src/Pure/drule.ML
author wenzelm
Wed Jan 25 00:21:35 2006 +0100 (2006-01-25)
changeset 18777 9d98d5705433
parent 18732 c0511e120f17
child 18799 f137c5e971f5
permissions -rw-r--r--
abs_def: improved error;
     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;
    10 
    11 signature BASIC_DRULE =
    12 sig
    13   val mk_implies: cterm * cterm -> cterm
    14   val list_implies: cterm list * cterm -> cterm
    15   val dest_implies: cterm -> cterm * cterm
    16   val dest_equals: cterm -> cterm * cterm
    17   val strip_imp_prems: cterm -> cterm list
    18   val strip_imp_concl: cterm -> cterm
    19   val cprems_of: thm -> cterm list
    20   val cterm_fun: (term -> term) -> (cterm -> cterm)
    21   val ctyp_fun: (typ -> typ) -> (ctyp -> ctyp)
    22   val read_insts: theory -> (indexname -> typ option) * (indexname -> sort option) ->
    23     (indexname -> typ option) * (indexname -> sort option) -> string list ->
    24     (indexname * string) list -> (ctyp * ctyp) list * (cterm * cterm) list
    25   val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
    26   val strip_shyps_warning: thm -> thm
    27   val forall_intr_list: cterm list -> thm -> thm
    28   val forall_intr_frees: thm -> thm
    29   val forall_intr_vars: thm -> thm
    30   val forall_elim_list: cterm list -> thm -> thm
    31   val forall_elim_var: int -> thm -> thm
    32   val forall_elim_vars: int -> thm -> thm
    33   val gen_all: thm -> thm
    34   val lift_all: cterm -> thm -> thm
    35   val freeze_thaw: thm -> thm * (thm -> thm)
    36   val freeze_thaw_robust: thm -> thm * (int -> thm -> thm)
    37   val implies_elim_list: thm -> thm list -> thm
    38   val implies_intr_list: cterm list -> thm -> thm
    39   val instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
    40   val zero_var_indexes: thm -> thm
    41   val implies_intr_hyps: thm -> thm
    42   val standard: thm -> thm
    43   val standard': thm -> thm
    44   val rotate_prems: int -> thm -> thm
    45   val rearrange_prems: int list -> thm -> thm
    46   val assume_ax: theory -> string -> thm
    47   val RSN: thm * (int * thm) -> thm
    48   val RS: thm * thm -> thm
    49   val RLN: thm list * (int * thm list) -> thm list
    50   val RL: thm list * thm list -> thm list
    51   val MRS: thm list * thm -> thm
    52   val MRL: thm list list * thm list -> thm list
    53   val OF: thm * thm list -> thm
    54   val compose: thm * int * thm -> thm list
    55   val COMP: thm * thm -> thm
    56   val read_instantiate_sg: theory -> (string*string)list -> thm -> thm
    57   val read_instantiate: (string*string)list -> thm -> thm
    58   val cterm_instantiate: (cterm*cterm)list -> thm -> thm
    59   val eq_thm_thy: thm * thm -> bool
    60   val eq_thm_prop: thm * thm -> bool
    61   val weak_eq_thm: thm * thm -> bool
    62   val size_of_thm: thm -> int
    63   val reflexive_thm: thm
    64   val symmetric_thm: thm
    65   val transitive_thm: thm
    66   val symmetric_fun: thm -> thm
    67   val extensional: thm -> thm
    68   val imp_cong: thm
    69   val swap_prems_eq: thm
    70   val equal_abs_elim: cterm  -> thm -> thm
    71   val equal_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 equal_elim_rule1: thm
    80   val inst: string -> string -> thm -> thm
    81   val instantiate': ctyp option list -> cterm option list -> thm -> thm
    82   val incr_indexes: thm -> thm -> thm
    83   val incr_indexes_wrt: int list -> ctyp list -> cterm list -> thm list -> thm -> thm
    84 end;
    85 
    86 signature DRULE =
    87 sig
    88   include BASIC_DRULE
    89   val list_comb: cterm * cterm list -> cterm
    90   val strip_comb: cterm -> cterm * cterm list
    91   val strip_type: ctyp -> ctyp list * ctyp
    92   val beta_conv: cterm -> cterm -> cterm
    93   val plain_prop_of: thm -> term
    94   val add_used: thm -> string list -> string list
    95   val map_tags: (tag list -> tag list) -> thm -> thm
    96   val tag_rule: tag -> thm -> thm
    97   val untag_rule: string -> thm -> thm
    98   val tag: tag -> attribute
    99   val untag: string -> attribute
   100   val get_kind: thm -> string
   101   val kind: string -> attribute
   102   val theoremK: string
   103   val lemmaK: string
   104   val corollaryK: string
   105   val internalK: string
   106   val kind_internal: attribute
   107   val has_internal: tag list -> bool
   108   val is_internal: thm -> bool
   109   val flexflex_unique: thm -> thm
   110   val close_derivation: thm -> thm
   111   val local_standard: thm -> thm
   112   val compose_single: thm * int * thm -> thm
   113   val add_rule: thm -> thm list -> thm list
   114   val del_rule: thm -> thm list -> thm list
   115   val add_rules: thm list -> thm list -> thm list
   116   val del_rules: thm list -> thm list -> thm list
   117   val merge_rules: thm list * thm list -> thm list
   118   val imp_cong_rule: thm -> thm -> thm
   119   val beta_eta_conversion: cterm -> thm
   120   val eta_long_conversion: cterm -> thm
   121   val forall_conv: int -> (cterm -> thm) -> cterm -> thm
   122   val concl_conv: int -> (cterm -> thm) -> cterm -> thm
   123   val prems_conv: int -> (int -> cterm -> thm) -> cterm -> thm
   124   val conjunction_conv: int -> (int -> cterm -> thm) -> cterm -> thm
   125   val goals_conv: (int -> bool) -> (cterm -> thm) -> cterm -> thm
   126   val fconv_rule: (cterm -> thm) -> thm -> thm
   127   val norm_hhf_eq: thm
   128   val is_norm_hhf: term -> bool
   129   val norm_hhf: theory -> term -> term
   130   val protect: cterm -> cterm
   131   val protectI: thm
   132   val protectD: thm
   133   val protect_cong: thm
   134   val implies_intr_protected: cterm list -> thm -> thm
   135   val freeze_all: thm -> thm
   136   val tvars_of_terms: term list -> (indexname * sort) list
   137   val vars_of_terms: term list -> (indexname * typ) list
   138   val tvars_of: thm -> (indexname * sort) list
   139   val vars_of: thm -> (indexname * typ) list
   140   val tfrees_of: thm -> (string * sort) list
   141   val frees_of: thm -> (string * typ) list
   142   val fold_terms: (term -> 'a -> 'a) -> thm -> 'a -> 'a
   143   val rename_bvars: (string * string) list -> thm -> thm
   144   val rename_bvars': string option list -> thm -> thm
   145   val unvarifyT: thm -> thm
   146   val unvarify: thm -> thm
   147   val tvars_intr_list: string list -> thm -> (string * (indexname * sort)) list * thm
   148   val remdups_rl: thm
   149   val multi_resolve: thm list -> thm -> thm Seq.seq
   150   val multi_resolves: thm list -> thm list -> thm Seq.seq
   151   val conj_intr: thm -> thm -> thm
   152   val conj_intr_list: thm list -> thm
   153   val conj_elim: thm -> thm * thm
   154   val conj_elim_list: thm -> thm list
   155   val conj_elim_precise: int list -> thm -> thm list list
   156   val conj_intr_thm: thm
   157   val conj_curry: thm -> thm
   158   val abs_def: thm -> thm
   159   val read_instantiate_sg': theory -> (indexname * string) list -> thm -> thm
   160   val read_instantiate': (indexname * string) list -> thm -> thm
   161 end;
   162 
   163 structure Drule: DRULE =
   164 struct
   165 
   166 
   167 (** some cterm->cterm operations: faster than calling cterm_of! **)
   168 
   169 fun dest_implies ct =
   170   (case Thm.term_of ct of
   171     (Const ("==>", _) $ _ $ _) =>
   172       let val (ct1, ct2) = Thm.dest_comb ct
   173       in (#2 (Thm.dest_comb ct1), ct2) end
   174   | _ => raise TERM ("dest_implies", [term_of ct]));
   175 
   176 fun dest_equals ct =
   177   (case Thm.term_of ct of
   178     (Const ("==", _) $ _ $ _) =>
   179       let val (ct1, ct2) = Thm.dest_comb ct
   180       in (#2 (Thm.dest_comb ct1), ct2) end
   181     | _ => raise TERM ("dest_equals", [term_of ct]));
   182 
   183 
   184 (* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
   185 fun strip_imp_prems ct =
   186     let val (cA,cB) = dest_implies ct
   187     in  cA :: strip_imp_prems cB  end
   188     handle TERM _ => [];
   189 
   190 (* A1==>...An==>B  goes to B, where B is not an implication *)
   191 fun strip_imp_concl ct =
   192     case term_of ct of (Const("==>", _) $ _ $ _) =>
   193         strip_imp_concl (#2 (Thm.dest_comb ct))
   194   | _ => ct;
   195 
   196 (*The premises of a theorem, as a cterm list*)
   197 val cprems_of = strip_imp_prems o cprop_of;
   198 
   199 fun cterm_fun f ct =
   200   let val {t, thy, ...} = Thm.rep_cterm ct
   201   in Thm.cterm_of thy (f t) end;
   202 
   203 fun ctyp_fun f cT =
   204   let val {T, thy, ...} = Thm.rep_ctyp cT
   205   in Thm.ctyp_of thy (f T) end;
   206 
   207 val implies = cterm_of ProtoPure.thy Term.implies;
   208 
   209 (*cterm version of mk_implies*)
   210 fun mk_implies(A,B) = Thm.capply (Thm.capply implies A) B;
   211 
   212 (*cterm version of list_implies: [A1,...,An], B  goes to [|A1;==>;An|]==>B *)
   213 fun list_implies([], B) = B
   214   | list_implies(A::AS, B) = mk_implies (A, list_implies(AS,B));
   215 
   216 (*cterm version of list_comb: maps  (f, [t1,...,tn])  to  f(t1,...,tn) *)
   217 fun list_comb (f, []) = f
   218   | list_comb (f, t::ts) = list_comb (Thm.capply f t, ts);
   219 
   220 (*cterm version of strip_comb: maps  f(t1,...,tn)  to  (f, [t1,...,tn]) *)
   221 fun strip_comb ct =
   222   let
   223     fun stripc (p as (ct, cts)) =
   224       let val (ct1, ct2) = Thm.dest_comb ct
   225       in stripc (ct1, ct2 :: cts) end handle CTERM _ => p
   226   in stripc (ct, []) end;
   227 
   228 (* cterm version of strip_type: maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T) *)
   229 fun strip_type cT = (case Thm.typ_of cT of
   230     Type ("fun", _) =>
   231       let
   232         val [cT1, cT2] = Thm.dest_ctyp cT;
   233         val (cTs, cT') = strip_type cT2
   234       in (cT1 :: cTs, cT') end
   235   | _ => ([], cT));
   236 
   237 (*Beta-conversion for cterms, where x is an abstraction. Simply returns the rhs
   238   of the meta-equality returned by the beta_conversion rule.*)
   239 fun beta_conv x y =
   240     #2 (Thm.dest_comb (cprop_of (Thm.beta_conversion false (Thm.capply x y))));
   241 
   242 fun plain_prop_of raw_thm =
   243   let
   244     val thm = Thm.strip_shyps raw_thm;
   245     fun err msg = raise THM ("plain_prop_of: " ^ msg, 0, [thm]);
   246     val {hyps, prop, tpairs, ...} = Thm.rep_thm thm;
   247   in
   248     if not (null hyps) then
   249       err "theorem may not contain hypotheses"
   250     else if not (null (Thm.extra_shyps thm)) then
   251       err "theorem may not contain sort hypotheses"
   252     else if not (null tpairs) then
   253       err "theorem may not contain flex-flex pairs"
   254     else prop
   255   end;
   256 
   257 
   258 
   259 (** reading of instantiations **)
   260 
   261 fun absent ixn =
   262   error("No such variable in term: " ^ Syntax.string_of_vname ixn);
   263 
   264 fun inst_failure ixn =
   265   error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails");
   266 
   267 fun read_insts thy (rtypes,rsorts) (types,sorts) used insts =
   268 let
   269     fun is_tv ((a, _), _) =
   270       (case Symbol.explode a of "'" :: _ => true | _ => false);
   271     val (tvs, vs) = List.partition is_tv insts;
   272     fun sort_of ixn = case rsorts ixn of SOME S => S | NONE => absent ixn;
   273     fun readT (ixn, st) =
   274         let val S = sort_of ixn;
   275             val T = Sign.read_typ (thy,sorts) st;
   276         in if Sign.typ_instance thy (T, TVar(ixn,S)) then (ixn,T)
   277            else inst_failure ixn
   278         end
   279     val tye = map readT tvs;
   280     fun mkty(ixn,st) = (case rtypes ixn of
   281                           SOME T => (ixn,(st,typ_subst_TVars tye T))
   282                         | NONE => absent ixn);
   283     val ixnsTs = map mkty vs;
   284     val ixns = map fst ixnsTs
   285     and sTs  = map snd ixnsTs
   286     val (cts,tye2) = read_def_cterms(thy,types,sorts) used false sTs;
   287     fun mkcVar(ixn,T) =
   288         let val U = typ_subst_TVars tye2 T
   289         in cterm_of thy (Var(ixn,U)) end
   290     val ixnTs = ListPair.zip(ixns, map snd sTs)
   291 in (map (fn (ixn, T) => (ctyp_of thy (TVar (ixn, sort_of ixn)),
   292       ctyp_of thy T)) (tye2 @ tye),
   293     ListPair.zip(map mkcVar ixnTs,cts))
   294 end;
   295 
   296 
   297 (*** Find the type (sort) associated with a (T)Var or (T)Free in a term
   298      Used for establishing default types (of variables) and sorts (of
   299      type variables) when reading another term.
   300      Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
   301 ***)
   302 
   303 fun types_sorts thm =
   304     let val {prop, hyps, tpairs, ...} = Thm.rep_thm thm;
   305         (* bogus term! *)
   306         val big = Term.list_comb
   307                     (Term.list_comb (prop, hyps), Thm.terms_of_tpairs tpairs);
   308         val vars = map dest_Var (term_vars big);
   309         val frees = map dest_Free (term_frees big);
   310         val tvars = term_tvars big;
   311         val tfrees = term_tfrees big;
   312         fun typ(a,i) = if i<0 then AList.lookup (op =) frees a else AList.lookup (op =) vars (a,i);
   313         fun sort(a,i) = if i<0 then AList.lookup (op =) tfrees a else AList.lookup (op =) tvars (a,i);
   314     in (typ,sort) end;
   315 
   316 fun add_used thm used =
   317   let val {prop, hyps, tpairs, ...} = Thm.rep_thm thm in
   318     add_term_tvarnames (prop, used)
   319     |> fold (curry add_term_tvarnames) hyps
   320     |> fold (curry add_term_tvarnames) (Thm.terms_of_tpairs tpairs)
   321   end;
   322 
   323 
   324 
   325 (** theorem tags **)
   326 
   327 (* add / delete tags *)
   328 
   329 fun map_tags f thm =
   330   Thm.put_name_tags (Thm.name_of_thm thm, f (#2 (Thm.get_name_tags thm))) thm;
   331 
   332 fun tag_rule tg = map_tags (fn tgs => if tg mem tgs then tgs else tgs @ [tg]);
   333 fun untag_rule s = map_tags (filter_out (equal s o #1));
   334 
   335 fun tag tg x = Thm.rule_attribute (K (tag_rule tg)) x;
   336 fun untag s x = Thm.rule_attribute (K (untag_rule s)) x;
   337 
   338 fun simple_tag name x = tag (name, []) x;
   339 
   340 
   341 (* theorem kinds *)
   342 
   343 val theoremK = "theorem";
   344 val lemmaK = "lemma";
   345 val corollaryK = "corollary";
   346 val internalK = "internal";
   347 
   348 fun get_kind thm =
   349   (case AList.lookup (op =) ((#2 o Thm.get_name_tags) thm) "kind" of
   350     SOME (k :: _) => k
   351   | _ => "unknown");
   352 
   353 fun kind_rule k = tag_rule ("kind", [k]) o untag_rule "kind";
   354 fun kind k x = if k = "" then x else Thm.rule_attribute (K (kind_rule k)) x;
   355 fun kind_internal x = kind internalK x;
   356 fun has_internal tags = exists (fn ("kind", [k]) => k = internalK | _ => false) tags;
   357 val is_internal = has_internal o Thm.tags_of_thm;
   358 
   359 
   360 
   361 (** Standardization of rules **)
   362 
   363 (*vars in left-to-right order*)
   364 fun tvars_of_terms ts = rev (fold Term.add_tvars ts []);
   365 fun vars_of_terms ts = rev (fold Term.add_vars ts []);
   366 fun tvars_of thm = tvars_of_terms [Thm.full_prop_of thm];
   367 fun vars_of thm = vars_of_terms [Thm.full_prop_of thm];
   368 
   369 fun fold_terms f th =
   370   let val {hyps, tpairs, prop, ...} = Thm.rep_thm th
   371   in f prop #> fold (fn (t, u) => f t #> f u) tpairs #> fold f hyps end;
   372 
   373 fun tfrees_of th = rev (fold_terms Term.add_tfrees th []);
   374 fun frees_of th = rev (fold_terms Term.add_frees th []);
   375 
   376 (*Strip extraneous shyps as far as possible*)
   377 fun strip_shyps_warning thm =
   378   let
   379     val str_of_sort = Pretty.str_of o Sign.pretty_sort (Thm.theory_of_thm thm);
   380     val thm' = Thm.strip_shyps thm;
   381     val xshyps = Thm.extra_shyps thm';
   382   in
   383     if null xshyps then ()
   384     else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps));
   385     thm'
   386   end;
   387 
   388 (*Generalization over a list of variables, IGNORING bad ones*)
   389 fun forall_intr_list [] th = th
   390   | forall_intr_list (y::ys) th =
   391         let val gth = forall_intr_list ys th
   392         in  forall_intr y gth   handle THM _ =>  gth  end;
   393 
   394 (*Generalization over all suitable Free variables*)
   395 fun forall_intr_frees th =
   396     let val {prop,thy,...} = rep_thm th
   397     in  forall_intr_list
   398          (map (cterm_of thy) (sort Term.term_ord (term_frees prop)))
   399          th
   400     end;
   401 
   402 (*Generalization over Vars -- canonical order*)
   403 fun forall_intr_vars th =
   404   let val cert = Thm.cterm_of (Thm.theory_of_thm th)
   405   in forall_intr_list (map (cert o Var) (vars_of th)) th end;
   406 
   407 val forall_elim_var = PureThy.forall_elim_var;
   408 val forall_elim_vars = PureThy.forall_elim_vars;
   409 
   410 fun outer_params t =
   411   let
   412     val vs = Term.strip_all_vars t;
   413     val xs = Term.variantlist (map (perhaps (try Syntax.dest_skolem) o #1) vs, []);
   414   in xs ~~ map #2 vs end;
   415 
   416 (*generalize outermost parameters*)
   417 fun gen_all th =
   418   let
   419     val {thy, prop, maxidx, ...} = Thm.rep_thm th;
   420     val cert = Thm.cterm_of thy;
   421     fun elim (x, T) = Thm.forall_elim (cert (Var ((x, maxidx + 1), T)));
   422   in fold elim (outer_params prop) th end;
   423 
   424 (*lift vars wrt. outermost goal parameters
   425   -- reverses the effect of gen_all modulo higher-order unification*)
   426 fun lift_all goal th =
   427   let
   428     val thy = Theory.merge (Thm.theory_of_cterm goal, Thm.theory_of_thm th);
   429     val cert = Thm.cterm_of thy;
   430     val {maxidx, ...} = Thm.rep_thm th;
   431     val ps = outer_params (Thm.term_of goal)
   432       |> map (fn (x, T) => Var ((x, maxidx + 1), Logic.incr_tvar (maxidx + 1) T));
   433     val Ts = map Term.fastype_of ps;
   434     val inst = vars_of th |> map (fn (xi, T) =>
   435       (cert (Var (xi, T)), cert (Term.list_comb (Var (xi, Ts ---> T), ps))));
   436   in
   437     th |> Thm.instantiate ([], inst)
   438     |> fold_rev (Thm.forall_intr o cert) ps
   439   end;
   440 
   441 
   442 (*specialization over a list of cterms*)
   443 val forall_elim_list = fold forall_elim;
   444 
   445 (*maps A1,...,An |- B  to  [| A1;...;An |] ==> B*)
   446 val implies_intr_list = fold_rev implies_intr;
   447 
   448 (*maps [| A1;...;An |] ==> B and [A1,...,An]  to  B*)
   449 fun implies_elim_list impth ths = Library.foldl (uncurry implies_elim) (impth,ths);
   450 
   451 (*Reset Var indexes to zero, renaming to preserve distinctness*)
   452 fun zero_var_indexes th =
   453   let
   454     val thy = Thm.theory_of_thm th;
   455     val certT = Thm.ctyp_of thy and cert = Thm.cterm_of thy;
   456     val (instT, inst) = Term.zero_var_indexes_inst (Thm.full_prop_of th);
   457     val cinstT = map (fn (v, T) => (certT (TVar v), certT T)) instT;
   458     val cinst = map (fn (v, t) => (cert (Var v), cert t)) inst;
   459   in Thm.adjust_maxidx_thm (Thm.instantiate (cinstT, cinst) th) end;
   460 
   461 
   462 (** Standard form of object-rule: no hypotheses, flexflex constraints,
   463     Frees, or outer quantifiers; all generality expressed by Vars of index 0.**)
   464 
   465 (*Discharge all hypotheses.*)
   466 fun implies_intr_hyps th =
   467   fold Thm.implies_intr (#hyps (Thm.crep_thm th)) th;
   468 
   469 (*Squash a theorem's flexflex constraints provided it can be done uniquely.
   470   This step can lose information.*)
   471 fun flexflex_unique th =
   472   if null (tpairs_of th) then th else
   473     case Seq.chop (2, flexflex_rule th) of
   474       ([th],_) => th
   475     | ([],_)   => raise THM("flexflex_unique: impossible constraints", 0, [th])
   476     |      _   => raise THM("flexflex_unique: multiple unifiers", 0, [th]);
   477 
   478 fun close_derivation thm =
   479   if Thm.get_name_tags thm = ("", []) then Thm.name_thm ("", thm)
   480   else thm;
   481 
   482 val standard' =
   483   implies_intr_hyps
   484   #> forall_intr_frees
   485   #> `(#maxidx o Thm.rep_thm)
   486   #-> (fn maxidx =>
   487     forall_elim_vars (maxidx + 1)
   488     #> strip_shyps_warning
   489     #> zero_var_indexes
   490     #> Thm.varifyT
   491     #> Thm.compress);
   492 
   493 val standard =
   494   flexflex_unique
   495   #> standard'
   496   #> close_derivation;
   497 
   498 val local_standard =
   499   strip_shyps
   500   #> zero_var_indexes
   501   #> Thm.compress
   502   #> close_derivation;
   503 
   504 
   505 (*Convert all Vars in a theorem to Frees.  Also return a function for
   506   reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
   507   Similar code in type/freeze_thaw*)
   508 
   509 fun freeze_thaw_robust th =
   510  let val fth = freezeT th
   511      val {prop, tpairs, thy, ...} = rep_thm fth
   512  in
   513    case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
   514        [] => (fth, fn i => fn x => x)   (*No vars: nothing to do!*)
   515      | vars =>
   516          let fun newName (Var(ix,_), pairs) =
   517                    let val v = gensym (string_of_indexname ix)
   518                    in  ((ix,v)::pairs)  end;
   519              val alist = foldr newName [] vars
   520              fun mk_inst (Var(v,T)) =
   521                  (cterm_of thy (Var(v,T)),
   522                   cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
   523              val insts = map mk_inst vars
   524              fun thaw i th' = (*i is non-negative increment for Var indexes*)
   525                  th' |> forall_intr_list (map #2 insts)
   526                      |> forall_elim_list (map (Thm.cterm_incr_indexes i o #1) insts)
   527          in  (Thm.instantiate ([],insts) fth, thaw)  end
   528  end;
   529 
   530 (*Basic version of the function above. No option to rename Vars apart in thaw.
   531   The Frees created from Vars have nice names.*)
   532 fun freeze_thaw th =
   533  let val fth = freezeT th
   534      val {prop, tpairs, thy, ...} = rep_thm fth
   535  in
   536    case foldr add_term_vars [] (prop :: Thm.terms_of_tpairs tpairs) of
   537        [] => (fth, fn x => x)
   538      | vars =>
   539          let fun newName (Var(ix,_), (pairs,used)) =
   540                    let val v = variant used (string_of_indexname ix)
   541                    in  ((ix,v)::pairs, v::used)  end;
   542              val (alist, _) = foldr newName ([], Library.foldr add_term_names
   543                (prop :: Thm.terms_of_tpairs tpairs, [])) vars
   544              fun mk_inst (Var(v,T)) =
   545                  (cterm_of thy (Var(v,T)),
   546                   cterm_of thy (Free(((the o AList.lookup (op =) alist) v), T)))
   547              val insts = map mk_inst vars
   548              fun thaw th' =
   549                  th' |> forall_intr_list (map #2 insts)
   550                      |> forall_elim_list (map #1 insts)
   551          in  (Thm.instantiate ([],insts) fth, thaw)  end
   552  end;
   553 
   554 (*Rotates a rule's premises to the left by k*)
   555 val rotate_prems = permute_prems 0;
   556 
   557 (* permute prems, where the i-th position in the argument list (counting from 0)
   558    gives the position within the original thm to be transferred to position i.
   559    Any remaining trailing positions are left unchanged. *)
   560 val rearrange_prems = let
   561   fun rearr new []      thm = thm
   562   |   rearr new (p::ps) thm = rearr (new+1)
   563      (map (fn q => if new<=q andalso q<p then q+1 else q) ps)
   564      (permute_prems (new+1) (new-p) (permute_prems new (p-new) thm))
   565   in rearr 0 end;
   566 
   567 (*Assume a new formula, read following the same conventions as axioms.
   568   Generalizes over Free variables,
   569   creates the assumption, and then strips quantifiers.
   570   Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
   571              [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
   572 fun assume_ax thy sP =
   573   let val prop = Logic.close_form (term_of (read_cterm thy (sP, propT)))
   574   in forall_elim_vars 0 (Thm.assume (cterm_of thy prop)) end;
   575 
   576 (*Resolution: exactly one resolvent must be produced.*)
   577 fun tha RSN (i,thb) =
   578   case Seq.chop (2, biresolution false [(false,tha)] i thb) of
   579       ([th],_) => th
   580     | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
   581     |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
   582 
   583 (*resolution: P==>Q, Q==>R gives P==>R. *)
   584 fun tha RS thb = tha RSN (1,thb);
   585 
   586 (*For joining lists of rules*)
   587 fun thas RLN (i,thbs) =
   588   let val resolve = biresolution false (map (pair false) thas) i
   589       fun resb thb = Seq.list_of (resolve thb) handle THM _ => []
   590   in  List.concat (map resb thbs)  end;
   591 
   592 fun thas RL thbs = thas RLN (1,thbs);
   593 
   594 (*Resolve a list of rules against bottom_rl from right to left;
   595   makes proof trees*)
   596 fun rls MRS bottom_rl =
   597   let fun rs_aux i [] = bottom_rl
   598         | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
   599   in  rs_aux 1 rls  end;
   600 
   601 (*As above, but for rule lists*)
   602 fun rlss MRL bottom_rls =
   603   let fun rs_aux i [] = bottom_rls
   604         | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
   605   in  rs_aux 1 rlss  end;
   606 
   607 (*A version of MRS with more appropriate argument order*)
   608 fun bottom_rl OF rls = rls MRS bottom_rl;
   609 
   610 (*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
   611   with no lifting or renaming!  Q may contain ==> or meta-quants
   612   ALWAYS deletes premise i *)
   613 fun compose(tha,i,thb) =
   614     Seq.list_of (bicompose false (false,tha,0) i thb);
   615 
   616 fun compose_single (tha,i,thb) =
   617   (case compose (tha,i,thb) of
   618     [th] => th
   619   | _ => raise THM ("compose: unique result expected", i, [tha,thb]));
   620 
   621 (*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
   622 fun tha COMP thb =
   623     case compose(tha,1,thb) of
   624         [th] => th
   625       | _ =>   raise THM("COMP", 1, [tha,thb]);
   626 
   627 
   628 (** theorem equality **)
   629 
   630 (*True if the two theorems have the same theory.*)
   631 val eq_thm_thy = eq_thy o pairself Thm.theory_of_thm;
   632 
   633 (*True if the two theorems have the same prop field, ignoring hyps, der, etc.*)
   634 val eq_thm_prop = op aconv o pairself Thm.full_prop_of;
   635 
   636 (*Useful "distance" function for BEST_FIRST*)
   637 val size_of_thm = size_of_term o Thm.full_prop_of;
   638 
   639 (*maintain lists of theorems --- preserving canonical order*)
   640 fun del_rules rs rules = Library.gen_rems eq_thm_prop (rules, rs);
   641 fun add_rules rs rules = rs @ del_rules rs rules;
   642 val del_rule = del_rules o single;
   643 val add_rule = add_rules o single;
   644 fun merge_rules (rules1, rules2) = gen_merge_lists' eq_thm_prop rules1 rules2;
   645 
   646 (*weak_eq_thm: ignores variable renaming and (some) type variable renaming*)
   647 val weak_eq_thm = Thm.eq_thm o pairself (forall_intr_vars o freezeT);
   648 
   649 
   650 (*** Meta-Rewriting Rules ***)
   651 
   652 fun read_prop s = read_cterm ProtoPure.thy (s, propT);
   653 
   654 fun store_thm name thm = hd (PureThy.smart_store_thms (name, [thm]));
   655 fun store_standard_thm name thm = store_thm name (standard thm);
   656 fun store_thm_open name thm = hd (PureThy.smart_store_thms_open (name, [thm]));
   657 fun store_standard_thm_open name thm = store_thm_open name (standard' thm);
   658 
   659 val reflexive_thm =
   660   let val cx = cterm_of ProtoPure.thy (Var(("x",0),TVar(("'a",0),[])))
   661   in store_standard_thm_open "reflexive" (Thm.reflexive cx) end;
   662 
   663 val symmetric_thm =
   664   let val xy = read_prop "x == y"
   665   in store_standard_thm_open "symmetric" (Thm.implies_intr xy (Thm.symmetric (Thm.assume xy))) end;
   666 
   667 val transitive_thm =
   668   let val xy = read_prop "x == y"
   669       val yz = read_prop "y == z"
   670       val xythm = Thm.assume xy and yzthm = Thm.assume yz
   671   in store_standard_thm_open "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
   672 
   673 fun symmetric_fun thm = thm RS symmetric_thm;
   674 
   675 fun extensional eq =
   676   let val eq' =
   677     abstract_rule "x" (snd (Thm.dest_comb (fst (dest_equals (cprop_of eq))))) eq
   678   in equal_elim (eta_conversion (cprop_of eq')) eq' end;
   679 
   680 val imp_cong =
   681   let
   682     val ABC = read_prop "PROP A ==> PROP B == PROP C"
   683     val AB = read_prop "PROP A ==> PROP B"
   684     val AC = read_prop "PROP A ==> PROP C"
   685     val A = read_prop "PROP A"
   686   in
   687     store_standard_thm_open "imp_cong" (implies_intr ABC (equal_intr
   688       (implies_intr AB (implies_intr A
   689         (equal_elim (implies_elim (assume ABC) (assume A))
   690           (implies_elim (assume AB) (assume A)))))
   691       (implies_intr AC (implies_intr A
   692         (equal_elim (symmetric (implies_elim (assume ABC) (assume A)))
   693           (implies_elim (assume AC) (assume A)))))))
   694   end;
   695 
   696 val swap_prems_eq =
   697   let
   698     val ABC = read_prop "PROP A ==> PROP B ==> PROP C"
   699     val BAC = read_prop "PROP B ==> PROP A ==> PROP C"
   700     val A = read_prop "PROP A"
   701     val B = read_prop "PROP B"
   702   in
   703     store_standard_thm_open "swap_prems_eq" (equal_intr
   704       (implies_intr ABC (implies_intr B (implies_intr A
   705         (implies_elim (implies_elim (assume ABC) (assume A)) (assume B)))))
   706       (implies_intr BAC (implies_intr A (implies_intr B
   707         (implies_elim (implies_elim (assume BAC) (assume B)) (assume A))))))
   708   end;
   709 
   710 val imp_cong_rule = combination o combination (reflexive implies);
   711 
   712 local
   713   val dest_eq = dest_equals o cprop_of
   714   val rhs_of = snd o dest_eq
   715 in
   716 fun beta_eta_conversion t =
   717   let val thm = beta_conversion true t
   718   in transitive thm (eta_conversion (rhs_of thm)) end
   719 end;
   720 
   721 fun eta_long_conversion ct = transitive (beta_eta_conversion ct)
   722   (symmetric (beta_eta_conversion (cterm_fun (Pattern.eta_long []) ct)));
   723 
   724 val abs_def =
   725   let
   726     fun contract_lhs th =
   727       Thm.transitive (Thm.symmetric (beta_eta_conversion (fst (dest_equals (cprop_of th))))) th;
   728     fun abstract cx th = Thm.abstract_rule
   729         (case Thm.term_of cx of Var ((x, _), _) => x | Free (x, _) => x | _ => "x") cx th
   730       handle THM _ => raise THM ("Malformed definitional equation", 0, [th]);
   731   in
   732     contract_lhs
   733     #> `(snd o strip_comb o fst o dest_equals o cprop_of)
   734     #-> fold_rev abstract
   735     #> contract_lhs
   736   end;
   737 
   738 (*rewrite B in !!x1 ... xn. B*)
   739 fun forall_conv 0 cv ct = cv ct
   740   | forall_conv n cv ct =
   741       (case try Thm.dest_comb ct of
   742         NONE => cv ct
   743       | SOME (A, B) =>
   744           (case (term_of A, term_of B) of
   745             (Const ("all", _), Abs (x, _, _)) =>
   746               let val (v, B') = Thm.dest_abs (SOME (gensym "all_")) B in
   747                 Thm.combination (Thm.reflexive A)
   748                   (Thm.abstract_rule x v (forall_conv (n - 1) cv B'))
   749               end
   750           | _ => cv ct));
   751 
   752 (*rewrite B in A1 ==> ... ==> An ==> B*)
   753 fun concl_conv 0 cv ct = cv ct
   754   | concl_conv n cv ct =
   755       (case try dest_implies ct of
   756         NONE => cv ct
   757       | SOME (A, B) => imp_cong_rule (reflexive A) (concl_conv (n - 1) cv B));
   758 
   759 (*rewrite the A's in A1 ==> ... ==> An ==> B*)
   760 fun prems_conv 0 _ = reflexive
   761   | prems_conv n cv =
   762       let
   763         fun conv i ct =
   764           if i = n + 1 then reflexive ct
   765           else
   766             (case try dest_implies ct of
   767               NONE => reflexive ct
   768             | SOME (A, B) => imp_cong_rule (cv i A) (conv (i + 1) B));
   769   in conv 1 end;
   770 
   771 (*rewrite the A's in A1 && ... && An*)
   772 fun conjunction_conv 0 _ = reflexive
   773   | conjunction_conv n cv =
   774       let
   775         fun conv i ct =
   776           if i <> n andalso can Logic.dest_conjunction (term_of ct) then
   777             forall_conv 1
   778               (prems_conv 1 (K (prems_conv 2 (fn 1 => cv i | 2 => conv (i + 1))))) ct
   779           else cv i ct;
   780       in conv 1 end;
   781 
   782 
   783 fun goals_conv pred cv = prems_conv ~1 (fn i => if pred i then cv else reflexive);
   784 fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
   785 
   786 
   787 (*** Some useful meta-theorems ***)
   788 
   789 (*The rule V/V, obtains assumption solving for eresolve_tac*)
   790 val asm_rl = store_standard_thm_open "asm_rl" (Thm.trivial (read_prop "PROP ?psi"));
   791 val _ = store_thm "_" asm_rl;
   792 
   793 (*Meta-level cut rule: [| V==>W; V |] ==> W *)
   794 val cut_rl =
   795   store_standard_thm_open "cut_rl"
   796     (Thm.trivial (read_prop "PROP ?psi ==> PROP ?theta"));
   797 
   798 (*Generalized elim rule for one conclusion; cut_rl with reversed premises:
   799      [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
   800 val revcut_rl =
   801   let val V = read_prop "PROP V"
   802       and VW = read_prop "PROP V ==> PROP W";
   803   in
   804     store_standard_thm_open "revcut_rl"
   805       (implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V))))
   806   end;
   807 
   808 (*for deleting an unwanted assumption*)
   809 val thin_rl =
   810   let val V = read_prop "PROP V"
   811       and W = read_prop "PROP W";
   812   in store_standard_thm_open "thin_rl" (implies_intr V (implies_intr W (assume W))) end;
   813 
   814 (* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
   815 val triv_forall_equality =
   816   let val V  = read_prop "PROP V"
   817       and QV = read_prop "!!x::'a. PROP V"
   818       and x  = read_cterm ProtoPure.thy ("x", TypeInfer.logicT);
   819   in
   820     store_standard_thm_open "triv_forall_equality"
   821       (equal_intr (implies_intr QV (forall_elim x (assume QV)))
   822         (implies_intr V  (forall_intr x (assume V))))
   823   end;
   824 
   825 (* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==>
   826    (PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi)
   827    `thm COMP swap_prems_rl' swaps the first two premises of `thm'
   828 *)
   829 val swap_prems_rl =
   830   let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi";
   831       val major = assume cmajor;
   832       val cminor1 = read_prop "PROP PhiA";
   833       val minor1 = assume cminor1;
   834       val cminor2 = read_prop "PROP PhiB";
   835       val minor2 = assume cminor2;
   836   in store_standard_thm_open "swap_prems_rl"
   837        (implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1
   838          (implies_elim (implies_elim major minor1) minor2))))
   839   end;
   840 
   841 (* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |]
   842    ==> PROP ?phi == PROP ?psi
   843    Introduction rule for == as a meta-theorem.
   844 *)
   845 val equal_intr_rule =
   846   let val PQ = read_prop "PROP phi ==> PROP psi"
   847       and QP = read_prop "PROP psi ==> PROP phi"
   848   in
   849     store_standard_thm_open "equal_intr_rule"
   850       (implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP))))
   851   end;
   852 
   853 (* [| PROP ?phi == PROP ?psi; PROP ?phi |] ==> PROP ?psi *)
   854 val equal_elim_rule1 =
   855   let val eq = read_prop "PROP phi == PROP psi"
   856       and P = read_prop "PROP phi"
   857   in store_standard_thm_open "equal_elim_rule1"
   858     (Thm.equal_elim (assume eq) (assume P) |> implies_intr_list [eq, P])
   859   end;
   860 
   861 (* "[| PROP ?phi; PROP ?phi; PROP ?psi |] ==> PROP ?psi" *)
   862 
   863 val remdups_rl =
   864   let val P = read_prop "PROP phi" and Q = read_prop "PROP psi";
   865   in store_standard_thm_open "remdups_rl" (implies_intr_list [P, P, Q] (Thm.assume Q)) end;
   866 
   867 
   868 (*(PROP ?phi ==> (!!x. PROP ?psi(x))) == (!!x. PROP ?phi ==> PROP ?psi(x))
   869   Rewrite rule for HHF normalization.*)
   870 
   871 val norm_hhf_eq =
   872   let
   873     val cert = Thm.cterm_of ProtoPure.thy;
   874     val aT = TFree ("'a", []);
   875     val all = Term.all aT;
   876     val x = Free ("x", aT);
   877     val phi = Free ("phi", propT);
   878     val psi = Free ("psi", aT --> propT);
   879 
   880     val cx = cert x;
   881     val cphi = cert phi;
   882     val lhs = cert (Logic.mk_implies (phi, all $ Abs ("x", aT, psi $ Bound 0)));
   883     val rhs = cert (all $ Abs ("x", aT, Logic.mk_implies (phi, psi $ Bound 0)));
   884   in
   885     Thm.equal_intr
   886       (Thm.implies_elim (Thm.assume lhs) (Thm.assume cphi)
   887         |> Thm.forall_elim cx
   888         |> Thm.implies_intr cphi
   889         |> Thm.forall_intr cx
   890         |> Thm.implies_intr lhs)
   891       (Thm.implies_elim
   892           (Thm.assume rhs |> Thm.forall_elim cx) (Thm.assume cphi)
   893         |> Thm.forall_intr cx
   894         |> Thm.implies_intr cphi
   895         |> Thm.implies_intr rhs)
   896     |> store_standard_thm_open "norm_hhf_eq"
   897   end;
   898 
   899 val norm_hhf_prop = Logic.dest_equals (Thm.prop_of norm_hhf_eq);
   900 
   901 fun is_norm_hhf tm =
   902   let
   903     fun is_norm (Const ("==>", _) $ _ $ (Const ("all", _) $ _)) = false
   904       | is_norm (t $ u) = is_norm t andalso is_norm u
   905       | is_norm (Abs (_, _, t)) = is_norm t
   906       | is_norm _ = true;
   907   in is_norm (Pattern.beta_eta_contract tm) end;
   908 
   909 fun norm_hhf thy t =
   910   if is_norm_hhf t then t
   911   else Pattern.rewrite_term thy [norm_hhf_prop] [] t;
   912 
   913 
   914 
   915 (*** Instantiate theorem th, reading instantiations in theory thy ****)
   916 
   917 (*Version that normalizes the result: Thm.instantiate no longer does that*)
   918 fun instantiate instpair th = Thm.instantiate instpair th  COMP   asm_rl;
   919 
   920 fun read_instantiate_sg' thy sinsts th =
   921     let val ts = types_sorts th;
   922         val used = add_used th [];
   923     in  instantiate (read_insts thy ts ts used sinsts) th  end;
   924 
   925 fun read_instantiate_sg thy sinsts th =
   926   read_instantiate_sg' thy (map (apfst Syntax.indexname) sinsts) th;
   927 
   928 (*Instantiate theorem th, reading instantiations under theory of th*)
   929 fun read_instantiate sinsts th =
   930     read_instantiate_sg (Thm.theory_of_thm th) sinsts th;
   931 
   932 fun read_instantiate' sinsts th =
   933     read_instantiate_sg' (Thm.theory_of_thm th) sinsts th;
   934 
   935 
   936 (*Left-to-right replacements: tpairs = [...,(vi,ti),...].
   937   Instantiates distinct Vars by terms, inferring type instantiations. *)
   938 local
   939   fun add_types ((ct,cu), (thy,tye,maxidx)) =
   940     let val {thy=thyt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct
   941         and {thy=thyu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu;
   942         val maxi = Int.max(maxidx, Int.max(maxt, maxu));
   943         val thy' = Theory.merge(thy, Theory.merge(thyt, thyu))
   944         val (tye',maxi') = Sign.typ_unify thy' (T, U) (tye, maxi)
   945           handle Type.TUNIFY => raise TYPE("Ill-typed instantiation", [T,U], [t,u])
   946     in  (thy', tye', maxi')  end;
   947 in
   948 fun cterm_instantiate ctpairs0 th =
   949   let val (thy,tye,_) = foldr add_types (Thm.theory_of_thm th, Vartab.empty, 0) ctpairs0
   950       fun instT(ct,cu) =
   951         let val inst = cterm_of thy o Envir.subst_TVars tye o term_of
   952         in (inst ct, inst cu) end
   953       fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy T)
   954   in  instantiate (map ctyp2 (Vartab.dest tye), map instT ctpairs0) th  end
   955   handle TERM _ =>
   956            raise THM("cterm_instantiate: incompatible theories",0,[th])
   957        | TYPE (msg, _, _) => raise THM(msg, 0, [th])
   958 end;
   959 
   960 
   961 (** Derived rules mainly for METAHYPS **)
   962 
   963 (*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
   964 fun equal_abs_elim ca eqth =
   965   let val {thy=thya, t=a, ...} = rep_cterm ca
   966       and combth = combination eqth (reflexive ca)
   967       val {thy,prop,...} = rep_thm eqth
   968       val (abst,absu) = Logic.dest_equals prop
   969       val cterm = cterm_of (Theory.merge (thy,thya))
   970   in  transitive (symmetric (beta_conversion false (cterm (abst$a))))
   971            (transitive combth (beta_conversion false (cterm (absu$a))))
   972   end
   973   handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
   974 
   975 (*Calling equal_abs_elim with multiple terms*)
   976 fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) th (rev cts);
   977 
   978 
   979 (** protected propositions **)
   980 
   981 local
   982   val cert = Thm.cterm_of ProtoPure.thy;
   983   val A = cert (Free ("A", propT));
   984   val prop_def = #1 (freeze_thaw ProtoPure.prop_def);
   985 in
   986   val protect = Thm.capply (cert Logic.protectC);
   987   val protectI = store_thm "protectI" (kind_rule internalK (standard
   988       (Thm.equal_elim (Thm.symmetric prop_def) (Thm.assume A))));
   989   val protectD = store_thm "protectD" (kind_rule internalK (standard
   990       (Thm.equal_elim prop_def (Thm.assume (protect A)))));
   991   val protect_cong = store_standard_thm_open "protect_cong" (Thm.reflexive (protect A));
   992 end;
   993 
   994 fun implies_intr_protected asms th =
   995   let val asms' = map protect asms in
   996     implies_elim_list
   997       (implies_intr_list asms th)
   998       (map (fn asm' => Thm.assume asm' RS protectD) asms')
   999     |> implies_intr_list asms'
  1000   end;
  1001 
  1002 
  1003 (** variations on instantiate **)
  1004 
  1005 (*shorthand for instantiating just one variable in the current theory*)
  1006 fun inst x t = read_instantiate_sg (the_context()) [(x,t)];
  1007 
  1008 
  1009 (* instantiate by left-to-right occurrence of variables *)
  1010 
  1011 fun instantiate' cTs cts thm =
  1012   let
  1013     fun err msg =
  1014       raise TYPE ("instantiate': " ^ msg,
  1015         List.mapPartial (Option.map Thm.typ_of) cTs,
  1016         List.mapPartial (Option.map Thm.term_of) cts);
  1017 
  1018     fun inst_of (v, ct) =
  1019       (Thm.cterm_of (Thm.theory_of_cterm ct) (Var v), ct)
  1020         handle TYPE (msg, _, _) => err msg;
  1021 
  1022     fun tyinst_of (v, cT) =
  1023       (Thm.ctyp_of (Thm.theory_of_ctyp cT) (TVar v), cT)
  1024         handle TYPE (msg, _, _) => err msg;
  1025 
  1026     fun zip_vars _ [] = []
  1027       | zip_vars (_ :: vs) (NONE :: opt_ts) = zip_vars vs opt_ts
  1028       | zip_vars (v :: vs) (SOME t :: opt_ts) = (v, t) :: zip_vars vs opt_ts
  1029       | zip_vars [] _ = err "more instantiations than variables in thm";
  1030 
  1031     (*instantiate types first!*)
  1032     val thm' =
  1033       if forall is_none cTs then thm
  1034       else Thm.instantiate (map tyinst_of (zip_vars (tvars_of thm) cTs), []) thm;
  1035     in
  1036       if forall is_none cts then thm'
  1037       else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm'
  1038     end;
  1039 
  1040 
  1041 
  1042 (** renaming of bound variables **)
  1043 
  1044 (* replace bound variables x_i in thm by y_i *)
  1045 (* where vs = [(x_1, y_1), ..., (x_n, y_n)]  *)
  1046 
  1047 fun rename_bvars [] thm = thm
  1048   | rename_bvars vs thm =
  1049     let
  1050       val {thy, prop, ...} = rep_thm thm;
  1051       fun ren (Abs (x, T, t)) = Abs (AList.lookup (op =) vs x |> the_default x, T, ren t)
  1052         | ren (t $ u) = ren t $ ren u
  1053         | ren t = t;
  1054     in equal_elim (reflexive (cterm_of thy (ren prop))) thm end;
  1055 
  1056 
  1057 (* renaming in left-to-right order *)
  1058 
  1059 fun rename_bvars' xs thm =
  1060   let
  1061     val {thy, prop, ...} = rep_thm thm;
  1062     fun rename [] t = ([], t)
  1063       | rename (x' :: xs) (Abs (x, T, t)) =
  1064           let val (xs', t') = rename xs t
  1065           in (xs', Abs (getOpt (x',x), T, t')) end
  1066       | rename xs (t $ u) =
  1067           let
  1068             val (xs', t') = rename xs t;
  1069             val (xs'', u') = rename xs' u
  1070           in (xs'', t' $ u') end
  1071       | rename xs t = (xs, t);
  1072   in case rename xs prop of
  1073       ([], prop') => equal_elim (reflexive (cterm_of thy prop')) thm
  1074     | _ => error "More names than abstractions in theorem"
  1075   end;
  1076 
  1077 
  1078 
  1079 (* unvarify(T) *)
  1080 
  1081 (*assume thm in standard form, i.e. no frees, 0 var indexes*)
  1082 
  1083 fun unvarifyT thm =
  1084   let
  1085     val cT = Thm.ctyp_of (Thm.theory_of_thm thm);
  1086     val tfrees = map (fn ((x, _), S) => SOME (cT (TFree (x, S)))) (tvars_of thm);
  1087   in instantiate' tfrees [] thm end;
  1088 
  1089 fun unvarify raw_thm =
  1090   let
  1091     val thm = unvarifyT raw_thm;
  1092     val ct = Thm.cterm_of (Thm.theory_of_thm thm);
  1093     val frees = map (fn ((x, _), T) => SOME (ct (Free (x, T)))) (vars_of thm);
  1094   in instantiate' [] frees thm end;
  1095 
  1096 
  1097 (* tvars_intr_list *)
  1098 
  1099 fun tvars_intr_list tfrees thm =
  1100   apfst (map (fn ((s, S), ixn) => (s, (ixn, S)))) (Thm.varifyT'
  1101     (gen_rems (op = o apfst fst) (tfrees_of thm, tfrees)) thm);
  1102 
  1103 
  1104 (* increment var indexes *)
  1105 
  1106 fun incr_indexes th = Thm.incr_indexes (#maxidx (Thm.rep_thm th) + 1);
  1107 
  1108 fun incr_indexes_wrt is cTs cts thms =
  1109   let
  1110     val maxidx =
  1111       Library.foldl Int.max (~1, is @
  1112         map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @
  1113         map (#maxidx o Thm.rep_cterm) cts @
  1114         map (#maxidx o Thm.rep_thm) thms);
  1115   in Thm.incr_indexes (maxidx + 1) end;
  1116 
  1117 
  1118 (* freeze_all *)
  1119 
  1120 (*freeze all (T)Vars; assumes thm in standard form*)
  1121 
  1122 fun freeze_all_TVars thm =
  1123   (case tvars_of thm of
  1124     [] => thm
  1125   | tvars =>
  1126       let val cert = Thm.ctyp_of (Thm.theory_of_thm thm)
  1127       in instantiate' (map (fn ((x, _), S) => SOME (cert (TFree (x, S)))) tvars) [] thm end);
  1128 
  1129 fun freeze_all_Vars thm =
  1130   (case vars_of thm of
  1131     [] => thm
  1132   | vars =>
  1133       let val cert = Thm.cterm_of (Thm.theory_of_thm thm)
  1134       in instantiate' [] (map (fn ((x, _), T) => SOME (cert (Free (x, T)))) vars) thm end);
  1135 
  1136 val freeze_all = freeze_all_Vars o freeze_all_TVars;
  1137 
  1138 
  1139 
  1140 (** multi_resolve **)
  1141 
  1142 local
  1143 
  1144 fun res th i rule =
  1145   Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
  1146 
  1147 fun multi_res _ [] rule = Seq.single rule
  1148   | multi_res i (th :: ths) rule = Seq.maps (res th i) (multi_res (i + 1) ths rule);
  1149 
  1150 in
  1151 
  1152 val multi_resolve = multi_res 1;
  1153 fun multi_resolves facts rules = Seq.maps (multi_resolve facts) (Seq.of_list rules);
  1154 
  1155 end;
  1156 
  1157 
  1158 
  1159 (** meta-level conjunction **)
  1160 
  1161 local
  1162   val A = read_prop "PROP A";
  1163   val B = read_prop "PROP B";
  1164   val C = read_prop "PROP C";
  1165   val ABC = read_prop "PROP A ==> PROP B ==> PROP C";
  1166 
  1167   val proj1 =
  1168     forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume A))
  1169     |> forall_elim_vars 0;
  1170 
  1171   val proj2 =
  1172     forall_intr_list [A, B] (implies_intr_list [A, B] (Thm.assume B))
  1173     |> forall_elim_vars 0;
  1174 
  1175   val conj_intr_rule =
  1176     forall_intr_list [A, B] (implies_intr_list [A, B]
  1177       (Thm.forall_intr C (Thm.implies_intr ABC
  1178         (implies_elim_list (Thm.assume ABC) [Thm.assume A, Thm.assume B]))))
  1179     |> forall_elim_vars 0;
  1180 in
  1181 
  1182 fun conj_intr tha thb = thb COMP (tha COMP incr_indexes_wrt [] [] [] [tha, thb] conj_intr_rule);
  1183 
  1184 fun conj_intr_list [] = asm_rl
  1185   | conj_intr_list ths = foldr1 (uncurry conj_intr) ths;
  1186 
  1187 fun conj_elim th =
  1188   let val th' = forall_elim_var (#maxidx (Thm.rep_thm th) + 1) th
  1189   in (incr_indexes th' proj1 COMP th', incr_indexes th' proj2 COMP th') end;
  1190 
  1191 (*((A && B) && C) && D && E -- flat*)
  1192 fun conj_elim_list th =
  1193   let val (th1, th2) = conj_elim th
  1194   in conj_elim_list th1 @ conj_elim_list th2 end handle THM _ => [th];
  1195 
  1196 (*(A1 && B1 && C1) && (A2 && B2 && C2 && D2) && A3 && B3 -- improper*)
  1197 fun conj_elim_precise spans =
  1198   let
  1199     fun elim 0 _ = []
  1200       | elim 1 th = [th]
  1201       | elim n th =
  1202           let val (th1, th2) = conj_elim th
  1203           in th1 :: elim (n - 1) th2 end;
  1204     fun elims (0 :: ns) ths = [] :: elims ns ths
  1205       | elims (n :: ns) (th :: ths) = elim n th :: elims ns ths
  1206       | elims _ _ = [];
  1207   in elims spans o elim (length (filter_out (equal 0) spans)) end;
  1208 
  1209 val conj_intr_thm = store_standard_thm_open "conjunctionI"
  1210   (implies_intr_list [A, B] (conj_intr (Thm.assume A) (Thm.assume B)));
  1211 
  1212 end;
  1213 
  1214 fun conj_curry th =
  1215   let
  1216     val {thy, maxidx, ...} = Thm.rep_thm th;
  1217     val n = Thm.nprems_of th;
  1218   in
  1219     if n < 2 then th
  1220     else
  1221       let
  1222         val cert = Thm.cterm_of thy;
  1223         val As = map (fn i => Free ("A" ^ string_of_int i, propT)) (1 upto n);
  1224         val B = Free ("B", propT);
  1225         val C = cert (Logic.mk_conjunction_list As);
  1226         val D = cert (Logic.list_implies (As, B));
  1227         val rule =
  1228           implies_elim_list (Thm.assume D) (conj_elim_list (Thm.assume C))
  1229           |> implies_intr_list [D, C]
  1230           |> forall_intr_frees
  1231           |> forall_elim_vars (maxidx + 1)
  1232       in Thm.adjust_maxidx_thm (th COMP rule) end
  1233   end;
  1234 
  1235 end;
  1236 
  1237 structure BasicDrule: BASIC_DRULE = Drule;
  1238 open BasicDrule;