(*  Title:      Pure/meta_simplifier.ML

     ID:         $Id$

     Author:     Tobias Nipkow and Stefan Berghofer

 Meta-level Simplification.

 *)

 infix 4

   addsimps delsimps addeqcongs deleqcongs addcongs delcongs addsimprocs delsimprocs

   setmksimps setmksimps2 setmkcong setmksym setmkeqTrue settermless setsubgoaler

   setloop addloop delloop setSSolver addSSolver setSolver addSolver;

 signature BASIC_META_SIMPLIFIER =

 sig

   val debug_simp: bool ref

   val trace_simp: bool ref

   val simp_depth_limit: int ref

   type rrule

   type cong

   type solver

   val mk_solver: string -> (thm list -> int -> tactic) -> solver

   type simpset

   type proc

   val rep_ss: simpset ->

    {rules: rrule Net.net,

     prems: thm list,

     bounds: string list,

     depth: int} *

    {congs: (string * cong) list * string list,

     procs: proc Net.net,

     mk_rews:

      {mk: thm -> thm list,

       mk2: thm list -> thm -> thm list,

       mk_cong: thm -> thm,

       mk_sym: thm -> thm option,

       mk_eq_True: thm -> thm option},

     termless: term * term -> bool,

     subgoal_tac: simpset -> int -> tactic,

     loop_tacs: (string * (int -> tactic)) list,

     solvers: solver list * solver list}

   val print_ss: simpset -> unit

   val empty_ss: simpset

   val merge_ss: simpset * simpset -> simpset

   type simproc

   val mk_simproc: string -> cterm list ->

     (Sign.sg -> simpset -> term -> thm option) -> simproc

   val add_prems: thm list -> simpset -> simpset

   val prems_of_ss: simpset -> thm list

   val addsimps: simpset * thm list -> simpset

   val delsimps: simpset * thm list -> simpset

   val addeqcongs: simpset * thm list -> simpset

   val deleqcongs: simpset * thm list -> simpset

   val addcongs: simpset * thm list -> simpset

   val delcongs: simpset * thm list -> simpset

   val addsimprocs: simpset * simproc list -> simpset

   val delsimprocs: simpset * simproc list -> simpset

   val setmksimps: simpset * (thm -> thm list) -> simpset

   val setmksimps2: simpset * (thm list -> thm -> thm list) -> simpset

   val setmkcong: simpset * (thm -> thm) -> simpset

   val setmksym: simpset * (thm -> thm option) -> simpset

   val setmkeqTrue: simpset * (thm -> thm option) -> simpset

   val settermless: simpset * (term * term -> bool) -> simpset

   val setsubgoaler: simpset * (simpset -> int -> tactic) -> simpset

   val setloop: simpset * (int -> tactic) -> simpset

   val addloop: simpset * (string * (int -> tactic)) -> simpset

   val delloop: simpset * string -> simpset

   val setSSolver: simpset * solver -> simpset

   val addSSolver: simpset * solver -> simpset

   val setSolver: simpset * solver -> simpset

   val addSolver: simpset * solver -> simpset

   val generic_simp_tac: bool -> bool * bool * bool -> simpset -> int -> tactic

 end;

 signature META_SIMPLIFIER =

 sig

   include BASIC_META_SIMPLIFIER

   exception SIMPLIFIER of string * thm

   val clear_ss: simpset -> simpset

   exception SIMPROC_FAIL of string * exn

   val simproc_i: Sign.sg -> string -> term list

     -> (Sign.sg -> simpset -> term -> thm option) -> simproc

   val simproc: Sign.sg -> string -> string list

     -> (Sign.sg -> simpset -> term -> thm option) -> simproc

   val rewrite_cterm: bool * bool * bool ->

     (simpset -> thm -> thm option) -> simpset -> cterm -> thm

   val rewrite_aux: (simpset -> thm -> thm option) -> bool -> thm list -> cterm -> thm

   val simplify_aux: (simpset -> thm -> thm option) -> bool -> thm list -> thm -> thm

   val rewrite_term: Sign.sg -> thm list -> (term -> term option) list -> term -> term

   val rewrite_thm: bool * bool * bool ->

     (simpset -> thm -> thm option) -> simpset -> thm -> thm

   val rewrite_goals_rule_aux: (simpset -> thm -> thm option) -> thm list -> thm -> thm

   val rewrite_goal_rule: bool * bool * bool ->

     (simpset -> thm -> thm option) -> simpset -> int -> thm -> thm

   val asm_rewrite_goal_tac: bool * bool * bool ->

     (simpset -> tactic) -> simpset -> int -> tactic

   val simp_thm: bool * bool * bool -> simpset -> thm -> thm

   val simp_cterm: bool * bool * bool -> simpset -> cterm -> thm

 end;

 structure MetaSimplifier: META_SIMPLIFIER =

 struct

 (** diagnostics **)

 exception SIMPLIFIER of string * thm;

 val debug_simp = ref false;

 val trace_simp = ref false;

 val simp_depth = ref 0;

 val simp_depth_limit = ref 1000;

 local

 fun println a =

   tracing (case ! simp_depth of 0 => a | n => enclose "[" "]" (string_of_int n) ^ a);

 fun prnt warn a = if warn then warning a else println a;

 fun prtm warn a sg t = prnt warn (a ^ "\n" ^ Sign.string_of_term sg t);

 fun prctm warn a t = prnt warn (a ^ "\n" ^ Display.string_of_cterm t);

 in

 fun debug warn a = if ! debug_simp then prnt warn a else ();

 fun trace warn a = if ! trace_simp then prnt warn a else ();

 fun debug_term warn a sign t = if ! debug_simp then prtm warn a sign t else ();

 fun trace_term warn a sign t = if ! trace_simp then prtm warn a sign t else ();

 fun trace_cterm warn a ct = if ! trace_simp then prctm warn a ct else ();

 fun trace_thm a th = if ! trace_simp then prctm false a (Thm.cprop_of th) else ();

 fun trace_named_thm a (thm, name) =

   if ! trace_simp then

     prctm false (if name = "" then a else a ^ " " ^ quote name ^ ":") (Thm.cprop_of thm)

   else ();

 fun warn_thm a = prctm true a o Thm.cprop_of;

 end;

 (** datatype simpset **)

 (* rewrite rules *)

 type rrule = {thm: thm, name: string, lhs: term, elhs: cterm, fo: bool, perm: bool};

 (*thm: the rewrite rule;

   name: name of theorem from which rewrite rule was extracted;

   lhs: the left-hand side;

   elhs: the etac-contracted lhs;

   fo: use first-order matching;

   perm: the rewrite rule is permutative;

 Remarks:

   - elhs is used for matching,

     lhs only for preservation of bound variable names;

   - fo is set iff

     either elhs is first-order (no Var is applied),

       in which case fo-matching is complete,

     or elhs is not a pattern,

       in which case there is nothing better to do;*)

 fun eq_rrule ({thm = thm1, ...}: rrule, {thm = thm2, ...}: rrule) =

   Drule.eq_thm_prop (thm1, thm2);

 (* congruences *)

 type cong = {thm: thm, lhs: cterm};

 fun eq_cong ({thm = thm1, ...}: cong, {thm = thm2, ...}: cong) =

   Drule.eq_thm_prop (thm1, thm2);

 (* solvers *)

 datatype solver =

   Solver of

    {name: string,

     solver: thm list -> int -> tactic,

     id: stamp};

 fun mk_solver name solver = Solver {name = name, solver = solver, id = stamp ()};

 fun solver_name (Solver {name, ...}) = name;

 fun solver ths (Solver {solver = tacf, ...}) = tacf ths;

 fun eq_solver (Solver {id = id1, ...}, Solver {id = id2, ...}) = (id1 = id2);

 val merge_solvers = gen_merge_lists eq_solver;

 (* simplification sets and procedures *)

 (*A simpset contains data required during conversion:

     rules: discrimination net of rewrite rules;

     prems: current premises;

     bounds: names of bound variables already used

       (for generating new names when rewriting under lambda abstractions);

     depth: depth of conditional rewriting;

     congs: association list of congruence rules and

            a list of `weak' congruence constants.

            A congruence is `weak' if it avoids normalization of some argument.

     procs: discrimination net of simplification procedures

       (functions that prove rewrite rules on the fly);

     mk_rews:

       mk: turn simplification thms into rewrite rules;

       mk2: like mk but may also depend on the other premises

       mk_cong: prepare congruence rules;

       mk_sym: turn == around;

       mk_eq_True: turn P into P == True;

     termless: relation for ordered rewriting;*)

 type mk_rews =

  {mk: thm -> thm list,

   mk2: thm list -> thm -> thm list,

   mk_cong: thm -> thm,

   mk_sym: thm -> thm option,

   mk_eq_True: thm -> thm option};

 datatype simpset =

   Simpset of

    {rules: rrule Net.net,

     prems: thm list,

     bounds: string list,

     depth: int} *

    {congs: (string * cong) list * string list,

     procs: proc Net.net,

     mk_rews: mk_rews,

     termless: term * term -> bool,

     subgoal_tac: simpset -> int -> tactic,

     loop_tacs: (string * (int -> tactic)) list,

     solvers: solver list * solver list}

 and proc =

   Proc of

    {name: string,

     lhs: cterm,

     proc: Sign.sg -> simpset -> term -> thm option,

     id: stamp};

 fun eq_proc (Proc {id = id1, ...}, Proc {id = id2, ...}) = (id1 = id2);

 fun rep_ss (Simpset args) = args;

 fun make_ss1 (rules, prems, bounds, depth) =

   {rules = rules, prems = prems, bounds = bounds, depth = depth};

 fun map_ss1 f {rules, prems, bounds, depth} =

   make_ss1 (f (rules, prems, bounds, depth));

 fun make_ss2 (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =

   {congs = congs, procs = procs, mk_rews = mk_rews, termless = termless,

     subgoal_tac = subgoal_tac, loop_tacs = loop_tacs, solvers = solvers};

 fun map_ss2 f {congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers} =

   make_ss2 (f (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));

 fun make_simpset (args1, args2) = Simpset (make_ss1 args1, make_ss2 args2);

 fun map_simpset f (Simpset ({rules, prems, bounds, depth},

     {congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers})) =

   make_simpset (f ((rules, prems, bounds, depth),

     (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers)));

 fun map_simpset1 f (Simpset (r1, r2)) = Simpset (map_ss1 f r1, r2);

 fun map_simpset2 f (Simpset (r1, r2)) = Simpset (r1, map_ss2 f r2);

 (* print simpsets *)

 fun print_ss ss =

   let

     val pretty_thms = map Display.pretty_thm;

     fun pretty_cong (name, th) =

       Pretty.block [Pretty.str (name ^ ":"), Pretty.brk 1, Display.pretty_thm th];

     fun pretty_proc (name, lhss) =

       Pretty.big_list (name ^ ":") (map Display.pretty_cterm lhss);

     val Simpset ({rules, ...}, {congs, procs, loop_tacs, solvers, ...}) = ss;

     val smps = map (#thm o #2) (Net.dest rules);

     val cngs = map (fn (name, {thm, ...}) => (name, thm)) (#1 congs);

     val prcs = Net.dest procs |>

       map (fn (_, Proc {name, lhs, id, ...}) => ((name, lhs), id))

       |> partition_eq eq_snd

       |> map (fn ps => (#1 (#1 (hd ps)), map (#2 o #1) ps))

       |> Library.sort_wrt #1;

   in

     [Pretty.big_list "simplification rules:" (pretty_thms smps),

       Pretty.big_list "simplification procedures:" (map pretty_proc prcs),

       Pretty.big_list "congruences:" (map pretty_cong cngs),

       Pretty.strs ("loopers:" :: map (quote o #1) loop_tacs),

       Pretty.strs ("unsafe solvers:" :: map (quote o solver_name) (#1 solvers)),

       Pretty.strs ("safe solvers:" :: map (quote o solver_name) (#2 solvers))]

     |> Pretty.chunks |> Pretty.writeln

   end;

 (* empty simpsets *)

 local

 fun init_ss mk_rews termless subgoal_tac solvers =

   make_simpset ((Net.empty, [], [], 0),

     (([], []), Net.empty, mk_rews, termless, subgoal_tac, [], solvers));

 val basic_mk_rews: mk_rews =

  {mk = fn th => if can Logic.dest_equals (Thm.concl_of th) then [th] else [],

   mk2 = fn thms => fn thm => [],

   mk_cong = I,

   mk_sym = Some o Drule.symmetric_fun,

   mk_eq_True = K None};

 in

 val empty_ss = init_ss basic_mk_rews Term.termless (K (K no_tac)) ([], []);

 fun clear_ss (Simpset (_, {mk_rews, termless, subgoal_tac, solvers, ...})) =

   init_ss mk_rews termless subgoal_tac solvers;

 end;

 (* merge simpsets *)            (*NOTE: ignores some fields of 2nd simpset*)

 fun merge_ss (ss1, ss2) =

   let

     val Simpset ({rules = rules1, prems = prems1, bounds = bounds1, depth},

      {congs = (congs1, weak1), procs = procs1, mk_rews, termless, subgoal_tac,

       loop_tacs = loop_tacs1, solvers = (unsafe_solvers1, solvers1)}) = ss1;

     val Simpset ({rules = rules2, prems = prems2, bounds = bounds2, depth = _},

      {congs = (congs2, weak2), procs = procs2, mk_rews = _, termless = _, subgoal_tac = _,

       loop_tacs = loop_tacs2, solvers = (unsafe_solvers2, solvers2)}) = ss2;

     val rules' = Net.merge (rules1, rules2, eq_rrule);

     val prems' = gen_merge_lists Drule.eq_thm_prop prems1 prems2;

     val bounds' = merge_lists bounds1 bounds2;

     val congs' = gen_merge_lists (eq_cong o pairself #2) congs1 congs2;

     val weak' = merge_lists weak1 weak2;

     val procs' = Net.merge (procs1, procs2, eq_proc);

     val loop_tacs' = merge_alists loop_tacs1 loop_tacs2;

     val unsafe_solvers' = merge_solvers unsafe_solvers1 unsafe_solvers2;

     val solvers' = merge_solvers solvers1 solvers2;

   in

     make_simpset ((rules', prems', bounds', depth), ((congs', weak'), procs',

       mk_rews, termless, subgoal_tac, loop_tacs', (unsafe_solvers', solvers')))

   end;

 (* simprocs *)

 exception SIMPROC_FAIL of string * exn;

 datatype simproc = Simproc of proc list;

 fun mk_simproc name lhss proc =

   let val id = stamp () in

     Simproc (lhss |> map (fn lhs =>

       Proc {name = name, lhs = lhs, proc = proc, id = id}))

   end;

 fun simproc_i sg name = mk_simproc name o map (Thm.cterm_of sg o Logic.varify);

 fun simproc sg name = simproc_i sg name o map (Sign.simple_read_term sg TypeInfer.logicT);

 (** simpset operations **)

 (* bounds and prems *)

 fun add_bound b = map_simpset1 (fn (rules, prems, bounds, depth) =>

   (rules, prems, b :: bounds, depth));

 fun add_prems ths = map_simpset1 (fn (rules, prems, bounds, depth) =>

   (rules, ths @ prems, bounds, depth));

 fun prems_of_ss (Simpset ({prems, ...}, _)) = prems;

 (* addsimps *)

 fun mk_rrule2 {thm, name, lhs, elhs, perm} =

   let

     val fo = Pattern.first_order (term_of elhs) orelse not (Pattern.pattern (term_of elhs))

   in {thm = thm, name = name, lhs = lhs, elhs = elhs, fo = fo, perm = perm} end;

 fun insert_rrule quiet (ss, rrule as {thm, name, lhs, elhs, perm}) =

  (trace_named_thm "Adding rewrite rule" (thm, name);

   ss |> map_simpset1 (fn (rules, prems, bounds, depth) =>

     let

       val rrule2 as {elhs, ...} = mk_rrule2 rrule;

       val rules' = Net.insert_term ((term_of elhs, rrule2), rules, eq_rrule);

     in (rules', prems, bounds, depth) end)

   handle Net.INSERT =>

     (if quiet then () else warn_thm "Ignoring duplicate rewrite rule:" thm; ss));

 fun vperm (Var _, Var _) = true

   | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)

   | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)

   | vperm (t, u) = (t = u);

 fun var_perm (t, u) =

   vperm (t, u) andalso eq_set (term_varnames t, term_varnames u);

 (* FIXME: it seems that the conditions on extra variables are too liberal if

 prems are nonempty: does solving the prems really guarantee instantiation of

 all its Vars? Better: a dynamic check each time a rule is applied.

 *)

 fun rewrite_rule_extra_vars prems elhs erhs =

   not (term_varnames erhs subset foldl add_term_varnames (term_varnames elhs, prems))

   orelse

   not (term_tvars erhs subset (term_tvars elhs union List.concat (map term_tvars prems)));

 (*simple test for looping rewrite rules and stupid orientations*)

 fun reorient sign prems lhs rhs =

   rewrite_rule_extra_vars prems lhs rhs

     orelse

   is_Var (head_of lhs)

     orelse

   exists (apl (lhs, Logic.occs)) (rhs :: prems)

     orelse

   null prems andalso Pattern.matches (Sign.tsig_of sign) (lhs, rhs)

     (*the condition "null prems" is necessary because conditional rewrites

       with extra variables in the conditions may terminate although

       the rhs is an instance of the lhs; example: ?m < ?n ==> f(?n) == f(?m)*)

     orelse

   is_Const lhs andalso not (is_Const rhs);

 fun decomp_simp thm =

   let

     val {sign, prop, ...} = Thm.rep_thm thm;

     val prems = Logic.strip_imp_prems prop;

     val concl = Drule.strip_imp_concl (Thm.cprop_of thm);

     val (lhs, rhs) = Drule.dest_equals concl handle TERM _ =>

       raise SIMPLIFIER ("Rewrite rule not a meta-equality", thm);

     val (_, elhs) = Drule.dest_equals (Thm.cprop_of (Thm.eta_conversion lhs));

     val elhs = if elhs = lhs then lhs else elhs;  (*share identical copies*)

     val erhs = Pattern.eta_contract (term_of rhs);

     val perm =

       var_perm (term_of elhs, erhs) andalso

       not (term_of elhs aconv erhs) andalso

       not (is_Var (term_of elhs));

   in (sign, prems, term_of lhs, elhs, term_of rhs, perm) end;

 fun decomp_simp' thm =

   let val (_, _, lhs, _, rhs, _) = decomp_simp thm in

     if Thm.nprems_of thm > 0 then raise SIMPLIFIER ("Bad conditional rewrite rule", thm)

     else (lhs, rhs)

   end;

 fun mk_eq_True (Simpset (_, {mk_rews = {mk_eq_True, ...}, ...})) (thm, name) =

   (case mk_eq_True thm of

     None => []

   | Some eq_True =>

       let val (_, _, lhs, elhs, _, _) = decomp_simp eq_True

       in [{thm = eq_True, name = name, lhs = lhs, elhs = elhs, perm = false}] end);

 (*create the rewrite rule and possibly also the eq_True variant,

   in case there are extra vars on the rhs*)

 fun rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm2) =

   let val rrule = {thm = thm, name = name, lhs = lhs, elhs = elhs, perm = false} in

     if term_varnames rhs subset term_varnames lhs andalso

       term_tvars rhs subset term_tvars lhs then [rrule]

     else mk_eq_True ss (thm2, name) @ [rrule]

   end;

 fun mk_rrule ss (thm, name) =

   let val (_, prems, lhs, elhs, rhs, perm) = decomp_simp thm in

     if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]

     else

       (*weak test for loops*)

       if rewrite_rule_extra_vars prems lhs rhs orelse is_Var (term_of elhs)

       then mk_eq_True ss (thm, name)

       else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)

   end;

 fun orient_rrule ss (thm, name) =

   let val (sign, prems, lhs, elhs, rhs, perm) = decomp_simp thm in

     if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]

     else if reorient sign prems lhs rhs then

       if reorient sign prems rhs lhs

       then mk_eq_True ss (thm, name)

       else

         let val Simpset (_, {mk_rews = {mk_sym, ...}, ...}) = ss in

           (case mk_sym thm of

             None => []

           | Some thm' =>

               let val (_, _, lhs', elhs', rhs', _) = decomp_simp thm'

               in rrule_eq_True (thm', name, lhs', elhs', rhs', ss, thm) end)

         end

     else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)

   end;

 fun extract_rews (Simpset ({prems, ...}, {mk_rews = {mk, ...}, ...}), thms)

   = flat (map (fn thm => map (rpair (Thm.name_of_thm thm)) (mk thm)) thms);

 fun extract_rews2 (Simpset ({prems, ...}, {mk_rews = {mk2, ...}, ...}), thms)

   = flat (map (fn thm => map (rpair (Thm.name_of_thm thm)) (mk2 prems thm)) thms);

 fun orient_comb_simps comb mk_rrule (ss, thms) =

   let

     val rews = extract_rews (ss, thms);

     val rrules = flat (map mk_rrule rews);

   in foldl comb (ss, rrules) end;

 fun extract_safe_rrules (ss, thm) =

   flat (map (orient_rrule ss) (extract_rews (ss, [thm])));

 fun extract_safe_rrules2 (ss, thm) =

   flat (map (orient_rrule ss) (extract_rews2 (ss, [thm])));

 (*add rewrite rules explicitly; do not reorient!*)

 fun ss addsimps thms =

   orient_comb_simps (insert_rrule false) (mk_rrule ss) (ss, thms);

 fun add_prem2(ss,thm) =

   foldl (insert_rrule true) (ss,extract_safe_rrules2(ss,thm))

   |> add_prems [thm];

 fun add_prems2 thms ss = foldl add_prem2 (ss,thms);

 (* delsimps *)

 fun del_rrule (ss, rrule as {thm, elhs, ...}) =

   ss |> map_simpset1 (fn (rules, prems, bounds, depth) =>

     (Net.delete_term ((term_of elhs, rrule), rules, eq_rrule), prems, bounds, depth))

   handle Net.DELETE => (warn_thm "Rewrite rule not in simpset:" thm; ss);

 fun ss delsimps thms =

   orient_comb_simps del_rrule (map mk_rrule2 o mk_rrule ss) (ss, thms);

 (* congs *)

 fun cong_name (Const (a, _)) = Some a

   | cong_name (Free (a, _)) = Some ("Free: " ^ a)

   | cong_name _ = None;

 local

 fun is_full_cong_prems [] [] = true

   | is_full_cong_prems [] _ = false

   | is_full_cong_prems (p :: prems) varpairs =

       (case Logic.strip_assums_concl p of

         Const ("==", _) $ lhs $ rhs =>

           let val (x, xs) = strip_comb lhs and (y, ys) = strip_comb rhs in

             is_Var x andalso forall is_Bound xs andalso

             null (findrep xs) andalso xs = ys andalso

             (x, y) mem varpairs andalso

             is_full_cong_prems prems (varpairs \ (x, y))

           end

       | _ => false);

 fun is_full_cong thm =

   let

     val prems = prems_of thm and concl = concl_of thm;

     val (lhs, rhs) = Logic.dest_equals concl;

     val (f, xs) = strip_comb lhs and (g, ys) = strip_comb rhs;

   in

     f = g andalso null (findrep (xs @ ys)) andalso length xs = length ys andalso

     is_full_cong_prems prems (xs ~~ ys)

   end;

 fun add_cong (ss, thm) = ss |>

   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>

     let

       val (lhs, _) = Drule.dest_equals (Drule.strip_imp_concl (Thm.cprop_of thm))

         handle TERM _ => raise SIMPLIFIER ("Congruence not a meta-equality", thm);

     (*val lhs = Pattern.eta_contract lhs;*)

       val a = the (cong_name (head_of (term_of lhs))) handle Library.OPTION =>

         raise SIMPLIFIER ("Congruence must start with a constant or free variable", thm);

       val (alist, weak) = congs;

       val alist2 = overwrite_warn (alist, (a, {lhs = lhs, thm = thm}))

         ("Overwriting congruence rule for " ^ quote a);

       val weak2 = if is_full_cong thm then weak else a :: weak;

     in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);

 fun del_cong (ss, thm) = ss |>

   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>

     let

       val (lhs, _) = Logic.dest_equals (Thm.concl_of thm) handle TERM _ =>

         raise SIMPLIFIER ("Congruence not a meta-equality", thm);

     (*val lhs = Pattern.eta_contract lhs;*)

       val a = the (cong_name (head_of lhs)) handle Library.OPTION =>

         raise SIMPLIFIER ("Congruence must start with a constant", thm);

       val (alist, _) = congs;

       val alist2 = filter (fn (x, _) => x <> a) alist;

       val weak2 = alist2 |> mapfilter (fn (a, {thm, ...}) =>

         if is_full_cong thm then None else Some a);

     in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);

 fun mk_cong (Simpset (_, {mk_rews = {mk_cong = f, ...}, ...})) = f;

 in

 val (op addeqcongs) = foldl add_cong;

 val (op deleqcongs) = foldl del_cong;

 fun ss addcongs congs = ss addeqcongs map (mk_cong ss) congs;

 fun ss delcongs congs = ss deleqcongs map (mk_cong ss) congs;

 end;

 (* simprocs *)

 local

 fun add_proc (ss, proc as Proc {name, lhs, ...}) =

  (trace_cterm false ("Adding simplification procedure " ^ quote name ^ " for") lhs;

   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>

     (congs, Net.insert_term ((term_of lhs, proc), procs, eq_proc),

       mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss

   handle Net.INSERT =>

     (warning ("Ignoring duplicate simplification procedure " ^ quote name); ss));

 fun del_proc (ss, proc as Proc {name, lhs, ...}) =

   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>

     (congs, Net.delete_term ((term_of lhs, proc), procs, eq_proc),

       mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss

   handle Net.DELETE =>

     (warning ("Simplification procedure " ^ quote name ^ " not in simpset"); ss);

 in

 val (op addsimprocs) = foldl (fn (ss, Simproc procs) => foldl add_proc (ss, procs));

 val (op delsimprocs) = foldl (fn (ss, Simproc procs) => foldl del_proc (ss, procs));

 end;

 (* mk_rews *)

 local

 fun map_mk_rews f = map_simpset2 (fn (congs, procs, {mk, mk2, mk_cong, mk_sym, mk_eq_True},

       termless, subgoal_tac, loop_tacs, solvers) =>

   let val (mk', mk2', mk_cong', mk_sym', mk_eq_True') = f (mk, mk2, mk_cong, mk_sym, mk_eq_True) in

     (congs, procs, {mk = mk', mk2 = mk2', mk_cong = mk_cong', mk_sym = mk_sym', mk_eq_True = mk_eq_True'},

       termless, subgoal_tac, loop_tacs, solvers)

   end);

 in

 fun ss setmksimps mk = ss |> map_mk_rews (fn (_, mk2, mk_cong, mk_sym, mk_eq_True) =>

   (mk, mk2, mk_cong, mk_sym, mk_eq_True));

 fun ss setmksimps2 mk2 = ss |> map_mk_rews (fn (mk, _, mk_cong, mk_sym, mk_eq_True) =>

   (mk, mk2, mk_cong, mk_sym, mk_eq_True));

 fun ss setmkcong mk_cong = ss |> map_mk_rews (fn (mk, mk2, _, mk_sym, mk_eq_True) =>

   (mk, mk2, mk_cong, mk_sym, mk_eq_True));

 fun ss setmksym mk_sym = ss |> map_mk_rews (fn (mk, mk2, mk_cong, _, mk_eq_True) =>

   (mk, mk2, mk_cong, mk_sym, mk_eq_True));

 fun ss setmkeqTrue mk_eq_True = ss |> map_mk_rews (fn (mk, mk2, mk_cong, mk_sym, _) =>

   (mk, mk2, mk_cong, mk_sym, mk_eq_True));

 end;

 (* termless *)

 fun ss settermless termless = ss |>

   map_simpset2 (fn (congs, procs, mk_rews, _, subgoal_tac, loop_tacs, solvers) =>

    (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));

 (* tactics *)

 fun ss setsubgoaler subgoal_tac = ss |>

   map_simpset2 (fn (congs, procs, mk_rews, termless, _, loop_tacs, solvers) =>

    (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));

 fun ss setloop tac = ss |>

   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, _, solvers) =>

    (congs, procs, mk_rews, termless, subgoal_tac, [("", tac)], solvers));

 fun ss addloop (name, tac) = ss |>

   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>

     (congs, procs, mk_rews, termless, subgoal_tac,

       overwrite_warn (loop_tacs, (name, tac)) ("Overwriting looper " ^ quote name),

       solvers));

 fun ss delloop name = ss |>

   map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>

     let val loop_tacs' = filter_out (equal name o #1) loop_tacs in

       if length loop_tacs <> length loop_tacs' then ()

       else warning ("No such looper in simpset: " ^ quote name);

       (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs', solvers)

     end);

 fun ss setSSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,

   subgoal_tac, loop_tacs, (unsafe_solvers, _)) =>

     (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, (unsafe_solvers, [solver])));

 fun ss addSSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,

   subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, termless,

     subgoal_tac, loop_tacs, (unsafe_solvers, merge_solvers solvers [solver])));

 fun ss setSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,

   subgoal_tac, loop_tacs, (_, solvers)) => (congs, procs, mk_rews, termless,

     subgoal_tac, loop_tacs, ([solver], solvers)));

 fun ss addSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,

   subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, termless,

     subgoal_tac, loop_tacs, (merge_solvers unsafe_solvers [solver], solvers)));

 fun set_solvers solvers = map_simpset2 (fn (congs, procs, mk_rews, termless,

   subgoal_tac, loop_tacs, _) => (congs, procs, mk_rews, termless,

   subgoal_tac, loop_tacs, (solvers, solvers)));

 (** rewriting **)

 (*

   Uses conversions, see:

     L C Paulson, A higher-order implementation of rewriting,

     Science of Computer Programming 3 (1983), pages 119-149.

 *)

 val dest_eq = Drule.dest_equals o Thm.cprop_of;

 val lhs_of = #1 o dest_eq;

 val rhs_of = #2 o dest_eq;

 fun check_conv msg thm thm' =

   let

     val thm'' = transitive thm (transitive

       (symmetric (Drule.beta_eta_conversion (lhs_of thm'))) thm')

   in if msg then trace_thm "SUCCEEDED" thm' else (); Some thm'' end

   handle THM _ =>

     let val {sign, prop = _ $ _ $ prop0, ...} = Thm.rep_thm thm in

       trace_thm "Proved wrong thm (Check subgoaler?)" thm';

       trace_term false "Should have proved:" sign prop0;

       None

     end;

 (* mk_procrule *)

 fun mk_procrule thm =

   let val (_, prems, lhs, elhs, rhs, _) = decomp_simp thm in

     if rewrite_rule_extra_vars prems lhs rhs

     then (warn_thm "Extra vars on rhs:" thm; [])

     else [mk_rrule2 {thm = thm, name = "", lhs = lhs, elhs = elhs, perm = false}]

   end;

 (* rewritec: conversion to apply the meta simpset to a term *)

 (*Since the rewriting strategy is bottom-up, we avoid re-normalizing already

   normalized terms by carrying around the rhs of the rewrite rule just

   applied. This is called the `skeleton'. It is decomposed in parallel

   with the term. Once a Var is encountered, the corresponding term is

   already in normal form.

   skel0 is a dummy skeleton that is to enforce complete normalization.*)

 val skel0 = Bound 0;

 (*Use rhs as skeleton only if the lhs does not contain unnormalized bits.

   The latter may happen iff there are weak congruence rules for constants

   in the lhs.*)

 fun uncond_skel ((_, weak), (lhs, rhs)) =

   if null weak then rhs  (*optimization*)

   else if exists_Const (fn (c, _) => c mem weak) lhs then skel0

   else rhs;

 (*Behaves like unconditional rule if rhs does not contain vars not in the lhs.

   Otherwise those vars may become instantiated with unnormalized terms

   while the premises are solved.*)

 fun cond_skel (args as (congs, (lhs, rhs))) =

   if term_varnames rhs subset term_varnames lhs then uncond_skel args

   else skel0;

 fun incr_depth ss =

   let

     val ss' = ss |> map_simpset1 (fn (rules, prems, bounds, depth) =>

       (rules, prems, bounds, depth + 1));

     val Simpset ({depth = depth', ...}, _) = ss';

   in

     if depth' > ! simp_depth_limit

     then (warning "simp_depth_limit exceeded - giving up"; None)

     else

      (if depth' mod 10 = 0

       then warning ("Simplification depth " ^ string_of_int depth')

       else ();

       Some ss')

   end;

 (*

   Rewriting -- we try in order:

     (1) beta reduction

     (2) unconditional rewrite rules

     (3) conditional rewrite rules

     (4) simplification procedures

   IMPORTANT: rewrite rules must not introduce new Vars or TVars!

 *)

 fun rewritec (prover, signt, maxt) ss t =

   let

     val Simpset ({rules, ...}, {congs, procs, termless, ...}) = ss;

     val eta_thm = Thm.eta_conversion t;

     val eta_t' = rhs_of eta_thm;

     val eta_t = term_of eta_t';

     val tsigt = Sign.tsig_of signt;

     fun rew {thm, name, lhs, elhs, fo, perm} =

       let

         val {sign, prop, maxidx, ...} = rep_thm thm;

         val _ = if Sign.subsig (sign, signt) then ()

                 else (warn_thm "Ignoring rewrite rule from different theory:" thm;

                       raise Pattern.MATCH);

         val (rthm, elhs') = if maxt = ~1 then (thm, elhs)

           else (Thm.incr_indexes (maxt+1) thm, Thm.cterm_incr_indexes (maxt+1) elhs);

         val insts = if fo then Thm.cterm_first_order_match (elhs', eta_t')

                           else Thm.cterm_match (elhs', eta_t');

         val thm' = Thm.instantiate insts (Thm.rename_boundvars lhs eta_t rthm);

         val prop' = Thm.prop_of thm';

         val unconditional = (Logic.count_prems (prop',0) = 0);

         val (lhs', rhs') = Logic.dest_equals (Logic.strip_imp_concl prop')

       in

         if perm andalso not (termless (rhs', lhs'))

         then (trace_named_thm "Cannot apply permutative rewrite rule" (thm, name);

               trace_thm "Term does not become smaller:" thm'; None)

         else (trace_named_thm "Applying instance of rewrite rule" (thm, name);

            if unconditional

            then

              (trace_thm "Rewriting:" thm';

               let val lr = Logic.dest_equals prop;

                   val Some thm'' = check_conv false eta_thm thm'

               in Some (thm'', uncond_skel (congs, lr)) end)

            else

              (trace_thm "Trying to rewrite:" thm';

               case incr_depth ss of

                 None => (trace_thm "FAILED - reached depth limit" thm'; None)

               | Some ss' =>

               (case prover ss' thm' of

                 None => (trace_thm "FAILED" thm'; None)

               | Some thm2 =>

                   (case check_conv true eta_thm thm2 of

                      None => None |

                      Some thm2' =>

                        let val concl = Logic.strip_imp_concl prop

                            val lr = Logic.dest_equals concl

                        in Some (thm2', cond_skel (congs, lr)) end))))

       end

     fun rews [] = None

       | rews (rrule :: rrules) =

           let val opt = rew rrule handle Pattern.MATCH => None

           in case opt of None => rews rrules | some => some end;

     fun sort_rrules rrs = let

       fun is_simple({thm, ...}:rrule) = case Thm.prop_of thm of

                                       Const("==",_) $ _ $ _ => true

                                       | _                   => false

       fun sort []        (re1,re2) = re1 @ re2

         | sort (rr::rrs) (re1,re2) = if is_simple rr

                                      then sort rrs (rr::re1,re2)

                                      else sort rrs (re1,rr::re2)

     in sort rrs ([],[]) end

     fun proc_rews [] = None

       | proc_rews (Proc {name, proc, lhs, ...} :: ps) =

           if Pattern.matches tsigt (Thm.term_of lhs, Thm.term_of t) then

             (debug_term false ("Trying procedure " ^ quote name ^ " on:") signt eta_t;

              case transform_failure (curry SIMPROC_FAIL name)

                  (fn () => proc signt ss eta_t) () of

                None => (debug false "FAILED"; proc_rews ps)

              | Some raw_thm =>

                  (trace_thm ("Procedure " ^ quote name ^ " produced rewrite rule:") raw_thm;

                   (case rews (mk_procrule raw_thm) of

                     None => (trace_cterm true ("IGNORED result of simproc " ^ quote name ^

                       " -- does not match") t; proc_rews ps)

                   | some => some)))

           else proc_rews ps;

   in case eta_t of

        Abs _ $ _ => Some (transitive eta_thm

          (beta_conversion false eta_t'), skel0)

      | _ => (case rews (sort_rrules (Net.match_term rules eta_t)) of

                None => proc_rews (Net.match_term procs eta_t)

              | some => some)

   end;

 (* conversion to apply a congruence rule to a term *)

 fun congc (prover,signt,maxt) {thm=cong,lhs=lhs} t =

   let val sign = Thm.sign_of_thm cong

       val _ = if Sign.subsig (sign, signt) then ()

                  else error("Congruence rule from different theory")

       val rthm = if maxt = ~1 then cong else Thm.incr_indexes (maxt+1) cong;

       val rlhs = fst (Drule.dest_equals (Drule.strip_imp_concl (cprop_of rthm)));

       val insts = Thm.cterm_match (rlhs, t)

       (* Pattern.match can raise Pattern.MATCH;

          is handled when congc is called *)

       val thm' = Thm.instantiate insts (Thm.rename_boundvars (term_of rlhs) (term_of t) rthm);

       val unit = trace_thm "Applying congruence rule:" thm';

       fun err (msg, thm) = (trace_thm msg thm; None)

   in case prover thm' of

        None => err ("Congruence proof failed.  Could not prove", thm')

      | Some thm2 => (case check_conv true (Drule.beta_eta_conversion t) thm2 of

           None => err ("Congruence proof failed.  Should not have proved", thm2)

         | Some thm2' =>

             if op aconv (pairself term_of (dest_equals (cprop_of thm2')))

             then None else Some thm2')

   end;

 val (cA, (cB, cC)) =

   apsnd dest_equals (dest_implies (hd (cprems_of Drule.imp_cong)));

 fun transitive1 None None = None

   | transitive1 (Some thm1) None = Some thm1

   | transitive1 None (Some thm2) = Some thm2

   | transitive1 (Some thm1) (Some thm2) = Some (transitive thm1 thm2)

 fun transitive2 thm = transitive1 (Some thm);

 fun transitive3 thm = transitive1 thm o Some;

 fun bottomc ((simprem, useprem, mutsimp), prover, sign, maxidx) =

   let

     fun botc skel ss t =

           if is_Var skel then None

           else

           (case subc skel ss t of

              some as Some thm1 =>

                (case rewritec (prover, sign, maxidx) ss (rhs_of thm1) of

                   Some (thm2, skel2) =>

                     transitive2 (transitive thm1 thm2)

                       (botc skel2 ss (rhs_of thm2))

                 | None => some)

            | None =>

                (case rewritec (prover, sign, maxidx) ss t of

                   Some (thm2, skel2) => transitive2 thm2

                     (botc skel2 ss (rhs_of thm2))

                 | None => None))

     and try_botc ss t =

           (case botc skel0 ss t of

              Some trec1 => trec1 | None => (reflexive t))

     and subc skel (ss as Simpset ({bounds, ...}, {congs, ...})) t0 =

        (case term_of t0 of

            Abs (a, T, t) =>

              let

                  val b = variant bounds a;

                  val (v, t') = Thm.dest_abs (Some ("." ^ b)) t0;

                  val ss' = add_bound b ss;

                  val skel' = case skel of Abs (_, _, sk) => sk | _ => skel0;

              in case botc skel' ss' t' of

                   Some thm => Some (abstract_rule a v thm)

                 | None => None

              end

          | t $ _ => (case t of

              Const ("==>", _) $ _  => impc t0 ss

            | Abs _ =>

                let val thm = beta_conversion false t0

                in case subc skel0 ss (rhs_of thm) of

                     None => Some thm

                   | Some thm' => Some (transitive thm thm')

                end

            | _  =>

                let fun appc () =

                      let

                        val (tskel, uskel) = case skel of

                            tskel $ uskel => (tskel, uskel)

                          | _ => (skel0, skel0);

                        val (ct, cu) = Thm.dest_comb t0

                      in

                      (case botc tskel ss ct of

                         Some thm1 =>

                           (case botc uskel ss cu of

                              Some thm2 => Some (combination thm1 thm2)

                            | None => Some (combination thm1 (reflexive cu)))

                       | None =>

                           (case botc uskel ss cu of

                              Some thm1 => Some (combination (reflexive ct) thm1)

                            | None => None))

                      end

                    val (h, ts) = strip_comb t

                in case cong_name h of

                     Some a =>

                       (case assoc_string (fst congs, a) of

                          None => appc ()

                        | Some cong =>

   (*post processing: some partial applications h t1 ... tj, j <= length ts,

     may be a redex. Example: map (%x. x) = (%xs. xs) wrt map_cong*)

                           (let

                              val thm = congc (prover ss, sign, maxidx) cong t0;

                              val t = if_none (apsome rhs_of thm) t0;

                              val (cl, cr) = Thm.dest_comb t

                              val dVar = Var(("", 0), dummyT)

                              val skel =

                                list_comb (h, replicate (length ts) dVar)

                            in case botc skel ss cl of

                                 None => thm

                               | Some thm' => transitive3 thm

                                   (combination thm' (reflexive cr))

                            end handle TERM _ => error "congc result"

                                     | Pattern.MATCH => appc ()))

                   | _ => appc ()

                end)

          | _ => None)

     and impc ct ss =

       if mutsimp then mut_impc0 [] ct [] [] ss else nonmut_impc ct ss

     and rules_of_prem ss prem =

       if maxidx_of_term (term_of prem) <> ~1

       then (trace_cterm true

         "Cannot add premise as rewrite rule because it contains (type) unknowns:" prem; ([], None))

       else

         let val asm = assume prem

         in (extract_safe_rrules (ss, asm), Some asm) end

     and add_rrules (rrss, asms) ss =

       let val Asms = mapfilter I asms

       in foldl (insert_rrule true) (ss, flat rrss) |> add_prems2 Asms end

     and disch r (prem, eq) =

       let

         val (lhs, rhs) = dest_eq eq;

         val eq' = implies_elim (Thm.instantiate

           ([], [(cA, prem), (cB, lhs), (cC, rhs)]) Drule.imp_cong)

           (implies_intr prem eq)

       in if not r then eq' else

         let

           val (prem', concl) = dest_implies lhs;

           val (prem'', _) = dest_implies rhs

         in transitive (transitive

           (Thm.instantiate ([], [(cA, prem'), (cB, prem), (cC, concl)])

              Drule.swap_prems_eq) eq')

           (Thm.instantiate ([], [(cA, prem), (cB, prem''), (cC, concl)])

              Drule.swap_prems_eq)

         end

       end

     and rebuild [] _ _ _ _ eq = eq

       | rebuild (prem :: prems) concl (rrs :: rrss) (asm :: asms) ss eq =

           let

             val ss' = add_rrules (rev rrss, rev asms) ss;

             val concl' =

               Drule.mk_implies (prem, if_none (apsome rhs_of eq) concl);

             val dprem = apsome (curry (disch false) prem)

           in case rewritec (prover, sign, maxidx) ss' concl' of

               None => rebuild prems concl' rrss asms ss (dprem eq)

             | Some (eq', _) => transitive2 (foldl (disch false o swap)

                   (the (transitive3 (dprem eq) eq'), prems))

                 (mut_impc0 (rev prems) (rhs_of eq') (rev rrss) (rev asms) ss)

           end

     and mut_impc0 prems concl rrss asms ss =

       let

         val prems' = strip_imp_prems concl;

         val (rrss', asms') = split_list (map (rules_of_prem ss) prems')

       in mut_impc (prems @ prems') (strip_imp_concl concl) (rrss @ rrss')

         (asms @ asms') [] [] [] [] ss ~1 ~1

       end

     and mut_impc [] concl [] [] prems' rrss' asms' eqns ss changed k =

         transitive1 (foldl (fn (eq2, (eq1, prem)) => transitive1 eq1

             (apsome (curry (disch false) prem) eq2)) (None, eqns ~~ prems'))

           (if changed > 0 then

              mut_impc (rev prems') concl (rev rrss') (rev asms')

                [] [] [] [] ss ~1 changed

            else rebuild prems' concl rrss' asms' ss

              (botc skel0 (add_rrules (rev rrss', rev asms') ss) concl))

       | mut_impc (prem :: prems) concl (rrs :: rrss) (asm :: asms)

           prems' rrss' asms' eqns ss changed k =

         case (if k = 0 then None else botc skel0 (add_rrules

           (rev rrss' @ rrss, rev asms' @ asms) ss) prem) of

             None => mut_impc prems concl rrss asms (prem :: prems')

               (rrs :: rrss') (asm :: asms') (None :: eqns) ss changed

               (if k = 0 then 0 else k - 1)

           | Some eqn =>

             let

               val prem' = rhs_of eqn;

               val tprems = map term_of prems;

               val i = 1 + foldl Int.max (~1, map (fn p =>

                 find_index_eq p tprems) (#hyps (rep_thm eqn)));

               val (rrs', asm') = rules_of_prem ss prem'

             in mut_impc prems concl rrss asms (prem' :: prems')

               (rrs' :: rrss') (asm' :: asms') (Some (foldr (disch true)

                 (take (i, prems), Drule.imp_cong' eqn (reflexive (Drule.list_implies

                   (drop (i, prems), concl))))) :: eqns) ss (length prems') ~1

             end

      (*legacy code - only for backwards compatibility*)

      and nonmut_impc ct ss =

        let val (prem, conc) = dest_implies ct;

            val thm1 = if simprem then botc skel0 ss prem else None;

            val prem1 = if_none (apsome rhs_of thm1) prem;

            val ss1 = if not useprem then ss else add_rrules

              (apsnd single (apfst single (rules_of_prem ss prem1))) ss

        in (case botc skel0 ss1 conc of

            None => (case thm1 of

                None => None

              | Some thm1' => Some (Drule.imp_cong' thm1' (reflexive conc)))

          | Some thm2 =>

            let val thm2' = disch false (prem1, thm2)

            in (case thm1 of

                None => Some thm2'

              | Some thm1' =>

                  Some (transitive (Drule.imp_cong' thm1' (reflexive conc)) thm2'))

            end)

        end

  in try_botc end;

 (* Meta-rewriting: rewrites t to u and returns the theorem t==u *)

 (*

   Parameters:

     mode = (simplify A,

             use A in simplifying B,

             use prems of B (if B is again a meta-impl.) to simplify A)

            when simplifying A ==> B

     prover: how to solve premises in conditional rewrites and congruences

 *)

 fun rewrite_cterm mode prover ss ct =

   let

     val Simpset ({depth, ...}, _) = ss;

     val {sign, t, maxidx, ...} = Thm.rep_cterm ct;

   in

     trace_cterm false "SIMPLIFIER INVOKED ON THE FOLLOWING TERM:" ct;

     simp_depth := depth;

     bottomc (mode, prover, sign, maxidx) ss ct

   end handle THM (s, _, thms) =>

     error ("Exception THM was raised in simplifier:\n" ^ s ^ "\n" ^

       Pretty.string_of (Display.pretty_thms thms));

 (*Rewrite a cterm*)

 fun rewrite_aux _ _ [] = (fn ct => Thm.reflexive ct)

   | rewrite_aux prover full thms =

       rewrite_cterm (full, false, false) prover (empty_ss addsimps thms);

 (*Rewrite a theorem*)

 fun simplify_aux _ _ [] = (fn th => th)

   | simplify_aux prover full thms =

       Drule.fconv_rule (rewrite_cterm (full, false, false) prover (empty_ss addsimps thms));

 (*simple term rewriting -- no proof*)

 fun rewrite_term sg rules procs =

   Pattern.rewrite_term (Sign.tsig_of sg) (map decomp_simp' rules) procs;

 fun rewrite_thm mode prover ss = Drule.fconv_rule (rewrite_cterm mode prover ss);

 (*Rewrite the subgoals of a proof state (represented by a theorem) *)

 fun rewrite_goals_rule_aux _ []   th = th

   | rewrite_goals_rule_aux prover thms th =

       Drule.fconv_rule (Drule.goals_conv (K true) (rewrite_cterm (true, true, false) prover

         (empty_ss addsimps thms))) th;

 (*Rewrite the subgoal of a proof state (represented by a theorem)*)

 fun rewrite_goal_rule mode prover ss i thm =

   if 0 < i  andalso  i <= nprems_of thm

   then Drule.fconv_rule (Drule.goals_conv (fn j => j=i) (rewrite_cterm mode prover ss)) thm

   else raise THM("rewrite_goal_rule",i,[thm]);

 (*Rewrite subgoal i only.  SELECT_GOAL avoids inefficiencies in goals_conv.*)

 fun asm_rewrite_goal_tac mode prover_tac ss =

   SELECT_GOAL

     (PRIMITIVE (rewrite_goal_rule mode (SINGLE o prover_tac) ss 1));

 (** simplification tactics and rules **)

 fun solve_all_tac solvers ss =

   let

     val Simpset (_, {subgoal_tac, ...}) = ss;

     val solve_tac = subgoal_tac (set_solvers solvers ss) THEN_ALL_NEW (K no_tac);

   in DEPTH_SOLVE (solve_tac 1) end;

 (*NOTE: may instantiate unknowns that appear also in other subgoals*)

 fun generic_simp_tac safe mode ss =

   let

     val Simpset ({prems, ...}, {loop_tacs, solvers = (unsafe_solvers, solvers), ...}) = ss;

     val loop_tac = FIRST' (map #2 loop_tacs);

     val solve_tac = FIRST' (map (solver prems) (if safe then solvers else unsafe_solvers));

     fun simp_loop_tac i =

       asm_rewrite_goal_tac mode (solve_all_tac unsafe_solvers) ss i THEN

       (solve_tac i ORELSE TRY ((loop_tac THEN_ALL_NEW simp_loop_tac) i));

   in simp_loop_tac end;

 fun simp rew mode ss thm =

   let

     val Simpset (_, {solvers = (unsafe_solvers, _), ...}) = ss;

     val tacf = solve_all_tac unsafe_solvers;

     fun prover s th = apsome #1 (Seq.pull (tacf s th));

   in rew mode prover ss thm end;

 val simp_thm = simp rewrite_thm;

 val simp_cterm = simp rewrite_cterm;

 end;

 structure BasicMetaSimplifier: BASIC_META_SIMPLIFIER = MetaSimplifier;

 open BasicMetaSimplifier;