src/Pure/meta_simplifier.ML
author skalberg
Fri Mar 04 15:07:34 2005 +0100 (2005-03-04)
changeset 15574 b1d1b5bfc464
parent 15570 8d8c70b41bab
child 16042 8e15ff79851a
permissions -rw-r--r--
Removed practically all references to Library.foldr.
     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   type rrule
    19   type cong
    20   type solver
    21   val mk_solver: string -> (thm list -> int -> tactic) -> solver
    22   type simpset
    23   type proc
    24   val rep_ss: simpset ->
    25    {rules: rrule Net.net,
    26     prems: thm list,
    27     bounds: int,
    28     depth: 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 
   111 local
   112 
   113 fun println a =
   114   tracing (case ! simp_depth of 0 => a | n => enclose "[" "]" (string_of_int n) ^ a);
   115 
   116 fun prnt warn a = if warn then warning a else println a;
   117 fun prtm warn a sg t = prnt warn (a ^ "\n" ^ Sign.string_of_term sg t);
   118 fun prctm warn a t = prnt warn (a ^ "\n" ^ Display.string_of_cterm t);
   119 
   120 in
   121 
   122 fun debug warn a = if ! debug_simp then prnt warn a else ();
   123 fun trace warn a = if ! trace_simp then prnt warn a else ();
   124 
   125 fun debug_term warn a sign t = if ! debug_simp then prtm warn a sign t else ();
   126 fun trace_term warn a sign t = if ! trace_simp then prtm warn a sign t else ();
   127 fun trace_cterm warn a ct = if ! trace_simp then prctm warn a ct else ();
   128 fun trace_thm a th = if ! trace_simp then prctm false a (Thm.cprop_of th) else ();
   129 
   130 fun trace_named_thm a (thm, name) =
   131   if ! trace_simp then
   132     prctm false (if name = "" then a else a ^ " " ^ quote name ^ ":") (Thm.cprop_of thm)
   133   else ();
   134 
   135 fun warn_thm a = prctm true a o Thm.cprop_of;
   136 
   137 end;
   138 
   139 
   140 
   141 (** datatype simpset **)
   142 
   143 (* rewrite rules *)
   144 
   145 type rrule = {thm: thm, name: string, lhs: term, elhs: cterm, fo: bool, perm: bool};
   146 
   147 (*thm: the rewrite rule;
   148   name: name of theorem from which rewrite rule was extracted;
   149   lhs: the left-hand side;
   150   elhs: the etac-contracted lhs;
   151   fo: use first-order matching;
   152   perm: the rewrite rule is permutative;
   153 
   154 Remarks:
   155   - elhs is used for matching,
   156     lhs only for preservation of bound variable names;
   157   - fo is set iff
   158     either elhs is first-order (no Var is applied),
   159       in which case fo-matching is complete,
   160     or elhs is not a pattern,
   161       in which case there is nothing better to do;*)
   162 
   163 fun eq_rrule ({thm = thm1, ...}: rrule, {thm = thm2, ...}: rrule) =
   164   Drule.eq_thm_prop (thm1, thm2);
   165 
   166 
   167 (* congruences *)
   168 
   169 type cong = {thm: thm, lhs: cterm};
   170 
   171 fun eq_cong ({thm = thm1, ...}: cong, {thm = thm2, ...}: cong) =
   172   Drule.eq_thm_prop (thm1, thm2);
   173 
   174 
   175 (* solvers *)
   176 
   177 datatype solver =
   178   Solver of
   179    {name: string,
   180     solver: thm list -> int -> tactic,
   181     id: stamp};
   182 
   183 fun mk_solver name solver = Solver {name = name, solver = solver, id = stamp ()};
   184 
   185 fun solver_name (Solver {name, ...}) = name;
   186 fun solver ths (Solver {solver = tacf, ...}) = tacf ths;
   187 fun eq_solver (Solver {id = id1, ...}, Solver {id = id2, ...}) = (id1 = id2);
   188 val merge_solvers = gen_merge_lists eq_solver;
   189 
   190 
   191 (* simplification sets and procedures *)
   192 
   193 (*A simpset contains data required during conversion:
   194     rules: discrimination net of rewrite rules;
   195     prems: current premises;
   196     bounds: maximal index of bound variables already used
   197       (for generating new names when rewriting under lambda abstractions);
   198     depth: depth of conditional rewriting;
   199     congs: association list of congruence rules and
   200            a list of `weak' congruence constants.
   201            A congruence is `weak' if it avoids normalization of some argument.
   202     procs: discrimination net of simplification procedures
   203       (functions that prove rewrite rules on the fly);
   204     mk_rews:
   205       mk: turn simplification thms into rewrite rules;
   206       mk_cong: prepare congruence rules;
   207       mk_sym: turn == around;
   208       mk_eq_True: turn P into P == True;
   209     termless: relation for ordered rewriting;*)
   210 
   211 type mk_rews =
   212  {mk: thm -> thm list,
   213   mk_cong: thm -> thm,
   214   mk_sym: thm -> thm option,
   215   mk_eq_True: thm -> thm option};
   216 
   217 datatype simpset =
   218   Simpset of
   219    {rules: rrule Net.net,
   220     prems: thm list,
   221     bounds: int,
   222     depth: 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, depth) =
   242   {rules = rules, prems = prems, bounds = bounds, depth = depth};
   243 
   244 fun map_ss1 f {rules, prems, bounds, depth} =
   245   make_ss1 (f (rules, prems, bounds, depth));
   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, depth},
   257     {congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers})) =
   258   make_simpset (f ((rules, prems, bounds, depth),
   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, 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, depth},
   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, depth = _},
   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', depth), ((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, depth) =>
   367   (rules, prems, bounds + 1, depth));
   368 
   369 fun add_prems ths = map_simpset1 (fn (rules, prems, bounds, depth) =>
   370   (rules, ths @ prems, bounds, depth));
   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, depth) =>
   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, depth) 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   exists (apl (lhs, Logic.occs)) (rhs :: prems)
   416     orelse
   417   null prems andalso Pattern.matches (Sign.tsig_of sign) (lhs, rhs)
   418     (*the condition "null prems" is necessary because conditional rewrites
   419       with extra variables in the conditions may terminate although
   420       the rhs is an instance of the lhs; example: ?m < ?n ==> f(?n) == f(?m)*)
   421     orelse
   422   is_Const lhs andalso not (is_Const rhs);
   423 
   424 fun decomp_simp thm =
   425   let
   426     val {sign, prop, ...} = Thm.rep_thm thm;
   427     val prems = Logic.strip_imp_prems prop;
   428     val concl = Drule.strip_imp_concl (Thm.cprop_of thm);
   429     val (lhs, rhs) = Drule.dest_equals concl handle TERM _ =>
   430       raise SIMPLIFIER ("Rewrite rule not a meta-equality", thm);
   431     val (_, elhs) = Drule.dest_equals (Thm.cprop_of (Thm.eta_conversion lhs));
   432     val elhs = if elhs = lhs then lhs else elhs;  (*share identical copies*)
   433     val erhs = Pattern.eta_contract (term_of rhs);
   434     val perm =
   435       var_perm (term_of elhs, erhs) andalso
   436       not (term_of elhs aconv erhs) andalso
   437       not (is_Var (term_of elhs));
   438   in (sign, prems, term_of lhs, elhs, term_of rhs, perm) end;
   439 
   440 fun decomp_simp' thm =
   441   let val (_, _, lhs, _, rhs, _) = decomp_simp thm in
   442     if Thm.nprems_of thm > 0 then raise SIMPLIFIER ("Bad conditional rewrite rule", thm)
   443     else (lhs, rhs)
   444   end;
   445 
   446 fun mk_eq_True (Simpset (_, {mk_rews = {mk_eq_True, ...}, ...})) (thm, name) =
   447   (case mk_eq_True thm of
   448     NONE => []
   449   | SOME eq_True =>
   450       let val (_, _, lhs, elhs, _, _) = decomp_simp eq_True
   451       in [{thm = eq_True, name = name, lhs = lhs, elhs = elhs, perm = false}] end);
   452 
   453 (*create the rewrite rule and possibly also the eq_True variant,
   454   in case there are extra vars on the rhs*)
   455 fun rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm2) =
   456   let val rrule = {thm = thm, name = name, lhs = lhs, elhs = elhs, perm = false} in
   457     if term_varnames rhs subset term_varnames lhs andalso
   458       term_tvars rhs subset term_tvars lhs then [rrule]
   459     else mk_eq_True ss (thm2, name) @ [rrule]
   460   end;
   461 
   462 fun mk_rrule ss (thm, name) =
   463   let val (_, prems, lhs, elhs, rhs, perm) = decomp_simp thm in
   464     if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]
   465     else
   466       (*weak test for loops*)
   467       if rewrite_rule_extra_vars prems lhs rhs orelse is_Var (term_of elhs)
   468       then mk_eq_True ss (thm, name)
   469       else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
   470   end;
   471 
   472 fun orient_rrule ss (thm, name) =
   473   let val (sign, prems, lhs, elhs, rhs, perm) = decomp_simp thm in
   474     if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]
   475     else if reorient sign prems lhs rhs then
   476       if reorient sign prems rhs lhs
   477       then mk_eq_True ss (thm, name)
   478       else
   479         let val Simpset (_, {mk_rews = {mk_sym, ...}, ...}) = ss in
   480           (case mk_sym thm of
   481             NONE => []
   482           | SOME thm' =>
   483               let val (_, _, lhs', elhs', rhs', _) = decomp_simp thm'
   484               in rrule_eq_True (thm', name, lhs', elhs', rhs', ss, thm) end)
   485         end
   486     else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
   487   end;
   488 
   489 fun extract_rews (Simpset (_, {mk_rews = {mk, ...}, ...}), thms) =
   490   List.concat (map (fn thm => map (rpair (Thm.name_of_thm thm)) (mk thm)) thms);
   491 
   492 fun orient_comb_simps comb mk_rrule (ss, thms) =
   493   let
   494     val rews = extract_rews (ss, thms);
   495     val rrules = List.concat (map mk_rrule rews);
   496   in Library.foldl comb (ss, rrules) end;
   497 
   498 fun extract_safe_rrules (ss, thm) =
   499   List.concat (map (orient_rrule ss) (extract_rews (ss, [thm])));
   500 
   501 (*add rewrite rules explicitly; do not reorient!*)
   502 fun ss addsimps thms =
   503   orient_comb_simps (insert_rrule false) (mk_rrule ss) (ss, thms);
   504 
   505 
   506 (* delsimps *)
   507 
   508 fun del_rrule (ss, rrule as {thm, elhs, ...}) =
   509   ss |> map_simpset1 (fn (rules, prems, bounds, depth) =>
   510     (Net.delete_term ((term_of elhs, rrule), rules, eq_rrule), prems, bounds, depth))
   511   handle Net.DELETE => (warn_thm "Rewrite rule not in simpset:" thm; ss);
   512 
   513 fun ss delsimps thms =
   514   orient_comb_simps del_rrule (map mk_rrule2 o mk_rrule ss) (ss, thms);
   515 
   516 
   517 (* congs *)
   518 
   519 fun cong_name (Const (a, _)) = SOME a
   520   | cong_name (Free (a, _)) = SOME ("Free: " ^ a)
   521   | cong_name _ = NONE;
   522 
   523 local
   524 
   525 fun is_full_cong_prems [] [] = true
   526   | is_full_cong_prems [] _ = false
   527   | is_full_cong_prems (p :: prems) varpairs =
   528       (case Logic.strip_assums_concl p of
   529         Const ("==", _) $ lhs $ rhs =>
   530           let val (x, xs) = strip_comb lhs and (y, ys) = strip_comb rhs in
   531             is_Var x andalso forall is_Bound xs andalso
   532             null (findrep xs) andalso xs = ys andalso
   533             (x, y) mem varpairs andalso
   534             is_full_cong_prems prems (varpairs \ (x, y))
   535           end
   536       | _ => false);
   537 
   538 fun is_full_cong thm =
   539   let
   540     val prems = prems_of thm and concl = concl_of thm;
   541     val (lhs, rhs) = Logic.dest_equals concl;
   542     val (f, xs) = strip_comb lhs and (g, ys) = strip_comb rhs;
   543   in
   544     f = g andalso null (findrep (xs @ ys)) andalso length xs = length ys andalso
   545     is_full_cong_prems prems (xs ~~ ys)
   546   end;
   547 
   548 fun add_cong (ss, thm) = ss |>
   549   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   550     let
   551       val (lhs, _) = Drule.dest_equals (Drule.strip_imp_concl (Thm.cprop_of thm))
   552         handle TERM _ => raise SIMPLIFIER ("Congruence not a meta-equality", thm);
   553     (*val lhs = Pattern.eta_contract lhs;*)
   554       val a = valOf (cong_name (head_of (term_of lhs))) handle Option =>
   555         raise SIMPLIFIER ("Congruence must start with a constant or free variable", thm);
   556       val (alist, weak) = congs;
   557       val alist2 = overwrite_warn (alist, (a, {lhs = lhs, thm = thm}))
   558         ("Overwriting congruence rule for " ^ quote a);
   559       val weak2 = if is_full_cong thm then weak else a :: weak;
   560     in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
   561 
   562 fun del_cong (ss, thm) = ss |>
   563   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   564     let
   565       val (lhs, _) = Logic.dest_equals (Thm.concl_of thm) handle TERM _ =>
   566         raise SIMPLIFIER ("Congruence not a meta-equality", thm);
   567     (*val lhs = Pattern.eta_contract lhs;*)
   568       val a = valOf (cong_name (head_of lhs)) handle Option =>
   569         raise SIMPLIFIER ("Congruence must start with a constant", thm);
   570       val (alist, _) = congs;
   571       val alist2 = List.filter (fn (x, _) => x <> a) alist;
   572       val weak2 = alist2 |> List.mapPartial (fn (a, {thm, ...}) =>
   573         if is_full_cong thm then NONE else SOME a);
   574     in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
   575 
   576 fun mk_cong (Simpset (_, {mk_rews = {mk_cong = f, ...}, ...})) = f;
   577 
   578 in
   579 
   580 val (op addeqcongs) = Library.foldl add_cong;
   581 val (op deleqcongs) = Library.foldl del_cong;
   582 
   583 fun ss addcongs congs = ss addeqcongs map (mk_cong ss) congs;
   584 fun ss delcongs congs = ss deleqcongs map (mk_cong ss) congs;
   585 
   586 end;
   587 
   588 
   589 (* simprocs *)
   590 
   591 local
   592 
   593 fun add_proc (ss, proc as Proc {name, lhs, ...}) =
   594  (trace_cterm false ("Adding simplification procedure " ^ quote name ^ " for") lhs;
   595   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   596     (congs, Net.insert_term ((term_of lhs, proc), procs, eq_proc),
   597       mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
   598   handle Net.INSERT =>
   599     (warning ("Ignoring duplicate simplification procedure " ^ quote name); ss));
   600 
   601 fun del_proc (ss, proc as Proc {name, lhs, ...}) =
   602   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   603     (congs, Net.delete_term ((term_of lhs, proc), procs, eq_proc),
   604       mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
   605   handle Net.DELETE =>
   606     (warning ("Simplification procedure " ^ quote name ^ " not in simpset"); ss);
   607 
   608 in
   609 
   610 val (op addsimprocs) = Library.foldl (fn (ss, Simproc procs) => Library.foldl add_proc (ss, procs));
   611 val (op delsimprocs) = Library.foldl (fn (ss, Simproc procs) => Library.foldl del_proc (ss, procs));
   612 
   613 end;
   614 
   615 
   616 (* mk_rews *)
   617 
   618 local
   619 
   620 fun map_mk_rews f = map_simpset2 (fn (congs, procs, {mk, mk_cong, mk_sym, mk_eq_True},
   621       termless, subgoal_tac, loop_tacs, solvers) =>
   622   let val (mk', mk_cong', mk_sym', mk_eq_True') = f (mk, mk_cong, mk_sym, mk_eq_True) in
   623     (congs, procs, {mk = mk', mk_cong = mk_cong', mk_sym = mk_sym', mk_eq_True = mk_eq_True'},
   624       termless, subgoal_tac, loop_tacs, solvers)
   625   end);
   626 
   627 in
   628 
   629 fun ss setmksimps mk = ss |> map_mk_rews (fn (_, mk_cong, mk_sym, mk_eq_True) =>
   630   (mk, mk_cong, mk_sym, mk_eq_True));
   631 
   632 fun ss setmkcong mk_cong = ss |> map_mk_rews (fn (mk, _, mk_sym, mk_eq_True) =>
   633   (mk, mk_cong, mk_sym, mk_eq_True));
   634 
   635 fun ss setmksym mk_sym = ss |> map_mk_rews (fn (mk, mk_cong, _, mk_eq_True) =>
   636   (mk, mk_cong, mk_sym, mk_eq_True));
   637 
   638 fun ss setmkeqTrue mk_eq_True = ss |> map_mk_rews (fn (mk, mk_cong, mk_sym, _) =>
   639   (mk, mk_cong, mk_sym, mk_eq_True));
   640 
   641 end;
   642 
   643 
   644 (* termless *)
   645 
   646 fun ss settermless termless = ss |>
   647   map_simpset2 (fn (congs, procs, mk_rews, _, subgoal_tac, loop_tacs, solvers) =>
   648    (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   649 
   650 
   651 (* tactics *)
   652 
   653 fun ss setsubgoaler subgoal_tac = ss |>
   654   map_simpset2 (fn (congs, procs, mk_rews, termless, _, loop_tacs, solvers) =>
   655    (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   656 
   657 fun ss setloop tac = ss |>
   658   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, _, solvers) =>
   659    (congs, procs, mk_rews, termless, subgoal_tac, [("", tac)], solvers));
   660 
   661 fun ss addloop (name, tac) = ss |>
   662   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   663     (congs, procs, mk_rews, termless, subgoal_tac,
   664       overwrite_warn (loop_tacs, (name, tac)) ("Overwriting looper " ^ quote name),
   665       solvers));
   666 
   667 fun ss delloop name = ss |>
   668   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   669     let val loop_tacs' = filter_out (equal name o #1) loop_tacs in
   670       if length loop_tacs <> length loop_tacs' then ()
   671       else warning ("No such looper in simpset: " ^ quote name);
   672       (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs', solvers)
   673     end);
   674 
   675 fun ss setSSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   676   subgoal_tac, loop_tacs, (unsafe_solvers, _)) =>
   677     (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, (unsafe_solvers, [solver])));
   678 
   679 fun ss addSSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   680   subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, termless,
   681     subgoal_tac, loop_tacs, (unsafe_solvers, merge_solvers solvers [solver])));
   682 
   683 fun ss setSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   684   subgoal_tac, loop_tacs, (_, solvers)) => (congs, procs, mk_rews, termless,
   685     subgoal_tac, loop_tacs, ([solver], solvers)));
   686 
   687 fun ss addSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   688   subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, termless,
   689     subgoal_tac, loop_tacs, (merge_solvers unsafe_solvers [solver], solvers)));
   690 
   691 fun set_solvers solvers = map_simpset2 (fn (congs, procs, mk_rews, termless,
   692   subgoal_tac, loop_tacs, _) => (congs, procs, mk_rews, termless,
   693   subgoal_tac, loop_tacs, (solvers, solvers)));
   694 
   695 
   696 
   697 (** rewriting **)
   698 
   699 (*
   700   Uses conversions, see:
   701     L C Paulson, A higher-order implementation of rewriting,
   702     Science of Computer Programming 3 (1983), pages 119-149.
   703 *)
   704 
   705 val dest_eq = Drule.dest_equals o Thm.cprop_of;
   706 val lhs_of = #1 o dest_eq;
   707 val rhs_of = #2 o dest_eq;
   708 
   709 fun check_conv msg thm thm' =
   710   let
   711     val thm'' = transitive thm (transitive
   712       (symmetric (Drule.beta_eta_conversion (lhs_of thm'))) thm')
   713   in if msg then trace_thm "SUCCEEDED" thm' else (); SOME thm'' end
   714   handle THM _ =>
   715     let val {sign, prop = _ $ _ $ prop0, ...} = Thm.rep_thm thm in
   716       trace_thm "Proved wrong thm (Check subgoaler?)" thm';
   717       trace_term false "Should have proved:" sign prop0;
   718       NONE
   719     end;
   720 
   721 
   722 (* mk_procrule *)
   723 
   724 fun mk_procrule thm =
   725   let val (_, prems, lhs, elhs, rhs, _) = decomp_simp thm in
   726     if rewrite_rule_extra_vars prems lhs rhs
   727     then (warn_thm "Extra vars on rhs:" thm; [])
   728     else [mk_rrule2 {thm = thm, name = "", lhs = lhs, elhs = elhs, perm = false}]
   729   end;
   730 
   731 
   732 (* rewritec: conversion to apply the meta simpset to a term *)
   733 
   734 (*Since the rewriting strategy is bottom-up, we avoid re-normalizing already
   735   normalized terms by carrying around the rhs of the rewrite rule just
   736   applied. This is called the `skeleton'. It is decomposed in parallel
   737   with the term. Once a Var is encountered, the corresponding term is
   738   already in normal form.
   739   skel0 is a dummy skeleton that is to enforce complete normalization.*)
   740 
   741 val skel0 = Bound 0;
   742 
   743 (*Use rhs as skeleton only if the lhs does not contain unnormalized bits.
   744   The latter may happen iff there are weak congruence rules for constants
   745   in the lhs.*)
   746 
   747 fun uncond_skel ((_, weak), (lhs, rhs)) =
   748   if null weak then rhs  (*optimization*)
   749   else if exists_Const (fn (c, _) => c mem weak) lhs then skel0
   750   else rhs;
   751 
   752 (*Behaves like unconditional rule if rhs does not contain vars not in the lhs.
   753   Otherwise those vars may become instantiated with unnormalized terms
   754   while the premises are solved.*)
   755 
   756 fun cond_skel (args as (congs, (lhs, rhs))) =
   757   if term_varnames rhs subset term_varnames lhs then uncond_skel args
   758   else skel0;
   759 
   760 fun incr_depth ss =
   761   let
   762     val ss' = ss |> map_simpset1 (fn (rules, prems, bounds, depth) =>
   763       (rules, prems, bounds, depth + 1));
   764     val Simpset ({depth = depth', ...}, _) = ss';
   765   in
   766     if depth' > ! simp_depth_limit
   767     then (warning "simp_depth_limit exceeded - giving up"; NONE)
   768     else
   769      (if depth' mod 10 = 0
   770       then warning ("Simplification depth " ^ string_of_int depth')
   771       else ();
   772       SOME ss')
   773   end;
   774 
   775 (*
   776   Rewriting -- we try in order:
   777     (1) beta reduction
   778     (2) unconditional rewrite rules
   779     (3) conditional rewrite rules
   780     (4) simplification procedures
   781 
   782   IMPORTANT: rewrite rules must not introduce new Vars or TVars!
   783 *)
   784 
   785 fun rewritec (prover, signt, maxt) ss t =
   786   let
   787     val Simpset ({rules, ...}, {congs, procs, termless, ...}) = ss;
   788     val eta_thm = Thm.eta_conversion t;
   789     val eta_t' = rhs_of eta_thm;
   790     val eta_t = term_of eta_t';
   791     val tsigt = Sign.tsig_of signt;
   792     fun rew {thm, name, lhs, elhs, fo, perm} =
   793       let
   794         val {sign, prop, maxidx, ...} = rep_thm thm;
   795         val (rthm, elhs') = if maxt = ~1 then (thm, elhs)
   796           else (Thm.incr_indexes (maxt+1) thm, Thm.cterm_incr_indexes (maxt+1) elhs);
   797         val insts = if fo then Thm.cterm_first_order_match (elhs', eta_t')
   798                           else Thm.cterm_match (elhs', eta_t');
   799         val thm' = Thm.instantiate insts (Thm.rename_boundvars lhs eta_t rthm);
   800         val prop' = Thm.prop_of thm';
   801         val unconditional = (Logic.count_prems (prop',0) = 0);
   802         val (lhs', rhs') = Logic.dest_equals (Logic.strip_imp_concl prop')
   803       in
   804         if perm andalso not (termless (rhs', lhs'))
   805         then (trace_named_thm "Cannot apply permutative rewrite rule" (thm, name);
   806               trace_thm "Term does not become smaller:" thm'; NONE)
   807         else (trace_named_thm "Applying instance of rewrite rule" (thm, name);
   808            if unconditional
   809            then
   810              (trace_thm "Rewriting:" thm';
   811               let val lr = Logic.dest_equals prop;
   812                   val SOME thm'' = check_conv false eta_thm thm'
   813               in SOME (thm'', uncond_skel (congs, lr)) end)
   814            else
   815              (trace_thm "Trying to rewrite:" thm';
   816               case incr_depth ss of
   817                 NONE => (trace_thm "FAILED - reached depth limit" thm'; NONE)
   818               | SOME ss' =>
   819               (case prover ss' thm' of
   820                 NONE => (trace_thm "FAILED" thm'; NONE)
   821               | SOME thm2 =>
   822                   (case check_conv true eta_thm thm2 of
   823                      NONE => NONE |
   824                      SOME thm2' =>
   825                        let val concl = Logic.strip_imp_concl prop
   826                            val lr = Logic.dest_equals concl
   827                        in SOME (thm2', cond_skel (congs, lr)) end))))
   828       end
   829 
   830     fun rews [] = NONE
   831       | rews (rrule :: rrules) =
   832           let val opt = rew rrule handle Pattern.MATCH => NONE
   833           in case opt of NONE => rews rrules | some => some end;
   834 
   835     fun sort_rrules rrs = let
   836       fun is_simple({thm, ...}:rrule) = case Thm.prop_of thm of
   837                                       Const("==",_) $ _ $ _ => true
   838                                       | _                   => false
   839       fun sort []        (re1,re2) = re1 @ re2
   840         | sort (rr::rrs) (re1,re2) = if is_simple rr
   841                                      then sort rrs (rr::re1,re2)
   842                                      else sort rrs (re1,rr::re2)
   843     in sort rrs ([],[]) end
   844 
   845     fun proc_rews [] = NONE
   846       | proc_rews (Proc {name, proc, lhs, ...} :: ps) =
   847           if Pattern.matches tsigt (Thm.term_of lhs, Thm.term_of t) then
   848             (debug_term false ("Trying procedure " ^ quote name ^ " on:") signt eta_t;
   849              case transform_failure (curry SIMPROC_FAIL name)
   850                  (fn () => proc signt ss eta_t) () of
   851                NONE => (debug false "FAILED"; proc_rews ps)
   852              | SOME raw_thm =>
   853                  (trace_thm ("Procedure " ^ quote name ^ " produced rewrite rule:") raw_thm;
   854                   (case rews (mk_procrule raw_thm) of
   855                     NONE => (trace_cterm true ("IGNORED result of simproc " ^ quote name ^
   856                       " -- does not match") t; proc_rews ps)
   857                   | some => some)))
   858           else proc_rews ps;
   859   in case eta_t of
   860        Abs _ $ _ => SOME (transitive eta_thm
   861          (beta_conversion false eta_t'), skel0)
   862      | _ => (case rews (sort_rrules (Net.match_term rules eta_t)) of
   863                NONE => proc_rews (Net.match_term procs eta_t)
   864              | some => some)
   865   end;
   866 
   867 
   868 (* conversion to apply a congruence rule to a term *)
   869 
   870 fun congc (prover,signt,maxt) {thm=cong,lhs=lhs} t =
   871   let val sign = Thm.sign_of_thm cong
   872       val rthm = if maxt = ~1 then cong else Thm.incr_indexes (maxt+1) cong;
   873       val rlhs = fst (Drule.dest_equals (Drule.strip_imp_concl (cprop_of rthm)));
   874       val insts = Thm.cterm_match (rlhs, t)
   875       (* Pattern.match can raise Pattern.MATCH;
   876          is handled when congc is called *)
   877       val thm' = Thm.instantiate insts (Thm.rename_boundvars (term_of rlhs) (term_of t) rthm);
   878       val unit = trace_thm "Applying congruence rule:" thm';
   879       fun err (msg, thm) = (trace_thm msg thm; NONE)
   880   in case prover thm' of
   881        NONE => err ("Congruence proof failed.  Could not prove", thm')
   882      | SOME thm2 => (case check_conv true (Drule.beta_eta_conversion t) thm2 of
   883           NONE => err ("Congruence proof failed.  Should not have proved", thm2)
   884         | SOME thm2' =>
   885             if op aconv (pairself term_of (dest_equals (cprop_of thm2')))
   886             then NONE else SOME thm2')
   887   end;
   888 
   889 val (cA, (cB, cC)) =
   890   apsnd dest_equals (dest_implies (hd (cprems_of Drule.imp_cong)));
   891 
   892 fun transitive1 NONE NONE = NONE
   893   | transitive1 (SOME thm1) NONE = SOME thm1
   894   | transitive1 NONE (SOME thm2) = SOME thm2
   895   | transitive1 (SOME thm1) (SOME thm2) = SOME (transitive thm1 thm2)
   896 
   897 fun transitive2 thm = transitive1 (SOME thm);
   898 fun transitive3 thm = transitive1 thm o SOME;
   899 
   900 fun bottomc ((simprem, useprem, mutsimp), prover, sign, maxidx) =
   901   let
   902     fun botc skel ss t =
   903           if is_Var skel then NONE
   904           else
   905           (case subc skel ss t of
   906              some as SOME thm1 =>
   907                (case rewritec (prover, sign, maxidx) ss (rhs_of thm1) of
   908                   SOME (thm2, skel2) =>
   909                     transitive2 (transitive thm1 thm2)
   910                       (botc skel2 ss (rhs_of thm2))
   911                 | NONE => some)
   912            | NONE =>
   913                (case rewritec (prover, sign, maxidx) ss t of
   914                   SOME (thm2, skel2) => transitive2 thm2
   915                     (botc skel2 ss (rhs_of thm2))
   916                 | NONE => NONE))
   917 
   918     and try_botc ss t =
   919           (case botc skel0 ss t of
   920              SOME trec1 => trec1 | NONE => (reflexive t))
   921 
   922     and subc skel (ss as Simpset ({bounds, ...}, {congs, ...})) t0 =
   923        (case term_of t0 of
   924            Abs (a, T, t) =>
   925              let
   926                  val (v, t') = Thm.dest_abs (SOME ("." ^ a ^ "." ^ string_of_int bounds)) t0;
   927                  val ss' = incr_bounds ss;
   928                  val skel' = case skel of Abs (_, _, sk) => sk | _ => skel0;
   929              in case botc skel' ss' t' of
   930                   SOME thm => SOME (abstract_rule a v thm)
   931                 | NONE => NONE
   932              end
   933          | t $ _ => (case t of
   934              Const ("==>", _) $ _  => impc t0 ss
   935            | Abs _ =>
   936                let val thm = beta_conversion false t0
   937                in case subc skel0 ss (rhs_of thm) of
   938                     NONE => SOME thm
   939                   | SOME thm' => SOME (transitive thm thm')
   940                end
   941            | _  =>
   942                let fun appc () =
   943                      let
   944                        val (tskel, uskel) = case skel of
   945                            tskel $ uskel => (tskel, uskel)
   946                          | _ => (skel0, skel0);
   947                        val (ct, cu) = Thm.dest_comb t0
   948                      in
   949                      (case botc tskel ss ct of
   950                         SOME thm1 =>
   951                           (case botc uskel ss cu of
   952                              SOME thm2 => SOME (combination thm1 thm2)
   953                            | NONE => SOME (combination thm1 (reflexive cu)))
   954                       | NONE =>
   955                           (case botc uskel ss cu of
   956                              SOME thm1 => SOME (combination (reflexive ct) thm1)
   957                            | NONE => NONE))
   958                      end
   959                    val (h, ts) = strip_comb t
   960                in case cong_name h of
   961                     SOME a =>
   962                       (case assoc_string (fst congs, a) of
   963                          NONE => appc ()
   964                        | SOME cong =>
   965   (*post processing: some partial applications h t1 ... tj, j <= length ts,
   966     may be a redex. Example: map (%x. x) = (%xs. xs) wrt map_cong*)
   967                           (let
   968                              val thm = congc (prover ss, sign, maxidx) cong t0;
   969                              val t = getOpt (Option.map rhs_of thm, t0);
   970                              val (cl, cr) = Thm.dest_comb t
   971                              val dVar = Var(("", 0), dummyT)
   972                              val skel =
   973                                list_comb (h, replicate (length ts) dVar)
   974                            in case botc skel ss cl of
   975                                 NONE => thm
   976                               | SOME thm' => transitive3 thm
   977                                   (combination thm' (reflexive cr))
   978                            end handle TERM _ => error "congc result"
   979                                     | Pattern.MATCH => appc ()))
   980                   | _ => appc ()
   981                end)
   982          | _ => NONE)
   983 
   984     and impc ct ss =
   985       if mutsimp then mut_impc0 [] ct [] [] ss else nonmut_impc ct ss
   986 
   987     and rules_of_prem ss prem =
   988       if maxidx_of_term (term_of prem) <> ~1
   989       then (trace_cterm true
   990         "Cannot add premise as rewrite rule because it contains (type) unknowns:" prem; ([], NONE))
   991       else
   992         let val asm = assume prem
   993         in (extract_safe_rrules (ss, asm), SOME asm) end
   994 
   995     and add_rrules (rrss, asms) ss =
   996       Library.foldl (insert_rrule true) (ss, List.concat rrss) |> add_prems (List.mapPartial I asms)
   997 
   998     and disch r (prem, eq) =
   999       let
  1000         val (lhs, rhs) = dest_eq eq;
  1001         val eq' = implies_elim (Thm.instantiate
  1002           ([], [(cA, prem), (cB, lhs), (cC, rhs)]) Drule.imp_cong)
  1003           (implies_intr prem eq)
  1004       in if not r then eq' else
  1005         let
  1006           val (prem', concl) = dest_implies lhs;
  1007           val (prem'', _) = dest_implies rhs
  1008         in transitive (transitive
  1009           (Thm.instantiate ([], [(cA, prem'), (cB, prem), (cC, concl)])
  1010              Drule.swap_prems_eq) eq')
  1011           (Thm.instantiate ([], [(cA, prem), (cB, prem''), (cC, concl)])
  1012              Drule.swap_prems_eq)
  1013         end
  1014       end
  1015 
  1016     and rebuild [] _ _ _ _ eq = eq
  1017       | rebuild (prem :: prems) concl (rrs :: rrss) (asm :: asms) ss eq =
  1018           let
  1019             val ss' = add_rrules (rev rrss, rev asms) ss;
  1020             val concl' =
  1021               Drule.mk_implies (prem, getOpt (Option.map rhs_of eq, concl));
  1022             val dprem = Option.map (curry (disch false) prem)
  1023           in case rewritec (prover, sign, maxidx) ss' concl' of
  1024               NONE => rebuild prems concl' rrss asms ss (dprem eq)
  1025             | SOME (eq', _) => transitive2 (Library.foldl (disch false o swap)
  1026                   (valOf (transitive3 (dprem eq) eq'), prems))
  1027                 (mut_impc0 (rev prems) (rhs_of eq') (rev rrss) (rev asms) ss)
  1028           end
  1029 
  1030     and mut_impc0 prems concl rrss asms ss =
  1031       let
  1032         val prems' = strip_imp_prems concl;
  1033         val (rrss', asms') = split_list (map (rules_of_prem ss) prems')
  1034       in mut_impc (prems @ prems') (strip_imp_concl concl) (rrss @ rrss')
  1035         (asms @ asms') [] [] [] [] ss ~1 ~1
  1036       end
  1037 
  1038     and mut_impc [] concl [] [] prems' rrss' asms' eqns ss changed k =
  1039         transitive1 (Library.foldl (fn (eq2, (eq1, prem)) => transitive1 eq1
  1040             (Option.map (curry (disch false) prem) eq2)) (NONE, eqns ~~ prems'))
  1041           (if changed > 0 then
  1042              mut_impc (rev prems') concl (rev rrss') (rev asms')
  1043                [] [] [] [] ss ~1 changed
  1044            else rebuild prems' concl rrss' asms' ss
  1045              (botc skel0 (add_rrules (rev rrss', rev asms') ss) concl))
  1046 
  1047       | mut_impc (prem :: prems) concl (rrs :: rrss) (asm :: asms)
  1048           prems' rrss' asms' eqns ss changed k =
  1049         case (if k = 0 then NONE else botc skel0 (add_rrules
  1050           (rev rrss' @ rrss, rev asms' @ asms) ss) prem) of
  1051             NONE => mut_impc prems concl rrss asms (prem :: prems')
  1052               (rrs :: rrss') (asm :: asms') (NONE :: eqns) ss changed
  1053               (if k = 0 then 0 else k - 1)
  1054           | SOME eqn =>
  1055             let
  1056               val prem' = rhs_of eqn;
  1057               val tprems = map term_of prems;
  1058               val i = 1 + Library.foldl Int.max (~1, map (fn p =>
  1059                 find_index_eq p tprems) (#hyps (rep_thm eqn)));
  1060               val (rrs', asm') = rules_of_prem ss prem'
  1061             in mut_impc prems concl rrss asms (prem' :: prems')
  1062               (rrs' :: rrss') (asm' :: asms') (SOME (foldr (disch true)
  1063                 (Drule.imp_cong' eqn (reflexive (Drule.list_implies
  1064                   (Library.drop (i, prems), concl)))) (Library.take (i, prems))) :: eqns) ss (length prems') ~1
  1065             end
  1066 
  1067      (*legacy code - only for backwards compatibility*)
  1068      and nonmut_impc ct ss =
  1069        let val (prem, conc) = dest_implies ct;
  1070            val thm1 = if simprem then botc skel0 ss prem else NONE;
  1071            val prem1 = getOpt (Option.map rhs_of thm1, prem);
  1072            val ss1 = if not useprem then ss else add_rrules
  1073              (apsnd single (apfst single (rules_of_prem ss prem1))) ss
  1074        in (case botc skel0 ss1 conc of
  1075            NONE => (case thm1 of
  1076                NONE => NONE
  1077              | SOME thm1' => SOME (Drule.imp_cong' thm1' (reflexive conc)))
  1078          | SOME thm2 =>
  1079            let val thm2' = disch false (prem1, thm2)
  1080            in (case thm1 of
  1081                NONE => SOME thm2'
  1082              | SOME thm1' =>
  1083                  SOME (transitive (Drule.imp_cong' thm1' (reflexive conc)) thm2'))
  1084            end)
  1085        end
  1086 
  1087  in try_botc end;
  1088 
  1089 
  1090 (* Meta-rewriting: rewrites t to u and returns the theorem t==u *)
  1091 
  1092 (*
  1093   Parameters:
  1094     mode = (simplify A,
  1095             use A in simplifying B,
  1096             use prems of B (if B is again a meta-impl.) to simplify A)
  1097            when simplifying A ==> B
  1098     prover: how to solve premises in conditional rewrites and congruences
  1099 *)
  1100 
  1101 fun rewrite_cterm mode prover ss ct =
  1102   let
  1103     val Simpset ({depth, ...}, _) = ss;
  1104     val {sign, t, maxidx, ...} = Thm.rep_cterm ct;
  1105   in
  1106     trace_cterm false "SIMPLIFIER INVOKED ON THE FOLLOWING TERM:" ct;
  1107     simp_depth := depth;
  1108     bottomc (mode, prover, sign, maxidx) ss ct
  1109   end handle THM (s, _, thms) =>
  1110     error ("Exception THM was raised in simplifier:\n" ^ s ^ "\n" ^
  1111       Pretty.string_of (Display.pretty_thms thms));
  1112 
  1113 (*Rewrite a cterm*)
  1114 fun rewrite_aux _ _ [] = (fn ct => Thm.reflexive ct)
  1115   | rewrite_aux prover full thms =
  1116       rewrite_cterm (full, false, false) prover (empty_ss addsimps thms);
  1117 
  1118 (*Rewrite a theorem*)
  1119 fun simplify_aux _ _ [] = (fn th => th)
  1120   | simplify_aux prover full thms =
  1121       Drule.fconv_rule (rewrite_cterm (full, false, false) prover (empty_ss addsimps thms));
  1122 
  1123 (*simple term rewriting -- no proof*)
  1124 fun rewrite_term sg rules procs =
  1125   Pattern.rewrite_term (Sign.tsig_of sg) (map decomp_simp' rules) procs;
  1126 
  1127 fun rewrite_thm mode prover ss = Drule.fconv_rule (rewrite_cterm mode prover ss);
  1128 
  1129 (*Rewrite the subgoals of a proof state (represented by a theorem) *)
  1130 fun rewrite_goals_rule_aux _ []   th = th
  1131   | rewrite_goals_rule_aux prover thms th =
  1132       Drule.fconv_rule (Drule.goals_conv (K true) (rewrite_cterm (true, true, false) prover
  1133         (empty_ss addsimps thms))) th;
  1134 
  1135 (*Rewrite the subgoal of a proof state (represented by a theorem)*)
  1136 fun rewrite_goal_rule mode prover ss i thm =
  1137   if 0 < i  andalso  i <= nprems_of thm
  1138   then Drule.fconv_rule (Drule.goals_conv (fn j => j=i) (rewrite_cterm mode prover ss)) thm
  1139   else raise THM("rewrite_goal_rule",i,[thm]);
  1140 
  1141 (*Rewrite subgoal i only.  SELECT_GOAL avoids inefficiencies in goals_conv.*)
  1142 fun asm_rewrite_goal_tac mode prover_tac ss =
  1143   SELECT_GOAL
  1144     (PRIMITIVE (rewrite_goal_rule mode (SINGLE o prover_tac) ss 1));
  1145 
  1146 
  1147 
  1148 (** simplification tactics and rules **)
  1149 
  1150 fun solve_all_tac solvers ss =
  1151   let
  1152     val Simpset (_, {subgoal_tac, ...}) = ss;
  1153     val solve_tac = subgoal_tac (set_solvers solvers ss) THEN_ALL_NEW (K no_tac);
  1154   in DEPTH_SOLVE (solve_tac 1) end;
  1155 
  1156 (*NOTE: may instantiate unknowns that appear also in other subgoals*)
  1157 fun generic_simp_tac safe mode ss =
  1158   let
  1159     val Simpset ({prems, ...}, {loop_tacs, solvers = (unsafe_solvers, solvers), ...}) = ss;
  1160     val loop_tac = FIRST' (map #2 loop_tacs);
  1161     val solve_tac = FIRST' (map (solver prems) (if safe then solvers else unsafe_solvers));
  1162 
  1163     fun simp_loop_tac i =
  1164       asm_rewrite_goal_tac mode (solve_all_tac unsafe_solvers) ss i THEN
  1165       (solve_tac i ORELSE TRY ((loop_tac THEN_ALL_NEW simp_loop_tac) i));
  1166   in simp_loop_tac end;
  1167 
  1168 fun simp rew mode ss thm =
  1169   let
  1170     val Simpset (_, {solvers = (unsafe_solvers, _), ...}) = ss;
  1171     val tacf = solve_all_tac unsafe_solvers;
  1172     fun prover s th = Option.map #1 (Seq.pull (tacf s th));
  1173   in rew mode prover ss thm end;
  1174 
  1175 val simp_thm = simp rewrite_thm;
  1176 val simp_cterm = simp rewrite_cterm;
  1177 
  1178 end;
  1179 
  1180 structure BasicMetaSimplifier: BASIC_META_SIMPLIFIER = MetaSimplifier;
  1181 open BasicMetaSimplifier;