivial A)));
   716 
   717 fun mk_term ct =
   718   let
   719     val thy = Thm.theory_of_cterm ct;
   720     val cert = Thm.cterm_of thy;
   721     val certT = Thm.ctyp_of thy;
   722     val T = Thm.typ_of (Thm.ctyp_of_term ct);
   723     val a = certT (TVar (("'a", 0), []));
   724     val x = cert (Var (("x", 0), T));
   725   in Thm.instantiate ([(a, certT T)], [(x, ct)]) termI end;
   726 
   727 fun dest_term th =
   728   let val cprop = strip_imp_concl (Thm.cprop_of th) in
   729     if can Logic.dest_term (Thm.term_of cprop) then
   730       Thm.dest_arg cprop
   731     else raise THM ("dest_term", 0, [th])
   732   end;
   733 
   734 fun cterm_rule f = dest_term o f o mk_term;
   735 fun term_rule thy f t = Thm.term_of (cterm_rule f (Thm.cterm_of thy t));
   736 
   737 val dummy_thm = mk_term (certify (Term.dummy_pattern propT));
   738 
   739 
   740 (* sort_constraint *)
   741 
   742 val sort_constraintI =
   743   store_standard_thm (Binding.conceal (Binding.name "sort_constraintI"))
   744     (Thm.equal_elim (Thm.symmetric sort_constraint_def) (mk_term T));
   745 
   746 val sort_constraint_eq =
   747   store_standard_thm (Binding.conceal (Binding.name "sort_constraint_eq"))
   748     (Thm.equal_intr
   749       (Thm.implies_intr CA (Thm.implies_elim (Thm.assume CA)
   750         (Thm.unvarify_global sort_constraintI)))
   751       (implies_intr_list [A, C] (Thm.assume A)));
   752 
   753 end;
   754 
   755 
   756 (* HHF normalization *)
   757 
   758 (* (PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x)) *)
   759 val norm_hhf_eq =
   760   let
   761     val aT = TFree ("'a", []);
   762     val all = Term.all aT;
   763     val x = Free ("x", aT);
   764     val phi = Free ("phi", propT);
   765     val psi = Free ("psi", aT --> propT);
   766 
   767     val cx = certify x;
   768     val cphi = certify phi;
   769     val lhs = certify (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
   770     val rhs = certify (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
   771   in
   772     Thm.equal_intr
   773       (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
   774         |> Thm.forall_elim cx
   775         |> Thm.implies_intr cphi
   776         |> Thm.forall_intr cx
   777         |> Thm.implies_intr lhs)
   778       (Thm.implies_elim
   779           (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
   780         |> Thm.forall_intr cx
   781         |> Thm.implies_intr cphi
   782         |> Thm.implies_intr rhs)
   783     |> store_standard_thm_open (Binding.name "norm_hhf_eq")
   784   end;
   785 
   786 val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
   787 val norm_hhf_eqs = [norm_hhf_eq, sort_constraint_eq];
   788 
   789 fun is_norm_hhf (Const ("Pure.sort_constraint", _)) = false
   790   | is_norm_hhf (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
   791   | is_norm_hhf (Abs _ $ _) = false
   792   | is_norm_hhf (t $ u) = is_norm_hhf t andalso is_norm_hhf u
   793   | is_norm_hhf (Abs (_, _, t)) = is_norm_hhf t
   794   | is_norm_hhf _ = true;
   795 
   796 fun norm_hhf thy t =
   797   if is_norm_hhf t then t
   798   else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
   799 
   800 fun norm_hhf_cterm ct =
   801   if is_norm_hhf (Thm.term_of ct) then ct
   802   else cterm_fun (Pattern.rewrite_term (Thm.theory_of_cterm ct) [norm_hhf_prop] []) ct;
   803 
   804 
   805 (* var indexes *)
   806 
   807 (*Increment the indexes of only the type variables*)
   808 fun incr_type_indexes inc th =
   809   let val tvs = OldTerm.term_tvars (prop_of th)
   810       and thy = Thm.theory_of_thm th
   811       fun inc_tvar ((a,i),s) = pairself (ctyp_of thy) (TVar ((a,i),s), TVar ((a,i+inc),s))
   812   in Thm.instantiate (map inc_tvar tvs, []) th end;
   813 
   814 fun incr_indexes th = Thm.incr_indexes (Thm.maxidx_of th + 1);
   815 
   816 fun incr_indexes2 th1 th2 =
   817   Thm.incr_indexes (Int.max (Thm.maxidx_of th1, Thm.maxidx_of th2) + 1);
   818 
   819 fun th1 INCR_COMP th2 = incr_indexes th2 th1 COMP th2;
   820 fun th1 COMP_INCR th2 = th1 COMP incr_indexes th1 th2;
   821 
   822 fun comp_no_flatten (th, n) i rule =
   823   (case distinct Thm.eq_thm (Seq.list_of
   824       (Thm.compose_no_flatten false (th, n) i (incr_indexes th rule))) of
   825     [th'] => th'
   826   | [] => raise THM ("comp_no_flatten", i, [th, rule])
   827   | _ => raise THM ("comp_no_flatten: unique result expected", i, [th, rule]));
   828 
   829 
   830 
   831 (*** Instantiate theorem th, reading instantiations in theory thy ****)
   832 
   833 (*Version that normalizes the result: Thm.instantiate no longer does that*)
   834 fun instantiate instpair th =
   835   Thm.adjust_maxidx_thm ~1 (Thm.instantiate instpair th COMP_INCR asm_rl);
   836 
   837 (*Left-to-right replacements: tpairs = [...,(vi,ti),...].
   838   Instantiates distinct Vars by terms, inferring type instantiations. *)
   839 local
   840   fun add_types ((ct,cu), (thy,tye,maxidx)) =
   841     let
   842         val thyt = Thm.theory_of_cterm ct;
   843         val thyu = Thm.theory_of_cterm cu;
   844         val {t, T, maxidx = maxt, ...} = Thm.rep_cterm ct;
   845         val {t = u, T = U, maxidx = maxu, ...} = Thm.rep_cterm cu;
   846         val maxi = Int.max(maxidx, Int.max(maxt, maxu));
   847         val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
   848         val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
   849           handle Type.TUNIFY => raise TYPE ("Ill-typed instantiation:\nType\n" ^
   850             Syntax.string_of_typ_global thy' (Envir.norm_type tye T) ^
   851             "\nof variable " ^
   852             Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) t) ^
   853             "\ncannot be unified with type\n" ^
   854             Syntax.string_of_typ_global thy' (Envir.norm_type tye U) ^ "\nof term " ^
   855             Syntax.string_of_term_global thy' (Term.map_types (Envir.norm_type tye) u),
   856             [T, U], [t, u])
   857     in  (thy', tye', maxi')  end;
   858 in
   859 fun cterm_instantiate [] th = th
   860   | cterm_instantiate ctpairs0 th =
   861   let val (thy,tye,_) = List.foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
   862       fun instT(ct,cu) =
   863         let val inst = cterm_of thy o Term.map_types (Envir.norm_type tye) o term_of
   864         in (inst ct, inst cu) end
   865       fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy (Envir.norm_type tye T))
   866   in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
   867   handle TERM _ =>
   868            raise THM("cterm_instantiate: incompatible theories",0,[th])
   869        | TYPE (msg, _, _) => raise THM(msg, 0, [th])
   870 end;
   871 
   872 
   873 
   874 (** variations on instantiate **)
   875 
   876 (* instantiate by left-to-right occurrence of variables *)
   877 
   878 fun instantiate' cTs cts thm =
   879   let
   880     fun err msg =
   881       raise TYPE ("instantiate': " ^ msg,
   882         map_filter (Option.map Thm.typ_of) cTs,
   883         map_filter (Option.map Thm.term_of) cts);
   884 
   885     fun inst_of (v, ct) =
   886       (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
   887         handle TYPE (msg, _, _) => err msg;
   888 
   889     fun tyinst_of (v, cT) =
   890       (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
   891         handle TYPE (msg, _, _) => err msg;
   892 
   893     fun zip_vars xs ys =
   894       zip_options xs ys handle Library.UnequalLengths =>
   895         err "more instantiations than variables in thm";
   896 
   897     (*instantiate types first!*)
   898     val thm' =
   899       if forall is_none cTs then thm
   900       else Thm.instantiate
   901         (map tyinst_of (zip_vars (rev (Thm.fold_terms Term.add_tvars thm [])) cTs), []) thm;
   902     val thm'' =
   903       if forall is_none cts then thm'
   904       else Thm.instantiate
   905         ([], map inst_of (zip_vars (rev (Thm.fold_terms Term.add_vars thm' [])) cts)) thm';
   906     in thm'' end;
   907 
   908 
   909 
   910 (** renaming of bound variables **)
   911 
   912 (* replace bound variables x_i in thm by y_i *)
   913 (* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
   914 
   915 fun rename_bvars [] thm = thm
   916   | rename_bvars vs thm =
   917       let
   918         val cert = Thm.cterm_of (Thm.theory_of_thm thm);
   919         fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
   920           | ren (t $ u) = ren t $ ren u
   921           | ren t = t;
   922       in Thm.equal_elim (Thm.reflexive (cert (ren (Thm.prop_of thm)))) thm end;
   923 
   924 
   925 (* renaming in left-to-right order *)
   926 
   927 fun rename_bvars' xs thm =
   928   let
   929     val cert = Thm.cterm_of (Thm.theory_of_thm thm);
   930     val prop = Thm.prop_of thm;
   931     fun rename [] t = ([], t)
   932       | rename (x' :: xs) (Abs (x, T, t)) =
   933           let val (xs', t') = rename xs t
   934           in (xs', Abs (the_default x x', T, t')) end
   935       | rename xs (t $ u) =
   936           let
   937             val (xs', t') = rename xs t;
   938             val (xs'', u') = rename xs' u
   939           in (xs'', t' $ u') end
   940       | rename xs t = (xs, t);
   941   in case rename xs prop of
   942       ([], prop') => Thm.equal_elim (Thm.reflexive (cert prop')) thm
   943     | _ => error "More names than abstractions in theorem"
   944   end;
   945 
   946 
   947 
   948 (** multi_resolve **)
   949 
   950 local
   951 
   952 fun res th i rule =
   953   Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
   954 
   955 fun multi_res _ [] rule = Seq.single rule
   956   | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
   957 
   958 in
   959 
   960 val multi_resolve = multi_res 1;
   961 fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
   962 
   963 end;
   964 
   965 end;
   966 
   967 structure Basic_Drule: BASIC_DRULE = Drule;
   968 open Basic_Drule;