src/Pure/meta_simplifier.ML
author wenzelm
Thu Jul 14 19:28:24 2005 +0200 (2005-07-14)
changeset 16842 5979c46853d1
parent 16807 730cace0ae48
child 16861 7446b4be013b
permissions -rw-r--r--
tuned;
     1 (*  Title:      Pure/meta_simplifier.ML
     2     ID:         $Id$
     3     Author:     Tobias Nipkow and Stefan Berghofer
     4 
     5 Meta-level Simplification.
     6 *)
     7 
     8 infix 4
     9   addsimps delsimps addeqcongs deleqcongs addcongs delcongs addsimprocs delsimprocs
    10   setmksimps setmkcong setmksym setmkeqTrue settermless setsubgoaler
    11   setloop addloop delloop setSSolver addSSolver setSolver addSolver;
    12 
    13 signature BASIC_META_SIMPLIFIER =
    14 sig
    15   val debug_simp: bool ref
    16   val trace_simp: bool ref
    17   val simp_depth_limit: int ref
    18   val trace_simp_depth_limit: int ref
    19   type rrule
    20   val eq_rrule: rrule * rrule -> bool
    21   type cong
    22   type solver
    23   val mk_solver: string -> (thm list -> int -> tactic) -> solver
    24   type simpset
    25   type proc
    26   val rep_ss: simpset ->
    27    {rules: rrule Net.net,
    28     prems: thm list,
    29     bounds: int} *
    30    {congs: (string * cong) list * string list,
    31     procs: proc Net.net,
    32     mk_rews:
    33      {mk: 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     (theory -> 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 setmkcong: simpset * (thm -> thm) -> simpset
    59   val setmksym: simpset * (thm -> thm option) -> simpset
    60   val setmkeqTrue: simpset * (thm -> thm option) -> simpset
    61   val settermless: simpset * (term * term -> bool) -> simpset
    62   val setsubgoaler: simpset * (simpset -> int -> tactic) -> simpset
    63   val setloop: simpset * (int -> tactic) -> simpset
    64   val addloop: simpset * (string * (int -> tactic)) -> simpset
    65   val delloop: simpset * string -> simpset
    66   val setSSolver: simpset * solver -> simpset
    67   val addSSolver: simpset * solver -> simpset
    68   val setSolver: simpset * solver -> simpset
    69   val addSolver: simpset * solver -> simpset
    70   val generic_simp_tac: bool -> bool * bool * bool -> simpset -> int -> tactic
    71 end;
    72 
    73 signature META_SIMPLIFIER =
    74 sig
    75   include BASIC_META_SIMPLIFIER
    76   exception SIMPLIFIER of string * thm
    77   val clear_ss: simpset -> simpset
    78   exception SIMPROC_FAIL of string * exn
    79   val simproc_i: theory -> string -> term list
    80     -> (theory -> simpset -> term -> thm option) -> simproc
    81   val simproc: theory -> string -> string list
    82     -> (theory -> simpset -> term -> thm option) -> simproc
    83   val rewrite_cterm: bool * bool * bool ->
    84     (simpset -> thm -> thm option) -> simpset -> cterm -> thm
    85   val rewrite_aux: (simpset -> thm -> thm option) -> bool -> thm list -> cterm -> thm
    86   val simplify_aux: (simpset -> thm -> thm option) -> bool -> thm list -> thm -> thm
    87   val rewrite_term: theory -> thm list -> (term -> term option) list -> term -> term
    88   val rewrite_thm: bool * bool * bool ->
    89     (simpset -> thm -> thm option) -> simpset -> thm -> thm
    90   val rewrite_goals_rule_aux: (simpset -> thm -> thm option) -> thm list -> thm -> thm
    91   val rewrite_goal_rule: bool * bool * bool ->
    92     (simpset -> thm -> thm option) -> simpset -> int -> thm -> thm
    93   val asm_rewrite_goal_tac: bool * bool * bool ->
    94     (simpset -> tactic) -> simpset -> int -> tactic
    95   val simp_thm: bool * bool * bool -> simpset -> thm -> thm
    96   val simp_cterm: bool * bool * bool -> simpset -> cterm -> thm
    97 end;
    98 
    99 structure MetaSimplifier: META_SIMPLIFIER =
   100 struct
   101 
   102 
   103 (** diagnostics **)
   104 
   105 exception SIMPLIFIER of string * thm;
   106 
   107 val debug_simp = ref false;
   108 val trace_simp = ref false;
   109 val simp_depth = ref 0;
   110 val simp_depth_limit = ref 100;
   111 val trace_simp_depth_limit = ref 100;
   112 
   113 local
   114 
   115 fun println a =
   116   if !simp_depth > !trace_simp_depth_limit then ()
   117   else tracing (enclose "[" "]" (string_of_int(!simp_depth)) ^ a);
   118 
   119 fun prnt warn a = if warn then warning a else println a;
   120 fun prtm warn a thy t = prnt warn (a ^ "\n" ^ Sign.string_of_term thy t);
   121 fun prctm warn a t = prnt warn (a ^ "\n" ^ Display.string_of_cterm t);
   122 
   123 in
   124 
   125 fun debug warn a = if ! debug_simp then prnt warn a else ();
   126 fun trace warn a = if ! trace_simp then prnt warn a else ();
   127 
   128 fun debug_term warn a thy t = if ! debug_simp then prtm warn a thy t else ();
   129 fun trace_term warn a thy t = if ! trace_simp then prtm warn a thy t else ();
   130 fun trace_cterm warn a ct = if ! trace_simp then prctm warn a ct else ();
   131 fun trace_thm a th = if ! trace_simp then prctm false a (Thm.cprop_of th) else ();
   132 
   133 fun trace_named_thm a (thm, name) =
   134   if ! trace_simp then
   135     prctm false (if name = "" then a else a ^ " " ^ quote name ^ ":") (Thm.cprop_of thm)
   136   else ();
   137 
   138 fun warn_thm a = prctm true a o Thm.cprop_of;
   139 
   140 end;
   141 
   142 
   143 
   144 (** datatype simpset **)
   145 
   146 (* rewrite rules *)
   147 
   148 type rrule = {thm: thm, name: string, lhs: term, elhs: cterm, fo: bool, perm: bool};
   149 
   150 (*thm: the rewrite rule;
   151   name: name of theorem from which rewrite rule was extracted;
   152   lhs: the left-hand side;
   153   elhs: the etac-contracted lhs;
   154   fo: use first-order matching;
   155   perm: the rewrite rule is permutative;
   156 
   157 Remarks:
   158   - elhs is used for matching,
   159     lhs only for preservation of bound variable names;
   160   - fo is set iff
   161     either elhs is first-order (no Var is applied),
   162       in which case fo-matching is complete,
   163     or elhs is not a pattern,
   164       in which case there is nothing better to do;*)
   165 
   166 fun eq_rrule ({thm = thm1, ...}: rrule, {thm = thm2, ...}: rrule) =
   167   Drule.eq_thm_prop (thm1, thm2);
   168 
   169 
   170 (* congruences *)
   171 
   172 type cong = {thm: thm, lhs: cterm};
   173 
   174 fun eq_cong ({thm = thm1, ...}: cong, {thm = thm2, ...}: cong) =
   175   Drule.eq_thm_prop (thm1, thm2);
   176 
   177 
   178 (* solvers *)
   179 
   180 datatype solver =
   181   Solver of
   182    {name: string,
   183     solver: thm list -> int -> tactic,
   184     id: stamp};
   185 
   186 fun mk_solver name solver = Solver {name = name, solver = solver, id = stamp ()};
   187 
   188 fun solver_name (Solver {name, ...}) = name;
   189 fun solver ths (Solver {solver = tacf, ...}) = tacf ths;
   190 fun eq_solver (Solver {id = id1, ...}, Solver {id = id2, ...}) = (id1 = id2);
   191 val merge_solvers = gen_merge_lists eq_solver;
   192 
   193 
   194 (* simplification sets and procedures *)
   195 
   196 (*A simpset contains data required during conversion:
   197     rules: discrimination net of rewrite rules;
   198     prems: current premises;
   199     bounds: maximal index of bound variables already used
   200       (for generating new names when rewriting under lambda abstractions);
   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       mk_cong: prepare congruence rules;
   209       mk_sym: turn == around;
   210       mk_eq_True: turn P into P == True;
   211     termless: relation for ordered rewriting;*)
   212 
   213 type mk_rews =
   214  {mk: thm -> thm list,
   215   mk_cong: thm -> thm,
   216   mk_sym: thm -> thm option,
   217   mk_eq_True: thm -> thm option};
   218 
   219 datatype simpset =
   220   Simpset of
   221    {rules: rrule Net.net,
   222     prems: thm list,
   223     bounds: int} *
   224    {congs: (string * cong) list * string list,
   225     procs: proc Net.net,
   226     mk_rews: mk_rews,
   227     termless: term * term -> bool,
   228     subgoal_tac: simpset -> int -> tactic,
   229     loop_tacs: (string * (int -> tactic)) list,
   230     solvers: solver list * solver list}
   231 and proc =
   232   Proc of
   233    {name: string,
   234     lhs: cterm,
   235     proc: theory -> simpset -> term -> thm option,
   236     id: stamp};
   237 
   238 fun eq_proc (Proc {id = id1, ...}, Proc {id = id2, ...}) = (id1 = id2);
   239 
   240 fun rep_ss (Simpset args) = args;
   241 
   242 fun make_ss1 (rules, prems, bounds) =
   243   {rules = rules, prems = prems, bounds = bounds};
   244 
   245 fun map_ss1 f {rules, prems, bounds} =
   246   make_ss1 (f (rules, prems, bounds));
   247 
   248 fun make_ss2 (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =
   249   {congs = congs, procs = procs, mk_rews = mk_rews, termless = termless,
   250     subgoal_tac = subgoal_tac, loop_tacs = loop_tacs, solvers = solvers};
   251 
   252 fun map_ss2 f {congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers} =
   253   make_ss2 (f (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   254 
   255 fun make_simpset (args1, args2) = Simpset (make_ss1 args1, make_ss2 args2);
   256 
   257 fun map_simpset f (Simpset ({rules, prems, bounds},
   258     {congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers})) =
   259   make_simpset (f ((rules, prems, bounds),
   260     (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers)));
   261 
   262 fun map_simpset1 f (Simpset (r1, r2)) = Simpset (map_ss1 f r1, r2);
   263 fun map_simpset2 f (Simpset (r1, r2)) = Simpset (r1, map_ss2 f r2);
   264 
   265 
   266 (* print simpsets *)
   267 
   268 fun print_ss ss =
   269   let
   270     val pretty_thms = map Display.pretty_thm;
   271 
   272     fun pretty_cong (name, th) =
   273       Pretty.block [Pretty.str (name ^ ":"), Pretty.brk 1, Display.pretty_thm th];
   274     fun pretty_proc (name, lhss) =
   275       Pretty.big_list (name ^ ":") (map Display.pretty_cterm lhss);
   276 
   277     val Simpset ({rules, ...}, {congs, procs, loop_tacs, solvers, ...}) = ss;
   278     val smps = map #thm (Net.entries rules);
   279     val cngs = map (fn (name, {thm, ...}) => (name, thm)) (#1 congs);
   280     val prcs = Net.entries procs |>
   281       map (fn Proc {name, lhs, id, ...} => ((name, lhs), id))
   282       |> partition_eq eq_snd
   283       |> map (fn ps => (#1 (#1 (hd ps)), map (#2 o #1) ps))
   284       |> Library.sort_wrt #1;
   285   in
   286     [Pretty.big_list "simplification rules:" (pretty_thms smps),
   287       Pretty.big_list "simplification procedures:" (map pretty_proc prcs),
   288       Pretty.big_list "congruences:" (map pretty_cong cngs),
   289       Pretty.strs ("loopers:" :: map (quote o #1) loop_tacs),
   290       Pretty.strs ("unsafe solvers:" :: map (quote o solver_name) (#1 solvers)),
   291       Pretty.strs ("safe solvers:" :: map (quote o solver_name) (#2 solvers))]
   292     |> Pretty.chunks |> Pretty.writeln
   293   end;
   294 
   295 
   296 (* empty simpsets *)
   297 
   298 local
   299 
   300 fun init_ss mk_rews termless subgoal_tac solvers =
   301   make_simpset ((Net.empty, [], 0),
   302     (([], []), Net.empty, mk_rews, termless, subgoal_tac, [], solvers));
   303 
   304 val basic_mk_rews: mk_rews =
   305  {mk = fn th => if can Logic.dest_equals (Thm.concl_of th) then [th] else [],
   306   mk_cong = I,
   307   mk_sym = SOME o Drule.symmetric_fun,
   308   mk_eq_True = K NONE};
   309 
   310 in
   311 
   312 val empty_ss = init_ss basic_mk_rews Term.termless (K (K no_tac)) ([], []);
   313 
   314 fun clear_ss (Simpset (_, {mk_rews, termless, subgoal_tac, solvers, ...})) =
   315   init_ss mk_rews termless subgoal_tac solvers;
   316 
   317 end;
   318 
   319 
   320 (* merge simpsets *)            (*NOTE: ignores some fields of 2nd simpset*)
   321 
   322 fun merge_ss (ss1, ss2) =
   323   let
   324     val Simpset ({rules = rules1, prems = prems1, bounds = bounds1},
   325      {congs = (congs1, weak1), procs = procs1, mk_rews, termless, subgoal_tac,
   326       loop_tacs = loop_tacs1, solvers = (unsafe_solvers1, solvers1)}) = ss1;
   327     val Simpset ({rules = rules2, prems = prems2, bounds = bounds2},
   328      {congs = (congs2, weak2), procs = procs2, mk_rews = _, termless = _, subgoal_tac = _,
   329       loop_tacs = loop_tacs2, solvers = (unsafe_solvers2, solvers2)}) = ss2;
   330 
   331     val rules' = Net.merge eq_rrule (rules1, rules2);
   332     val prems' = gen_merge_lists Drule.eq_thm_prop prems1 prems2;
   333     val bounds' = Int.max (bounds1, bounds2);
   334     val congs' = gen_merge_lists (eq_cong o pairself #2) congs1 congs2;
   335     val weak' = merge_lists weak1 weak2;
   336     val procs' = Net.merge eq_proc (procs1, procs2);
   337     val loop_tacs' = merge_alists loop_tacs1 loop_tacs2;
   338     val unsafe_solvers' = merge_solvers unsafe_solvers1 unsafe_solvers2;
   339     val solvers' = merge_solvers solvers1 solvers2;
   340   in
   341     make_simpset ((rules', prems', bounds'), ((congs', weak'), procs',
   342       mk_rews, termless, subgoal_tac, loop_tacs', (unsafe_solvers', solvers')))
   343   end;
   344 
   345 
   346 (* simprocs *)
   347 
   348 exception SIMPROC_FAIL of string * exn;
   349 
   350 datatype simproc = Simproc of proc list;
   351 
   352 fun mk_simproc name lhss proc =
   353   let val id = stamp () in
   354     Simproc (lhss |> map (fn lhs =>
   355       Proc {name = name, lhs = lhs, proc = proc, id = id}))
   356   end;
   357 
   358 fun simproc_i thy name = mk_simproc name o map (Thm.cterm_of thy o Logic.varify);
   359 fun simproc thy name = simproc_i thy name o map (Sign.read_term thy);
   360 
   361 
   362 
   363 (** simpset operations **)
   364 
   365 (* bounds and prems *)
   366 
   367 val incr_bounds = map_simpset1 (fn (rules, prems, bounds) =>
   368   (rules, prems, bounds + 1));
   369 
   370 fun add_prems ths = map_simpset1 (fn (rules, prems, bounds) =>
   371   (rules, ths @ prems, bounds));
   372 
   373 fun prems_of_ss (Simpset ({prems, ...}, _)) = prems;
   374 
   375 
   376 (* addsimps *)
   377 
   378 fun mk_rrule2 {thm, name, lhs, elhs, perm} =
   379   let
   380     val fo = Pattern.first_order (term_of elhs) orelse not (Pattern.pattern (term_of elhs))
   381   in {thm = thm, name = name, lhs = lhs, elhs = elhs, fo = fo, perm = perm} end;
   382 
   383 fun insert_rrule quiet (ss, rrule as {thm, name, lhs, elhs, perm}) =
   384  (trace_named_thm "Adding rewrite rule" (thm, name);
   385   ss |> map_simpset1 (fn (rules, prems, bounds) =>
   386     let
   387       val rrule2 as {elhs, ...} = mk_rrule2 rrule;
   388       val rules' = Net.insert_term eq_rrule (term_of elhs, rrule2) rules;
   389     in (rules', prems, bounds) end)
   390   handle Net.INSERT =>
   391     (if quiet then () else warn_thm "Ignoring duplicate rewrite rule:" thm; ss));
   392 
   393 fun vperm (Var _, Var _) = true
   394   | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)
   395   | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)
   396   | vperm (t, u) = (t = u);
   397 
   398 fun var_perm (t, u) =
   399   vperm (t, u) andalso eq_set (term_varnames t, term_varnames u);
   400 
   401 (* FIXME: it seems that the conditions on extra variables are too liberal if
   402 prems are nonempty: does solving the prems really guarantee instantiation of
   403 all its Vars? Better: a dynamic check each time a rule is applied.
   404 *)
   405 fun rewrite_rule_extra_vars prems elhs erhs =
   406   not (term_varnames erhs subset Library.foldl add_term_varnames (term_varnames elhs, prems))
   407   orelse
   408   not (term_tvars erhs subset (term_tvars elhs union List.concat (map term_tvars prems)));
   409 
   410 (*simple test for looping rewrite rules and stupid orientations*)
   411 fun reorient thy prems lhs rhs =
   412   rewrite_rule_extra_vars prems lhs rhs
   413     orelse
   414   is_Var (head_of lhs)
   415     orelse
   416 (* turns t = x around, which causes a headache if x is a local variable -
   417    usually it is very useful :-(
   418   is_Free rhs andalso not(is_Free lhs) andalso not(Logic.occs(rhs,lhs))
   419   andalso not(exists_subterm is_Var lhs)
   420     orelse
   421 *)
   422   exists (fn t => Logic.occs (lhs, t)) (rhs :: prems)
   423     orelse
   424   null prems andalso Pattern.matches (Sign.tsig_of thy) (lhs, rhs)
   425     (*the condition "null prems" is necessary because conditional rewrites
   426       with extra variables in the conditions may terminate although
   427       the rhs is an instance of the lhs; example: ?m < ?n ==> f(?n) == f(?m)*)
   428     orelse
   429   is_Const lhs andalso not (is_Const rhs);
   430 
   431 fun decomp_simp thm =
   432   let
   433     val {thy, prop, ...} = Thm.rep_thm thm;
   434     val prems = Logic.strip_imp_prems prop;
   435     val concl = Drule.strip_imp_concl (Thm.cprop_of thm);
   436     val (lhs, rhs) = Drule.dest_equals concl handle TERM _ =>
   437       raise SIMPLIFIER ("Rewrite rule not a meta-equality", thm);
   438     val (_, elhs) = Drule.dest_equals (Thm.cprop_of (Thm.eta_conversion lhs));
   439     val elhs = if term_of elhs aconv term_of lhs then lhs else elhs;  (*share identical copies*)
   440     val erhs = Pattern.eta_contract (term_of rhs);
   441     val perm =
   442       var_perm (term_of elhs, erhs) andalso
   443       not (term_of elhs aconv erhs) andalso
   444       not (is_Var (term_of elhs));
   445   in (thy, prems, term_of lhs, elhs, term_of rhs, perm) end;
   446 
   447 fun decomp_simp' thm =
   448   let val (_, _, lhs, _, rhs, _) = decomp_simp thm in
   449     if Thm.nprems_of thm > 0 then raise SIMPLIFIER ("Bad conditional rewrite rule", thm)
   450     else (lhs, rhs)
   451   end;
   452 
   453 fun mk_eq_True (Simpset (_, {mk_rews = {mk_eq_True, ...}, ...})) (thm, name) =
   454   (case mk_eq_True thm of
   455     NONE => []
   456   | SOME eq_True =>
   457       let val (_, _, lhs, elhs, _, _) = decomp_simp eq_True
   458       in [{thm = eq_True, name = name, lhs = lhs, elhs = elhs, perm = false}] end);
   459 
   460 (*create the rewrite rule and possibly also the eq_True variant,
   461   in case there are extra vars on the rhs*)
   462 fun rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm2) =
   463   let val rrule = {thm = thm, name = name, lhs = lhs, elhs = elhs, perm = false} in
   464     if term_varnames rhs subset term_varnames lhs andalso
   465       term_tvars rhs subset term_tvars lhs then [rrule]
   466     else mk_eq_True ss (thm2, name) @ [rrule]
   467   end;
   468 
   469 fun mk_rrule ss (thm, name) =
   470   let val (_, prems, lhs, elhs, rhs, perm) = decomp_simp thm in
   471     if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]
   472     else
   473       (*weak test for loops*)
   474       if rewrite_rule_extra_vars prems lhs rhs orelse is_Var (term_of elhs)
   475       then mk_eq_True ss (thm, name)
   476       else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
   477   end;
   478 
   479 fun orient_rrule ss (thm, name) =
   480   let val (thy, prems, lhs, elhs, rhs, perm) = decomp_simp thm in
   481     if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]
   482     else if reorient thy prems lhs rhs then
   483       if reorient thy prems rhs lhs
   484       then mk_eq_True ss (thm, name)
   485       else
   486         let val Simpset (_, {mk_rews = {mk_sym, ...}, ...}) = ss in
   487           (case mk_sym thm of
   488             NONE => []
   489           | SOME thm' =>
   490               let val (_, _, lhs', elhs', rhs', _) = decomp_simp thm'
   491               in rrule_eq_True (thm', name, lhs', elhs', rhs', ss, thm) end)
   492         end
   493     else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
   494   end;
   495 
   496 fun extract_rews (Simpset (_, {mk_rews = {mk, ...}, ...}), thms) =
   497   List.concat (map (fn thm => map (rpair (Thm.name_of_thm thm)) (mk thm)) thms);
   498 
   499 fun orient_comb_simps comb mk_rrule (ss, thms) =
   500   let
   501     val rews = extract_rews (ss, thms);
   502     val rrules = List.concat (map mk_rrule rews);
   503   in Library.foldl comb (ss, rrules) end;
   504 
   505 fun extract_safe_rrules (ss, thm) =
   506   List.concat (map (orient_rrule ss) (extract_rews (ss, [thm])));
   507 
   508 (*add rewrite rules explicitly; do not reorient!*)
   509 fun ss addsimps thms =
   510   orient_comb_simps (insert_rrule false) (mk_rrule ss) (ss, thms);
   511 
   512 
   513 (* delsimps *)
   514 
   515 fun del_rrule (ss, rrule as {thm, elhs, ...}) =
   516   ss |> map_simpset1 (fn (rules, prems, bounds) =>
   517     (Net.delete_term eq_rrule (term_of elhs, rrule) rules, prems, bounds))
   518   handle Net.DELETE => (warn_thm "Rewrite rule not in simpset:" thm; ss);
   519 
   520 fun ss delsimps thms =
   521   orient_comb_simps del_rrule (map mk_rrule2 o mk_rrule ss) (ss, thms);
   522 
   523 
   524 (* congs *)
   525 
   526 fun cong_name (Const (a, _)) = SOME a
   527   | cong_name (Free (a, _)) = SOME ("Free: " ^ a)
   528   | cong_name _ = NONE;
   529 
   530 local
   531 
   532 fun is_full_cong_prems [] [] = true
   533   | is_full_cong_prems [] _ = false
   534   | is_full_cong_prems (p :: prems) varpairs =
   535       (case Logic.strip_assums_concl p of
   536         Const ("==", _) $ lhs $ rhs =>
   537           let val (x, xs) = strip_comb lhs and (y, ys) = strip_comb rhs in
   538             is_Var x andalso forall is_Bound xs andalso
   539             null (findrep xs) andalso xs = ys andalso
   540             (x, y) mem varpairs andalso
   541             is_full_cong_prems prems (varpairs \ (x, y))
   542           end
   543       | _ => false);
   544 
   545 fun is_full_cong thm =
   546   let
   547     val prems = prems_of thm and concl = concl_of thm;
   548     val (lhs, rhs) = Logic.dest_equals concl;
   549     val (f, xs) = strip_comb lhs and (g, ys) = strip_comb rhs;
   550   in
   551     f = g andalso null (findrep (xs @ ys)) andalso length xs = length ys andalso
   552     is_full_cong_prems prems (xs ~~ ys)
   553   end;
   554 
   555 fun add_cong (ss, thm) = ss |>
   556   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   557     let
   558       val (lhs, _) = Drule.dest_equals (Drule.strip_imp_concl (Thm.cprop_of thm))
   559         handle TERM _ => raise SIMPLIFIER ("Congruence not a meta-equality", thm);
   560     (*val lhs = Pattern.eta_contract lhs;*)
   561       val a = valOf (cong_name (head_of (term_of lhs))) handle Option =>
   562         raise SIMPLIFIER ("Congruence must start with a constant or free variable", thm);
   563       val (alist, weak) = congs;
   564       val alist2 = overwrite_warn (alist, (a, {lhs = lhs, thm = thm}))
   565         ("Overwriting congruence rule for " ^ quote a);
   566       val weak2 = if is_full_cong thm then weak else a :: weak;
   567     in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
   568 
   569 fun del_cong (ss, thm) = ss |>
   570   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   571     let
   572       val (lhs, _) = Logic.dest_equals (Thm.concl_of thm) handle TERM _ =>
   573         raise SIMPLIFIER ("Congruence not a meta-equality", thm);
   574     (*val lhs = Pattern.eta_contract lhs;*)
   575       val a = valOf (cong_name (head_of lhs)) handle Option =>
   576         raise SIMPLIFIER ("Congruence must start with a constant", thm);
   577       val (alist, _) = congs;
   578       val alist2 = List.filter (fn (x, _) => x <> a) alist;
   579       val weak2 = alist2 |> List.mapPartial (fn (a, {thm, ...}) =>
   580         if is_full_cong thm then NONE else SOME a);
   581     in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
   582 
   583 fun mk_cong (Simpset (_, {mk_rews = {mk_cong = f, ...}, ...})) = f;
   584 
   585 in
   586 
   587 val (op addeqcongs) = Library.foldl add_cong;
   588 val (op deleqcongs) = Library.foldl del_cong;
   589 
   590 fun ss addcongs congs = ss addeqcongs map (mk_cong ss) congs;
   591 fun ss delcongs congs = ss deleqcongs map (mk_cong ss) congs;
   592 
   593 end;
   594 
   595 
   596 (* simprocs *)
   597 
   598 local
   599 
   600 fun add_proc (ss, proc as Proc {name, lhs, ...}) =
   601  (trace_cterm false ("Adding simplification procedure " ^ quote name ^ " for") lhs;
   602   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   603     (congs, Net.insert_term eq_proc (term_of lhs, proc) procs,
   604       mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
   605   handle Net.INSERT =>
   606     (warning ("Ignoring duplicate simplification procedure " ^ quote name); ss));
   607 
   608 fun del_proc (ss, proc as Proc {name, lhs, ...}) =
   609   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   610     (congs, Net.delete_term eq_proc (term_of lhs, proc) procs,
   611       mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
   612   handle Net.DELETE =>
   613     (warning ("Simplification procedure " ^ quote name ^ " not in simpset"); ss);
   614 
   615 in
   616 
   617 val (op addsimprocs) = Library.foldl (fn (ss, Simproc procs) => Library.foldl add_proc (ss, procs));
   618 val (op delsimprocs) = Library.foldl (fn (ss, Simproc procs) => Library.foldl del_proc (ss, procs));
   619 
   620 end;
   621 
   622 
   623 (* mk_rews *)
   624 
   625 local
   626 
   627 fun map_mk_rews f = map_simpset2 (fn (congs, procs, {mk, mk_cong, mk_sym, mk_eq_True},
   628       termless, subgoal_tac, loop_tacs, solvers) =>
   629   let val (mk', mk_cong', mk_sym', mk_eq_True') = f (mk, mk_cong, mk_sym, mk_eq_True) in
   630     (congs, procs, {mk = mk', mk_cong = mk_cong', mk_sym = mk_sym', mk_eq_True = mk_eq_True'},
   631       termless, subgoal_tac, loop_tacs, solvers)
   632   end);
   633 
   634 in
   635 
   636 fun ss setmksimps mk = ss |> map_mk_rews (fn (_, mk_cong, mk_sym, mk_eq_True) =>
   637   (mk, mk_cong, mk_sym, mk_eq_True));
   638 
   639 fun ss setmkcong mk_cong = ss |> map_mk_rews (fn (mk, _, mk_sym, mk_eq_True) =>
   640   (mk, mk_cong, mk_sym, mk_eq_True));
   641 
   642 fun ss setmksym mk_sym = ss |> map_mk_rews (fn (mk, mk_cong, _, mk_eq_True) =>
   643   (mk, mk_cong, mk_sym, mk_eq_True));
   644 
   645 fun ss setmkeqTrue mk_eq_True = ss |> map_mk_rews (fn (mk, mk_cong, mk_sym, _) =>
   646   (mk, mk_cong, mk_sym, mk_eq_True));
   647 
   648 end;
   649 
   650 
   651 (* termless *)
   652 
   653 fun ss settermless termless = ss |>
   654   map_simpset2 (fn (congs, procs, mk_rews, _, subgoal_tac, loop_tacs, solvers) =>
   655    (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   656 
   657 
   658 (* tactics *)
   659 
   660 fun ss setsubgoaler subgoal_tac = ss |>
   661   map_simpset2 (fn (congs, procs, mk_rews, termless, _, loop_tacs, solvers) =>
   662    (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
   663 
   664 fun ss setloop tac = ss |>
   665   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, _, solvers) =>
   666    (congs, procs, mk_rews, termless, subgoal_tac, [("", tac)], solvers));
   667 
   668 fun ss addloop (name, tac) = ss |>
   669   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   670     (congs, procs, mk_rews, termless, subgoal_tac,
   671       overwrite_warn (loop_tacs, (name, tac)) ("Overwriting looper " ^ quote name),
   672       solvers));
   673 
   674 fun ss delloop name = ss |>
   675   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
   676     let val loop_tacs' = filter_out (equal name o #1) loop_tacs in
   677       if length loop_tacs <> length loop_tacs' then ()
   678       else warning ("No such looper in simpset: " ^ quote name);
   679       (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs', solvers)
   680     end);
   681 
   682 fun ss setSSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   683   subgoal_tac, loop_tacs, (unsafe_solvers, _)) =>
   684     (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, (unsafe_solvers, [solver])));
   685 
   686 fun ss addSSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   687   subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, termless,
   688     subgoal_tac, loop_tacs, (unsafe_solvers, merge_solvers solvers [solver])));
   689 
   690 fun ss setSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   691   subgoal_tac, loop_tacs, (_, solvers)) => (congs, procs, mk_rews, termless,
   692     subgoal_tac, loop_tacs, ([solver], solvers)));
   693 
   694 fun ss addSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
   695   subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, termless,
   696     subgoal_tac, loop_tacs, (merge_solvers unsafe_solvers [solver], solvers)));
   697 
   698 fun set_solvers solvers = map_simpset2 (fn (congs, procs, mk_rews, termless,
   699   subgoal_tac, loop_tacs, _) => (congs, procs, mk_rews, termless,
   700   subgoal_tac, loop_tacs, (solvers, solvers)));
   701 
   702 
   703 
   704 (** rewriting **)
   705 
   706 (*
   707   Uses conversions, see:
   708     L C Paulson, A higher-order implementation of rewriting,
   709     Science of Computer Programming 3 (1983), pages 119-149.
   710 *)
   711 
   712 val dest_eq = Drule.dest_equals o Thm.cprop_of;
   713 val lhs_of = #1 o dest_eq;
   714 val rhs_of = #2 o dest_eq;
   715 
   716 fun check_conv msg thm thm' =
   717   let
   718     val thm'' = transitive thm (transitive
   719       (symmetric (Drule.beta_eta_conversion (lhs_of thm'))) thm')
   720   in if msg then trace_thm "SUCCEEDED" thm' else (); SOME thm'' end
   721   handle THM _ =>
   722     let val {thy, prop = _ $ _ $ prop0, ...} = Thm.rep_thm thm in
   723       trace_thm "Proved wrong thm (Check subgoaler?)" thm';
   724       trace_term false "Should have proved:" thy prop0;
   725       NONE
   726     end;
   727 
   728 
   729 (* mk_procrule *)
   730 
   731 fun mk_procrule thm =
   732   let val (_, prems, lhs, elhs, rhs, _) = decomp_simp thm in
   733     if rewrite_rule_extra_vars prems lhs rhs
   734     then (warn_thm "Extra vars on rhs:" thm; [])
   735     else [mk_rrule2 {thm = thm, name = "", lhs = lhs, elhs = elhs, perm = false}]
   736   end;
   737 
   738 
   739 (* rewritec: conversion to apply the meta simpset to a term *)
   740 
   741 (*Since the rewriting strategy is bottom-up, we avoid re-normalizing already
   742   normalized terms by carrying around the rhs of the rewrite rule just
   743   applied. This is called the `skeleton'. It is decomposed in parallel
   744   with the term. Once a Var is encountered, the corresponding term is
   745   already in normal form.
   746   skel0 is a dummy skeleton that is to enforce complete normalization.*)
   747 
   748 val skel0 = Bound 0;
   749 
   750 (*Use rhs as skeleton only if the lhs does not contain unnormalized bits.
   751   The latter may happen iff there are weak congruence rules for constants
   752   in the lhs.*)
   753 
   754 fun uncond_skel ((_, weak), (lhs, rhs)) =
   755   if null weak then rhs  (*optimization*)
   756   else if exists_Const (fn (c, _) => c mem weak) lhs then skel0
   757   else rhs;
   758 
   759 (*Behaves like unconditional rule if rhs does not contain vars not in the lhs.
   760   Otherwise those vars may become instantiated with unnormalized terms
   761   while the premises are solved.*)
   762 
   763 fun cond_skel (args as (congs, (lhs, rhs))) =
   764   if term_varnames rhs subset term_varnames lhs then uncond_skel args
   765   else skel0;
   766 
   767 (*
   768   Rewriting -- we try in order:
   769     (1) beta reduction
   770     (2) unconditional rewrite rules
   771     (3) conditional rewrite rules
   772     (4) simplification procedures
   773 
   774   IMPORTANT: rewrite rules must not introduce new Vars or TVars!
   775 *)
   776 
   777 fun rewritec (prover, thyt, maxt) ss t =
   778   let
   779     val Simpset ({rules, ...}, {congs, procs, termless, ...}) = ss;
   780     val eta_thm = Thm.eta_conversion t;
   781     val eta_t' = rhs_of eta_thm;
   782     val eta_t = term_of eta_t';
   783     val tsigt = Sign.tsig_of thyt;
   784     fun rew {thm, name, lhs, elhs, fo, perm} =
   785       let
   786         val {thy, prop, maxidx, ...} = rep_thm thm;
   787         val (rthm, elhs') = if maxt = ~1 then (thm, elhs)
   788           else (Thm.incr_indexes (maxt+1) thm, Thm.cterm_incr_indexes (maxt+1) elhs);
   789         val insts = if fo then Thm.cterm_first_order_match (elhs', eta_t')
   790                           else Thm.cterm_match (elhs', eta_t');
   791         val thm' = Thm.instantiate insts (Thm.rename_boundvars lhs eta_t rthm);
   792         val prop' = Thm.prop_of thm';
   793         val unconditional = (Logic.count_prems (prop',0) = 0);
   794         val (lhs', rhs') = Logic.dest_equals (Logic.strip_imp_concl prop')
   795       in
   796         if perm andalso not (termless (rhs', lhs'))
   797         then (trace_named_thm "Cannot apply permutative rewrite rule" (thm, name);
   798               trace_thm "Term does not become smaller:" thm'; NONE)
   799         else (trace_named_thm "Applying instance of rewrite rule" (thm, name);
   800            if unconditional
   801            then
   802              (trace_thm "Rewriting:" thm';
   803               let val lr = Logic.dest_equals prop;
   804                   val SOME thm'' = check_conv false eta_thm thm'
   805               in SOME (thm'', uncond_skel (congs, lr)) end)
   806            else
   807              (trace_thm "Trying to rewrite:" thm';
   808               if !simp_depth > !simp_depth_limit
   809               then let val s = "simp_depth_limit exceeded - giving up"
   810                    in trace false s; warning s; NONE end
   811               else
   812               case prover ss thm' of
   813                 NONE => (trace_thm "FAILED" thm'; NONE)
   814               | SOME thm2 =>
   815                   (case check_conv true eta_thm thm2 of
   816                      NONE => NONE |
   817                      SOME thm2' =>
   818                        let val concl = Logic.strip_imp_concl prop
   819                            val lr = Logic.dest_equals concl
   820                        in SOME (thm2', cond_skel (congs, lr)) end)))
   821       end
   822 
   823     fun rews [] = NONE
   824       | rews (rrule :: rrules) =
   825           let val opt = rew rrule handle Pattern.MATCH => NONE
   826           in case opt of NONE => rews rrules | some => some end;
   827 
   828     fun sort_rrules rrs = let
   829       fun is_simple({thm, ...}:rrule) = case Thm.prop_of thm of
   830                                       Const("==",_) $ _ $ _ => true
   831                                       | _                   => false
   832       fun sort []        (re1,re2) = re1 @ re2
   833         | sort (rr::rrs) (re1,re2) = if is_simple rr
   834                                      then sort rrs (rr::re1,re2)
   835                                      else sort rrs (re1,rr::re2)
   836     in sort rrs ([],[]) end
   837 
   838     fun proc_rews [] = NONE
   839       | proc_rews (Proc {name, proc, lhs, ...} :: ps) =
   840           if Pattern.matches tsigt (Thm.term_of lhs, Thm.term_of t) then
   841             (debug_term false ("Trying procedure " ^ quote name ^ " on:") thyt eta_t;
   842              case transform_failure (curry SIMPROC_FAIL name)
   843                  (fn () => proc thyt ss eta_t) () of
   844                NONE => (debug false "FAILED"; proc_rews ps)
   845              | SOME raw_thm =>
   846                  (trace_thm ("Procedure " ^ quote name ^ " produced rewrite rule:") raw_thm;
   847                   (case rews (mk_procrule raw_thm) of
   848                     NONE => (trace_cterm true ("IGNORED result of simproc " ^ quote name ^
   849                       " -- does not match") t; proc_rews ps)
   850                   | some => some)))
   851           else proc_rews ps;
   852   in case eta_t of
   853        Abs _ $ _ => SOME (transitive eta_thm
   854          (beta_conversion false eta_t'), skel0)
   855      | _ => (case rews (sort_rrules (Net.match_term rules eta_t)) of
   856                NONE => proc_rews (Net.match_term procs eta_t)
   857              | some => some)
   858   end;
   859 
   860 
   861 (* conversion to apply a congruence rule to a term *)
   862 
   863 fun congc (prover,thyt,maxt) {thm=cong,lhs=lhs} t =
   864   let val thy = Thm.theory_of_thm cong
   865       val rthm = if maxt = ~1 then cong else Thm.incr_indexes (maxt+1) cong;
   866       val rlhs = fst (Drule.dest_equals (Drule.strip_imp_concl (cprop_of rthm)));
   867       val insts = Thm.cterm_match (rlhs, t)
   868       (* Pattern.match can raise Pattern.MATCH;
   869          is handled when congc is called *)
   870       val thm' = Thm.instantiate insts (Thm.rename_boundvars (term_of rlhs) (term_of t) rthm);
   871       val unit = trace_thm "Applying congruence rule:" thm';
   872       fun err (msg, thm) = (trace_thm msg thm; NONE)
   873   in case prover thm' of
   874        NONE => err ("Congruence proof failed.  Could not prove", thm')
   875      | SOME thm2 => (case check_conv true (Drule.beta_eta_conversion t) thm2 of
   876           NONE => err ("Congruence proof failed.  Should not have proved", thm2)
   877         | SOME thm2' =>
   878             if op aconv (pairself term_of (dest_equals (cprop_of thm2')))
   879             then NONE else SOME thm2')
   880   end;
   881 
   882 val (cA, (cB, cC)) =
   883   apsnd dest_equals (dest_implies (hd (cprems_of Drule.imp_cong)));
   884 
   885 fun transitive1 NONE NONE = NONE
   886   | transitive1 (SOME thm1) NONE = SOME thm1
   887   | transitive1 NONE (SOME thm2) = SOME thm2
   888   | transitive1 (SOME thm1) (SOME thm2) = SOME (transitive thm1 thm2)
   889 
   890 fun transitive2 thm = transitive1 (SOME thm);
   891 fun transitive3 thm = transitive1 thm o SOME;
   892 
   893 fun bottomc ((simprem, useprem, mutsimp), prover, thy, maxidx) =
   894   let
   895     fun botc skel ss t =
   896           if is_Var skel then NONE
   897           else
   898           (case subc skel ss t of
   899              some as SOME thm1 =>
   900                (case rewritec (prover, thy, maxidx) ss (rhs_of thm1) of
   901                   SOME (thm2, skel2) =>
   902                     transitive2 (transitive thm1 thm2)
   903                       (botc skel2 ss (rhs_of thm2))
   904                 | NONE => some)
   905            | NONE =>
   906                (case rewritec (prover, thy, maxidx) ss t of
   907                   SOME (thm2, skel2) => transitive2 thm2
   908                     (botc skel2 ss (rhs_of thm2))
   909                 | NONE => NONE))
   910 
   911     and try_botc ss t =
   912           (case botc skel0 ss t of
   913              SOME trec1 => trec1 | NONE => (reflexive t))
   914 
   915     and subc skel (ss as Simpset ({bounds, ...}, {congs, ...})) t0 =
   916        (case term_of t0 of
   917            Abs (a, T, t) =>
   918              let
   919                  val (v, t') = Thm.dest_abs (SOME ("." ^ a ^ "." ^ string_of_int bounds)) t0;
   920                  val ss' = incr_bounds ss;
   921                  val skel' = case skel of Abs (_, _, sk) => sk | _ => skel0;
   922              in case botc skel' ss' t' of
   923                   SOME thm => SOME (abstract_rule a v thm)
   924                 | NONE => NONE
   925              end
   926          | t $ _ => (case t of
   927              Const ("==>", _) $ _  => impc t0 ss
   928            | Abs _ =>
   929                let val thm = beta_conversion false t0
   930                in case subc skel0 ss (rhs_of thm) of
   931                     NONE => SOME thm
   932                   | SOME thm' => SOME (transitive thm thm')
   933                end
   934            | _  =>
   935                let fun appc () =
   936                      let
   937                        val (tskel, uskel) = case skel of
   938                            tskel $ uskel => (tskel, uskel)
   939                          | _ => (skel0, skel0);
   940                        val (ct, cu) = Thm.dest_comb t0
   941                      in
   942                      (case botc tskel ss ct of
   943                         SOME thm1 =>
   944                           (case botc uskel ss cu of
   945                              SOME thm2 => SOME (combination thm1 thm2)
   946                            | NONE => SOME (combination thm1 (reflexive cu)))
   947                       | NONE =>
   948                           (case botc uskel ss cu of
   949                              SOME thm1 => SOME (combination (reflexive ct) thm1)
   950                            | NONE => NONE))
   951                      end
   952                    val (h, ts) = strip_comb t
   953                in case cong_name h of
   954                     SOME a =>
   955                       (case assoc_string (fst congs, a) of
   956                          NONE => appc ()
   957                        | SOME cong =>
   958   (*post processing: some partial applications h t1 ... tj, j <= length ts,
   959     may be a redex. Example: map (%x. x) = (%xs. xs) wrt map_cong*)
   960                           (let
   961                              val thm = congc (prover ss, thy, maxidx) cong t0;
   962                              val t = getOpt (Option.map rhs_of thm, t0);
   963                              val (cl, cr) = Thm.dest_comb t
   964                              val dVar = Var(("", 0), dummyT)
   965                              val skel =
   966                                list_comb (h, replicate (length ts) dVar)
   967                            in case botc skel ss cl of
   968                                 NONE => thm
   969                               | SOME thm' => transitive3 thm
   970                                   (combination thm' (reflexive cr))
   971                            end handle TERM _ => error "congc result"
   972                                     | Pattern.MATCH => appc ()))
   973                   | _ => appc ()
   974                end)
   975          | _ => NONE)
   976 
   977     and impc ct ss =
   978       if mutsimp then mut_impc0 [] ct [] [] ss else nonmut_impc ct ss
   979 
   980     and rules_of_prem ss prem =
   981       if maxidx_of_term (term_of prem) <> ~1
   982       then (trace_cterm true
   983         "Cannot add premise as rewrite rule because it contains (type) unknowns:" prem; ([], NONE))
   984       else
   985         let val asm = assume prem
   986         in (extract_safe_rrules (ss, asm), SOME asm) end
   987 
   988     and add_rrules (rrss, asms) ss =
   989       Library.foldl (insert_rrule true) (ss, List.concat rrss) |> add_prems (List.mapPartial I asms)
   990 
   991     and disch r (prem, eq) =
   992       let
   993         val (lhs, rhs) = dest_eq eq;
   994         val eq' = implies_elim (Thm.instantiate
   995           ([], [(cA, prem), (cB, lhs), (cC, rhs)]) Drule.imp_cong)
   996           (implies_intr prem eq)
   997       in if not r then eq' else
   998         let
   999           val (prem', concl) = dest_implies lhs;
  1000           val (prem'', _) = dest_implies rhs
  1001         in transitive (transitive
  1002           (Thm.instantiate ([], [(cA, prem'), (cB, prem), (cC, concl)])
  1003              Drule.swap_prems_eq) eq')
  1004           (Thm.instantiate ([], [(cA, prem), (cB, prem''), (cC, concl)])
  1005              Drule.swap_prems_eq)
  1006         end
  1007       end
  1008 
  1009     and rebuild [] _ _ _ _ eq = eq
  1010       | rebuild (prem :: prems) concl (rrs :: rrss) (asm :: asms) ss eq =
  1011           let
  1012             val ss' = add_rrules (rev rrss, rev asms) ss;
  1013             val concl' =
  1014               Drule.mk_implies (prem, getOpt (Option.map rhs_of eq, concl));
  1015             val dprem = Option.map (curry (disch false) prem)
  1016           in case rewritec (prover, thy, maxidx) ss' concl' of
  1017               NONE => rebuild prems concl' rrss asms ss (dprem eq)
  1018             | SOME (eq', _) => transitive2 (Library.foldl (disch false o swap)
  1019                   (valOf (transitive3 (dprem eq) eq'), prems))
  1020                 (mut_impc0 (rev prems) (rhs_of eq') (rev rrss) (rev asms) ss)
  1021           end
  1022 
  1023     and mut_impc0 prems concl rrss asms ss =
  1024       let
  1025         val prems' = strip_imp_prems concl;
  1026         val (rrss', asms') = split_list (map (rules_of_prem ss) prems')
  1027       in mut_impc (prems @ prems') (strip_imp_concl concl) (rrss @ rrss')
  1028         (asms @ asms') [] [] [] [] ss ~1 ~1
  1029       end
  1030 
  1031     and mut_impc [] concl [] [] prems' rrss' asms' eqns ss changed k =
  1032         transitive1 (Library.foldl (fn (eq2, (eq1, prem)) => transitive1 eq1
  1033             (Option.map (curry (disch false) prem) eq2)) (NONE, eqns ~~ prems'))
  1034           (if changed > 0 then
  1035              mut_impc (rev prems') concl (rev rrss') (rev asms')
  1036                [] [] [] [] ss ~1 changed
  1037            else rebuild prems' concl rrss' asms' ss
  1038              (botc skel0 (add_rrules (rev rrss', rev asms') ss) concl))
  1039 
  1040       | mut_impc (prem :: prems) concl (rrs :: rrss) (asm :: asms)
  1041           prems' rrss' asms' eqns ss changed k =
  1042         case (if k = 0 then NONE else botc skel0 (add_rrules
  1043           (rev rrss' @ rrss, rev asms' @ asms) ss) prem) of
  1044             NONE => mut_impc prems concl rrss asms (prem :: prems')
  1045               (rrs :: rrss') (asm :: asms') (NONE :: eqns) ss changed
  1046               (if k = 0 then 0 else k - 1)
  1047           | SOME eqn =>
  1048             let
  1049               val prem' = rhs_of eqn;
  1050               val tprems = map term_of prems;
  1051               val i = 1 + Library.foldl Int.max (~1, map (fn p =>
  1052                 find_index_eq p tprems) (#hyps (rep_thm eqn)));
  1053               val (rrs', asm') = rules_of_prem ss prem'
  1054             in mut_impc prems concl rrss asms (prem' :: prems')
  1055               (rrs' :: rrss') (asm' :: asms') (SOME (foldr (disch true)
  1056                 (Drule.imp_cong' eqn (reflexive (Drule.list_implies
  1057                   (Library.drop (i, prems), concl)))) (Library.take (i, prems))) :: eqns) ss (length prems') ~1
  1058             end
  1059 
  1060      (*legacy code - only for backwards compatibility*)
  1061      and nonmut_impc ct ss =
  1062        let val (prem, conc) = dest_implies ct;
  1063            val thm1 = if simprem then botc skel0 ss prem else NONE;
  1064            val prem1 = getOpt (Option.map rhs_of thm1, prem);
  1065            val ss1 = if not useprem then ss else add_rrules
  1066              (apsnd single (apfst single (rules_of_prem ss prem1))) ss
  1067        in (case botc skel0 ss1 conc of
  1068            NONE => (case thm1 of
  1069                NONE => NONE
  1070              | SOME thm1' => SOME (Drule.imp_cong' thm1' (reflexive conc)))
  1071          | SOME thm2 =>
  1072            let val thm2' = disch false (prem1, thm2)
  1073            in (case thm1 of
  1074                NONE => SOME thm2'
  1075              | SOME thm1' =>
  1076                  SOME (transitive (Drule.imp_cong' thm1' (reflexive conc)) thm2'))
  1077            end)
  1078        end
  1079 
  1080  in try_botc end;
  1081 
  1082 
  1083 (* Meta-rewriting: rewrites t to u and returns the theorem t==u *)
  1084 
  1085 (*
  1086   Parameters:
  1087     mode = (simplify A,
  1088             use A in simplifying B,
  1089             use prems of B (if B is again a meta-impl.) to simplify A)
  1090            when simplifying A ==> B
  1091     prover: how to solve premises in conditional rewrites and congruences
  1092 *)
  1093 
  1094 fun rewrite_cterm mode prover ss ct =
  1095   (simp_depth := !simp_depth + 1;
  1096    if !simp_depth mod 10 = 0
  1097    then warning ("Simplification depth " ^ string_of_int (!simp_depth))
  1098    else ();
  1099    trace_cterm false "SIMPLIFIER INVOKED ON THE FOLLOWING TERM:" ct;
  1100    let val {thy, t, maxidx, ...} = Thm.rep_cterm ct
  1101        val res = bottomc (mode, prover, thy, maxidx) ss ct
  1102          handle THM (s, _, thms) =>
  1103          error ("Exception THM was raised in simplifier:\n" ^ s ^ "\n" ^
  1104            Pretty.string_of (Display.pretty_thms thms))
  1105    in simp_depth := !simp_depth - 1; res end
  1106   ) handle exn => (simp_depth := !simp_depth - 1; raise exn);
  1107 
  1108 (*Rewrite a cterm*)
  1109 fun rewrite_aux _ _ [] = (fn ct => Thm.reflexive ct)
  1110   | rewrite_aux prover full thms =
  1111       rewrite_cterm (full, false, false) prover (empty_ss addsimps thms);
  1112 
  1113 (*Rewrite a theorem*)
  1114 fun simplify_aux _ _ [] = (fn th => th)
  1115   | simplify_aux prover full thms =
  1116       Drule.fconv_rule (rewrite_cterm (full, false, false) prover (empty_ss addsimps thms));
  1117 
  1118 (*simple term rewriting -- no proof*)
  1119 fun rewrite_term thy rules procs =
  1120   Pattern.rewrite_term (Sign.tsig_of thy) (map decomp_simp' rules) procs;
  1121 
  1122 fun rewrite_thm mode prover ss = Drule.fconv_rule (rewrite_cterm mode prover ss);
  1123 
  1124 (*Rewrite the subgoals of a proof state (represented by a theorem) *)
  1125 fun rewrite_goals_rule_aux _ []   th = th
  1126   | rewrite_goals_rule_aux prover thms th =
  1127       Drule.fconv_rule (Drule.goals_conv (K true) (rewrite_cterm (true, true, false) prover
  1128         (empty_ss addsimps thms))) th;
  1129 
  1130 (*Rewrite the subgoal of a proof state (represented by a theorem)*)
  1131 fun rewrite_goal_rule mode prover ss i thm =
  1132   if 0 < i  andalso  i <= nprems_of thm
  1133   then Drule.fconv_rule (Drule.goals_conv (fn j => j=i) (rewrite_cterm mode prover ss)) thm
  1134   else raise THM("rewrite_goal_rule",i,[thm]);
  1135 
  1136 (*Rewrite subgoal i only.  SELECT_GOAL avoids inefficiencies in goals_conv.*)
  1137 fun asm_rewrite_goal_tac mode prover_tac ss =
  1138   SELECT_GOAL
  1139     (PRIMITIVE (rewrite_goal_rule mode (SINGLE o prover_tac) ss 1));
  1140 
  1141 
  1142 
  1143 (** simplification tactics and rules **)
  1144 
  1145 fun solve_all_tac solvers ss =
  1146   let
  1147     val Simpset (_, {subgoal_tac, ...}) = ss;
  1148     val solve_tac = subgoal_tac (set_solvers solvers ss) THEN_ALL_NEW (K no_tac);
  1149   in DEPTH_SOLVE (solve_tac 1) end;
  1150 
  1151 (*NOTE: may instantiate unknowns that appear also in other subgoals*)
  1152 fun generic_simp_tac safe mode ss =
  1153   let
  1154     val Simpset ({prems, ...}, {loop_tacs, solvers = (unsafe_solvers, solvers), ...}) = ss;
  1155     val loop_tac = FIRST' (map #2 loop_tacs);
  1156     val solve_tac = FIRST' (map (solver prems) (if safe then solvers else unsafe_solvers));
  1157 
  1158     fun simp_loop_tac i =
  1159       asm_rewrite_goal_tac mode (solve_all_tac unsafe_solvers) ss i THEN
  1160       (solve_tac i ORELSE TRY ((loop_tac THEN_ALL_NEW simp_loop_tac) i));
  1161   in simp_loop_tac end;
  1162 
  1163 fun simp rew mode ss thm =
  1164   let
  1165     val Simpset (_, {solvers = (unsafe_solvers, _), ...}) = ss;
  1166     val tacf = solve_all_tac unsafe_solvers;
  1167     fun prover s th = Option.map #1 (Seq.pull (tacf s th));
  1168   in rew mode prover ss thm end;
  1169 
  1170 val simp_thm = simp rewrite_thm;
  1171 val simp_cterm = simp rewrite_cterm;
  1172 
  1173 end;
  1174 
  1175 structure BasicMetaSimplifier: BASIC_META_SIMPLIFIER = MetaSimplifier;
  1176 open BasicMetaSimplifier;