src/Pure/meta_simplifier.ML
author nipkow
Mon Jun 06 19:09:49 2005 +0200 (2005-06-06)
changeset 16305 5e7b6731b004
parent 16042 8e15ff79851a
child 16378 8af448f67cef
permissions -rw-r--r--
Added the t = x "fix" - in (* ... *) :-(
     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 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   type cong
    21   type solver
    22   val mk_solver: string -> (thm list -> int -> tactic) -> solver
    23   type simpset
    24   type proc
    25   val rep_ss: simpset ->
    26    {rules: rrule Net.net,
    27     prems: thm list,
    28     bounds: int} *
    29    {congs: (string * cong) list * string list,
    30     procs: proc Net.net,
    31     mk_rews:
    32      {mk: thm -> thm list,
    33       mk_cong: thm -> thm,
    34       mk_sym: thm -> thm option,
    35       mk_eq_True: thm -> thm option},
    36     termless: term * term -> bool,
    37     subgoal_tac: simpset -> int -> tactic,
    38     loop_tacs: (string * (int -> tactic)) list,
    39     solvers: solver list * solver list}
    40   val print_ss: simpset -> unit
    41   val empty_ss: simpset
    42   val merge_ss: simpset * simpset -> simpset
    43   type simproc
    44   val mk_simproc: string -> cterm list ->
    45     (Sign.sg -> simpset -> term -> thm option) -> simproc
    46   val add_prems: thm list -> simpset -> simpset
    47   val prems_of_ss: simpset -> thm list
    48   val addsimps: simpset * thm list -> simpset
    49   val delsimps: simpset * thm list -> simpset
    50   val addeqcongs: simpset * thm list -> simpset
    51   val deleqcongs: simpset * thm list -> simpset
    52   val addcongs: simpset * thm list -> simpset
    53   val delcongs: simpset * thm list -> simpset
    54   val addsimprocs: simpset * simproc list -> simpset
    55   val delsimprocs: simpset * simproc list -> simpset
    56   val setmksimps: simpset * (thm -> thm list) -> simpset
    57   val setmkcong: simpset * (thm -> thm) -> simpset
    58   val setmksym: simpset * (thm -> thm option) -> simpset
    59   val setmkeqTrue: simpset * (thm -> thm option) -> simpset
    60   val settermless: simpset * (term * term -> bool) -> simpset
    61   val setsubgoaler: simpset * (simpset -> int -> tactic) -> simpset
    62   val setloop: simpset * (int -> tactic) -> simpset
    63   val addloop: simpset * (string * (int -> tactic)) -> simpset
    64   val delloop: simpset * string -> simpset
    65   val setSSolver: simpset * solver -> simpset
    66   val addSSolver: simpset * solver -> simpset
    67   val setSolver: simpset * solver -> simpset
    68   val addSolver: simpset * solver -> simpset
    69   val generic_simp_tac: bool -> bool * bool * bool -> simpset -> int -> tactic
    70 end;
    71 
    72 signature META_SIMPLIFIER =
    73 sig
    74   include BASIC_META_SIMPLIFIER
    75   exception SIMPLIFIER of string * thm
    76   val clear_ss: simpset -> simpset
    77   exception SIMPROC_FAIL of string * exn
    78   val simproc_i: Sign.sg -> string -> term list
    79     -> (Sign.sg -> simpset -> term -> thm option) -> simproc
    80   val simproc: Sign.sg -> string -> string list
    81     -> (Sign.sg -> simpset -> term -> thm option) -> simproc
    82   val rewrite_cterm: bool * bool * bool ->
    83     (simpset -> thm -> thm option) -> simpset -> cterm -> thm
    84   val rewrite_aux: (simpset -> thm -> thm option) -> bool -> thm list -> cterm -> thm
    85   val simplify_aux: (simpset -> thm -> thm option) -> bool -> thm list -> thm -> thm
    86   val rewrite_term: Sign.sg -> thm list -> (term -> term option) list -> term -> term
    87   val rewrite_thm: bool * bool * bool ->
    88     (simpset -> thm -> thm option) -> simpset -> thm -> thm
    89   val rewrite_goals_rule_aux: (simpset -> thm -> thm option) -> thm list -> thm -> thm
    90   val rewrite_goal_rule: bool * bool * bool ->
    91     (simpset -> thm -> thm option) -> simpset -> int -> thm -> thm
    92   val asm_rewrite_goal_tac: bool * bool * bool ->
    93     (simpset -> tactic) -> simpset -> int -> tactic
    94   val simp_thm: bool * bool * bool -> simpset -> thm -> thm
    95   val simp_cterm: bool * bool * bool -> simpset -> cterm -> thm
    96 end;
    97 
    98 structure MetaSimplifier: META_SIMPLIFIER =
    99 struct
   100 
   101 
   102 (** diagnostics **)
   103 
   104 exception SIMPLIFIER of string * thm;
   105 
   106 val debug_simp = ref false;
   107 val trace_simp = ref false;
   108 val simp_depth = ref 0;
   109 val simp_depth_limit = ref 1000;
   110 val trace_simp_depth_limit = ref 1000;
   111 
   112 local
   113 
   114 fun println a =
   115   if !simp_depth > !trace_simp_depth_limit then ()
   116   else tracing (enclose "[" "]" (string_of_int(!simp_depth)) ^ a);
   117 
   118 fun prnt warn a = if warn then warning a else println a;
   119 fun prtm warn a sg t = prnt warn (a ^ "\n" ^ Sign.string_of_term sg t);
   120 fun prctm warn a t = prnt warn (a ^ "\n" ^ Display.string_of_cterm t);
   121 
   122 in
   123 
   124 fun debug warn a = if ! debug_simp then prnt warn a else ();
   125 fun trace warn a = if ! trace_simp then prnt warn a else ();
   126 
   127 fun debug_term warn a sign t = if ! debug_simp then prtm warn a sign t else ();
   128 fun trace_term warn a sign t = if ! trace_simp then prtm warn a sign t else ();
   129 fun trace_cterm warn a ct = if ! trace_simp then prctm warn a ct else ();
   130 fun trace_thm a th = if ! trace_simp then prctm false a (Thm.cprop_of th) else ();
   131 
   132 fun trace_named_thm a (thm, name) =
   133   if ! trace_simp then
   134     prctm false (if name = "" then a else a ^ " " ^ quote name ^ ":") (Thm.cprop_of thm)
   135   else ();
   136 
   137 fun warn_thm a = prctm true a o Thm.cprop_of;
   138 
   139 end;
   140 
   141 
   142 
   143 (** datatype simpset **)
   144 
   145 (* rewrite rules *)
   146 
   147 type rrule = {thm: thm, name: string, lhs: term, elhs: cterm, fo: bool, perm: bool};
   148 
   149 (*thm: the rewrite rule;
   150   name: name of theorem from which rewrite rule was extracted;
   151   lhs: the left-hand side;
   152   elhs: the etac-contracted lhs;
   153   fo: use first-order matching;
   154   perm: the rewrite rule is permutative;
   155 
   156 Remarks:
   157   - elhs is used for matching,
   158     lhs only for preservation of bound variable names;
   159   - fo is set iff
   160     either elhs is first-order (no Var is applied),
   161       in which case fo-matching is complete,
   162     or elhs is not a pattern,
   163       in which case there is nothing better to do;*)
   164 
   165 fun eq_rrule ({thm = thm1, ...}: rrule, {thm = thm2, ...}: rrule) =
   166   Drule.eq_thm_prop (thm1, thm2);
   167 
   168 
   169 (* congruences *)
   170 
   171 type cong = {thm: thm, lhs: cterm};
   172 
   173 fun eq_cong ({thm = thm1, ...}: cong, {thm = thm2, ...}: cong) =
   174   Drule.eq_thm_prop (thm1, thm2);
   175 
   176 
   177 (* solvers *)
   178 
   179 datatype solver =
   180   Solver of
   181    {name: string,
   182     solver: thm list -> int -> tactic,
   183     id: stamp};
   184 
   185 fun mk_solver name solver = Solver {name = name, solver = solver, id = stamp ()};
   186 
   187 fun solver_name (Solver {name, ...}) = name;
   188 fun solver ths (Solver {solver = tacf, ...}) = tacf ths;
   189 fun eq_solver (Solver {id = id1, ...}, Solver {id = id2, ...}) = (id1 = id2);
   190 val merge_solvers = gen_merge_lists eq_solver;
   191 
   192 
   193 (* simplification sets and procedures *)
   194 
   195 (*A simpset contains data required during conversion:
   196     rules: discrimination net of rewrite rules;
   197     prems: current premises;
   198     bounds: maximal index of bound variables already used
   199       (for generating new names when rewriting under lambda abstractions);
   200     congs: association list of congruence rules and
   201            a list of `weak' congruence constants.
   202            A congruence is `weak' if it avoids normalization of some argument.
   203     procs: discrimination net of simplification procedures
   204       (functions that prove rewrite rules on the fly);
   205     mk_rews:
   206       mk: turn simplification thms into rewrite rules;
   207       mk_cong: prepare congruence rules;
   208       mk_sym: turn == around;
   209       mk_eq_True: turn P into P == True;
   210     termless: relation for ordered rewriting;*)
   211 
   212 type mk_rews =
   213  {mk: thm -> thm list,
   214   mk_cong: thm -> thm,
   215   mk_sym: thm -> thm option,
   216   mk_eq_True: thm -> thm option};
   217 
   218 datatype simpset =
   219   Simpset of
   220    {rules: rrule Net.net,
   221     prems: thm list,
   222     bounds: int} *
   223    {congs: (string * cong) list * string list,
   224     procs: proc Net.net,
   225     mk_rews: mk_rews,
   226     termless: term * term -> bool,
   227     subgoal_tac: simpset -> int -> tactic,
   228     loop_tacs: (string * (int -> tactic)) list,
   229     solvers: solver list * solver list}
   230 and proc =
   231   Proc of
   232    {name: string,
   233     lhs: cterm,
   234     proc: Sign.sg -> simpset -> term -> thm option,
   235     id: stamp};
   236 
   237 fun eq_proc (Proc {id = id1, ...}, Proc {id = id2, ...}) = (id1 = id2);
   238 
   239 fun rep_ss (Simpset args) = args;
   240 
   241 fun make_ss1 (rules, prems, bounds) =
   242   {rules = rules, prems = prems, bounds = bounds};
   243 
   244 fun map_ss1 f {rules, prems, bounds} =
   245   make_ss1 (f (rules, prems, bounds));
   246 
   247 fun make_ss2 (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =
   248   {congs = congs, procs = procs, mk_rews = mk_rews, termless = termless,
   249     subgoal_tac = subgoal_tac, loop_tacs = loop_tacs, solvers = solvers};
   250 
   251 fun map_ss2 f {congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers} =
   252   make_ss2 (f (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   253 
   254 fun make_simpset (args1, args2) = Simpset (make_ss1 args1, make_ss2 args2);
   255 
   256 fun map_simpset f (Simpset ({rules, prems, bounds},
   257     {congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers})) =
   258   make_simpset (f ((rules, prems, bounds),
   259     (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers)));
   260 
   261 fun map_simpset1 f (Simpset (r1, r2)) = Simpset (map_ss1 f r1, r2);
   262 fun map_simpset2 f (Simpset (r1, r2)) = Simpset (r1, map_ss2 f r2);
   263 
   264 
   265 (* print simpsets *)
   266 
   267 fun print_ss ss =
   268   let
   269     val pretty_thms = map Display.pretty_thm;
   270 
   271     fun pretty_cong (name, th) =
   272       Pretty.block [Pretty.str (name ^ ":"), Pretty.brk 1, Display.pretty_thm th];
   273     fun pretty_proc (name, lhss) =
   274       Pretty.big_list (name ^ ":") (map Display.pretty_cterm lhss);
   275 
   276     val Simpset ({rules, ...}, {congs, procs, loop_tacs, solvers, ...}) = ss;
   277     val smps = map (#thm o #2) (Net.dest rules);
   278     val cngs = map (fn (name, {thm, ...}) => (name, thm)) (#1 congs);
   279     val prcs = Net.dest procs |>
   280       map (fn (_, Proc {name, lhs, id, ...}) => ((name, lhs), id))
   281       |> partition_eq eq_snd
   282       |> map (fn ps => (#1 (#1 (hd ps)), map (#2 o #1) ps))
   283       |> Library.sort_wrt #1;
   284   in
   285     [Pretty.big_list "simplification rules:" (pretty_thms smps),
   286       Pretty.big_list "simplification procedures:" (map pretty_proc prcs),
   287       Pretty.big_list "congruences:" (map pretty_cong cngs),
   288       Pretty.strs ("loopers:" :: map (quote o #1) loop_tacs),
   289       Pretty.strs ("unsafe solvers:" :: map (quote o solver_name) (#1 solvers)),
   290       Pretty.strs ("safe solvers:" :: map (quote o solver_name) (#2 solvers))]
   291     |> Pretty.chunks |> Pretty.writeln
   292   end;
   293 
   294 
   295 (* empty simpsets *)
   296 
   297 local
   298 
   299 fun init_ss mk_rews termless subgoal_tac solvers =
   300   make_simpset ((Net.empty, [], 0),
   301     (([], []), Net.empty, mk_rews, termless, subgoal_tac, [], solvers));
   302 
   303 val basic_mk_rews: mk_rews =
   304  {mk = fn th => if can Logic.dest_equals (Thm.concl_of th) then [th] else [],
   305   mk_cong = I,
   306   mk_sym = SOME o Drule.symmetric_fun,
   307   mk_eq_True = K NONE};
   308 
   309 in
   310 
   311 val empty_ss = init_ss basic_mk_rews Term.termless (K (K no_tac)) ([], []);
   312 
   313 fun clear_ss (Simpset (_, {mk_rews, termless, subgoal_tac, solvers, ...})) =
   314   init_ss mk_rews termless subgoal_tac solvers;
   315 
   316 end;
   317 
   318 
   319 (* merge simpsets *)            (*NOTE: ignores some fields of 2nd simpset*)
   320 
   321 fun merge_ss (ss1, ss2) =
   322   let
   323     val Simpset ({rules = rules1, prems = prems1, bounds = bounds1},
   324      {congs = (congs1, weak1), procs = procs1, mk_rews, termless, subgoal_tac,
   325       loop_tacs = loop_tacs1, solvers = (unsafe_solvers1, solvers1)}) = ss1;
   326     val Simpset ({rules = rules2, prems = prems2, bounds = bounds2},
   327      {congs = (congs2, weak2), procs = procs2, mk_rews = _, termless = _, subgoal_tac = _,
   328       loop_tacs = loop_tacs2, solvers = (unsafe_solvers2, solvers2)}) = ss2;
   329 
   330     val rules' = Net.merge (rules1, rules2, eq_rrule);
   331     val prems' = gen_merge_lists Drule.eq_thm_prop prems1 prems2;
   332     val bounds' = Int.max (bounds1, bounds2);
   333     val congs' = gen_merge_lists (eq_cong o pairself #2) congs1 congs2;
   334     val weak' = merge_lists weak1 weak2;
   335     val procs' = Net.merge (procs1, procs2, eq_proc);
   336     val loop_tacs' = merge_alists loop_tacs1 loop_tacs2;
   337     val unsafe_solvers' = merge_solvers unsafe_solvers1 unsafe_solvers2;
   338     val solvers' = merge_solvers solvers1 solvers2;
   339   in
   340     make_simpset ((rules', prems', bounds'), ((congs', weak'), procs',
   341       mk_rews, termless, subgoal_tac, loop_tacs', (unsafe_solvers', solvers')))
   342   end;
   343 
   344 
   345 (* simprocs *)
   346 
   347 exception SIMPROC_FAIL of string * exn;
   348 
   349 datatype simproc = Simproc of proc list;
   350 
   351 fun mk_simproc name lhss proc =
   352   let val id = stamp () in
   353     Simproc (lhss |> map (fn lhs =>
   354       Proc {name = name, lhs = lhs, proc = proc, id = id}))
   355   end;
   356 
   357 fun simproc_i sg name = mk_simproc name o map (Thm.cterm_of sg o Logic.varify);
   358 fun simproc sg name = simproc_i sg name o map (Sign.simple_read_term sg TypeInfer.logicT);
   359 
   360 
   361 
   362 (** simpset operations **)
   363 
   364 (* bounds and prems *)
   365 
   366 val incr_bounds = map_simpset1 (fn (rules, prems, bounds) =>
   367   (rules, prems, bounds + 1));
   368 
   369 fun add_prems ths = map_simpset1 (fn (rules, prems, bounds) =>
   370   (rules, ths @ prems, bounds));
   371 
   372 fun prems_of_ss (Simpset ({prems, ...}, _)) = prems;
   373 
   374 
   375 (* addsimps *)
   376 
   377 fun mk_rrule2 {thm, name, lhs, elhs, perm} =
   378   let
   379     val fo = Pattern.first_order (term_of elhs) orelse not (Pattern.pattern (term_of elhs))
   380   in {thm = thm, name = name, lhs = lhs, elhs = elhs, fo = fo, perm = perm} end;
   381 
   382 fun insert_rrule quiet (ss, rrule as {thm, name, lhs, elhs, perm}) =
   383  (trace_named_thm "Adding rewrite rule" (thm, name);
   384   ss |> map_simpset1 (fn (rules, prems, bounds) =>
   385     let
   386       val rrule2 as {elhs, ...} = mk_rrule2 rrule;
   387       val rules' = Net.insert_term ((term_of elhs, rrule2), rules, eq_rrule);
   388     in (rules', prems, bounds) end)
   389   handle Net.INSERT =>
   390     (if quiet then () else warn_thm "Ignoring duplicate rewrite rule:" thm; ss));
   391 
   392 fun vperm (Var _, Var _) = true
   393   | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)
   394   | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)
   395   | vperm (t, u) = (t = u);
   396 
   397 fun var_perm (t, u) =
   398   vperm (t, u) andalso eq_set (term_varnames t, term_varnames u);
   399 
   400 (* FIXME: it seems that the conditions on extra variables are too liberal if
   401 prems are nonempty: does solving the prems really guarantee instantiation of
   402 all its Vars? Better: a dynamic check each time a rule is applied.
   403 *)
   404 fun rewrite_rule_extra_vars prems elhs erhs =
   405   not (term_varnames erhs subset Library.foldl add_term_varnames (term_varnames elhs, prems))
   406   orelse
   407   not (term_tvars erhs subset (term_tvars elhs union List.concat (map term_tvars prems)));
   408 
   409 (*simple test for looping rewrite rules and stupid orientations*)
   410 fun reorient sign prems lhs rhs =
   411   rewrite_rule_extra_vars prems lhs rhs
   412     orelse
   413   is_Var (head_of lhs)
   414     orelse
   415 (* turns t = x around, which causes a headache if x is a local variable -
   416    usually it is very useful :-(
   417   is_Free rhs andalso not(is_Free lhs) andalso not(Logic.occs(rhs,lhs))
   418   andalso not(exists_subterm is_Var lhs)
   419     orelse
   420 *)
   421   exists (apl (lhs, Logic.occs)) (rhs :: prems)
   422     orelse
   423   null prems andalso Pattern.matches (Sign.tsig_of sign) (lhs, rhs)
   424     (*the condition "null prems" is necessary because conditional rewrites
   425       with extra variables in the conditions may terminate although
   426       the rhs is an instance of the lhs; example: ?m < ?n ==> f(?n) == f(?m)*)
   427     orelse
   428   is_Const lhs andalso not (is_Const rhs);
   429 
   430 fun decomp_simp thm =
   431   let
   432     val {sign, prop, ...} = Thm.rep_thm thm;
   433     val prems = Logic.strip_imp_prems prop;
   434     val concl = Drule.strip_imp_concl (Thm.cprop_of thm);
   435     val (lhs, rhs) = Drule.dest_equals concl handle TERM _ =>
   436       raise SIMPLIFIER ("Rewrite rule not a meta-equality", thm);
   437     val (_, elhs) = Drule.dest_equals (Thm.cprop_of (Thm.eta_conversion lhs));
   438     val elhs = if elhs = lhs then lhs else elhs;  (*share identical copies*)
   439     val erhs = Pattern.eta_contract (term_of rhs);
   440     val perm =
   441       var_perm (term_of elhs, erhs) andalso
   442       not (term_of elhs aconv erhs) andalso
   443       not (is_Var (term_of elhs));
   444   in (sign, prems, term_of lhs, elhs, term_of rhs, perm) end;
   445 
   446 fun decomp_simp' thm =
   447   let val (_, _, lhs, _, rhs, _) = decomp_simp thm in
   448     if Thm.nprems_of thm > 0 then raise SIMPLIFIER ("Bad conditional rewrite rule", thm)
   449     else (lhs, rhs)
   450   end;
   451 
   452 fun mk_eq_True (Simpset (_, {mk_rews = {mk_eq_True, ...}, ...})) (thm, name) =
   453   (case mk_eq_True thm of
   454     NONE => []
   455   | SOME eq_True =>
   456       let val (_, _, lhs, elhs, _, _) = decomp_simp eq_True
   457       in [{thm = eq_True, name = name, lhs = lhs, elhs = elhs, perm = false}] end);
   458 
   459 (*create the rewrite rule and possibly also the eq_True variant,
   460   in case there are extra vars on the rhs*)
   461 fun rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm2) =
   462   let val rrule = {thm = thm, name = name, lhs = lhs, elhs = elhs, perm = false} in
   463     if term_varnames rhs subset term_varnames lhs andalso
   464       term_tvars rhs subset term_tvars lhs then [rrule]
   465     else mk_eq_True ss (thm2, name) @ [rrule]
   466   end;
   467 
   468 fun mk_rrule ss (thm, name) =
   469   let val (_, prems, lhs, elhs, rhs, perm) = decomp_simp thm in
   470     if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]
   471     else
   472       (*weak test for loops*)
   473       if rewrite_rule_extra_vars prems lhs rhs orelse is_Var (term_of elhs)
   474       then mk_eq_True ss (thm, name)
   475       else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
   476   end;
   477 
   478 fun orient_rrule ss (thm, name) =
   479   let val (sign, prems, lhs, elhs, rhs, perm) = decomp_simp thm in
   480     if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]
   481     else if reorient sign prems lhs rhs then
   482       if reorient sign prems rhs lhs
   483       then mk_eq_True ss (thm, name)
   484       else
   485         let val Simpset (_, {mk_rews = {mk_sym, ...}, ...}) = ss in
   486           (case mk_sym thm of
   487             NONE => []
   488           | SOME thm' =>
   489               let val (_, _, lhs', elhs', rhs', _) = decomp_simp thm'
   490               in rrule_eq_True (thm', name, lhs', elhs', rhs', ss, thm) end)
   491         end
   492     else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
   493   end;
   494 
   495 fun extract_rews (Simpset (_, {mk_rews = {mk, ...}, ...}), thms) =
   496   List.concat (map (fn thm => map (rpair (Thm.name_of_thm thm)) (mk thm)) thms);
   497 
   498 fun orient_comb_simps comb mk_rrule (ss, thms) =
   499   let
   500     val rews = extract_rews (ss, thms);
   501     val rrules = List.concat (map mk_rrule rews);
   502   in Library.foldl comb (ss, rrules) end;
   503 
   504 fun extract_safe_rrules (ss, thm) =
   505   List.concat (map (orient_rrule ss) (extract_rews (ss, [thm])));
   506 
   507 (*add rewrite rules explicitly; do not reorient!*)
   508 fun ss addsimps thms =
   509   orient_comb_simps (insert_rrule false) (mk_rrule ss) (ss, thms);
   510 
   511 
   512 (* delsimps *)
   513 
   514 fun del_rrule (ss, rrule as {thm, elhs, ...}) =
   515   ss |> map_simpset1 (fn (rules, prems, bounds) =>
   516     (Net.delete_term ((term_of elhs, rrule), rules, eq_rrule), prems, bounds))
   517   handle Net.DELETE => (warn_thm "Rewrite rule not in simpset:" thm; ss);
   518 
   519 fun ss delsimps thms =
   520   orient_comb_simps del_rrule (map mk_rrule2 o mk_rrule ss) (ss, thms);
   521 
   522 
   523 (* congs *)
   524 
   525 fun cong_name (Const (a, _)) = SOME a
   526   | cong_name (Free (a, _)) = SOME ("Free: " ^ a)
   527   | cong_name _ = NONE;
   528 
   529 local
   530 
   531 fun is_full_cong_prems [] [] = true
   532   | is_full_cong_prems [] _ = false
   533   | is_full_cong_prems (p :: prems) varpairs =
   534       (case Logic.strip_assums_concl p of
   535         Const ("==", _) $ lhs $ rhs =>
   536           let val (x, xs) = strip_comb lhs and (y, ys) = strip_comb rhs in
   537             is_Var x andalso forall is_Bound xs andalso
   538             null (findrep xs) andalso xs = ys andalso
   539             (x, y) mem varpairs andalso
   540             is_full_cong_prems prems (varpairs \ (x, y))
   541           end
   542       | _ => false);
   543 
   544 fun is_full_cong thm =
   545   let
   546     val prems = prems_of thm and concl = concl_of thm;
   547     val (lhs, rhs) = Logic.dest_equals concl;
   548     val (f, xs) = strip_comb lhs and (g, ys) = strip_comb rhs;
   549   in
   550     f = g andalso null (findrep (xs @ ys)) andalso length xs = length ys andalso
   551     is_full_cong_prems prems (xs ~~ ys)
   552   end;
   553 
   554 fun add_cong (ss, thm) = ss |>
   555   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   556     let
   557       val (lhs, _) = Drule.dest_equals (Drule.strip_imp_concl (Thm.cprop_of thm))
   558         handle TERM _ => raise SIMPLIFIER ("Congruence not a meta-equality", thm);
   559     (*val lhs = Pattern.eta_contract lhs;*)
   560       val a = valOf (cong_name (head_of (term_of lhs))) handle Option =>
   561         raise SIMPLIFIER ("Congruence must start with a constant or free variable", thm);
   562       val (alist, weak) = congs;
   563       val alist2 = overwrite_warn (alist, (a, {lhs = lhs, thm = thm}))
   564         ("Overwriting congruence rule for " ^ quote a);
   565       val weak2 = if is_full_cong thm then weak else a :: weak;
   566     in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
   567 
   568 fun del_cong (ss, thm) = ss |>
   569   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   570     let
   571       val (lhs, _) = Logic.dest_equals (Thm.concl_of thm) handle TERM _ =>
   572         raise SIMPLIFIER ("Congruence not a meta-equality", thm);
   573     (*val lhs = Pattern.eta_contract lhs;*)
   574       val a = valOf (cong_name (head_of lhs)) handle Option =>
   575         raise SIMPLIFIER ("Congruence must start with a constant", thm);
   576       val (alist, _) = congs;
   577       val alist2 = List.filter (fn (x, _) => x <> a) alist;
   578       val weak2 = alist2 |> List.mapPartial (fn (a, {thm, ...}) =>
   579         if is_full_cong thm then NONE else SOME a);
   580     in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
   581 
   582 fun mk_cong (Simpset (_, {mk_rews = {mk_cong = f, ...}, ...})) = f;
   583 
   584 in
   585 
   586 val (op addeqcongs) = Library.foldl add_cong;
   587 val (op deleqcongs) = Library.foldl del_cong;
   588 
   589 fun ss addcongs congs = ss addeqcongs map (mk_cong ss) congs;
   590 fun ss delcongs congs = ss deleqcongs map (mk_cong ss) congs;
   591 
   592 end;
   593 
   594 
   595 (* simprocs *)
   596 
   597 local
   598 
   599 fun add_proc (ss, proc as Proc {name, lhs, ...}) =
   600  (trace_cterm false ("Adding simplification procedure " ^ quote name ^ " for") lhs;
   601   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   602     (congs, Net.insert_term ((term_of lhs, proc), procs, eq_proc),
   603       mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
   604   handle Net.INSERT =>
   605     (warning ("Ignoring duplicate simplification procedure " ^ quote name); ss));
   606 
   607 fun del_proc (ss, proc as Proc {name, lhs, ...}) =
   608   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   609     (congs, Net.delete_term ((term_of lhs, proc), procs, eq_proc),
   610       mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
   611   handle Net.DELETE =>
   612     (warning ("Simplification procedure " ^ quote name ^ " not in simpset"); ss);
   613 
   614 in
   615 
   616 val (op addsimprocs) = Library.foldl (fn (ss, Simproc procs) => Library.foldl add_proc (ss, procs));
   617 val (op delsimprocs) = Library.foldl (fn (ss, Simproc procs) => Library.foldl del_proc (ss, procs));
   618 
   619 end;
   620 
   621 
   622 (* mk_rews *)
   623 
   624 local
   625 
   626 fun map_mk_rews f = map_simpset2 (fn (congs, procs, {mk, mk_cong, mk_sym, mk_eq_True},
   627       termless, subgoal_tac, loop_tacs, solvers) =>
   628   let val (mk', mk_cong', mk_sym', mk_eq_True') = f (mk, mk_cong, mk_sym, mk_eq_True) in
   629     (congs, procs, {mk = mk', mk_cong = mk_cong', mk_sym = mk_sym', mk_eq_True = mk_eq_True'},
   630       termless, subgoal_tac, loop_tacs, solvers)
   631   end);
   632 
   633 in
   634 
   635 fun ss setmksimps mk = ss |> map_mk_rews (fn (_, mk_cong, mk_sym, mk_eq_True) =>
   636   (mk, mk_cong, mk_sym, mk_eq_True));
   637 
   638 fun ss setmkcong mk_cong = ss |> map_mk_rews (fn (mk, _, mk_sym, mk_eq_True) =>
   639   (mk, mk_cong, mk_sym, mk_eq_True));
   640 
   641 fun ss setmksym mk_sym = ss |> map_mk_rews (fn (mk, mk_cong, _, mk_eq_True) =>
   642   (mk, mk_cong, mk_sym, mk_eq_True));
   643 
   644 fun ss setmkeqTrue mk_eq_True = ss |> map_mk_rews (fn (mk, mk_cong, mk_sym, _) =>
   645   (mk, mk_cong, mk_sym, mk_eq_True));
   646 
   647 end;
   648 
   649 
   650 (* termless *)
   651 
   652 fun ss settermless termless = ss |>
   653   map_simpset2 (fn (congs, procs, mk_rews, _, subgoal_tac, loop_tacs, solvers) =>
   654    (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   655 
   656 
   657 (* tactics *)
   658 
   659 fun ss setsubgoaler subgoal_tac = ss |>
   660   map_simpset2 (fn (congs, procs, mk_rews, termless, _, loop_tacs, solvers) =>
   661    (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   662 
   663 fun ss setloop tac = ss |>
   664   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, _, solvers) =>
   665    (congs, procs, mk_rews, termless, subgoal_tac, [("", tac)], solvers));
   666 
   667 fun ss addloop (name, tac) = ss |>
   668   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   669     (congs, procs, mk_rews, termless, subgoal_tac,
   670       overwrite_warn (loop_tacs, (name, tac)) ("Overwriting looper " ^ quote name),
   671       solvers));
   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 #1) 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 
   703 (** rewriting **)
   704 
   705 (*
   706   Uses conversions, see:
   707     L C Paulson, A higher-order implementation of rewriting,
   708     Science of Computer Programming 3 (1983), pages 119-149.
   709 *)
   710 
   711 val dest_eq = Drule.dest_equals o Thm.cprop_of;
   712 val lhs_of = #1 o dest_eq;
   713 val rhs_of = #2 o dest_eq;
   714 
   715 fun check_conv msg thm thm' =
   716   let
   717     val thm'' = transitive thm (transitive
   718       (symmetric (Drule.beta_eta_conversion (lhs_of thm'))) thm')
   719   in if msg then trace_thm "SUCCEEDED" thm' else (); SOME thm'' end
   720   handle THM _ =>
   721     let val {sign, prop = _ $ _ $ prop0, ...} = Thm.rep_thm thm in
   722       trace_thm "Proved wrong thm (Check subgoaler?)" thm';
   723       trace_term false "Should have proved:" sign prop0;
   724       NONE
   725     end;
   726 
   727 
   728 (* mk_procrule *)
   729 
   730 fun mk_procrule thm =
   731   let val (_, prems, lhs, elhs, rhs, _) = decomp_simp thm in
   732     if rewrite_rule_extra_vars prems lhs rhs
   733     then (warn_thm "Extra vars on rhs:" thm; [])
   734     else [mk_rrule2 {thm = thm, name = "", lhs = lhs, elhs = elhs, perm = false}]
   735   end;
   736 
   737 
   738 (* rewritec: conversion to apply the meta simpset to a term *)
   739 
   740 (*Since the rewriting strategy is bottom-up, we avoid re-normalizing already
   741   normalized terms by carrying around the rhs of the rewrite rule just
   742   applied. This is called the `skeleton'. It is decomposed in parallel
   743   with the term. Once a Var is encountered, the corresponding term is
   744   already in normal form.
   745   skel0 is a dummy skeleton that is to enforce complete normalization.*)
   746 
   747 val skel0 = Bound 0;
   748 
   749 (*Use rhs as skeleton only if the lhs does not contain unnormalized bits.
   750   The latter may happen iff there are weak congruence rules for constants
   751   in the lhs.*)
   752 
   753 fun uncond_skel ((_, weak), (lhs, rhs)) =
   754   if null weak then rhs  (*optimization*)
   755   else if exists_Const (fn (c, _) => c mem weak) lhs then skel0
   756   else rhs;
   757 
   758 (*Behaves like unconditional rule if rhs does not contain vars not in the lhs.
   759   Otherwise those vars may become instantiated with unnormalized terms
   760   while the premises are solved.*)
   761 
   762 fun cond_skel (args as (congs, (lhs, rhs))) =
   763   if term_varnames rhs subset term_varnames lhs then uncond_skel args
   764   else skel0;
   765 
   766 (*
   767   Rewriting -- we try in order:
   768     (1) beta reduction
   769     (2) unconditional rewrite rules
   770     (3) conditional rewrite rules
   771     (4) simplification procedures
   772 
   773   IMPORTANT: rewrite rules must not introduce new Vars or TVars!
   774 *)
   775 
   776 fun rewritec (prover, signt, maxt) ss t =
   777   let
   778     val Simpset ({rules, ...}, {congs, procs, termless, ...}) = ss;
   779     val eta_thm = Thm.eta_conversion t;
   780     val eta_t' = rhs_of eta_thm;
   781     val eta_t = term_of eta_t';
   782     val tsigt = Sign.tsig_of signt;
   783     fun rew {thm, name, lhs, elhs, fo, perm} =
   784       let
   785         val {sign, prop, maxidx, ...} = rep_thm thm;
   786         val (rthm, elhs') = if maxt = ~1 then (thm, elhs)
   787           else (Thm.incr_indexes (maxt+1) thm, Thm.cterm_incr_indexes (maxt+1) elhs);
   788         val insts = if fo then Thm.cterm_first_order_match (elhs', eta_t')
   789                           else Thm.cterm_match (elhs', eta_t');
   790         val thm' = Thm.instantiate insts (Thm.rename_boundvars lhs eta_t rthm);
   791         val prop' = Thm.prop_of thm';
   792         val unconditional = (Logic.count_prems (prop',0) = 0);
   793         val (lhs', rhs') = Logic.dest_equals (Logic.strip_imp_concl prop')
   794       in
   795         if perm andalso not (termless (rhs', lhs'))
   796         then (trace_named_thm "Cannot apply permutative rewrite rule" (thm, name);
   797               trace_thm "Term does not become smaller:" thm'; NONE)
   798         else (trace_named_thm "Applying instance of rewrite rule" (thm, name);
   799            if unconditional
   800            then
   801              (trace_thm "Rewriting:" thm';
   802               let val lr = Logic.dest_equals prop;
   803                   val SOME thm'' = check_conv false eta_thm thm'
   804               in SOME (thm'', uncond_skel (congs, lr)) end)
   805            else
   806              (trace_thm "Trying to rewrite:" thm';
   807               if !simp_depth > !simp_depth_limit
   808               then let val s = "simp_depth_limit exceeded - giving up"
   809                    in trace false s; warning s; NONE end
   810               else
   811               case prover ss thm' of
   812                 NONE => (trace_thm "FAILED" thm'; NONE)
   813               | SOME thm2 =>
   814                   (case check_conv true eta_thm thm2 of
   815                      NONE => NONE |
   816                      SOME thm2' =>
   817                        let val concl = Logic.strip_imp_concl prop
   818                            val lr = Logic.dest_equals concl
   819                        in SOME (thm2', cond_skel (congs, lr)) end)))
   820       end
   821 
   822     fun rews [] = NONE
   823       | rews (rrule :: rrules) =
   824           let val opt = rew rrule handle Pattern.MATCH => NONE
   825           in case opt of NONE => rews rrules | some => some end;
   826 
   827     fun sort_rrules rrs = let
   828       fun is_simple({thm, ...}:rrule) = case Thm.prop_of thm of
   829                                       Const("==",_) $ _ $ _ => true
   830                                       | _                   => false
   831       fun sort []        (re1,re2) = re1 @ re2
   832         | sort (rr::rrs) (re1,re2) = if is_simple rr
   833                                      then sort rrs (rr::re1,re2)
   834                                      else sort rrs (re1,rr::re2)
   835     in sort rrs ([],[]) end
   836 
   837     fun proc_rews [] = NONE
   838       | proc_rews (Proc {name, proc, lhs, ...} :: ps) =
   839           if Pattern.matches tsigt (Thm.term_of lhs, Thm.term_of t) then
   840             (debug_term false ("Trying procedure " ^ quote name ^ " on:") signt eta_t;
   841              case transform_failure (curry SIMPROC_FAIL name)
   842                  (fn () => proc signt ss eta_t) () of
   843                NONE => (debug false "FAILED"; proc_rews ps)
   844              | SOME raw_thm =>
   845                  (trace_thm ("Procedure " ^ quote name ^ " produced rewrite rule:") raw_thm;
   846                   (case rews (mk_procrule raw_thm) of
   847                     NONE => (trace_cterm true ("IGNORED result of simproc " ^ quote name ^
   848                       " -- does not match") t; proc_rews ps)
   849                   | some => some)))
   850           else proc_rews ps;
   851   in case eta_t of
   852        Abs _ $ _ => SOME (transitive eta_thm
   853          (beta_conversion false eta_t'), skel0)
   854      | _ => (case rews (sort_rrules (Net.match_term rules eta_t)) of
   855                NONE => proc_rews (Net.match_term procs eta_t)
   856              | some => some)
   857   end;
   858 
   859 
   860 (* conversion to apply a congruence rule to a term *)
   861 
   862 fun congc (prover,signt,maxt) {thm=cong,lhs=lhs} t =
   863   let val sign = Thm.sign_of_thm cong
   864       val rthm = if maxt = ~1 then cong else Thm.incr_indexes (maxt+1) cong;
   865       val rlhs = fst (Drule.dest_equals (Drule.strip_imp_concl (cprop_of rthm)));
   866       val insts = Thm.cterm_match (rlhs, t)
   867       (* Pattern.match can raise Pattern.MATCH;
   868          is handled when congc is called *)
   869       val thm' = Thm.instantiate insts (Thm.rename_boundvars (term_of rlhs) (term_of t) rthm);
   870       val unit = trace_thm "Applying congruence rule:" thm';
   871       fun err (msg, thm) = (trace_thm msg thm; NONE)
   872   in case prover thm' of
   873        NONE => err ("Congruence proof failed.  Could not prove", thm')
   874      | SOME thm2 => (case check_conv true (Drule.beta_eta_conversion t) thm2 of
   875           NONE => err ("Congruence proof failed.  Should not have proved", thm2)
   876         | SOME thm2' =>
   877             if op aconv (pairself term_of (dest_equals (cprop_of thm2')))
   878             then NONE else SOME thm2')
   879   end;
   880 
   881 val (cA, (cB, cC)) =
   882   apsnd dest_equals (dest_implies (hd (cprems_of Drule.imp_cong)));
   883 
   884 fun transitive1 NONE NONE = NONE
   885   | transitive1 (SOME thm1) NONE = SOME thm1
   886   | transitive1 NONE (SOME thm2) = SOME thm2
   887   | transitive1 (SOME thm1) (SOME thm2) = SOME (transitive thm1 thm2)
   888 
   889 fun transitive2 thm = transitive1 (SOME thm);
   890 fun transitive3 thm = transitive1 thm o SOME;
   891 
   892 fun bottomc ((simprem, useprem, mutsimp), prover, sign, maxidx) =
   893   let
   894     fun botc skel ss t =
   895           if is_Var skel then NONE
   896           else
   897           (case subc skel ss t of
   898              some as SOME thm1 =>
   899                (case rewritec (prover, sign, maxidx) ss (rhs_of thm1) of
   900                   SOME (thm2, skel2) =>
   901                     transitive2 (transitive thm1 thm2)
   902                       (botc skel2 ss (rhs_of thm2))
   903                 | NONE => some)
   904            | NONE =>
   905                (case rewritec (prover, sign, maxidx) ss t of
   906                   SOME (thm2, skel2) => transitive2 thm2
   907                     (botc skel2 ss (rhs_of thm2))
   908                 | NONE => NONE))
   909 
   910     and try_botc ss t =
   911           (case botc skel0 ss t of
   912              SOME trec1 => trec1 | NONE => (reflexive t))
   913 
   914     and subc skel (ss as Simpset ({bounds, ...}, {congs, ...})) t0 =
   915        (case term_of t0 of
   916            Abs (a, T, t) =>
   917              let
   918                  val (v, t') = Thm.dest_abs (SOME ("." ^ a ^ "." ^ string_of_int bounds)) t0;
   919                  val ss' = incr_bounds ss;
   920                  val skel' = case skel of Abs (_, _, sk) => sk | _ => skel0;
   921              in case botc skel' ss' t' of
   922                   SOME thm => SOME (abstract_rule a v thm)
   923                 | NONE => NONE
   924              end
   925          | t $ _ => (case t of
   926              Const ("==>", _) $ _  => impc t0 ss
   927            | Abs _ =>
   928                let val thm = beta_conversion false t0
   929                in case subc skel0 ss (rhs_of thm) of
   930                     NONE => SOME thm
   931                   | SOME thm' => SOME (transitive thm thm')
   932                end
   933            | _  =>
   934                let fun appc () =
   935                      let
   936                        val (tskel, uskel) = case skel of
   937                            tskel $ uskel => (tskel, uskel)
   938                          | _ => (skel0, skel0);
   939                        val (ct, cu) = Thm.dest_comb t0
   940                      in
   941                      (case botc tskel ss ct of
   942                         SOME thm1 =>
   943                           (case botc uskel ss cu of
   944                              SOME thm2 => SOME (combination thm1 thm2)
   945                            | NONE => SOME (combination thm1 (reflexive cu)))
   946                       | NONE =>
   947                           (case botc uskel ss cu of
   948                              SOME thm1 => SOME (combination (reflexive ct) thm1)
   949                            | NONE => NONE))
   950                      end
   951                    val (h, ts) = strip_comb t
   952                in case cong_name h of
   953                     SOME a =>
   954                       (case assoc_string (fst congs, a) of
   955                          NONE => appc ()
   956                        | SOME cong =>
   957   (*post processing: some partial applications h t1 ... tj, j <= length ts,
   958     may be a redex. Example: map (%x. x) = (%xs. xs) wrt map_cong*)
   959                           (let
   960                              val thm = congc (prover ss, sign, maxidx) cong t0;
   961                              val t = getOpt (Option.map rhs_of thm, t0);
   962                              val (cl, cr) = Thm.dest_comb t
   963                              val dVar = Var(("", 0), dummyT)
   964                              val skel =
   965                                list_comb (h, replicate (length ts) dVar)
   966                            in case botc skel ss cl of
   967                                 NONE => thm
   968                               | SOME thm' => transitive3 thm
   969                                   (combination thm' (reflexive cr))
   970                            end handle TERM _ => error "congc result"
   971                                     | Pattern.MATCH => appc ()))
   972                   | _ => appc ()
   973                end)
   974          | _ => NONE)
   975 
   976     and impc ct ss =
   977       if mutsimp then mut_impc0 [] ct [] [] ss else nonmut_impc ct ss
   978 
   979     and rules_of_prem ss prem =
   980       if maxidx_of_term (term_of prem) <> ~1
   981       then (trace_cterm true
   982         "Cannot add premise as rewrite rule because it contains (type) unknowns:" prem; ([], NONE))
   983       else
   984         let val asm = assume prem
   985         in (extract_safe_rrules (ss, asm), SOME asm) end
   986 
   987     and add_rrules (rrss, asms) ss =
   988       Library.foldl (insert_rrule true) (ss, List.concat rrss) |> add_prems (List.mapPartial I asms)
   989 
   990     and disch r (prem, eq) =
   991       let
   992         val (lhs, rhs) = dest_eq eq;
   993         val eq' = implies_elim (Thm.instantiate
   994           ([], [(cA, prem), (cB, lhs), (cC, rhs)]) Drule.imp_cong)
   995           (implies_intr prem eq)
   996       in if not r then eq' else
   997         let
   998           val (prem', concl) = dest_implies lhs;
   999           val (prem'', _) = dest_implies rhs
  1000         in transitive (transitive
  1001           (Thm.instantiate ([], [(cA, prem'), (cB, prem), (cC, concl)])
  1002              Drule.swap_prems_eq) eq')
  1003           (Thm.instantiate ([], [(cA, prem), (cB, prem''), (cC, concl)])
  1004              Drule.swap_prems_eq)
  1005         end
  1006       end
  1007 
  1008     and rebuild [] _ _ _ _ eq = eq
  1009       | rebuild (prem :: prems) concl (rrs :: rrss) (asm :: asms) ss eq =
  1010           let
  1011             val ss' = add_rrules (rev rrss, rev asms) ss;
  1012             val concl' =
  1013               Drule.mk_implies (prem, getOpt (Option.map rhs_of eq, concl));
  1014             val dprem = Option.map (curry (disch false) prem)
  1015           in case rewritec (prover, sign, maxidx) ss' concl' of
  1016               NONE => rebuild prems concl' rrss asms ss (dprem eq)
  1017             | SOME (eq', _) => transitive2 (Library.foldl (disch false o swap)
  1018                   (valOf (transitive3 (dprem eq) eq'), prems))
  1019                 (mut_impc0 (rev prems) (rhs_of eq') (rev rrss) (rev asms) ss)
  1020           end
  1021 
  1022     and mut_impc0 prems concl rrss asms ss =
  1023       let
  1024         val prems' = strip_imp_prems concl;
  1025         val (rrss', asms') = split_list (map (rules_of_prem ss) prems')
  1026       in mut_impc (prems @ prems') (strip_imp_concl concl) (rrss @ rrss')
  1027         (asms @ asms') [] [] [] [] ss ~1 ~1
  1028       end
  1029 
  1030     and mut_impc [] concl [] [] prems' rrss' asms' eqns ss changed k =
  1031         transitive1 (Library.foldl (fn (eq2, (eq1, prem)) => transitive1 eq1
  1032             (Option.map (curry (disch false) prem) eq2)) (NONE, eqns ~~ prems'))
  1033           (if changed > 0 then
  1034              mut_impc (rev prems') concl (rev rrss') (rev asms')
  1035                [] [] [] [] ss ~1 changed
  1036            else rebuild prems' concl rrss' asms' ss
  1037              (botc skel0 (add_rrules (rev rrss', rev asms') ss) concl))
  1038 
  1039       | mut_impc (prem :: prems) concl (rrs :: rrss) (asm :: asms)
  1040           prems' rrss' asms' eqns ss changed k =
  1041         case (if k = 0 then NONE else botc skel0 (add_rrules
  1042           (rev rrss' @ rrss, rev asms' @ asms) ss) prem) of
  1043             NONE => mut_impc prems concl rrss asms (prem :: prems')
  1044               (rrs :: rrss') (asm :: asms') (NONE :: eqns) ss changed
  1045               (if k = 0 then 0 else k - 1)
  1046           | SOME eqn =>
  1047             let
  1048               val prem' = rhs_of eqn;
  1049               val tprems = map term_of prems;
  1050               val i = 1 + Library.foldl Int.max (~1, map (fn p =>
  1051                 find_index_eq p tprems) (#hyps (rep_thm eqn)));
  1052               val (rrs', asm') = rules_of_prem ss prem'
  1053             in mut_impc prems concl rrss asms (prem' :: prems')
  1054               (rrs' :: rrss') (asm' :: asms') (SOME (foldr (disch true)
  1055                 (Drule.imp_cong' eqn (reflexive (Drule.list_implies
  1056                   (Library.drop (i, prems), concl)))) (Library.take (i, prems))) :: eqns) ss (length prems') ~1
  1057             end
  1058 
  1059      (*legacy code - only for backwards compatibility*)
  1060      and nonmut_impc ct ss =
  1061        let val (prem, conc) = dest_implies ct;
  1062            val thm1 = if simprem then botc skel0 ss prem else NONE;
  1063            val prem1 = getOpt (Option.map rhs_of thm1, prem);
  1064            val ss1 = if not useprem then ss else add_rrules
  1065              (apsnd single (apfst single (rules_of_prem ss prem1))) ss
  1066        in (case botc skel0 ss1 conc of
  1067            NONE => (case thm1 of
  1068                NONE => NONE
  1069              | SOME thm1' => SOME (Drule.imp_cong' thm1' (reflexive conc)))
  1070          | SOME thm2 =>
  1071            let val thm2' = disch false (prem1, thm2)
  1072            in (case thm1 of
  1073                NONE => SOME thm2'
  1074              | SOME thm1' =>
  1075                  SOME (transitive (Drule.imp_cong' thm1' (reflexive conc)) thm2'))
  1076            end)
  1077        end
  1078 
  1079  in try_botc end;
  1080 
  1081 
  1082 (* Meta-rewriting: rewrites t to u and returns the theorem t==u *)
  1083 
  1084 (*
  1085   Parameters:
  1086     mode = (simplify A,
  1087             use A in simplifying B,
  1088             use prems of B (if B is again a meta-impl.) to simplify A)
  1089            when simplifying A ==> B
  1090     prover: how to solve premises in conditional rewrites and congruences
  1091 *)
  1092 
  1093 fun rewrite_cterm mode prover ss ct =
  1094   (simp_depth := !simp_depth + 1;
  1095    if !simp_depth mod 10 = 0
  1096    then warning ("Simplification depth " ^ string_of_int (!simp_depth))
  1097    else ();
  1098    trace_cterm false "SIMPLIFIER INVOKED ON THE FOLLOWING TERM:" ct;
  1099    let val {sign, t, maxidx, ...} = Thm.rep_cterm ct
  1100        val res = bottomc (mode, prover, sign, maxidx) ss ct
  1101          handle THM (s, _, thms) =>
  1102          error ("Exception THM was raised in simplifier:\n" ^ s ^ "\n" ^
  1103            Pretty.string_of (Display.pretty_thms thms))
  1104    in simp_depth := !simp_depth - 1; res end
  1105   ) handle exn => (simp_depth := 0; raise exn);
  1106 
  1107 (*Rewrite a cterm*)
  1108 fun rewrite_aux _ _ [] = (fn ct => Thm.reflexive ct)
  1109   | rewrite_aux prover full thms =
  1110       rewrite_cterm (full, false, false) prover (empty_ss addsimps thms);
  1111 
  1112 (*Rewrite a theorem*)
  1113 fun simplify_aux _ _ [] = (fn th => th)
  1114   | simplify_aux prover full thms =
  1115       Drule.fconv_rule (rewrite_cterm (full, false, false) prover (empty_ss addsimps thms));
  1116 
  1117 (*simple term rewriting -- no proof*)
  1118 fun rewrite_term sg rules procs =
  1119   Pattern.rewrite_term (Sign.tsig_of sg) (map decomp_simp' rules) procs;
  1120 
  1121 fun rewrite_thm mode prover ss = Drule.fconv_rule (rewrite_cterm mode prover ss);
  1122 
  1123 (*Rewrite the subgoals of a proof state (represented by a theorem) *)
  1124 fun rewrite_goals_rule_aux _ []   th = th
  1125   | rewrite_goals_rule_aux prover thms th =
  1126       Drule.fconv_rule (Drule.goals_conv (K true) (rewrite_cterm (true, true, false) prover
  1127         (empty_ss addsimps thms))) th;
  1128 
  1129 (*Rewrite the subgoal of a proof state (represented by a theorem)*)
  1130 fun rewrite_goal_rule mode prover ss i thm =
  1131   if 0 < i  andalso  i <= nprems_of thm
  1132   then Drule.fconv_rule (Drule.goals_conv (fn j => j=i) (rewrite_cterm mode prover ss)) thm
  1133   else raise THM("rewrite_goal_rule",i,[thm]);
  1134 
  1135 (*Rewrite subgoal i only.  SELECT_GOAL avoids inefficiencies in goals_conv.*)
  1136 fun asm_rewrite_goal_tac mode prover_tac ss =
  1137   SELECT_GOAL
  1138     (PRIMITIVE (rewrite_goal_rule mode (SINGLE o prover_tac) ss 1));
  1139 
  1140 
  1141 
  1142 (** simplification tactics and rules **)
  1143 
  1144 fun solve_all_tac solvers ss =
  1145   let
  1146     val Simpset (_, {subgoal_tac, ...}) = ss;
  1147     val solve_tac = subgoal_tac (set_solvers solvers ss) THEN_ALL_NEW (K no_tac);
  1148   in DEPTH_SOLVE (solve_tac 1) end;
  1149 
  1150 (*NOTE: may instantiate unknowns that appear also in other subgoals*)
  1151 fun generic_simp_tac safe mode ss =
  1152   let
  1153     val Simpset ({prems, ...}, {loop_tacs, solvers = (unsafe_solvers, solvers), ...}) = ss;
  1154     val loop_tac = FIRST' (map #2 loop_tacs);
  1155     val solve_tac = FIRST' (map (solver prems) (if safe then solvers else unsafe_solvers));
  1156 
  1157     fun simp_loop_tac i =
  1158       asm_rewrite_goal_tac mode (solve_all_tac unsafe_solvers) ss i THEN
  1159       (solve_tac i ORELSE TRY ((loop_tac THEN_ALL_NEW simp_loop_tac) i));
  1160   in simp_loop_tac end;
  1161 
  1162 fun simp rew mode ss thm =
  1163   let
  1164     val Simpset (_, {solvers = (unsafe_solvers, _), ...}) = ss;
  1165     val tacf = solve_all_tac unsafe_solvers;
  1166     fun prover s th = Option.map #1 (Seq.pull (tacf s th));
  1167   in rew mode prover ss thm end;
  1168 
  1169 val simp_thm = simp rewrite_thm;
  1170 val simp_cterm = simp rewrite_cterm;
  1171 
  1172 end;
  1173 
  1174 structure BasicMetaSimplifier: BASIC_META_SIMPLIFIER = MetaSimplifier;
  1175 open BasicMetaSimplifier;