src/Pure/meta_simplifier.ML
author nipkow
Fri Sep 10 00:19:15 2004 +0200 (2004-09-10)
changeset 15195 197e00ce3f20
parent 15088 b8a95eadbc14
child 15199 29ca1fe63e7b
permissions -rw-r--r--
new forward deduction capability for simplifier
     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 setmksimps2 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: string list,
    28     depth: int} *
    29    {congs: (string * cong) list * string list,
    30     procs: proc Net.net,
    31     mk_rews:
    32      {mk: thm -> thm list,
    33       mk2: thm list -> thm -> thm list,
    34       mk_cong: thm -> thm,
    35       mk_sym: thm -> thm option,
    36       mk_eq_True: thm -> thm option},
    37     termless: term * term -> bool,
    38     subgoal_tac: simpset -> int -> tactic,
    39     loop_tacs: (string * (int -> tactic)) list,
    40     solvers: solver list * solver list}
    41   val print_ss: simpset -> unit
    42   val empty_ss: simpset
    43   val merge_ss: simpset * simpset -> simpset
    44   type simproc
    45   val mk_simproc: string -> cterm list ->
    46     (Sign.sg -> simpset -> term -> thm option) -> simproc
    47   val add_prems: thm list -> simpset -> simpset
    48   val prems_of_ss: simpset -> thm list
    49   val addsimps: simpset * thm list -> simpset
    50   val delsimps: simpset * thm list -> simpset
    51   val addeqcongs: simpset * thm list -> simpset
    52   val deleqcongs: simpset * thm list -> simpset
    53   val addcongs: simpset * thm list -> simpset
    54   val delcongs: simpset * thm list -> simpset
    55   val addsimprocs: simpset * simproc list -> simpset
    56   val delsimprocs: simpset * simproc list -> simpset
    57   val setmksimps: simpset * (thm -> thm list) -> simpset
    58   val setmksimps2: simpset * (thm list -> thm -> thm list) -> simpset
    59   val setmkcong: simpset * (thm -> thm) -> simpset
    60   val setmksym: simpset * (thm -> thm option) -> simpset
    61   val setmkeqTrue: simpset * (thm -> thm option) -> simpset
    62   val settermless: simpset * (term * term -> bool) -> simpset
    63   val setsubgoaler: simpset * (simpset -> int -> tactic) -> simpset
    64   val setloop: simpset * (int -> tactic) -> simpset
    65   val addloop: simpset * (string * (int -> tactic)) -> simpset
    66   val delloop: simpset * string -> simpset
    67   val setSSolver: simpset * solver -> simpset
    68   val addSSolver: simpset * solver -> simpset
    69   val setSolver: simpset * solver -> simpset
    70   val addSolver: simpset * solver -> simpset
    71   val generic_simp_tac: bool -> bool * bool * bool -> simpset -> int -> tactic
    72 end;
    73 
    74 signature META_SIMPLIFIER =
    75 sig
    76   include BASIC_META_SIMPLIFIER
    77   exception SIMPLIFIER of string * thm
    78   val clear_ss: simpset -> simpset
    79   exception SIMPROC_FAIL of string * exn
    80   val simproc_i: Sign.sg -> string -> term list
    81     -> (Sign.sg -> simpset -> term -> thm option) -> simproc
    82   val simproc: Sign.sg -> string -> string list
    83     -> (Sign.sg -> simpset -> term -> thm option) -> simproc
    84   val rewrite_cterm: bool * bool * bool ->
    85     (simpset -> thm -> thm option) -> simpset -> cterm -> thm
    86   val rewrite_aux: (simpset -> thm -> thm option) -> bool -> thm list -> cterm -> thm
    87   val simplify_aux: (simpset -> thm -> thm option) -> bool -> thm list -> thm -> thm
    88   val rewrite_term: Sign.sg -> thm list -> (term -> term option) list -> term -> term
    89   val rewrite_thm: bool * bool * bool ->
    90     (simpset -> thm -> thm option) -> simpset -> thm -> thm
    91   val rewrite_goals_rule_aux: (simpset -> thm -> thm option) -> thm list -> thm -> thm
    92   val rewrite_goal_rule: bool * bool * bool ->
    93     (simpset -> thm -> thm option) -> simpset -> int -> thm -> thm
    94   val asm_rewrite_goal_tac: bool * bool * bool ->
    95     (simpset -> tactic) -> simpset -> int -> tactic
    96   val simp_thm: bool * bool * bool -> simpset -> thm -> thm
    97   val simp_cterm: bool * bool * bool -> simpset -> cterm -> thm
    98 end;
    99 
   100 structure MetaSimplifier: META_SIMPLIFIER =
   101 struct
   102 
   103 
   104 (** diagnostics **)
   105 
   106 exception SIMPLIFIER of string * thm;
   107 
   108 val debug_simp = ref false;
   109 val trace_simp = ref false;
   110 val simp_depth = ref 0;
   111 val simp_depth_limit = ref 1000;
   112 
   113 local
   114 
   115 fun println a =
   116   tracing (case ! simp_depth of 0 => a | n => enclose "[" "]" (string_of_int n) ^ 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: names of bound variables already used
   199       (for generating new names when rewriting under lambda abstractions);
   200     depth: depth of conditional rewriting;
   201     congs: association list of congruence rules and
   202            a list of `weak' congruence constants.
   203            A congruence is `weak' if it avoids normalization of some argument.
   204     procs: discrimination net of simplification procedures
   205       (functions that prove rewrite rules on the fly);
   206     mk_rews:
   207       mk: turn simplification thms into rewrite rules;
   208       mk2: like mk but may also depend on the other premises
   209       mk_cong: prepare congruence rules;
   210       mk_sym: turn == around;
   211       mk_eq_True: turn P into P == True;
   212     termless: relation for ordered rewriting;*)
   213 
   214 type mk_rews =
   215  {mk: thm -> thm list,
   216   mk2: thm list -> thm -> thm list,
   217   mk_cong: thm -> thm,
   218   mk_sym: thm -> thm option,
   219   mk_eq_True: thm -> thm option};
   220 
   221 datatype simpset =
   222   Simpset of
   223    {rules: rrule Net.net,
   224     prems: thm list,
   225     bounds: string list,
   226     depth: int} *
   227    {congs: (string * cong) list * string list,
   228     procs: proc Net.net,
   229     mk_rews: mk_rews,
   230     termless: term * term -> bool,
   231     subgoal_tac: simpset -> int -> tactic,
   232     loop_tacs: (string * (int -> tactic)) list,
   233     solvers: solver list * solver list}
   234 and proc =
   235   Proc of
   236    {name: string,
   237     lhs: cterm,
   238     proc: Sign.sg -> simpset -> term -> thm option,
   239     id: stamp};
   240 
   241 fun eq_proc (Proc {id = id1, ...}, Proc {id = id2, ...}) = (id1 = id2);
   242 
   243 fun rep_ss (Simpset args) = args;
   244 
   245 fun make_ss1 (rules, prems, bounds, depth) =
   246   {rules = rules, prems = prems, bounds = bounds, depth = depth};
   247 
   248 fun map_ss1 f {rules, prems, bounds, depth} =
   249   make_ss1 (f (rules, prems, bounds, depth));
   250 
   251 fun make_ss2 (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =
   252   {congs = congs, procs = procs, mk_rews = mk_rews, termless = termless,
   253     subgoal_tac = subgoal_tac, loop_tacs = loop_tacs, solvers = solvers};
   254 
   255 fun map_ss2 f {congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers} =
   256   make_ss2 (f (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   257 
   258 fun make_simpset (args1, args2) = Simpset (make_ss1 args1, make_ss2 args2);
   259 
   260 fun map_simpset f (Simpset ({rules, prems, bounds, depth},
   261     {congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers})) =
   262   make_simpset (f ((rules, prems, bounds, depth),
   263     (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers)));
   264 
   265 fun map_simpset1 f (Simpset (r1, r2)) = Simpset (map_ss1 f r1, r2);
   266 fun map_simpset2 f (Simpset (r1, r2)) = Simpset (r1, map_ss2 f r2);
   267 
   268 
   269 (* print simpsets *)
   270 
   271 fun print_ss ss =
   272   let
   273     val pretty_thms = map Display.pretty_thm;
   274 
   275     fun pretty_cong (name, th) =
   276       Pretty.block [Pretty.str (name ^ ":"), Pretty.brk 1, Display.pretty_thm th];
   277     fun pretty_proc (name, lhss) =
   278       Pretty.big_list (name ^ ":") (map Display.pretty_cterm lhss);
   279 
   280     val Simpset ({rules, ...}, {congs, procs, loop_tacs, solvers, ...}) = ss;
   281     val smps = map (#thm o #2) (Net.dest rules);
   282     val cngs = map (fn (name, {thm, ...}) => (name, thm)) (#1 congs);
   283     val prcs = Net.dest procs |>
   284       map (fn (_, Proc {name, lhs, id, ...}) => ((name, lhs), id))
   285       |> partition_eq eq_snd
   286       |> map (fn ps => (#1 (#1 (hd ps)), map (#2 o #1) ps))
   287       |> Library.sort_wrt #1;
   288   in
   289     [Pretty.big_list "simplification rules:" (pretty_thms smps),
   290       Pretty.big_list "simplification procedures:" (map pretty_proc prcs),
   291       Pretty.big_list "congruences:" (map pretty_cong cngs),
   292       Pretty.strs ("loopers:" :: map (quote o #1) loop_tacs),
   293       Pretty.strs ("unsafe solvers:" :: map (quote o solver_name) (#1 solvers)),
   294       Pretty.strs ("safe solvers:" :: map (quote o solver_name) (#2 solvers))]
   295     |> Pretty.chunks |> Pretty.writeln
   296   end;
   297 
   298 
   299 (* empty simpsets *)
   300 
   301 local
   302 
   303 fun init_ss mk_rews termless subgoal_tac solvers =
   304   make_simpset ((Net.empty, [], [], 0),
   305     (([], []), Net.empty, mk_rews, termless, subgoal_tac, [], solvers));
   306 
   307 val basic_mk_rews: mk_rews =
   308  {mk = fn th => if can Logic.dest_equals (Thm.concl_of th) then [th] else [],
   309   mk2 = fn thms => fn thm => [],
   310   mk_cong = I,
   311   mk_sym = Some o Drule.symmetric_fun,
   312   mk_eq_True = K None};
   313 
   314 in
   315 
   316 val empty_ss = init_ss basic_mk_rews Term.termless (K (K no_tac)) ([], []);
   317 
   318 fun clear_ss (Simpset (_, {mk_rews, termless, subgoal_tac, solvers, ...})) =
   319   init_ss mk_rews termless subgoal_tac solvers;
   320 
   321 end;
   322 
   323 
   324 (* merge simpsets *)            (*NOTE: ignores some fields of 2nd simpset*)
   325 
   326 fun merge_ss (ss1, ss2) =
   327   let
   328     val Simpset ({rules = rules1, prems = prems1, bounds = bounds1, depth},
   329      {congs = (congs1, weak1), procs = procs1, mk_rews, termless, subgoal_tac,
   330       loop_tacs = loop_tacs1, solvers = (unsafe_solvers1, solvers1)}) = ss1;
   331     val Simpset ({rules = rules2, prems = prems2, bounds = bounds2, depth = _},
   332      {congs = (congs2, weak2), procs = procs2, mk_rews = _, termless = _, subgoal_tac = _,
   333       loop_tacs = loop_tacs2, solvers = (unsafe_solvers2, solvers2)}) = ss2;
   334 
   335     val rules' = Net.merge (rules1, rules2, eq_rrule);
   336     val prems' = gen_merge_lists Drule.eq_thm_prop prems1 prems2;
   337     val bounds' = merge_lists bounds1 bounds2;
   338     val congs' = gen_merge_lists (eq_cong o pairself #2) congs1 congs2;
   339     val weak' = merge_lists weak1 weak2;
   340     val procs' = Net.merge (procs1, procs2, eq_proc);
   341     val loop_tacs' = merge_alists loop_tacs1 loop_tacs2;
   342     val unsafe_solvers' = merge_solvers unsafe_solvers1 unsafe_solvers2;
   343     val solvers' = merge_solvers solvers1 solvers2;
   344   in
   345     make_simpset ((rules', prems', bounds', depth), ((congs', weak'), procs',
   346       mk_rews, termless, subgoal_tac, loop_tacs', (unsafe_solvers', solvers')))
   347   end;
   348 
   349 
   350 (* simprocs *)
   351 
   352 exception SIMPROC_FAIL of string * exn;
   353 
   354 datatype simproc = Simproc of proc list;
   355 
   356 fun mk_simproc name lhss proc =
   357   let val id = stamp () in
   358     Simproc (lhss |> map (fn lhs =>
   359       Proc {name = name, lhs = lhs, proc = proc, id = id}))
   360   end;
   361 
   362 fun simproc_i sg name = mk_simproc name o map (Thm.cterm_of sg o Logic.varify);
   363 fun simproc sg name = simproc_i sg name o map (Sign.simple_read_term sg TypeInfer.logicT);
   364 
   365 
   366 
   367 (** simpset operations **)
   368 
   369 (* bounds and prems *)
   370 
   371 fun add_bound b = map_simpset1 (fn (rules, prems, bounds, depth) =>
   372   (rules, prems, b :: bounds, depth));
   373 
   374 fun add_prems ths = map_simpset1 (fn (rules, prems, bounds, depth) =>
   375   (rules, ths @ prems, bounds, depth));
   376 
   377 fun prems_of_ss (Simpset ({prems, ...}, _)) = prems;
   378 
   379 
   380 (* addsimps *)
   381 
   382 fun mk_rrule2 {thm, name, lhs, elhs, perm} =
   383   let
   384     val fo = Pattern.first_order (term_of elhs) orelse not (Pattern.pattern (term_of elhs))
   385   in {thm = thm, name = name, lhs = lhs, elhs = elhs, fo = fo, perm = perm} end;
   386 
   387 fun insert_rrule quiet (ss, rrule as {thm, name, lhs, elhs, perm}) =
   388  (trace_named_thm "Adding rewrite rule" (thm, name);
   389   ss |> map_simpset1 (fn (rules, prems, bounds, depth) =>
   390     let
   391       val rrule2 as {elhs, ...} = mk_rrule2 rrule;
   392       val rules' = Net.insert_term ((term_of elhs, rrule2), rules, eq_rrule);
   393     in (rules', prems, bounds, depth) end)
   394   handle Net.INSERT =>
   395     (if quiet then () else warn_thm "Ignoring duplicate rewrite rule:" thm; ss));
   396 
   397 fun vperm (Var _, Var _) = true
   398   | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)
   399   | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)
   400   | vperm (t, u) = (t = u);
   401 
   402 fun var_perm (t, u) =
   403   vperm (t, u) andalso eq_set (term_varnames t, term_varnames u);
   404 
   405 (* FIXME: it seems that the conditions on extra variables are too liberal if
   406 prems are nonempty: does solving the prems really guarantee instantiation of
   407 all its Vars? Better: a dynamic check each time a rule is applied.
   408 *)
   409 fun rewrite_rule_extra_vars prems elhs erhs =
   410   not (term_varnames erhs subset foldl add_term_varnames (term_varnames elhs, prems))
   411   orelse
   412   not (term_tvars erhs subset (term_tvars elhs union List.concat (map term_tvars prems)));
   413 
   414 (*simple test for looping rewrite rules and stupid orientations*)
   415 fun reorient sign prems lhs rhs =
   416   rewrite_rule_extra_vars prems lhs rhs
   417     orelse
   418   is_Var (head_of lhs)
   419     orelse
   420   exists (apl (lhs, Logic.occs)) (rhs :: prems)
   421     orelse
   422   null prems andalso Pattern.matches (Sign.tsig_of sign) (lhs, rhs)
   423     (*the condition "null prems" is necessary because conditional rewrites
   424       with extra variables in the conditions may terminate although
   425       the rhs is an instance of the lhs; example: ?m < ?n ==> f(?n) == f(?m)*)
   426     orelse
   427   is_Const lhs andalso not (is_Const rhs);
   428 
   429 fun decomp_simp thm =
   430   let
   431     val {sign, prop, ...} = Thm.rep_thm thm;
   432     val prems = Logic.strip_imp_prems prop;
   433     val concl = Drule.strip_imp_concl (Thm.cprop_of thm);
   434     val (lhs, rhs) = Drule.dest_equals concl handle TERM _ =>
   435       raise SIMPLIFIER ("Rewrite rule not a meta-equality", thm);
   436     val (_, elhs) = Drule.dest_equals (Thm.cprop_of (Thm.eta_conversion lhs));
   437     val elhs = if elhs = lhs then lhs else elhs;  (*share identical copies*)
   438     val erhs = Pattern.eta_contract (term_of rhs);
   439     val perm =
   440       var_perm (term_of elhs, erhs) andalso
   441       not (term_of elhs aconv erhs) andalso
   442       not (is_Var (term_of elhs));
   443   in (sign, prems, term_of lhs, elhs, term_of rhs, perm) end;
   444 
   445 fun decomp_simp' thm =
   446   let val (_, _, lhs, _, rhs, _) = decomp_simp thm in
   447     if Thm.nprems_of thm > 0 then raise SIMPLIFIER ("Bad conditional rewrite rule", thm)
   448     else (lhs, rhs)
   449   end;
   450 
   451 fun mk_eq_True (Simpset (_, {mk_rews = {mk_eq_True, ...}, ...})) (thm, name) =
   452   (case mk_eq_True thm of
   453     None => []
   454   | Some eq_True =>
   455       let val (_, _, lhs, elhs, _, _) = decomp_simp eq_True
   456       in [{thm = eq_True, name = name, lhs = lhs, elhs = elhs, perm = false}] end);
   457 
   458 (*create the rewrite rule and possibly also the eq_True variant,
   459   in case there are extra vars on the rhs*)
   460 fun rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm2) =
   461   let val rrule = {thm = thm, name = name, lhs = lhs, elhs = elhs, perm = false} in
   462     if term_varnames rhs subset term_varnames lhs andalso
   463       term_tvars rhs subset term_tvars lhs then [rrule]
   464     else mk_eq_True ss (thm2, name) @ [rrule]
   465   end;
   466 
   467 fun mk_rrule ss (thm, name) =
   468   let val (_, prems, lhs, elhs, rhs, perm) = decomp_simp thm in
   469     if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]
   470     else
   471       (*weak test for loops*)
   472       if rewrite_rule_extra_vars prems lhs rhs orelse is_Var (term_of elhs)
   473       then mk_eq_True ss (thm, name)
   474       else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
   475   end;
   476 
   477 fun orient_rrule ss (thm, name) =
   478   let val (sign, prems, lhs, elhs, rhs, perm) = decomp_simp thm in
   479     if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]
   480     else if reorient sign prems lhs rhs then
   481       if reorient sign prems rhs lhs
   482       then mk_eq_True ss (thm, name)
   483       else
   484         let val Simpset (_, {mk_rews = {mk_sym, ...}, ...}) = ss in
   485           (case mk_sym thm of
   486             None => []
   487           | Some thm' =>
   488               let val (_, _, lhs', elhs', rhs', _) = decomp_simp thm'
   489               in rrule_eq_True (thm', name, lhs', elhs', rhs', ss, thm) end)
   490         end
   491     else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
   492   end;
   493 
   494 fun extract_rews (Simpset ({prems, ...}, {mk_rews = {mk, ...}, ...}), thms)
   495   = flat (map (fn thm => map (rpair (Thm.name_of_thm thm)) (mk thm)) thms);
   496 
   497 fun extract_rews2 (Simpset ({prems, ...}, {mk_rews = {mk2, ...}, ...}), thms)
   498   = flat (map (fn thm => map (rpair (Thm.name_of_thm thm)) (mk2 prems thm)) thms);
   499 
   500 fun orient_comb_simps comb mk_rrule (ss, thms) =
   501   let
   502     val rews = extract_rews (ss, thms);
   503     val rrules = flat (map mk_rrule rews);
   504   in foldl comb (ss, rrules) end;
   505 
   506 fun extract_safe_rrules (ss, thm) =
   507   flat (map (orient_rrule ss) (extract_rews (ss, [thm])));
   508 
   509 fun extract_safe_rrules2 (ss, thm) =
   510   flat (map (orient_rrule ss) (extract_rews2 (ss, [thm])));
   511 
   512 (*add rewrite rules explicitly; do not reorient!*)
   513 fun ss addsimps thms =
   514   orient_comb_simps (insert_rrule false) (mk_rrule ss) (ss, thms);
   515 
   516 
   517 fun add_prem2(ss,thm) =
   518   foldl (insert_rrule true) (ss,extract_safe_rrules2(ss,thm))
   519   |> add_prems [thm];
   520 
   521 fun add_prems2 thms ss = foldl add_prem2 (ss,thms);
   522 
   523 (* delsimps *)
   524 
   525 fun del_rrule (ss, rrule as {thm, elhs, ...}) =
   526   ss |> map_simpset1 (fn (rules, prems, bounds, depth) =>
   527     (Net.delete_term ((term_of elhs, rrule), rules, eq_rrule), prems, bounds, depth))
   528   handle Net.DELETE => (warn_thm "Rewrite rule not in simpset:" thm; ss);
   529 
   530 fun ss delsimps thms =
   531   orient_comb_simps del_rrule (map mk_rrule2 o mk_rrule ss) (ss, thms);
   532 
   533 
   534 (* congs *)
   535 
   536 fun cong_name (Const (a, _)) = Some a
   537   | cong_name (Free (a, _)) = Some ("Free: " ^ a)
   538   | cong_name _ = None;
   539 
   540 local
   541 
   542 fun is_full_cong_prems [] [] = true
   543   | is_full_cong_prems [] _ = false
   544   | is_full_cong_prems (p :: prems) varpairs =
   545       (case Logic.strip_assums_concl p of
   546         Const ("==", _) $ lhs $ rhs =>
   547           let val (x, xs) = strip_comb lhs and (y, ys) = strip_comb rhs in
   548             is_Var x andalso forall is_Bound xs andalso
   549             null (findrep xs) andalso xs = ys andalso
   550             (x, y) mem varpairs andalso
   551             is_full_cong_prems prems (varpairs \ (x, y))
   552           end
   553       | _ => false);
   554 
   555 fun is_full_cong thm =
   556   let
   557     val prems = prems_of thm and concl = concl_of thm;
   558     val (lhs, rhs) = Logic.dest_equals concl;
   559     val (f, xs) = strip_comb lhs and (g, ys) = strip_comb rhs;
   560   in
   561     f = g andalso null (findrep (xs @ ys)) andalso length xs = length ys andalso
   562     is_full_cong_prems prems (xs ~~ ys)
   563   end;
   564 
   565 fun add_cong (ss, thm) = ss |>
   566   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   567     let
   568       val (lhs, _) = Drule.dest_equals (Drule.strip_imp_concl (Thm.cprop_of thm))
   569         handle TERM _ => raise SIMPLIFIER ("Congruence not a meta-equality", thm);
   570     (*val lhs = Pattern.eta_contract lhs;*)
   571       val a = the (cong_name (head_of (term_of lhs))) handle Library.OPTION =>
   572         raise SIMPLIFIER ("Congruence must start with a constant or free variable", thm);
   573       val (alist, weak) = congs;
   574       val alist2 = overwrite_warn (alist, (a, {lhs = lhs, thm = thm}))
   575         ("Overwriting congruence rule for " ^ quote a);
   576       val weak2 = if is_full_cong thm then weak else a :: weak;
   577     in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
   578 
   579 fun del_cong (ss, thm) = ss |>
   580   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   581     let
   582       val (lhs, _) = Logic.dest_equals (Thm.concl_of thm) handle TERM _ =>
   583         raise SIMPLIFIER ("Congruence not a meta-equality", thm);
   584     (*val lhs = Pattern.eta_contract lhs;*)
   585       val a = the (cong_name (head_of lhs)) handle Library.OPTION =>
   586         raise SIMPLIFIER ("Congruence must start with a constant", thm);
   587       val (alist, _) = congs;
   588       val alist2 = filter (fn (x, _) => x <> a) alist;
   589       val weak2 = alist2 |> mapfilter (fn (a, {thm, ...}) =>
   590         if is_full_cong thm then None else Some a);
   591     in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
   592 
   593 fun mk_cong (Simpset (_, {mk_rews = {mk_cong = f, ...}, ...})) = f;
   594 
   595 in
   596 
   597 val (op addeqcongs) = foldl add_cong;
   598 val (op deleqcongs) = foldl del_cong;
   599 
   600 fun ss addcongs congs = ss addeqcongs map (mk_cong ss) congs;
   601 fun ss delcongs congs = ss deleqcongs map (mk_cong ss) congs;
   602 
   603 end;
   604 
   605 
   606 (* simprocs *)
   607 
   608 local
   609 
   610 fun add_proc (ss, proc as Proc {name, lhs, ...}) =
   611  (trace_cterm false ("Adding simplification procedure " ^ quote name ^ " for") lhs;
   612   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   613     (congs, Net.insert_term ((term_of lhs, proc), procs, eq_proc),
   614       mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
   615   handle Net.INSERT =>
   616     (warning ("Ignoring duplicate simplification procedure " ^ quote name); ss));
   617 
   618 fun del_proc (ss, proc as Proc {name, lhs, ...}) =
   619   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   620     (congs, Net.delete_term ((term_of lhs, proc), procs, eq_proc),
   621       mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
   622   handle Net.DELETE =>
   623     (warning ("Simplification procedure " ^ quote name ^ " not in simpset"); ss);
   624 
   625 in
   626 
   627 val (op addsimprocs) = foldl (fn (ss, Simproc procs) => foldl add_proc (ss, procs));
   628 val (op delsimprocs) = foldl (fn (ss, Simproc procs) => foldl del_proc (ss, procs));
   629 
   630 end;
   631 
   632 
   633 (* mk_rews *)
   634 
   635 local
   636 
   637 fun map_mk_rews f = map_simpset2 (fn (congs, procs, {mk, mk2, mk_cong, mk_sym, mk_eq_True},
   638       termless, subgoal_tac, loop_tacs, solvers) =>
   639   let val (mk', mk2', mk_cong', mk_sym', mk_eq_True') = f (mk, mk2, mk_cong, mk_sym, mk_eq_True) in
   640     (congs, procs, {mk = mk', mk2 = mk2', mk_cong = mk_cong', mk_sym = mk_sym', mk_eq_True = mk_eq_True'},
   641       termless, subgoal_tac, loop_tacs, solvers)
   642   end);
   643 
   644 in
   645 
   646 fun ss setmksimps mk = ss |> map_mk_rews (fn (_, mk2, mk_cong, mk_sym, mk_eq_True) =>
   647   (mk, mk2, mk_cong, mk_sym, mk_eq_True));
   648 
   649 fun ss setmksimps2 mk2 = ss |> map_mk_rews (fn (mk, _, mk_cong, mk_sym, mk_eq_True) =>
   650   (mk, mk2, mk_cong, mk_sym, mk_eq_True));
   651 
   652 fun ss setmkcong mk_cong = ss |> map_mk_rews (fn (mk, mk2, _, mk_sym, mk_eq_True) =>
   653   (mk, mk2, mk_cong, mk_sym, mk_eq_True));
   654 
   655 fun ss setmksym mk_sym = ss |> map_mk_rews (fn (mk, mk2, mk_cong, _, mk_eq_True) =>
   656   (mk, mk2, mk_cong, mk_sym, mk_eq_True));
   657 
   658 fun ss setmkeqTrue mk_eq_True = ss |> map_mk_rews (fn (mk, mk2, mk_cong, mk_sym, _) =>
   659   (mk, mk2, mk_cong, mk_sym, mk_eq_True));
   660 
   661 end;
   662 
   663 
   664 (* termless *)
   665 
   666 fun ss settermless termless = ss |>
   667   map_simpset2 (fn (congs, procs, mk_rews, _, subgoal_tac, loop_tacs, solvers) =>
   668    (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   669 
   670 
   671 (* tactics *)
   672 
   673 fun ss setsubgoaler subgoal_tac = ss |>
   674   map_simpset2 (fn (congs, procs, mk_rews, termless, _, loop_tacs, solvers) =>
   675    (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   676 
   677 fun ss setloop tac = ss |>
   678   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, _, solvers) =>
   679    (congs, procs, mk_rews, termless, subgoal_tac, [("", tac)], solvers));
   680 
   681 fun ss addloop (name, tac) = ss |>
   682   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   683     (congs, procs, mk_rews, termless, subgoal_tac,
   684       overwrite_warn (loop_tacs, (name, tac)) ("Overwriting looper " ^ quote name),
   685       solvers));
   686 
   687 fun ss delloop name = ss |>
   688   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   689     let val loop_tacs' = filter_out (equal name o #1) loop_tacs in
   690       if length loop_tacs <> length loop_tacs' then ()
   691       else warning ("No such looper in simpset: " ^ quote name);
   692       (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs', solvers)
   693     end);
   694 
   695 fun ss setSSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   696   subgoal_tac, loop_tacs, (unsafe_solvers, _)) =>
   697     (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, (unsafe_solvers, [solver])));
   698 
   699 fun ss addSSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   700   subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, termless,
   701     subgoal_tac, loop_tacs, (unsafe_solvers, merge_solvers solvers [solver])));
   702 
   703 fun ss setSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   704   subgoal_tac, loop_tacs, (_, solvers)) => (congs, procs, mk_rews, termless,
   705     subgoal_tac, loop_tacs, ([solver], solvers)));
   706 
   707 fun ss addSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   708   subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, termless,
   709     subgoal_tac, loop_tacs, (merge_solvers unsafe_solvers [solver], solvers)));
   710 
   711 fun set_solvers solvers = map_simpset2 (fn (congs, procs, mk_rews, termless,
   712   subgoal_tac, loop_tacs, _) => (congs, procs, mk_rews, termless,
   713   subgoal_tac, loop_tacs, (solvers, solvers)));
   714 
   715 
   716 
   717 (** rewriting **)
   718 
   719 (*
   720   Uses conversions, see:
   721     L C Paulson, A higher-order implementation of rewriting,
   722     Science of Computer Programming 3 (1983), pages 119-149.
   723 *)
   724 
   725 val dest_eq = Drule.dest_equals o Thm.cprop_of;
   726 val lhs_of = #1 o dest_eq;
   727 val rhs_of = #2 o dest_eq;
   728 
   729 fun check_conv msg thm thm' =
   730   let
   731     val thm'' = transitive thm (transitive
   732       (symmetric (Drule.beta_eta_conversion (lhs_of thm'))) thm')
   733   in if msg then trace_thm "SUCCEEDED" thm' else (); Some thm'' end
   734   handle THM _ =>
   735     let val {sign, prop = _ $ _ $ prop0, ...} = Thm.rep_thm thm in
   736       trace_thm "Proved wrong thm (Check subgoaler?)" thm';
   737       trace_term false "Should have proved:" sign prop0;
   738       None
   739     end;
   740 
   741 
   742 (* mk_procrule *)
   743 
   744 fun mk_procrule thm =
   745   let val (_, prems, lhs, elhs, rhs, _) = decomp_simp thm in
   746     if rewrite_rule_extra_vars prems lhs rhs
   747     then (warn_thm "Extra vars on rhs:" thm; [])
   748     else [mk_rrule2 {thm = thm, name = "", lhs = lhs, elhs = elhs, perm = false}]
   749   end;
   750 
   751 
   752 (* rewritec: conversion to apply the meta simpset to a term *)
   753 
   754 (*Since the rewriting strategy is bottom-up, we avoid re-normalizing already
   755   normalized terms by carrying around the rhs of the rewrite rule just
   756   applied. This is called the `skeleton'. It is decomposed in parallel
   757   with the term. Once a Var is encountered, the corresponding term is
   758   already in normal form.
   759   skel0 is a dummy skeleton that is to enforce complete normalization.*)
   760 
   761 val skel0 = Bound 0;
   762 
   763 (*Use rhs as skeleton only if the lhs does not contain unnormalized bits.
   764   The latter may happen iff there are weak congruence rules for constants
   765   in the lhs.*)
   766 
   767 fun uncond_skel ((_, weak), (lhs, rhs)) =
   768   if null weak then rhs  (*optimization*)
   769   else if exists_Const (fn (c, _) => c mem weak) lhs then skel0
   770   else rhs;
   771 
   772 (*Behaves like unconditional rule if rhs does not contain vars not in the lhs.
   773   Otherwise those vars may become instantiated with unnormalized terms
   774   while the premises are solved.*)
   775 
   776 fun cond_skel (args as (congs, (lhs, rhs))) =
   777   if term_varnames rhs subset term_varnames lhs then uncond_skel args
   778   else skel0;
   779 
   780 fun incr_depth ss =
   781   let
   782     val ss' = ss |> map_simpset1 (fn (rules, prems, bounds, depth) =>
   783       (rules, prems, bounds, depth + 1));
   784     val Simpset ({depth = depth', ...}, _) = ss';
   785   in
   786     if depth' > ! simp_depth_limit
   787     then (warning "simp_depth_limit exceeded - giving up"; None)
   788     else
   789      (if depth' mod 10 = 0
   790       then warning ("Simplification depth " ^ string_of_int depth')
   791       else ();
   792       Some ss')
   793   end;
   794 
   795 (*
   796   Rewriting -- we try in order:
   797     (1) beta reduction
   798     (2) unconditional rewrite rules
   799     (3) conditional rewrite rules
   800     (4) simplification procedures
   801 
   802   IMPORTANT: rewrite rules must not introduce new Vars or TVars!
   803 *)
   804 
   805 fun rewritec (prover, signt, maxt) ss t =
   806   let
   807     val Simpset ({rules, ...}, {congs, procs, termless, ...}) = ss;
   808     val eta_thm = Thm.eta_conversion t;
   809     val eta_t' = rhs_of eta_thm;
   810     val eta_t = term_of eta_t';
   811     val tsigt = Sign.tsig_of signt;
   812     fun rew {thm, name, lhs, elhs, fo, perm} =
   813       let
   814         val {sign, prop, maxidx, ...} = rep_thm thm;
   815         val _ = if Sign.subsig (sign, signt) then ()
   816                 else (warn_thm "Ignoring rewrite rule from different theory:" thm;
   817                       raise Pattern.MATCH);
   818         val (rthm, elhs') = if maxt = ~1 then (thm, elhs)
   819           else (Thm.incr_indexes (maxt+1) thm, Thm.cterm_incr_indexes (maxt+1) elhs);
   820         val insts = if fo then Thm.cterm_first_order_match (elhs', eta_t')
   821                           else Thm.cterm_match (elhs', eta_t');
   822         val thm' = Thm.instantiate insts (Thm.rename_boundvars lhs eta_t rthm);
   823         val prop' = Thm.prop_of thm';
   824         val unconditional = (Logic.count_prems (prop',0) = 0);
   825         val (lhs', rhs') = Logic.dest_equals (Logic.strip_imp_concl prop')
   826       in
   827         if perm andalso not (termless (rhs', lhs'))
   828         then (trace_named_thm "Cannot apply permutative rewrite rule" (thm, name);
   829               trace_thm "Term does not become smaller:" thm'; None)
   830         else (trace_named_thm "Applying instance of rewrite rule" (thm, name);
   831            if unconditional
   832            then
   833              (trace_thm "Rewriting:" thm';
   834               let val lr = Logic.dest_equals prop;
   835                   val Some thm'' = check_conv false eta_thm thm'
   836               in Some (thm'', uncond_skel (congs, lr)) end)
   837            else
   838              (trace_thm "Trying to rewrite:" thm';
   839               case incr_depth ss of
   840                 None => (trace_thm "FAILED - reached depth limit" thm'; None)
   841               | Some ss' =>
   842               (case prover ss' thm' of
   843                 None => (trace_thm "FAILED" thm'; None)
   844               | Some thm2 =>
   845                   (case check_conv true eta_thm thm2 of
   846                      None => None |
   847                      Some thm2' =>
   848                        let val concl = Logic.strip_imp_concl prop
   849                            val lr = Logic.dest_equals concl
   850                        in Some (thm2', cond_skel (congs, lr)) end))))
   851       end
   852 
   853     fun rews [] = None
   854       | rews (rrule :: rrules) =
   855           let val opt = rew rrule handle Pattern.MATCH => None
   856           in case opt of None => rews rrules | some => some end;
   857 
   858     fun sort_rrules rrs = let
   859       fun is_simple({thm, ...}:rrule) = case Thm.prop_of thm of
   860                                       Const("==",_) $ _ $ _ => true
   861                                       | _                   => false
   862       fun sort []        (re1,re2) = re1 @ re2
   863         | sort (rr::rrs) (re1,re2) = if is_simple rr
   864                                      then sort rrs (rr::re1,re2)
   865                                      else sort rrs (re1,rr::re2)
   866     in sort rrs ([],[]) end
   867 
   868     fun proc_rews [] = None
   869       | proc_rews (Proc {name, proc, lhs, ...} :: ps) =
   870           if Pattern.matches tsigt (Thm.term_of lhs, Thm.term_of t) then
   871             (debug_term false ("Trying procedure " ^ quote name ^ " on:") signt eta_t;
   872              case transform_failure (curry SIMPROC_FAIL name)
   873                  (fn () => proc signt ss eta_t) () of
   874                None => (debug false "FAILED"; proc_rews ps)
   875              | Some raw_thm =>
   876                  (trace_thm ("Procedure " ^ quote name ^ " produced rewrite rule:") raw_thm;
   877                   (case rews (mk_procrule raw_thm) of
   878                     None => (trace_cterm true ("IGNORED result of simproc " ^ quote name ^
   879                       " -- does not match") t; proc_rews ps)
   880                   | some => some)))
   881           else proc_rews ps;
   882   in case eta_t of
   883        Abs _ $ _ => Some (transitive eta_thm
   884          (beta_conversion false eta_t'), skel0)
   885      | _ => (case rews (sort_rrules (Net.match_term rules eta_t)) of
   886                None => proc_rews (Net.match_term procs eta_t)
   887              | some => some)
   888   end;
   889 
   890 
   891 (* conversion to apply a congruence rule to a term *)
   892 
   893 fun congc (prover,signt,maxt) {thm=cong,lhs=lhs} t =
   894   let val sign = Thm.sign_of_thm cong
   895       val _ = if Sign.subsig (sign, signt) then ()
   896                  else error("Congruence rule from different theory")
   897       val rthm = if maxt = ~1 then cong else Thm.incr_indexes (maxt+1) cong;
   898       val rlhs = fst (Drule.dest_equals (Drule.strip_imp_concl (cprop_of rthm)));
   899       val insts = Thm.cterm_match (rlhs, t)
   900       (* Pattern.match can raise Pattern.MATCH;
   901          is handled when congc is called *)
   902       val thm' = Thm.instantiate insts (Thm.rename_boundvars (term_of rlhs) (term_of t) rthm);
   903       val unit = trace_thm "Applying congruence rule:" thm';
   904       fun err (msg, thm) = (trace_thm msg thm; None)
   905   in case prover thm' of
   906        None => err ("Congruence proof failed.  Could not prove", thm')
   907      | Some thm2 => (case check_conv true (Drule.beta_eta_conversion t) thm2 of
   908           None => err ("Congruence proof failed.  Should not have proved", thm2)
   909         | Some thm2' =>
   910             if op aconv (pairself term_of (dest_equals (cprop_of thm2')))
   911             then None else Some thm2')
   912   end;
   913 
   914 val (cA, (cB, cC)) =
   915   apsnd dest_equals (dest_implies (hd (cprems_of Drule.imp_cong)));
   916 
   917 fun transitive1 None None = None
   918   | transitive1 (Some thm1) None = Some thm1
   919   | transitive1 None (Some thm2) = Some thm2
   920   | transitive1 (Some thm1) (Some thm2) = Some (transitive thm1 thm2)
   921 
   922 fun transitive2 thm = transitive1 (Some thm);
   923 fun transitive3 thm = transitive1 thm o Some;
   924 
   925 fun bottomc ((simprem, useprem, mutsimp), prover, sign, maxidx) =
   926   let
   927     fun botc skel ss t =
   928           if is_Var skel then None
   929           else
   930           (case subc skel ss t of
   931              some as Some thm1 =>
   932                (case rewritec (prover, sign, maxidx) ss (rhs_of thm1) of
   933                   Some (thm2, skel2) =>
   934                     transitive2 (transitive thm1 thm2)
   935                       (botc skel2 ss (rhs_of thm2))
   936                 | None => some)
   937            | None =>
   938                (case rewritec (prover, sign, maxidx) ss t of
   939                   Some (thm2, skel2) => transitive2 thm2
   940                     (botc skel2 ss (rhs_of thm2))
   941                 | None => None))
   942 
   943     and try_botc ss t =
   944           (case botc skel0 ss t of
   945              Some trec1 => trec1 | None => (reflexive t))
   946 
   947     and subc skel (ss as Simpset ({bounds, ...}, {congs, ...})) t0 =
   948        (case term_of t0 of
   949            Abs (a, T, t) =>
   950              let
   951                  val b = variant bounds a;
   952                  val (v, t') = Thm.dest_abs (Some ("." ^ b)) t0;
   953                  val ss' = add_bound b ss;
   954                  val skel' = case skel of Abs (_, _, sk) => sk | _ => skel0;
   955              in case botc skel' ss' t' of
   956                   Some thm => Some (abstract_rule a v thm)
   957                 | None => None
   958              end
   959          | t $ _ => (case t of
   960              Const ("==>", _) $ _  => impc t0 ss
   961            | Abs _ =>
   962                let val thm = beta_conversion false t0
   963                in case subc skel0 ss (rhs_of thm) of
   964                     None => Some thm
   965                   | Some thm' => Some (transitive thm thm')
   966                end
   967            | _  =>
   968                let fun appc () =
   969                      let
   970                        val (tskel, uskel) = case skel of
   971                            tskel $ uskel => (tskel, uskel)
   972                          | _ => (skel0, skel0);
   973                        val (ct, cu) = Thm.dest_comb t0
   974                      in
   975                      (case botc tskel ss ct of
   976                         Some thm1 =>
   977                           (case botc uskel ss cu of
   978                              Some thm2 => Some (combination thm1 thm2)
   979                            | None => Some (combination thm1 (reflexive cu)))
   980                       | None =>
   981                           (case botc uskel ss cu of
   982                              Some thm1 => Some (combination (reflexive ct) thm1)
   983                            | None => None))
   984                      end
   985                    val (h, ts) = strip_comb t
   986                in case cong_name h of
   987                     Some a =>
   988                       (case assoc_string (fst congs, a) of
   989                          None => appc ()
   990                        | Some cong =>
   991   (*post processing: some partial applications h t1 ... tj, j <= length ts,
   992     may be a redex. Example: map (%x. x) = (%xs. xs) wrt map_cong*)
   993                           (let
   994                              val thm = congc (prover ss, sign, maxidx) cong t0;
   995                              val t = if_none (apsome rhs_of thm) t0;
   996                              val (cl, cr) = Thm.dest_comb t
   997                              val dVar = Var(("", 0), dummyT)
   998                              val skel =
   999                                list_comb (h, replicate (length ts) dVar)
  1000                            in case botc skel ss cl of
  1001                                 None => thm
  1002                               | Some thm' => transitive3 thm
  1003                                   (combination thm' (reflexive cr))
  1004                            end handle TERM _ => error "congc result"
  1005                                     | Pattern.MATCH => appc ()))
  1006                   | _ => appc ()
  1007                end)
  1008          | _ => None)
  1009 
  1010     and impc ct ss =
  1011       if mutsimp then mut_impc0 [] ct [] [] ss else nonmut_impc ct ss
  1012 
  1013     and rules_of_prem ss prem =
  1014       if maxidx_of_term (term_of prem) <> ~1
  1015       then (trace_cterm true
  1016         "Cannot add premise as rewrite rule because it contains (type) unknowns:" prem; ([], None))
  1017       else
  1018         let val asm = assume prem
  1019         in (extract_safe_rrules (ss, asm), Some asm) end
  1020 
  1021     and add_rrules (rrss, asms) ss =
  1022       let val Asms = mapfilter I asms
  1023       in foldl (insert_rrule true) (ss, flat rrss) |> add_prems2 Asms end
  1024 
  1025     and disch r (prem, eq) =
  1026       let
  1027         val (lhs, rhs) = dest_eq eq;
  1028         val eq' = implies_elim (Thm.instantiate
  1029           ([], [(cA, prem), (cB, lhs), (cC, rhs)]) Drule.imp_cong)
  1030           (implies_intr prem eq)
  1031       in if not r then eq' else
  1032         let
  1033           val (prem', concl) = dest_implies lhs;
  1034           val (prem'', _) = dest_implies rhs
  1035         in transitive (transitive
  1036           (Thm.instantiate ([], [(cA, prem'), (cB, prem), (cC, concl)])
  1037              Drule.swap_prems_eq) eq')
  1038           (Thm.instantiate ([], [(cA, prem), (cB, prem''), (cC, concl)])
  1039              Drule.swap_prems_eq)
  1040         end
  1041       end
  1042 
  1043     and rebuild [] _ _ _ _ eq = eq
  1044       | rebuild (prem :: prems) concl (rrs :: rrss) (asm :: asms) ss eq =
  1045           let
  1046             val ss' = add_rrules (rev rrss, rev asms) ss;
  1047             val concl' =
  1048               Drule.mk_implies (prem, if_none (apsome rhs_of eq) concl);
  1049             val dprem = apsome (curry (disch false) prem)
  1050           in case rewritec (prover, sign, maxidx) ss' concl' of
  1051               None => rebuild prems concl' rrss asms ss (dprem eq)
  1052             | Some (eq', _) => transitive2 (foldl (disch false o swap)
  1053                   (the (transitive3 (dprem eq) eq'), prems))
  1054                 (mut_impc0 (rev prems) (rhs_of eq') (rev rrss) (rev asms) ss)
  1055           end
  1056 
  1057     and mut_impc0 prems concl rrss asms ss =
  1058       let
  1059         val prems' = strip_imp_prems concl;
  1060         val (rrss', asms') = split_list (map (rules_of_prem ss) prems')
  1061       in mut_impc (prems @ prems') (strip_imp_concl concl) (rrss @ rrss')
  1062         (asms @ asms') [] [] [] [] ss ~1 ~1
  1063       end
  1064 
  1065     and mut_impc [] concl [] [] prems' rrss' asms' eqns ss changed k =
  1066         transitive1 (foldl (fn (eq2, (eq1, prem)) => transitive1 eq1
  1067             (apsome (curry (disch false) prem) eq2)) (None, eqns ~~ prems'))
  1068           (if changed > 0 then
  1069              mut_impc (rev prems') concl (rev rrss') (rev asms')
  1070                [] [] [] [] ss ~1 changed
  1071            else rebuild prems' concl rrss' asms' ss
  1072              (botc skel0 (add_rrules (rev rrss', rev asms') ss) concl))
  1073 
  1074       | mut_impc (prem :: prems) concl (rrs :: rrss) (asm :: asms)
  1075           prems' rrss' asms' eqns ss changed k =
  1076         case (if k = 0 then None else botc skel0 (add_rrules
  1077           (rev rrss' @ rrss, rev asms' @ asms) ss) prem) of
  1078             None => mut_impc prems concl rrss asms (prem :: prems')
  1079               (rrs :: rrss') (asm :: asms') (None :: eqns) ss changed
  1080               (if k = 0 then 0 else k - 1)
  1081           | Some eqn =>
  1082             let
  1083               val prem' = rhs_of eqn;
  1084               val tprems = map term_of prems;
  1085               val i = 1 + foldl Int.max (~1, map (fn p =>
  1086                 find_index_eq p tprems) (#hyps (rep_thm eqn)));
  1087               val (rrs', asm') = rules_of_prem ss prem'
  1088             in mut_impc prems concl rrss asms (prem' :: prems')
  1089               (rrs' :: rrss') (asm' :: asms') (Some (foldr (disch true)
  1090                 (take (i, prems), Drule.imp_cong' eqn (reflexive (Drule.list_implies
  1091                   (drop (i, prems), concl))))) :: eqns) ss (length prems') ~1
  1092             end
  1093 
  1094      (*legacy code - only for backwards compatibility*)
  1095      and nonmut_impc ct ss =
  1096        let val (prem, conc) = dest_implies ct;
  1097            val thm1 = if simprem then botc skel0 ss prem else None;
  1098            val prem1 = if_none (apsome rhs_of thm1) prem;
  1099            val ss1 = if not useprem then ss else add_rrules
  1100              (apsnd single (apfst single (rules_of_prem ss prem1))) ss
  1101        in (case botc skel0 ss1 conc of
  1102            None => (case thm1 of
  1103                None => None
  1104              | Some thm1' => Some (Drule.imp_cong' thm1' (reflexive conc)))
  1105          | Some thm2 =>
  1106            let val thm2' = disch false (prem1, thm2)
  1107            in (case thm1 of
  1108                None => Some thm2'
  1109              | Some thm1' =>
  1110                  Some (transitive (Drule.imp_cong' thm1' (reflexive conc)) thm2'))
  1111            end)
  1112        end
  1113 
  1114  in try_botc end;
  1115 
  1116 
  1117 (* Meta-rewriting: rewrites t to u and returns the theorem t==u *)
  1118 
  1119 (*
  1120   Parameters:
  1121     mode = (simplify A,
  1122             use A in simplifying B,
  1123             use prems of B (if B is again a meta-impl.) to simplify A)
  1124            when simplifying A ==> B
  1125     prover: how to solve premises in conditional rewrites and congruences
  1126 *)
  1127 
  1128 fun rewrite_cterm mode prover ss ct =
  1129   let
  1130     val Simpset ({depth, ...}, _) = ss;
  1131     val {sign, t, maxidx, ...} = Thm.rep_cterm ct;
  1132   in
  1133     trace_cterm false "SIMPLIFIER INVOKED ON THE FOLLOWING TERM:" ct;
  1134     simp_depth := depth;
  1135     bottomc (mode, prover, sign, maxidx) ss ct
  1136   end handle THM (s, _, thms) =>
  1137     error ("Exception THM was raised in simplifier:\n" ^ s ^ "\n" ^
  1138       Pretty.string_of (Display.pretty_thms thms));
  1139 
  1140 (*Rewrite a cterm*)
  1141 fun rewrite_aux _ _ [] = (fn ct => Thm.reflexive ct)
  1142   | rewrite_aux prover full thms =
  1143       rewrite_cterm (full, false, false) prover (empty_ss addsimps thms);
  1144 
  1145 (*Rewrite a theorem*)
  1146 fun simplify_aux _ _ [] = (fn th => th)
  1147   | simplify_aux prover full thms =
  1148       Drule.fconv_rule (rewrite_cterm (full, false, false) prover (empty_ss addsimps thms));
  1149 
  1150 (*simple term rewriting -- no proof*)
  1151 fun rewrite_term sg rules procs =
  1152   Pattern.rewrite_term (Sign.tsig_of sg) (map decomp_simp' rules) procs;
  1153 
  1154 fun rewrite_thm mode prover ss = Drule.fconv_rule (rewrite_cterm mode prover ss);
  1155 
  1156 (*Rewrite the subgoals of a proof state (represented by a theorem) *)
  1157 fun rewrite_goals_rule_aux _ []   th = th
  1158   | rewrite_goals_rule_aux prover thms th =
  1159       Drule.fconv_rule (Drule.goals_conv (K true) (rewrite_cterm (true, true, false) prover
  1160         (empty_ss addsimps thms))) th;
  1161 
  1162 (*Rewrite the subgoal of a proof state (represented by a theorem)*)
  1163 fun rewrite_goal_rule mode prover ss i thm =
  1164   if 0 < i  andalso  i <= nprems_of thm
  1165   then Drule.fconv_rule (Drule.goals_conv (fn j => j=i) (rewrite_cterm mode prover ss)) thm
  1166   else raise THM("rewrite_goal_rule",i,[thm]);
  1167 
  1168 (*Rewrite subgoal i only.  SELECT_GOAL avoids inefficiencies in goals_conv.*)
  1169 fun asm_rewrite_goal_tac mode prover_tac ss =
  1170   SELECT_GOAL
  1171     (PRIMITIVE (rewrite_goal_rule mode (SINGLE o prover_tac) ss 1));
  1172 
  1173 
  1174 
  1175 (** simplification tactics and rules **)
  1176 
  1177 fun solve_all_tac solvers ss =
  1178   let
  1179     val Simpset (_, {subgoal_tac, ...}) = ss;
  1180     val solve_tac = subgoal_tac (set_solvers solvers ss) THEN_ALL_NEW (K no_tac);
  1181   in DEPTH_SOLVE (solve_tac 1) end;
  1182 
  1183 (*NOTE: may instantiate unknowns that appear also in other subgoals*)
  1184 fun generic_simp_tac safe mode ss =
  1185   let
  1186     val Simpset ({prems, ...}, {loop_tacs, solvers = (unsafe_solvers, solvers), ...}) = ss;
  1187     val loop_tac = FIRST' (map #2 loop_tacs);
  1188     val solve_tac = FIRST' (map (solver prems) (if safe then solvers else unsafe_solvers));
  1189 
  1190     fun simp_loop_tac i =
  1191       asm_rewrite_goal_tac mode (solve_all_tac unsafe_solvers) ss i THEN
  1192       (solve_tac i ORELSE TRY ((loop_tac THEN_ALL_NEW simp_loop_tac) i));
  1193   in simp_loop_tac end;
  1194 
  1195 fun simp rew mode ss thm =
  1196   let
  1197     val Simpset (_, {solvers = (unsafe_solvers, _), ...}) = ss;
  1198     val tacf = solve_all_tac unsafe_solvers;
  1199     fun prover s th = apsome #1 (Seq.pull (tacf s th));
  1200   in rew mode prover ss thm end;
  1201 
  1202 val simp_thm = simp rewrite_thm;
  1203 val simp_cterm = simp rewrite_cterm;
  1204 
  1205 end;
  1206 
  1207 structure BasicMetaSimplifier: BASIC_META_SIMPLIFIER = MetaSimplifier;
  1208 open BasicMetaSimplifier;