src/Pure/meta_simplifier.ML
author wenzelm
Thu Dec 22 00:29:00 2005 +0100 (2005-12-22)
changeset 18470 19be817913c4
parent 18208 dbdcf366db53
child 18573 0ee7eab8c845
permissions -rw-r--r--
renamed imp_cong' to imp_cong_rule;
     1 (*  Title:      Pure/meta_simplifier.ML
     2     ID:         $Id$
     3     Author:     Tobias Nipkow and Stefan Berghofer
     4 
     5 Meta-level Simplification.
     6 *)
     7 
     8 infix 4
     9   addsimps delsimps addeqcongs deleqcongs addcongs delcongs addsimprocs delsimprocs
    10   setmksimps setmkcong setmksym setmkeqTrue settermless setsubgoaler
    11   setloop' setloop addloop addloop' delloop setSSolver addSSolver setSolver addSolver;
    12 
    13 signature BASIC_META_SIMPLIFIER =
    14 sig
    15   val debug_simp: bool ref
    16   val trace_simp: bool ref
    17   val simp_depth_limit: int ref
    18   val trace_simp_depth_limit: int ref
    19   type rrule
    20   val eq_rrule: rrule * rrule -> bool
    21   type cong
    22   type simpset
    23   type proc
    24   type solver
    25   val mk_solver': string -> (simpset -> int -> tactic) -> solver
    26   val mk_solver: string -> (thm list -> int -> tactic) -> solver
    27   val rep_ss: simpset ->
    28    {rules: rrule Net.net,
    29     prems: thm list,
    30     bounds: int * ((string * typ) * string) list,
    31     context: Context.proof option} *
    32    {congs: (string * cong) list * string list,
    33     procs: proc Net.net,
    34     mk_rews:
    35      {mk: thm -> thm list,
    36       mk_cong: thm -> thm,
    37       mk_sym: thm -> thm option,
    38       mk_eq_True: thm -> thm option,
    39       reorient: theory -> term list -> term -> term -> bool},
    40     termless: term * term -> bool,
    41     subgoal_tac: simpset -> int -> tactic,
    42     loop_tacs: (string * (simpset -> int -> tactic)) list,
    43     solvers: solver list * solver list}
    44   val print_ss: simpset -> unit
    45   val empty_ss: simpset
    46   val merge_ss: simpset * simpset -> simpset
    47   type simproc
    48   val mk_simproc: string -> cterm list ->
    49     (theory -> simpset -> term -> thm option) -> simproc
    50   val add_prems: thm list -> simpset -> simpset
    51   val prems_of_ss: simpset -> thm list
    52   val addsimps: simpset * thm list -> simpset
    53   val delsimps: simpset * thm list -> simpset
    54   val addeqcongs: simpset * thm list -> simpset
    55   val deleqcongs: simpset * thm list -> simpset
    56   val addcongs: simpset * thm list -> simpset
    57   val delcongs: simpset * thm list -> simpset
    58   val addsimprocs: simpset * simproc list -> simpset
    59   val delsimprocs: simpset * simproc list -> simpset
    60   val setmksimps: simpset * (thm -> thm list) -> simpset
    61   val setmkcong: simpset * (thm -> thm) -> simpset
    62   val setmksym: simpset * (thm -> thm option) -> simpset
    63   val setmkeqTrue: simpset * (thm -> thm option) -> simpset
    64   val settermless: simpset * (term * term -> bool) -> simpset
    65   val setsubgoaler: simpset * (simpset -> int -> tactic) -> simpset
    66   val setloop': simpset * (simpset -> int -> tactic) -> simpset
    67   val setloop: simpset * (int -> tactic) -> simpset
    68   val addloop': simpset * (string * (simpset -> int -> tactic)) -> simpset
    69   val addloop: simpset * (string * (int -> tactic)) -> simpset
    70   val delloop: simpset * string -> simpset
    71   val setSSolver: simpset * solver -> simpset
    72   val addSSolver: simpset * solver -> simpset
    73   val setSolver: simpset * solver -> simpset
    74   val addSolver: simpset * solver -> simpset
    75 end;
    76 
    77 signature META_SIMPLIFIER =
    78 sig
    79   include BASIC_META_SIMPLIFIER
    80   exception SIMPLIFIER of string * thm
    81   val solver: simpset -> solver -> int -> tactic
    82   val clear_ss: simpset -> simpset
    83   exception SIMPROC_FAIL of string * exn
    84   val simproc_i: theory -> string -> term list
    85     -> (theory -> simpset -> term -> thm option) -> simproc
    86   val simproc: theory -> string -> string list
    87     -> (theory -> simpset -> term -> thm option) -> simproc
    88   val inherit_context: simpset -> simpset -> simpset
    89   val the_context: simpset -> Context.proof
    90   val context: Context.proof -> simpset -> simpset
    91   val theory_context: theory  -> simpset -> simpset
    92   val debug_bounds: bool ref
    93   val set_reorient: (theory -> term list -> term -> term -> bool) -> simpset -> simpset
    94   val set_solvers: solver list -> simpset -> simpset
    95   val rewrite_cterm: bool * bool * bool ->
    96     (simpset -> thm -> thm option) -> simpset -> cterm -> thm
    97   val rewrite_aux: (simpset -> thm -> thm option) -> bool -> thm list -> cterm -> thm
    98   val simplify_aux: (simpset -> thm -> thm option) -> bool -> thm list -> thm -> thm
    99   val rewrite_term: theory -> thm list -> (term -> term option) list -> term -> term
   100   val rewrite_thm: bool * bool * bool ->
   101     (simpset -> thm -> thm option) -> simpset -> thm -> thm
   102   val rewrite_goals_rule_aux: (simpset -> thm -> thm option) -> thm list -> thm -> thm
   103   val rewrite_goal_rule: bool * bool * bool ->
   104     (simpset -> thm -> thm option) -> simpset -> int -> thm -> thm
   105 end;
   106 
   107 structure MetaSimplifier: META_SIMPLIFIER =
   108 struct
   109 
   110 
   111 (** datatype simpset **)
   112 
   113 (* rewrite rules *)
   114 
   115 type rrule = {thm: thm, name: string, lhs: term, elhs: cterm, fo: bool, perm: bool};
   116 
   117 (*thm: the rewrite rule;
   118   name: name of theorem from which rewrite rule was extracted;
   119   lhs: the left-hand side;
   120   elhs: the etac-contracted lhs;
   121   fo: use first-order matching;
   122   perm: the rewrite rule is permutative;
   123 
   124 Remarks:
   125   - elhs is used for matching,
   126     lhs only for preservation of bound variable names;
   127   - fo is set iff
   128     either elhs is first-order (no Var is applied),
   129       in which case fo-matching is complete,
   130     or elhs is not a pattern,
   131       in which case there is nothing better to do;*)
   132 
   133 fun eq_rrule ({thm = thm1, ...}: rrule, {thm = thm2, ...}: rrule) =
   134   Drule.eq_thm_prop (thm1, thm2);
   135 
   136 
   137 (* congruences *)
   138 
   139 type cong = {thm: thm, lhs: cterm};
   140 
   141 fun eq_cong ({thm = thm1, ...}: cong, {thm = thm2, ...}: cong) =
   142   Drule.eq_thm_prop (thm1, thm2);
   143 
   144 
   145 (* simplification sets, procedures, and solvers *)
   146 
   147 (*A simpset contains data required during conversion:
   148     rules: discrimination net of rewrite rules;
   149     prems: current premises;
   150     bounds: maximal index of bound variables already used
   151       (for generating new names when rewriting under lambda abstractions);
   152     congs: association list of congruence rules and
   153            a list of `weak' congruence constants.
   154            A congruence is `weak' if it avoids normalization of some argument.
   155     procs: discrimination net of simplification procedures
   156       (functions that prove rewrite rules on the fly);
   157     mk_rews:
   158       mk: turn simplification thms into rewrite rules;
   159       mk_cong: prepare congruence rules;
   160       mk_sym: turn == around;
   161       mk_eq_True: turn P into P == True;
   162     termless: relation for ordered rewriting;*)
   163 
   164 type mk_rews =
   165  {mk: thm -> thm list,
   166   mk_cong: thm -> thm,
   167   mk_sym: thm -> thm option,
   168   mk_eq_True: thm -> thm option,
   169   reorient: theory -> term list -> term -> term -> bool};
   170 
   171 datatype simpset =
   172   Simpset of
   173    {rules: rrule Net.net,
   174     prems: thm list,
   175     bounds: int * ((string * typ) * string) list,
   176     context: Context.proof option} *
   177    {congs: (string * cong) list * string list,
   178     procs: proc Net.net,
   179     mk_rews: mk_rews,
   180     termless: term * term -> bool,
   181     subgoal_tac: simpset -> int -> tactic,
   182     loop_tacs: (string * (simpset -> int -> tactic)) list,
   183     solvers: solver list * solver list}
   184 and proc =
   185   Proc of
   186    {name: string,
   187     lhs: cterm,
   188     proc: theory -> simpset -> term -> thm option,
   189     id: stamp}
   190 and solver =
   191   Solver of
   192    {name: string,
   193     solver: simpset -> int -> tactic,
   194     id: stamp};
   195 
   196 
   197 fun rep_ss (Simpset args) = args;
   198 
   199 fun make_ss1 (rules, prems, bounds, context) =
   200   {rules = rules, prems = prems, bounds = bounds, context = context};
   201 
   202 fun map_ss1 f {rules, prems, bounds, context} =
   203   make_ss1 (f (rules, prems, bounds, context));
   204 
   205 fun make_ss2 (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =
   206   {congs = congs, procs = procs, mk_rews = mk_rews, termless = termless,
   207     subgoal_tac = subgoal_tac, loop_tacs = loop_tacs, solvers = solvers};
   208 
   209 fun map_ss2 f {congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers} =
   210   make_ss2 (f (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   211 
   212 fun make_simpset (args1, args2) = Simpset (make_ss1 args1, make_ss2 args2);
   213 
   214 fun map_simpset f (Simpset ({rules, prems, bounds, context},
   215     {congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers})) =
   216   make_simpset (f ((rules, prems, bounds, context),
   217     (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers)));
   218 
   219 fun map_simpset1 f (Simpset (r1, r2)) = Simpset (map_ss1 f r1, r2);
   220 fun map_simpset2 f (Simpset (r1, r2)) = Simpset (r1, map_ss2 f r2);
   221 
   222 fun prems_of_ss (Simpset ({prems, ...}, _)) = prems;
   223 
   224 
   225 fun eq_proc (Proc {id = id1, ...}, Proc {id = id2, ...}) = (id1 = id2);
   226 
   227 fun mk_solver' name solver = Solver {name = name, solver = solver, id = stamp ()};
   228 fun mk_solver name solver = mk_solver' name (solver o prems_of_ss);
   229 
   230 fun solver_name (Solver {name, ...}) = name;
   231 fun solver ss (Solver {solver = tac, ...}) = tac ss;
   232 fun eq_solver (Solver {id = id1, ...}, Solver {id = id2, ...}) = (id1 = id2);
   233 val merge_solvers = gen_merge_lists eq_solver;
   234 
   235 
   236 (* diagnostics *)
   237 
   238 exception SIMPLIFIER of string * thm;
   239 
   240 val debug_simp = ref false;
   241 val trace_simp = ref false;
   242 val simp_depth = ref 0;
   243 val simp_depth_limit = ref 100;
   244 val trace_simp_depth_limit = ref 100;
   245 
   246 local
   247 
   248 fun println a =
   249   if ! simp_depth > ! trace_simp_depth_limit then ()
   250   else tracing (enclose "[" "]" (string_of_int (! simp_depth)) ^ a);
   251 
   252 fun prnt warn a = if warn then warning a else println a;
   253 
   254 fun show_bounds (Simpset ({bounds = (_, bs), ...}, _)) t =
   255   let
   256     val used = Term.add_term_names (t, []);
   257     val xs = rev (Term.variantlist (rev (map #2 bs), used));
   258     fun subst (((b, T), _), x') = (Free (b, T), Syntax.mark_boundT (x', T));
   259   in Term.subst_atomic (ListPair.map subst (bs, xs)) t end;
   260 
   261 in
   262 
   263 fun print_term warn a ss thy t = prnt warn (a ^ "\n" ^
   264   Sign.string_of_term thy (if ! debug_simp then t else show_bounds ss t));
   265 
   266 fun debug warn a = if ! debug_simp then prnt warn a else ();
   267 fun trace warn a = if ! trace_simp then prnt warn a else ();
   268 
   269 fun debug_term warn a ss thy t = if ! debug_simp then print_term warn a ss thy t else ();
   270 fun trace_term warn a ss thy t = if ! trace_simp then print_term warn a ss thy t else ();
   271 
   272 fun trace_cterm warn a ss ct =
   273   if ! trace_simp then print_term warn a ss (Thm.theory_of_cterm ct) (Thm.term_of ct) else ();
   274 
   275 fun trace_thm a ss th =
   276   if ! trace_simp then print_term false a ss (Thm.theory_of_thm th) (Thm.full_prop_of th) else ();
   277 
   278 fun trace_named_thm a ss (th, name) =
   279   if ! trace_simp then
   280     print_term false (if name = "" then a else a ^ " " ^ quote name ^ ":") ss
   281       (Thm.theory_of_thm th) (Thm.full_prop_of th)
   282   else ();
   283 
   284 fun warn_thm a ss th = print_term true a ss (Thm.theory_of_thm th) (Thm.full_prop_of th);
   285 
   286 end;
   287 
   288 
   289 (* print simpsets *)
   290 
   291 fun print_ss ss =
   292   let
   293     val pretty_thms = map Display.pretty_thm;
   294 
   295     fun pretty_cong (name, th) =
   296       Pretty.block [Pretty.str (name ^ ":"), Pretty.brk 1, Display.pretty_thm th];
   297     fun pretty_proc (name, lhss) =
   298       Pretty.big_list (name ^ ":") (map Display.pretty_cterm lhss);
   299 
   300     val Simpset ({rules, ...}, {congs, procs, loop_tacs, solvers, ...}) = ss;
   301     val smps = map #thm (Net.entries rules);
   302     val cngs = map (fn (name, {thm, ...}) => (name, thm)) (#1 congs);
   303     val prcs = Net.entries procs |>
   304       map (fn Proc {name, lhs, id, ...} => ((name, lhs), id))
   305       |> partition_eq (eq_snd (op =))
   306       |> map (fn ps => (fst (fst (hd ps)), map (snd o fst) ps))
   307       |> Library.sort_wrt fst;
   308   in
   309     [Pretty.big_list "simplification rules:" (pretty_thms smps),
   310       Pretty.big_list "simplification procedures:" (map pretty_proc prcs),
   311       Pretty.big_list "congruences:" (map pretty_cong cngs),
   312       Pretty.strs ("loopers:" :: map (quote o #1) loop_tacs),
   313       Pretty.strs ("unsafe solvers:" :: map (quote o solver_name) (#1 solvers)),
   314       Pretty.strs ("safe solvers:" :: map (quote o solver_name) (#2 solvers))]
   315     |> Pretty.chunks |> Pretty.writeln
   316   end;
   317 
   318 
   319 (* simprocs *)
   320 
   321 exception SIMPROC_FAIL of string * exn;
   322 
   323 datatype simproc = Simproc of proc list;
   324 
   325 fun mk_simproc name lhss proc =
   326   let val id = stamp () in
   327     Simproc (lhss |> map (fn lhs =>
   328       Proc {name = name, lhs = lhs, proc = proc, id = id}))
   329   end;
   330 
   331 fun simproc_i thy name = mk_simproc name o map (Thm.cterm_of thy o Logic.varify);
   332 fun simproc thy name = simproc_i thy name o map (Sign.read_term thy);
   333 
   334 
   335 
   336 (** simpset operations **)
   337 
   338 (* context *)
   339 
   340 fun eq_bound (x: string, (y, _)) = x = y;
   341 
   342 fun add_bound bound = map_simpset1 (fn (rules, prems, (count, bounds), context) =>
   343   (rules, prems, (count + 1, bound :: bounds), context));
   344 
   345 fun add_prems ths = map_simpset1 (fn (rules, prems, bounds, context) =>
   346   (rules, ths @ prems, bounds, context));
   347 
   348 fun inherit_context (Simpset ({bounds, context, ...}, _)) =
   349   map_simpset1 (fn (rules, prems, _, _) => (rules, prems, bounds, context));
   350 
   351 fun the_context (Simpset ({context = SOME ctxt, ...}, _)) = ctxt
   352   | the_context _ = raise Fail "Simplifier: no proof context in simpset";
   353 
   354 fun context ctxt =
   355   map_simpset1 (fn (rules, prems, bounds, _) => (rules, prems, bounds, SOME ctxt));
   356 
   357 val theory_context = context o Context.init_proof;
   358 
   359 fun fallback_context _ (ss as Simpset ({context = SOME _, ...}, _)) = ss
   360   | fallback_context thy ss =
   361      (warning "Simplifier: no proof context in simpset -- fallback to theory context!";
   362       theory_context thy ss);
   363 
   364 
   365 (* addsimps *)
   366 
   367 fun mk_rrule2 {thm, name, lhs, elhs, perm} =
   368   let
   369     val fo = Pattern.first_order (term_of elhs) orelse not (Pattern.pattern (term_of elhs))
   370   in {thm = thm, name = name, lhs = lhs, elhs = elhs, fo = fo, perm = perm} end;
   371 
   372 fun insert_rrule quiet (ss, rrule as {thm, name, lhs, elhs, perm}) =
   373  (trace_named_thm "Adding rewrite rule" ss (thm, name);
   374   ss |> map_simpset1 (fn (rules, prems, bounds, context) =>
   375     let
   376       val rrule2 as {elhs, ...} = mk_rrule2 rrule;
   377       val rules' = Net.insert_term eq_rrule (term_of elhs, rrule2) rules;
   378     in (rules', prems, bounds, context) end)
   379   handle Net.INSERT =>
   380     (if quiet then () else warn_thm "Ignoring duplicate rewrite rule:" ss thm; ss));
   381 
   382 fun vperm (Var _, Var _) = true
   383   | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)
   384   | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)
   385   | vperm (t, u) = (t = u);
   386 
   387 fun var_perm (t, u) =
   388   vperm (t, u) andalso eq_set (term_varnames t, term_varnames u);
   389 
   390 (* FIXME: it seems that the conditions on extra variables are too liberal if
   391 prems are nonempty: does solving the prems really guarantee instantiation of
   392 all its Vars? Better: a dynamic check each time a rule is applied.
   393 *)
   394 fun rewrite_rule_extra_vars prems elhs erhs =
   395   not (term_varnames erhs subset fold add_term_varnames prems (term_varnames elhs))
   396   orelse
   397   not (term_tvars erhs subset (term_tvars elhs union List.concat (map term_tvars prems)));
   398 
   399 (*simple test for looping rewrite rules and stupid orientations*)
   400 fun default_reorient thy prems lhs rhs =
   401   rewrite_rule_extra_vars prems lhs rhs
   402     orelse
   403   is_Var (head_of lhs)
   404     orelse
   405 (* turns t = x around, which causes a headache if x is a local variable -
   406    usually it is very useful :-(
   407   is_Free rhs andalso not(is_Free lhs) andalso not(Logic.occs(rhs,lhs))
   408   andalso not(exists_subterm is_Var lhs)
   409     orelse
   410 *)
   411   exists (fn t => Logic.occs (lhs, t)) (rhs :: prems)
   412     orelse
   413   null prems andalso Pattern.matches thy (lhs, rhs)
   414     (*the condition "null prems" is necessary because conditional rewrites
   415       with extra variables in the conditions may terminate although
   416       the rhs is an instance of the lhs; example: ?m < ?n ==> f(?n) == f(?m)*)
   417     orelse
   418   is_Const lhs andalso not (is_Const rhs);
   419 
   420 fun decomp_simp thm =
   421   let
   422     val {thy, prop, ...} = Thm.rep_thm thm;
   423     val prems = Logic.strip_imp_prems prop;
   424     val concl = Drule.strip_imp_concl (Thm.cprop_of thm);
   425     val (lhs, rhs) = Drule.dest_equals concl handle TERM _ =>
   426       raise SIMPLIFIER ("Rewrite rule not a meta-equality", thm);
   427     val (_, elhs) = Drule.dest_equals (Thm.cprop_of (Thm.eta_conversion lhs));
   428     val elhs = if term_of elhs aconv term_of lhs then lhs else elhs;  (*share identical copies*)
   429     val erhs = Pattern.eta_contract (term_of rhs);
   430     val perm =
   431       var_perm (term_of elhs, erhs) andalso
   432       not (term_of elhs aconv erhs) andalso
   433       not (is_Var (term_of elhs));
   434   in (thy, prems, term_of lhs, elhs, term_of rhs, perm) end;
   435 
   436 fun decomp_simp' thm =
   437   let val (_, _, lhs, _, rhs, _) = decomp_simp thm in
   438     if Thm.nprems_of thm > 0 then raise SIMPLIFIER ("Bad conditional rewrite rule", thm)
   439     else (lhs, rhs)
   440   end;
   441 
   442 fun mk_eq_True (Simpset (_, {mk_rews = {mk_eq_True, ...}, ...})) (thm, name) =
   443   (case mk_eq_True thm of
   444     NONE => []
   445   | SOME eq_True =>
   446       let val (_, _, lhs, elhs, _, _) = decomp_simp eq_True
   447       in [{thm = eq_True, name = name, lhs = lhs, elhs = elhs, perm = false}] end);
   448 
   449 (*create the rewrite rule and possibly also the eq_True variant,
   450   in case there are extra vars on the rhs*)
   451 fun rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm2) =
   452   let val rrule = {thm = thm, name = name, lhs = lhs, elhs = elhs, perm = false} in
   453     if term_varnames rhs subset term_varnames lhs andalso
   454       term_tvars rhs subset term_tvars lhs then [rrule]
   455     else mk_eq_True ss (thm2, name) @ [rrule]
   456   end;
   457 
   458 fun mk_rrule ss (thm, name) =
   459   let val (_, prems, lhs, elhs, rhs, perm) = decomp_simp thm in
   460     if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]
   461     else
   462       (*weak test for loops*)
   463       if rewrite_rule_extra_vars prems lhs rhs orelse is_Var (term_of elhs)
   464       then mk_eq_True ss (thm, name)
   465       else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
   466   end;
   467 
   468 fun orient_rrule ss (thm, name) =
   469   let
   470     val (thy, prems, lhs, elhs, rhs, perm) = decomp_simp thm;
   471     val Simpset (_, {mk_rews = {reorient, mk_sym, ...}, ...}) = ss;
   472   in
   473     if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]
   474     else if reorient thy prems lhs rhs then
   475       if reorient thy prems rhs lhs
   476       then mk_eq_True ss (thm, name)
   477       else
   478         (case mk_sym thm of
   479           NONE => []
   480         | SOME thm' =>
   481             let val (_, _, lhs', elhs', rhs', _) = decomp_simp thm'
   482             in rrule_eq_True (thm', name, lhs', elhs', rhs', ss, thm) end)
   483     else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
   484   end;
   485 
   486 fun extract_rews (Simpset (_, {mk_rews = {mk, ...}, ...}), thms) =
   487   List.concat (map (fn thm => map (rpair (Thm.name_of_thm thm)) (mk thm)) thms);
   488 
   489 fun orient_comb_simps comb mk_rrule (ss, thms) =
   490   let
   491     val rews = extract_rews (ss, thms);
   492     val rrules = List.concat (map mk_rrule rews);
   493   in Library.foldl comb (ss, rrules) end;
   494 
   495 fun extract_safe_rrules (ss, thm) =
   496   List.concat (map (orient_rrule ss) (extract_rews (ss, [thm])));
   497 
   498 (*add rewrite rules explicitly; do not reorient!*)
   499 fun ss addsimps thms =
   500   orient_comb_simps (insert_rrule false) (mk_rrule ss) (ss, thms);
   501 
   502 
   503 (* delsimps *)
   504 
   505 fun del_rrule (ss, rrule as {thm, elhs, ...}) =
   506   ss |> map_simpset1 (fn (rules, prems, bounds, context) =>
   507     (Net.delete_term eq_rrule (term_of elhs, rrule) rules, prems, bounds, context))
   508   handle Net.DELETE => (warn_thm "Rewrite rule not in simpset:" ss thm; ss);
   509 
   510 fun ss delsimps thms =
   511   orient_comb_simps del_rrule (map mk_rrule2 o mk_rrule ss) (ss, thms);
   512 
   513 
   514 (* congs *)
   515 
   516 fun cong_name (Const (a, _)) = SOME a
   517   | cong_name (Free (a, _)) = SOME ("Free: " ^ a)
   518   | cong_name _ = NONE;
   519 
   520 local
   521 
   522 fun is_full_cong_prems [] [] = true
   523   | is_full_cong_prems [] _ = false
   524   | is_full_cong_prems (p :: prems) varpairs =
   525       (case Logic.strip_assums_concl p of
   526         Const ("==", _) $ lhs $ rhs =>
   527           let val (x, xs) = strip_comb lhs and (y, ys) = strip_comb rhs in
   528             is_Var x andalso forall is_Bound xs andalso
   529             null (findrep xs) andalso xs = ys andalso
   530             (x, y) mem varpairs andalso
   531             is_full_cong_prems prems (varpairs \ (x, y))
   532           end
   533       | _ => false);
   534 
   535 fun is_full_cong thm =
   536   let
   537     val prems = prems_of thm and concl = concl_of thm;
   538     val (lhs, rhs) = Logic.dest_equals concl;
   539     val (f, xs) = strip_comb lhs and (g, ys) = strip_comb rhs;
   540   in
   541     f = g andalso null (findrep (xs @ ys)) andalso length xs = length ys andalso
   542     is_full_cong_prems prems (xs ~~ ys)
   543   end;
   544 
   545 fun add_cong (ss, thm) = ss |>
   546   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   547     let
   548       val (lhs, _) = Drule.dest_equals (Drule.strip_imp_concl (Thm.cprop_of thm))
   549         handle TERM _ => raise SIMPLIFIER ("Congruence not a meta-equality", thm);
   550     (*val lhs = Pattern.eta_contract lhs;*)
   551       val a = valOf (cong_name (head_of (term_of lhs))) handle Option =>
   552         raise SIMPLIFIER ("Congruence must start with a constant or free variable", thm);
   553       val (alist, weak) = congs;
   554       val alist2 = overwrite_warn (alist, (a, {lhs = lhs, thm = thm}))
   555         ("Overwriting congruence rule for " ^ quote a);
   556       val weak2 = if is_full_cong thm then weak else a :: weak;
   557     in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
   558 
   559 fun del_cong (ss, thm) = ss |>
   560   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   561     let
   562       val (lhs, _) = Logic.dest_equals (Thm.concl_of thm) handle TERM _ =>
   563         raise SIMPLIFIER ("Congruence not a meta-equality", thm);
   564     (*val lhs = Pattern.eta_contract lhs;*)
   565       val a = valOf (cong_name (head_of lhs)) handle Option =>
   566         raise SIMPLIFIER ("Congruence must start with a constant", thm);
   567       val (alist, _) = congs;
   568       val alist2 = List.filter (fn (x, _) => x <> a) alist;
   569       val weak2 = alist2 |> List.mapPartial (fn (a, {thm, ...}: cong) =>
   570         if is_full_cong thm then NONE else SOME a);
   571     in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
   572 
   573 fun mk_cong (Simpset (_, {mk_rews = {mk_cong = f, ...}, ...})) = f;
   574 
   575 in
   576 
   577 val (op addeqcongs) = Library.foldl add_cong;
   578 val (op deleqcongs) = Library.foldl del_cong;
   579 
   580 fun ss addcongs congs = ss addeqcongs map (mk_cong ss) congs;
   581 fun ss delcongs congs = ss deleqcongs map (mk_cong ss) congs;
   582 
   583 end;
   584 
   585 
   586 (* simprocs *)
   587 
   588 local
   589 
   590 fun add_proc (proc as Proc {name, lhs, ...}) ss =
   591  (trace_cterm false ("Adding simplification procedure " ^ quote name ^ " for") ss lhs;
   592   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   593     (congs, Net.insert_term eq_proc (term_of lhs, proc) procs,
   594       mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
   595   handle Net.INSERT =>
   596     (warning ("Ignoring duplicate simplification procedure " ^ quote name); ss));
   597 
   598 fun del_proc (proc as Proc {name, lhs, ...}) ss =
   599   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   600     (congs, Net.delete_term eq_proc (term_of lhs, proc) procs,
   601       mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
   602   handle Net.DELETE =>
   603     (warning ("Simplification procedure " ^ quote name ^ " not in simpset"); ss);
   604 
   605 in
   606 
   607 fun ss addsimprocs ps = fold (fn Simproc procs => fold add_proc procs) ps ss;
   608 fun ss delsimprocs ps = fold (fn Simproc procs => fold del_proc procs) ps ss;
   609 
   610 end;
   611 
   612 
   613 (* mk_rews *)
   614 
   615 local
   616 
   617 fun map_mk_rews f = map_simpset2 (fn (congs, procs, {mk, mk_cong, mk_sym, mk_eq_True, reorient},
   618       termless, subgoal_tac, loop_tacs, solvers) =>
   619   let
   620     val (mk', mk_cong', mk_sym', mk_eq_True', reorient') =
   621       f (mk, mk_cong, mk_sym, mk_eq_True, reorient);
   622     val mk_rews' = {mk = mk', mk_cong = mk_cong', mk_sym = mk_sym', mk_eq_True = mk_eq_True',
   623       reorient = reorient'};
   624   in (congs, procs, mk_rews', termless, subgoal_tac, loop_tacs, solvers) end);
   625 
   626 in
   627 
   628 fun ss setmksimps mk = ss |> map_mk_rews (fn (_, mk_cong, mk_sym, mk_eq_True, reorient) =>
   629   (mk, mk_cong, mk_sym, mk_eq_True, reorient));
   630 
   631 fun ss setmkcong mk_cong = ss |> map_mk_rews (fn (mk, _, mk_sym, mk_eq_True, reorient) =>
   632   (mk, mk_cong, mk_sym, mk_eq_True, reorient));
   633 
   634 fun ss setmksym mk_sym = ss |> map_mk_rews (fn (mk, mk_cong, _, mk_eq_True, reorient) =>
   635   (mk, mk_cong, mk_sym, mk_eq_True, reorient));
   636 
   637 fun ss setmkeqTrue mk_eq_True = ss |> map_mk_rews (fn (mk, mk_cong, mk_sym, _, reorient) =>
   638   (mk, mk_cong, mk_sym, mk_eq_True, reorient));
   639 
   640 fun set_reorient reorient = map_mk_rews (fn (mk, mk_cong, mk_sym, mk_eq_True, _) =>
   641   (mk, mk_cong, mk_sym, mk_eq_True, reorient));
   642 
   643 end;
   644 
   645 
   646 (* termless *)
   647 
   648 fun ss settermless termless = ss |>
   649   map_simpset2 (fn (congs, procs, mk_rews, _, subgoal_tac, loop_tacs, solvers) =>
   650    (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   651 
   652 
   653 (* tactics *)
   654 
   655 fun ss setsubgoaler subgoal_tac = ss |>
   656   map_simpset2 (fn (congs, procs, mk_rews, termless, _, loop_tacs, solvers) =>
   657    (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   658 
   659 fun ss setloop' tac = ss |>
   660   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, _, solvers) =>
   661    (congs, procs, mk_rews, termless, subgoal_tac, [("", tac)], solvers));
   662 
   663 fun ss setloop tac = ss setloop' (K tac);
   664 
   665 fun ss addloop' (name, tac) = ss |>
   666   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   667     (congs, procs, mk_rews, termless, subgoal_tac,
   668       overwrite_warn (loop_tacs, (name, tac)) ("Overwriting looper " ^ quote name),
   669       solvers));
   670 
   671 fun ss addloop (name, tac) = ss addloop' (name, K tac);
   672 
   673 fun ss delloop name = ss |>
   674   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   675     let val loop_tacs' = filter_out (equal name o fst) loop_tacs in
   676       if length loop_tacs <> length loop_tacs' then ()
   677       else warning ("No such looper in simpset: " ^ quote name);
   678       (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs', solvers)
   679     end);
   680 
   681 fun ss setSSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   682   subgoal_tac, loop_tacs, (unsafe_solvers, _)) =>
   683     (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, (unsafe_solvers, [solver])));
   684 
   685 fun ss addSSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   686   subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, termless,
   687     subgoal_tac, loop_tacs, (unsafe_solvers, merge_solvers solvers [solver])));
   688 
   689 fun ss setSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   690   subgoal_tac, loop_tacs, (_, solvers)) => (congs, procs, mk_rews, termless,
   691     subgoal_tac, loop_tacs, ([solver], solvers)));
   692 
   693 fun ss addSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   694   subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, termless,
   695     subgoal_tac, loop_tacs, (merge_solvers unsafe_solvers [solver], solvers)));
   696 
   697 fun set_solvers solvers = map_simpset2 (fn (congs, procs, mk_rews, termless,
   698   subgoal_tac, loop_tacs, _) => (congs, procs, mk_rews, termless,
   699   subgoal_tac, loop_tacs, (solvers, solvers)));
   700 
   701 
   702 (* empty *)
   703 
   704 fun init_ss mk_rews termless subgoal_tac solvers =
   705   make_simpset ((Net.empty, [], (0, []), NONE),
   706     (([], []), Net.empty, mk_rews, termless, subgoal_tac, [], solvers));
   707 
   708 fun clear_ss (ss as Simpset (_, {mk_rews, termless, subgoal_tac, solvers, ...})) =
   709   init_ss mk_rews termless subgoal_tac solvers
   710   |> inherit_context ss;
   711 
   712 val basic_mk_rews: mk_rews =
   713  {mk = fn th => if can Logic.dest_equals (Thm.concl_of th) then [th] else [],
   714   mk_cong = I,
   715   mk_sym = SOME o Drule.symmetric_fun,
   716   mk_eq_True = K NONE,
   717   reorient = default_reorient};
   718 
   719 val empty_ss = init_ss basic_mk_rews Term.termless (K (K no_tac)) ([], []);
   720 
   721 
   722 (* merge *)  (*NOTE: ignores some fields of 2nd simpset*)
   723 
   724 fun merge_ss (ss1, ss2) =
   725   let
   726     val Simpset ({rules = rules1, prems = prems1, bounds = bounds1, context = _},
   727      {congs = (congs1, weak1), procs = procs1, mk_rews, termless, subgoal_tac,
   728       loop_tacs = loop_tacs1, solvers = (unsafe_solvers1, solvers1)}) = ss1;
   729     val Simpset ({rules = rules2, prems = prems2, bounds = bounds2, context = _},
   730      {congs = (congs2, weak2), procs = procs2, mk_rews = _, termless = _, subgoal_tac = _,
   731       loop_tacs = loop_tacs2, solvers = (unsafe_solvers2, solvers2)}) = ss2;
   732 
   733     val rules' = Net.merge eq_rrule (rules1, rules2);
   734     val prems' = gen_merge_lists Drule.eq_thm_prop prems1 prems2;
   735     val bounds' = if #1 bounds1 < #1 bounds2 then bounds2 else bounds1;
   736     val congs' = gen_merge_lists (eq_cong o pairself #2) congs1 congs2;
   737     val weak' = merge_lists weak1 weak2;
   738     val procs' = Net.merge eq_proc (procs1, procs2);
   739     val loop_tacs' = merge_alists loop_tacs1 loop_tacs2;
   740     val unsafe_solvers' = merge_solvers unsafe_solvers1 unsafe_solvers2;
   741     val solvers' = merge_solvers solvers1 solvers2;
   742   in
   743     make_simpset ((rules', prems', bounds', NONE), ((congs', weak'), procs',
   744       mk_rews, termless, subgoal_tac, loop_tacs', (unsafe_solvers', solvers')))
   745   end;
   746 
   747 
   748 
   749 (** rewriting **)
   750 
   751 (*
   752   Uses conversions, see:
   753     L C Paulson, A higher-order implementation of rewriting,
   754     Science of Computer Programming 3 (1983), pages 119-149.
   755 *)
   756 
   757 val dest_eq = Drule.dest_equals o Thm.cprop_of;
   758 val lhs_of = #1 o dest_eq;
   759 val rhs_of = #2 o dest_eq;
   760 
   761 fun check_conv msg ss thm thm' =
   762   let
   763     val thm'' = transitive thm (transitive
   764       (symmetric (Drule.beta_eta_conversion (lhs_of thm'))) thm')
   765   in if msg then trace_thm "SUCCEEDED" ss thm' else (); SOME thm'' end
   766   handle THM _ =>
   767     let val {thy, prop = _ $ _ $ prop0, ...} = Thm.rep_thm thm in
   768       trace_thm "Proved wrong thm (Check subgoaler?)" ss thm';
   769       trace_term false "Should have proved:" ss thy prop0;
   770       NONE
   771     end;
   772 
   773 
   774 (* mk_procrule *)
   775 
   776 fun mk_procrule ss thm =
   777   let val (_, prems, lhs, elhs, rhs, _) = decomp_simp thm in
   778     if rewrite_rule_extra_vars prems lhs rhs
   779     then (warn_thm "Extra vars on rhs:" ss thm; [])
   780     else [mk_rrule2 {thm = thm, name = "", lhs = lhs, elhs = elhs, perm = false}]
   781   end;
   782 
   783 
   784 (* rewritec: conversion to apply the meta simpset to a term *)
   785 
   786 (*Since the rewriting strategy is bottom-up, we avoid re-normalizing already
   787   normalized terms by carrying around the rhs of the rewrite rule just
   788   applied. This is called the `skeleton'. It is decomposed in parallel
   789   with the term. Once a Var is encountered, the corresponding term is
   790   already in normal form.
   791   skel0 is a dummy skeleton that is to enforce complete normalization.*)
   792 
   793 val skel0 = Bound 0;
   794 
   795 (*Use rhs as skeleton only if the lhs does not contain unnormalized bits.
   796   The latter may happen iff there are weak congruence rules for constants
   797   in the lhs.*)
   798 
   799 fun uncond_skel ((_, weak), (lhs, rhs)) =
   800   if null weak then rhs  (*optimization*)
   801   else if exists_Const (fn (c, _) => c mem weak) lhs then skel0
   802   else rhs;
   803 
   804 (*Behaves like unconditional rule if rhs does not contain vars not in the lhs.
   805   Otherwise those vars may become instantiated with unnormalized terms
   806   while the premises are solved.*)
   807 
   808 fun cond_skel (args as (congs, (lhs, rhs))) =
   809   if term_varnames rhs subset term_varnames lhs then uncond_skel args
   810   else skel0;
   811 
   812 (*
   813   Rewriting -- we try in order:
   814     (1) beta reduction
   815     (2) unconditional rewrite rules
   816     (3) conditional rewrite rules
   817     (4) simplification procedures
   818 
   819   IMPORTANT: rewrite rules must not introduce new Vars or TVars!
   820 *)
   821 
   822 fun rewritec (prover, thyt, maxt) ss t =
   823   let
   824     val Simpset ({rules, ...}, {congs, procs, termless, ...}) = ss;
   825     val eta_thm = Thm.eta_conversion t;
   826     val eta_t' = rhs_of eta_thm;
   827     val eta_t = term_of eta_t';
   828     fun rew {thm, name, lhs, elhs, fo, perm} =
   829       let
   830         val {thy, prop, maxidx, ...} = rep_thm thm;
   831         val (rthm, elhs') = if maxt = ~1 then (thm, elhs)
   832           else (Thm.incr_indexes (maxt+1) thm, Thm.cterm_incr_indexes (maxt+1) elhs);
   833         val insts = if fo then Thm.cterm_first_order_match (elhs', eta_t')
   834                           else Thm.cterm_match (elhs', eta_t');
   835         val thm' = Thm.instantiate insts (Thm.rename_boundvars lhs eta_t rthm);
   836         val prop' = Thm.prop_of thm';
   837         val unconditional = (Logic.count_prems (prop',0) = 0);
   838         val (lhs', rhs') = Logic.dest_equals (Logic.strip_imp_concl prop')
   839       in
   840         if perm andalso not (termless (rhs', lhs'))
   841         then (trace_named_thm "Cannot apply permutative rewrite rule" ss (thm, name);
   842               trace_thm "Term does not become smaller:" ss thm'; NONE)
   843         else (trace_named_thm "Applying instance of rewrite rule" ss (thm, name);
   844            if unconditional
   845            then
   846              (trace_thm "Rewriting:" ss thm';
   847               let val lr = Logic.dest_equals prop;
   848                   val SOME thm'' = check_conv false ss eta_thm thm'
   849               in SOME (thm'', uncond_skel (congs, lr)) end)
   850            else
   851              (trace_thm "Trying to rewrite:" ss thm';
   852               if !simp_depth > !simp_depth_limit
   853               then let val s = "simp_depth_limit exceeded - giving up"
   854                    in trace false s; warning s; NONE end
   855               else
   856               case prover ss thm' of
   857                 NONE => (trace_thm "FAILED" ss thm'; NONE)
   858               | SOME thm2 =>
   859                   (case check_conv true ss eta_thm thm2 of
   860                      NONE => NONE |
   861                      SOME thm2' =>
   862                        let val concl = Logic.strip_imp_concl prop
   863                            val lr = Logic.dest_equals concl
   864                        in SOME (thm2', cond_skel (congs, lr)) end)))
   865       end
   866 
   867     fun rews [] = NONE
   868       | rews (rrule :: rrules) =
   869           let val opt = rew rrule handle Pattern.MATCH => NONE
   870           in case opt of NONE => rews rrules | some => some end;
   871 
   872     fun sort_rrules rrs = let
   873       fun is_simple({thm, ...}:rrule) = case Thm.prop_of thm of
   874                                       Const("==",_) $ _ $ _ => true
   875                                       | _                   => false
   876       fun sort []        (re1,re2) = re1 @ re2
   877         | sort (rr::rrs) (re1,re2) = if is_simple rr
   878                                      then sort rrs (rr::re1,re2)
   879                                      else sort rrs (re1,rr::re2)
   880     in sort rrs ([],[]) end
   881 
   882     fun proc_rews [] = NONE
   883       | proc_rews (Proc {name, proc, lhs, ...} :: ps) =
   884           if Pattern.matches thyt (Thm.term_of lhs, Thm.term_of t) then
   885             (debug_term false ("Trying procedure " ^ quote name ^ " on:") ss thyt eta_t;
   886              case transform_failure (curry SIMPROC_FAIL name)
   887                  (fn () => proc thyt ss eta_t) () of
   888                NONE => (debug false "FAILED"; proc_rews ps)
   889              | SOME raw_thm =>
   890                  (trace_thm ("Procedure " ^ quote name ^ " produced rewrite rule:") ss raw_thm;
   891                   (case rews (mk_procrule ss raw_thm) of
   892                     NONE => (trace_cterm true ("IGNORED result of simproc " ^ quote name ^
   893                       " -- does not match") ss t; proc_rews ps)
   894                   | some => some)))
   895           else proc_rews ps;
   896   in case eta_t of
   897        Abs _ $ _ => SOME (transitive eta_thm
   898          (beta_conversion false eta_t'), skel0)
   899      | _ => (case rews (sort_rrules (Net.match_term rules eta_t)) of
   900                NONE => proc_rews (Net.match_term procs eta_t)
   901              | some => some)
   902   end;
   903 
   904 
   905 (* conversion to apply a congruence rule to a term *)
   906 
   907 fun congc prover ss maxt {thm=cong,lhs=lhs} t =
   908   let val rthm = Thm.incr_indexes (maxt+1) cong;
   909       val rlhs = fst (Drule.dest_equals (Drule.strip_imp_concl (cprop_of rthm)));
   910       val insts = Thm.cterm_match (rlhs, t)
   911       (* Pattern.match can raise Pattern.MATCH;
   912          is handled when congc is called *)
   913       val thm' = Thm.instantiate insts (Thm.rename_boundvars (term_of rlhs) (term_of t) rthm);
   914       val unit = trace_thm "Applying congruence rule:" ss thm';
   915       fun err (msg, thm) = (trace_thm msg ss thm; NONE)
   916   in case prover thm' of
   917        NONE => err ("Congruence proof failed.  Could not prove", thm')
   918      | SOME thm2 => (case check_conv true ss (Drule.beta_eta_conversion t) thm2 of
   919           NONE => err ("Congruence proof failed.  Should not have proved", thm2)
   920         | SOME thm2' =>
   921             if op aconv (pairself term_of (dest_equals (cprop_of thm2')))
   922             then NONE else SOME thm2')
   923   end;
   924 
   925 val (cA, (cB, cC)) =
   926   apsnd dest_equals (dest_implies (hd (cprems_of Drule.imp_cong)));
   927 
   928 fun transitive1 NONE NONE = NONE
   929   | transitive1 (SOME thm1) NONE = SOME thm1
   930   | transitive1 NONE (SOME thm2) = SOME thm2
   931   | transitive1 (SOME thm1) (SOME thm2) = SOME (transitive thm1 thm2)
   932 
   933 fun transitive2 thm = transitive1 (SOME thm);
   934 fun transitive3 thm = transitive1 thm o SOME;
   935 
   936 fun bottomc ((simprem, useprem, mutsimp), prover, thy, maxidx) =
   937   let
   938     fun botc skel ss t =
   939           if is_Var skel then NONE
   940           else
   941           (case subc skel ss t of
   942              some as SOME thm1 =>
   943                (case rewritec (prover, thy, maxidx) ss (rhs_of thm1) of
   944                   SOME (thm2, skel2) =>
   945                     transitive2 (transitive thm1 thm2)
   946                       (botc skel2 ss (rhs_of thm2))
   947                 | NONE => some)
   948            | NONE =>
   949                (case rewritec (prover, thy, maxidx) ss t of
   950                   SOME (thm2, skel2) => transitive2 thm2
   951                     (botc skel2 ss (rhs_of thm2))
   952                 | NONE => NONE))
   953 
   954     and try_botc ss t =
   955           (case botc skel0 ss t of
   956              SOME trec1 => trec1 | NONE => (reflexive t))
   957 
   958     and subc skel (ss as Simpset ({bounds, ...}, {congs, ...})) t0 =
   959        (case term_of t0 of
   960            Abs (a, T, t) =>
   961              let
   962                  val b = Term.bound (#1 bounds);
   963                  val (v, t') = Thm.dest_abs (SOME b) t0;
   964                  val b' = #1 (Term.dest_Free (Thm.term_of v));
   965                  val _ = conditional (b <> b') (fn () =>
   966                    warning ("Simplifier: renamed bound variable " ^ quote b ^ " to " ^ quote b'));
   967                  val ss' = add_bound ((b', T), a) ss;
   968                  val skel' = case skel of Abs (_, _, sk) => sk | _ => skel0;
   969              in case botc skel' ss' t' of
   970                   SOME thm => SOME (abstract_rule a v thm)
   971                 | NONE => NONE
   972              end
   973          | t $ _ => (case t of
   974              Const ("==>", _) $ _  => impc t0 ss
   975            | Abs _ =>
   976                let val thm = beta_conversion false t0
   977                in case subc skel0 ss (rhs_of thm) of
   978                     NONE => SOME thm
   979                   | SOME thm' => SOME (transitive thm thm')
   980                end
   981            | _  =>
   982                let fun appc () =
   983                      let
   984                        val (tskel, uskel) = case skel of
   985                            tskel $ uskel => (tskel, uskel)
   986                          | _ => (skel0, skel0);
   987                        val (ct, cu) = Thm.dest_comb t0
   988                      in
   989                      (case botc tskel ss ct of
   990                         SOME thm1 =>
   991                           (case botc uskel ss cu of
   992                              SOME thm2 => SOME (combination thm1 thm2)
   993                            | NONE => SOME (combination thm1 (reflexive cu)))
   994                       | NONE =>
   995                           (case botc uskel ss cu of
   996                              SOME thm1 => SOME (combination (reflexive ct) thm1)
   997                            | NONE => NONE))
   998                      end
   999                    val (h, ts) = strip_comb t
  1000                in case cong_name h of
  1001                     SOME a =>
  1002                       (case AList.lookup (op =) (fst congs) a of
  1003                          NONE => appc ()
  1004                        | SOME cong =>
  1005   (*post processing: some partial applications h t1 ... tj, j <= length ts,
  1006     may be a redex. Example: map (%x. x) = (%xs. xs) wrt map_cong*)
  1007                           (let
  1008                              val thm = congc (prover ss) ss maxidx cong t0;
  1009                              val t = getOpt (Option.map rhs_of thm, t0);
  1010                              val (cl, cr) = Thm.dest_comb t
  1011                              val dVar = Var(("", 0), dummyT)
  1012                              val skel =
  1013                                list_comb (h, replicate (length ts) dVar)
  1014                            in case botc skel ss cl of
  1015                                 NONE => thm
  1016                               | SOME thm' => transitive3 thm
  1017                                   (combination thm' (reflexive cr))
  1018                            end handle TERM _ => error "congc result"
  1019                                     | Pattern.MATCH => appc ()))
  1020                   | _ => appc ()
  1021                end)
  1022          | _ => NONE)
  1023 
  1024     and impc ct ss =
  1025       if mutsimp then mut_impc0 [] ct [] [] ss else nonmut_impc ct ss
  1026 
  1027     and rules_of_prem ss prem =
  1028       if maxidx_of_term (term_of prem) <> ~1
  1029       then (trace_cterm true
  1030         "Cannot add premise as rewrite rule because it contains (type) unknowns:" ss prem; ([], NONE))
  1031       else
  1032         let val asm = assume prem
  1033         in (extract_safe_rrules (ss, asm), SOME asm) end
  1034 
  1035     and add_rrules (rrss, asms) ss =
  1036       Library.foldl (insert_rrule true) (ss, List.concat rrss) |> add_prems (List.mapPartial I asms)
  1037 
  1038     and disch r (prem, eq) =
  1039       let
  1040         val (lhs, rhs) = dest_eq eq;
  1041         val eq' = implies_elim (Thm.instantiate
  1042           ([], [(cA, prem), (cB, lhs), (cC, rhs)]) Drule.imp_cong)
  1043           (implies_intr prem eq)
  1044       in if not r then eq' else
  1045         let
  1046           val (prem', concl) = dest_implies lhs;
  1047           val (prem'', _) = dest_implies rhs
  1048         in transitive (transitive
  1049           (Thm.instantiate ([], [(cA, prem'), (cB, prem), (cC, concl)])
  1050              Drule.swap_prems_eq) eq')
  1051           (Thm.instantiate ([], [(cA, prem), (cB, prem''), (cC, concl)])
  1052              Drule.swap_prems_eq)
  1053         end
  1054       end
  1055 
  1056     and rebuild [] _ _ _ _ eq = eq
  1057       | rebuild (prem :: prems) concl (rrs :: rrss) (asm :: asms) ss eq =
  1058           let
  1059             val ss' = add_rrules (rev rrss, rev asms) ss;
  1060             val concl' =
  1061               Drule.mk_implies (prem, getOpt (Option.map rhs_of eq, concl));
  1062             val dprem = Option.map (curry (disch false) prem)
  1063           in case rewritec (prover, thy, maxidx) ss' concl' of
  1064               NONE => rebuild prems concl' rrss asms ss (dprem eq)
  1065             | SOME (eq', _) => transitive2 (Library.foldl (disch false o swap)
  1066                   (valOf (transitive3 (dprem eq) eq'), prems))
  1067                 (mut_impc0 (rev prems) (rhs_of eq') (rev rrss) (rev asms) ss)
  1068           end
  1069 
  1070     and mut_impc0 prems concl rrss asms ss =
  1071       let
  1072         val prems' = strip_imp_prems concl;
  1073         val (rrss', asms') = split_list (map (rules_of_prem ss) prems')
  1074       in mut_impc (prems @ prems') (strip_imp_concl concl) (rrss @ rrss')
  1075         (asms @ asms') [] [] [] [] ss ~1 ~1
  1076       end
  1077 
  1078     and mut_impc [] concl [] [] prems' rrss' asms' eqns ss changed k =
  1079         transitive1 (Library.foldl (fn (eq2, (eq1, prem)) => transitive1 eq1
  1080             (Option.map (curry (disch false) prem) eq2)) (NONE, eqns ~~ prems'))
  1081           (if changed > 0 then
  1082              mut_impc (rev prems') concl (rev rrss') (rev asms')
  1083                [] [] [] [] ss ~1 changed
  1084            else rebuild prems' concl rrss' asms' ss
  1085              (botc skel0 (add_rrules (rev rrss', rev asms') ss) concl))
  1086 
  1087       | mut_impc (prem :: prems) concl (rrs :: rrss) (asm :: asms)
  1088           prems' rrss' asms' eqns ss changed k =
  1089         case (if k = 0 then NONE else botc skel0 (add_rrules
  1090           (rev rrss' @ rrss, rev asms' @ asms) ss) prem) of
  1091             NONE => mut_impc prems concl rrss asms (prem :: prems')
  1092               (rrs :: rrss') (asm :: asms') (NONE :: eqns) ss changed
  1093               (if k = 0 then 0 else k - 1)
  1094           | SOME eqn =>
  1095             let
  1096               val prem' = rhs_of eqn;
  1097               val tprems = map term_of prems;
  1098               val i = 1 + Library.foldl Int.max (~1, map (fn p =>
  1099                 find_index_eq p tprems) (#hyps (rep_thm eqn)));
  1100               val (rrs', asm') = rules_of_prem ss prem'
  1101             in mut_impc prems concl rrss asms (prem' :: prems')
  1102               (rrs' :: rrss') (asm' :: asms') (SOME (foldr (disch true)
  1103                 (Drule.imp_cong_rule eqn (reflexive (Drule.list_implies
  1104                   (Library.drop (i, prems), concl)))) (Library.take (i, prems))) :: eqns) ss (length prems') ~1
  1105             end
  1106 
  1107      (*legacy code - only for backwards compatibility*)
  1108      and nonmut_impc ct ss =
  1109        let val (prem, conc) = dest_implies ct;
  1110            val thm1 = if simprem then botc skel0 ss prem else NONE;
  1111            val prem1 = getOpt (Option.map rhs_of thm1, prem);
  1112            val ss1 = if not useprem then ss else add_rrules
  1113              (apsnd single (apfst single (rules_of_prem ss prem1))) ss
  1114        in (case botc skel0 ss1 conc of
  1115            NONE => (case thm1 of
  1116                NONE => NONE
  1117              | SOME thm1' => SOME (Drule.imp_cong_rule thm1' (reflexive conc)))
  1118          | SOME thm2 =>
  1119            let val thm2' = disch false (prem1, thm2)
  1120            in (case thm1 of
  1121                NONE => SOME thm2'
  1122              | SOME thm1' =>
  1123                  SOME (transitive (Drule.imp_cong_rule thm1' (reflexive conc)) thm2'))
  1124            end)
  1125        end
  1126 
  1127  in try_botc end;
  1128 
  1129 
  1130 (* Meta-rewriting: rewrites t to u and returns the theorem t==u *)
  1131 
  1132 (*
  1133   Parameters:
  1134     mode = (simplify A,
  1135             use A in simplifying B,
  1136             use prems of B (if B is again a meta-impl.) to simplify A)
  1137            when simplifying A ==> B
  1138     prover: how to solve premises in conditional rewrites and congruences
  1139 *)
  1140 
  1141 val debug_bounds = ref false;
  1142 
  1143 fun check_bounds ss ct = conditional (! debug_bounds) (fn () =>
  1144   let
  1145     val Simpset ({bounds = (_, bounds), ...}, _) = ss;
  1146     val bs = fold_aterms (fn Free (x, _) =>
  1147         if Term.is_bound x andalso not (AList.defined eq_bound bounds x)
  1148         then insert (op =) x else I
  1149       | _ => I) (term_of ct) [];
  1150   in
  1151     if null bs then ()
  1152     else print_term true ("Simplifier: term contains loose bounds: " ^ commas_quote bs) ss
  1153       (Thm.theory_of_cterm ct) (Thm.term_of ct)
  1154   end);
  1155 
  1156 fun rewrite_cterm mode prover raw_ss ct =
  1157   let
  1158     val {thy, t, maxidx, ...} = Thm.rep_cterm ct;
  1159     val ss = fallback_context thy raw_ss;
  1160     val _ = inc simp_depth;
  1161     val _ = conditional (!simp_depth mod 20 = 0) (fn () =>
  1162       warning ("Simplification depth " ^ string_of_int (! simp_depth)));
  1163     val _ = trace_cterm false "SIMPLIFIER INVOKED ON THE FOLLOWING TERM:" ss ct;
  1164     val _ = check_bounds ss ct;
  1165     val res = bottomc (mode, Option.map Drule.flexflex_unique oo prover, thy, maxidx) ss ct
  1166   in dec simp_depth; res end
  1167   handle exn => (dec simp_depth; raise exn);
  1168 
  1169 (*Rewrite a cterm*)
  1170 fun rewrite_aux _ _ [] ct = Thm.reflexive ct
  1171   | rewrite_aux prover full thms ct =
  1172       rewrite_cterm (full, false, false) prover
  1173       (theory_context (Thm.theory_of_cterm ct) empty_ss addsimps thms) ct;
  1174 
  1175 (*Rewrite a theorem*)
  1176 fun simplify_aux _ _ [] th = th
  1177   | simplify_aux prover full thms th =
  1178       Drule.fconv_rule (rewrite_cterm (full, false, false) prover
  1179         (theory_context (Thm.theory_of_thm th) empty_ss addsimps thms)) th;
  1180 
  1181 (*simple term rewriting -- no proof*)
  1182 fun rewrite_term thy rules procs =
  1183   Pattern.rewrite_term thy (map decomp_simp' rules) procs;
  1184 
  1185 fun rewrite_thm mode prover ss = Drule.fconv_rule (rewrite_cterm mode prover ss);
  1186 
  1187 (*Rewrite the subgoals of a proof state (represented by a theorem) *)
  1188 fun rewrite_goals_rule_aux _ []   th = th
  1189   | rewrite_goals_rule_aux prover thms th =
  1190       Drule.fconv_rule (Drule.goals_conv (K true) (rewrite_cterm (true, true, false) prover
  1191         (theory_context (Thm.theory_of_thm th) empty_ss addsimps thms))) th;
  1192 
  1193 (*Rewrite the subgoal of a proof state (represented by a theorem)*)
  1194 fun rewrite_goal_rule mode prover ss i thm =
  1195   if 0 < i  andalso  i <= nprems_of thm
  1196   then Drule.fconv_rule (Drule.goals_conv (fn j => j=i) (rewrite_cterm mode prover ss)) thm
  1197   else raise THM("rewrite_goal_rule",i,[thm]);
  1198 
  1199 end;
  1200 
  1201 structure BasicMetaSimplifier: BASIC_META_SIMPLIFIER = MetaSimplifier;
  1202 open BasicMetaSimplifier;