(*  Title:      Pure/raw_simplifier.ML

    Author:     Tobias Nipkow and Stefan Berghofer, TU Muenchen

Higher-order Simplification.

*)

infix 4

  addsimps delsimps addeqcongs deleqcongs addcongs delcongs addsimprocs delsimprocs

  setmksimps setmkcong setmksym setmkeqTrue settermless setsubgoaler

  setloop' setloop addloop addloop' delloop setSSolver addSSolver setSolver addSolver;

signature BASIC_RAW_SIMPLIFIER =

sig

  val simp_depth_limit: int Config.T

  val simp_trace_depth_limit: int Config.T

  val simp_debug: bool Config.T

  val simp_trace: bool Config.T

  type rrule

  val eq_rrule: rrule * rrule -> bool

  type simpset

  type proc

  type solver

  val mk_solver: string -> (simpset -> int -> tactic) -> solver

  val empty_ss: simpset

  val merge_ss: simpset * simpset -> simpset

  val dest_ss: simpset ->

   {simps: (string * thm) list,

    procs: (string * cterm list) list,

    congs: (string * thm) list,

    weak_congs: string list,

    loopers: string list,

    unsafe_solvers: string list,

    safe_solvers: string list}

  type simproc

  val eq_simproc: simproc * simproc -> bool

  val morph_simproc: morphism -> simproc -> simproc

  val make_simproc: {name: string, lhss: cterm list,

    proc: morphism -> simpset -> cterm -> thm option, identifier: thm list} -> simproc

  val mk_simproc: string -> cterm list -> (theory -> simpset -> term -> thm option) -> simproc

  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 mksimps: simpset -> thm -> thm list

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

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

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

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

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

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

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

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

  val addloop': simpset * (string * (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 rewrite_rule: thm list -> thm -> thm

  val rewrite_goals_rule: thm list -> thm -> thm

  val rewrite_goals_tac: thm list -> tactic

  val rewrite_goal_tac: thm list -> int -> tactic

  val rewtac: thm -> tactic

  val prune_params_tac: tactic

  val fold_rule: thm list -> thm -> thm

  val fold_goals_tac: thm list -> tactic

  val norm_hhf: thm -> thm

  val norm_hhf_protect: thm -> thm

end;

signature RAW_SIMPLIFIER =

sig

  include BASIC_RAW_SIMPLIFIER

  exception SIMPLIFIER of string * thm

  val internal_ss: simpset ->

   {rules: rrule Net.net,

    prems: thm list,

    bounds: int * ((string * typ) * string) list,

    depth: int * bool Unsynchronized.ref,

    context: Proof.context option} *

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

    procs: proc Net.net,

    mk_rews:

     {mk: simpset -> thm -> thm list,

      mk_cong: simpset -> thm -> thm,

      mk_sym: simpset -> thm -> thm option,

      mk_eq_True: simpset -> thm -> thm option,

      reorient: theory -> term list -> term -> term -> bool},

    termless: term * term -> bool,

    subgoal_tac: simpset -> int -> tactic,

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

    solvers: solver list * solver list}

  val add_simp: thm -> simpset -> simpset

  val del_simp: thm -> simpset -> simpset

  val solver: simpset -> solver -> int -> tactic

  val simp_depth_limit_raw: Config.raw

  val clear_ss: simpset -> simpset

  val simproc_global_i: theory -> string -> term list

    -> (theory -> simpset -> term -> thm option) -> simproc

  val simproc_global: theory -> string -> string list

    -> (theory -> simpset -> term -> thm option) -> simproc

  val simp_trace_depth_limit_raw: Config.raw

  val simp_trace_depth_limit_default: int Unsynchronized.ref

  val simp_trace_default: bool Unsynchronized.ref

  val simp_trace_raw: Config.raw

  val simp_debug_raw: Config.raw

  val add_prems: thm list -> simpset -> simpset

  val inherit_context: simpset -> simpset -> simpset

  val the_context: simpset -> Proof.context

  val context: Proof.context -> simpset -> simpset

  val global_context: theory -> simpset -> simpset

  val with_context: Proof.context -> (simpset -> simpset) -> simpset -> simpset

  val debug_bounds: bool Unsynchronized.ref

  val set_reorient: (theory -> term list -> term -> term -> bool) -> simpset -> simpset

  val set_solvers: solver list -> simpset -> simpset

  val rewrite_cterm: bool * bool * bool -> (simpset -> thm -> thm option) -> simpset -> conv

  val rewrite_term: theory -> thm list -> (term -> term option) list -> term -> term

  val rewrite_thm: bool * bool * bool ->

    (simpset -> thm -> thm option) -> simpset -> 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 rewrite: bool -> thm list -> conv

  val simplify: bool -> thm list -> thm -> thm

end;

structure Raw_Simplifier: RAW_SIMPLIFIER =

struct

(** datatype simpset **)

(* rewrite rules *)

type rrule =

 {thm: thm,         (*the rewrite rule*)

  name: string,     (*name of theorem from which rewrite rule was extracted*)

  lhs: term,        (*the left-hand side*)

  elhs: cterm,      (*the etac-contracted lhs*)

  extra: bool,      (*extra variables outside of elhs*)

  fo: bool,         (*use first-order matching*)

  perm: bool};      (*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) =

  Thm.eq_thm_prop (thm1, thm2);

(* simplification sets, procedures, and solvers *)

(*A simpset contains data required during conversion:

    rules: discrimination net of rewrite rules;

    prems: current premises;

    bounds: maximal index of bound variables already used

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

    depth: simp_depth and exceeded flag;

    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;

      mk_cong: prepare congruence rules;

      mk_sym: turn == around;

      mk_eq_True: turn P into P == True;

    termless: relation for ordered rewriting;*)

datatype simpset =

  Simpset of

   {rules: rrule Net.net,

    prems: thm list,

    bounds: int * ((string * typ) * string) list,

    depth: int * bool Unsynchronized.ref,

    context: Proof.context option} *

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

    procs: proc Net.net,

    mk_rews:

     {mk: simpset -> thm -> thm list,

      mk_cong: simpset -> thm -> thm,

      mk_sym: simpset -> thm -> thm option,

      mk_eq_True: simpset -> thm -> thm option,

      reorient: theory -> term list -> term -> term -> bool},

    termless: term * term -> bool,

    subgoal_tac: simpset -> int -> tactic,

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

    solvers: solver list * solver list}

and proc =

  Proc of

   {name: string,

    lhs: cterm,

    proc: simpset -> cterm -> thm option,

    id: stamp * thm list}

and solver =

  Solver of

   {name: string,

    solver: simpset -> int -> tactic,

    id: stamp};

fun internal_ss (Simpset args) = args;

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

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

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

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

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_simpset1 f (Simpset (r1, r2)) = Simpset (map_ss1 f r1, r2);

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

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

fun eq_procid ((s1: stamp, ths1: thm list), (s2, ths2)) =

  s1 = s2 andalso eq_list Thm.eq_thm (ths1, ths2);

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

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

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

fun solver ss (Solver {solver = tac, ...}) = tac ss;

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

(* simp depth *)

val simp_depth_limit_raw = Config.declare "simp_depth_limit" (K (Config.Int 100));

val simp_depth_limit = Config.int simp_depth_limit_raw;

val simp_trace_depth_limit_default = Unsynchronized.ref 1;

val simp_trace_depth_limit_raw = Config.declare "simp_trace_depth_limit"

  (fn _ => Config.Int (! simp_trace_depth_limit_default));

val simp_trace_depth_limit = Config.int simp_trace_depth_limit_raw;

fun simp_trace_depth_limit_of NONE = ! simp_trace_depth_limit_default

  | simp_trace_depth_limit_of (SOME ctxt) = Config.get ctxt simp_trace_depth_limit;

fun trace_depth (Simpset ({depth = (depth, exceeded), context, ...}, _)) msg =

  if depth > simp_trace_depth_limit_of context then

    if ! exceeded then () else (tracing "simp_trace_depth_limit exceeded!"; exceeded := true)

  else

    (tracing (enclose "[" "]" (string_of_int depth) ^ msg); exceeded := false);

val inc_simp_depth = map_simpset1 (fn (rules, prems, bounds, (depth, exceeded), context) =>

  (rules, prems, bounds,

    (depth + 1,

      if depth = simp_trace_depth_limit_of context then Unsynchronized.ref false else exceeded), context));

fun simp_depth (Simpset ({depth = (depth, _), ...}, _)) = depth;

(* diagnostics *)

exception SIMPLIFIER of string * thm;

val simp_debug_raw = Config.declare "simp_debug" (K (Config.Bool false));

val simp_debug = Config.bool simp_debug_raw;

val simp_trace_default = Unsynchronized.ref false;

val simp_trace_raw = Config.declare "simp_trace" (fn _ => Config.Bool (! simp_trace_default));

val simp_trace = Config.bool simp_trace_raw;

fun if_enabled (Simpset ({context, ...}, _)) flag f =

  (case context of

    SOME ctxt => if Config.get ctxt flag then f ctxt else ()

  | NONE => ())

fun if_visible (Simpset ({context, ...}, _)) f x =

  (case context of

    SOME ctxt => Context_Position.if_visible ctxt f x

  | NONE => ());

local

fun prnt ss warn a = if warn then warning a else trace_depth ss a;

fun show_bounds (Simpset ({bounds = (_, bs), ...}, _)) t =

  let

    val names = Term.declare_term_names t Name.context;

    val xs = rev (#1 (fold_map Name.variant (rev (map #2 bs)) names));

    fun subst (((b, T), _), x') = (Free (b, T), Syntax_Trans.mark_boundT (x', T));

  in Term.subst_atomic (ListPair.map subst (bs, xs)) t end;

fun print_term ss warn a t ctxt = prnt ss warn (a () ^ "\n" ^

  Syntax.string_of_term ctxt

    (if Config.get ctxt simp_debug then t else show_bounds ss t));

in

fun print_term_global ss warn a thy t =

  print_term ss warn (K a) t (Proof_Context.init_global thy);

fun debug warn a ss = if_enabled ss simp_debug (fn _ => prnt ss warn (a ()));

fun trace warn a ss = if_enabled ss simp_trace (fn _ => prnt ss warn (a ()));

fun debug_term warn a ss t = if_enabled ss simp_debug (print_term ss warn a t);

fun trace_term warn a ss t = if_enabled ss simp_trace (print_term ss warn a t);

fun trace_cterm warn a ss ct =

  if_enabled ss simp_trace (print_term ss warn a (Thm.term_of ct));

fun trace_thm a ss th =

  if_enabled ss simp_trace (print_term ss false a (Thm.full_prop_of th));

fun trace_named_thm a ss (th, name) =

  if_enabled ss simp_trace (print_term ss false

    (fn () => if name = "" then a () else a () ^ " " ^ quote name ^ ":")

    (Thm.full_prop_of th));

fun warn_thm a ss th =

  print_term_global ss true a (Thm.theory_of_thm th) (Thm.full_prop_of th);

fun cond_warn_thm a ss th = if_visible ss (fn () => warn_thm a ss th) ();

end;

(** simpset operations **)

(* context *)

fun eq_bound (x: string, (y, _)) = x = y;

fun add_bound bound = map_simpset1 (fn (rules, prems, (count, bounds), depth, context) =>

  (rules, prems, (count + 1, bound :: bounds), depth, context));

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

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

fun inherit_context (Simpset ({bounds, depth, context, ...}, _)) =

  map_simpset1 (fn (rules, prems, _, _, _) => (rules, prems, bounds, depth, context));

fun the_context (Simpset ({context = SOME ctxt, ...}, _)) = ctxt

  | the_context _ = raise Fail "Simplifier: no proof context in simpset";

fun context ctxt =

  map_simpset1 (fn (rules, prems, bounds, depth, _) => (rules, prems, bounds, depth, SOME ctxt));

val global_context = context o Proof_Context.init_global;

fun activate_context thy ss =

  let

    val ctxt = the_context ss;

    val ctxt' = ctxt

      |> Context.raw_transfer (Theory.merge (thy, Proof_Context.theory_of ctxt))

      |> Context_Position.set_visible false;

  in context ctxt' ss end;

fun with_context ctxt f ss = inherit_context ss (f (context ctxt ss));

(* maintain simp rules *)

(* 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 =

  let

    val elhss = elhs :: prems;

    val tvars = fold Term.add_tvars elhss [];

    val vars = fold Term.add_vars elhss [];

  in

    erhs |> Term.exists_type (Term.exists_subtype

      (fn TVar v => not (member (op =) tvars v) | _ => false)) orelse

    erhs |> Term.exists_subterm

      (fn Var v => not (member (op =) vars v) | _ => false)

  end;

fun rrule_extra_vars elhs thm =

  rewrite_rule_extra_vars [] (term_of elhs) (Thm.full_prop_of thm);

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

  let

    val t = term_of elhs;

    val fo = Pattern.first_order t orelse not (Pattern.pattern t);

    val extra = rrule_extra_vars elhs thm;

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

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

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

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

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

fun insert_rrule (rrule as {thm, name, ...}) ss =

 (trace_named_thm (fn () => "Adding rewrite rule") ss (thm, name);

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

    let

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

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

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

  handle Net.INSERT => (cond_warn_thm "Ignoring duplicate rewrite rule:" ss 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 (op =) (Term.add_vars t [], Term.add_vars u []);

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

fun default_reorient thy prems lhs rhs =

  rewrite_rule_extra_vars prems lhs rhs

    orelse

  is_Var (head_of lhs)

    orelse

(* turns t = x around, which causes a headache if x is a local variable -

   usually it is very useful :-(

  is_Free rhs andalso not(is_Free lhs) andalso not(Logic.occs(rhs,lhs))

  andalso not(exists_subterm is_Var lhs)

    orelse

*)

  exists (fn t => Logic.occs (lhs, t)) (rhs :: prems)

    orelse

  null prems andalso Pattern.matches thy (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 thy = Thm.theory_of_thm thm;

    val prop = Thm.prop_of thm;

    val prems = Logic.strip_imp_prems prop;

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

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

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

    val elhs = Thm.dest_arg (Thm.cprop_of (Thm.eta_conversion lhs));

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

    val erhs = Envir.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 (thy, 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 (ss as Simpset (_, {mk_rews = {mk_eq_True, ...}, ...})) (thm, name) =

  (case mk_eq_True ss 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 rewrite_rule_extra_vars [] lhs rhs then

      mk_eq_True ss (thm2, name) @ [rrule]

    else [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 (thy, prems, lhs, elhs, rhs, perm) = decomp_simp thm;

    val Simpset (_, {mk_rews = {reorient, mk_sym, ...}, ...}) = ss;

  in

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

    else if reorient thy prems lhs rhs then

      if reorient thy prems rhs lhs

      then mk_eq_True ss (thm, name)

      else

        (case mk_sym ss 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)

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

  end;

fun extract_rews (ss as Simpset (_, {mk_rews = {mk, ...}, ...}), thms) =

  maps (fn thm => map (rpair (Thm.get_name_hint thm)) (mk ss thm)) thms;

fun extract_safe_rrules (ss, thm) =

  maps (orient_rrule ss) (extract_rews (ss, [thm]));

(* add/del rules explicitly *)

fun comb_simps comb mk_rrule (ss, thms) =

  let

    val rews = extract_rews (ss, thms);

  in fold (fold comb o mk_rrule) rews ss end;

fun ss addsimps thms =

  comb_simps insert_rrule (mk_rrule ss) (ss, thms);

fun ss delsimps thms =

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

fun add_simp thm ss = ss addsimps [thm];

fun del_simp thm ss = ss delsimps [thm];

(* 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

            not (has_duplicates (op =) xs) andalso xs = ys andalso

            member (op =) varpairs (x, y) andalso

            is_full_cong_prems prems (remove (op =) (x, y) varpairs)

          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 not (has_duplicates (op =) (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, _) = Thm.dest_equals (Drule.strip_imp_concl (Thm.cprop_of thm))

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

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

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

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

      val (xs, weak) = congs;

      val _ =

        if AList.defined (op =) xs a

        then if_visible ss warning ("Overwriting congruence rule for " ^ quote a)

        else ();

      val xs' = AList.update (op =) (a, thm) xs;

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

    in ((xs', weak'), 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 = Envir.eta_contract lhs;*)

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

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

      val (xs, _) = congs;

      val xs' = filter_out (fn (x : string, _) => x = a) xs;

      val weak' = xs' |> map_filter (fn (a, thm) =>

        if is_full_cong thm then NONE else SOME a);

    in ((xs', weak'), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);

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

in

val (op addeqcongs) = Library.foldl add_cong;

val (op deleqcongs) = Library.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 *)

datatype simproc =

  Simproc of

    {name: string,

     lhss: cterm list,

     proc: morphism -> simpset -> cterm -> thm option,

     id: stamp * thm list};

fun eq_simproc (Simproc {id = id1, ...}, Simproc {id = id2, ...}) = eq_procid (id1, id2);

fun morph_simproc phi (Simproc {name, lhss, proc, id = (s, ths)}) =

  Simproc

   {name = name,

    lhss = map (Morphism.cterm phi) lhss,

    proc = Morphism.transform phi proc,

    id = (s, Morphism.fact phi ths)};

fun make_simproc {name, lhss, proc, identifier} =

  Simproc {name = name, lhss = lhss, proc = proc, id = (stamp (), identifier)};

fun mk_simproc name lhss proc =

  make_simproc {name = name, lhss = lhss, proc = fn _ => fn ss => fn ct =>

    proc (Proof_Context.theory_of (the_context ss)) ss (Thm.term_of ct), identifier = []};

(* FIXME avoid global thy and Logic.varify_global *)

fun simproc_global_i thy name = mk_simproc name o map (Thm.cterm_of thy o Logic.varify_global);

fun simproc_global thy name = simproc_global_i thy name o map (Syntax.read_term_global thy);

local

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

 (trace_cterm false (fn () => "Adding simplification procedure " ^ quote name ^ " for") ss lhs;

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

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

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

  handle Net.INSERT =>

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

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

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

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

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

  handle Net.DELETE =>

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

fun prep_procs (Simproc {name, lhss, proc, id}) =

  lhss |> map (fn lhs => Proc {name = name, lhs = lhs, proc = Morphism.form proc, id = id});

in

fun ss addsimprocs ps = fold (fold add_proc o prep_procs) ps ss;

fun ss delsimprocs ps = fold (fold del_proc o prep_procs) ps ss;

end;

(* mk_rews *)

local

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

      termless, subgoal_tac, loop_tacs, solvers) =>

  let

    val (mk', mk_cong', mk_sym', mk_eq_True', reorient') =

      f (mk, mk_cong, mk_sym, mk_eq_True, reorient);

    val mk_rews' = {mk = mk', mk_cong = mk_cong', mk_sym = mk_sym', mk_eq_True = mk_eq_True',

      reorient = reorient'};

  in (congs, procs, mk_rews', termless, subgoal_tac, loop_tacs, solvers) end);

in

fun mksimps (ss as Simpset (_, {mk_rews = {mk, ...}, ...})) = mk ss;

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

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

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

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

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

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

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

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

fun set_reorient reorient = map_mk_rews (fn (mk, mk_cong, mk_sym, mk_eq_True, _) =>

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

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 setloop tac = ss setloop' (K tac);

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,

     (if AList.defined (op =) loop_tacs name

      then if_visible ss warning ("Overwriting looper " ^ quote name)

      else (); AList.update (op =) (name, tac) loop_tacs), solvers));

fun ss addloop (name, tac) = ss addloop' (name, K tac);

fun ss delloop name = ss |>

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

    (congs, procs, mk_rews, termless, subgoal_tac,

     (if AList.defined (op =) loop_tacs name then ()

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

      AList.delete (op =) name loop_tacs), solvers));

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, insert eq_solver solver solvers)));

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, (insert eq_solver solver unsafe_solvers, 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)));

(* empty *)

fun init_ss mk_rews termless subgoal_tac solvers =

  make_simpset ((Net.empty, [], (0, []), (0, Unsynchronized.ref false), NONE),

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

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

  init_ss mk_rews termless subgoal_tac solvers

  |> inherit_context ss;

val empty_ss =

  init_ss

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

      mk_cong = K I,

      mk_sym = K (SOME o Drule.symmetric_fun),

      mk_eq_True = K (K NONE),

      reorient = default_reorient}

    Term_Ord.termless (K (K no_tac)) ([], []);

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

fun merge_ss (ss1, ss2) =

  if pointer_eq (ss1, ss2) then ss1

  else

    let

      val Simpset ({rules = rules1, prems = prems1, bounds = bounds1, depth = depth1, context = _},

       {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 = depth2, context = _},

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

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

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

      val prems' = Thm.merge_thms (prems1, prems2);

      val bounds' = if #1 bounds1 < #1 bounds2 then bounds2 else bounds1;

      val depth' = if #1 depth1 < #1 depth2 then depth2 else depth1;

      val congs' = merge (Thm.eq_thm_prop o pairself #2) (congs1, congs2);

      val weak' = merge (op =) (weak1, weak2);

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

      val loop_tacs' = AList.merge (op =) (K true) (loop_tacs1, loop_tacs2);

      val unsafe_solvers' = merge eq_solver (unsafe_solvers1, unsafe_solvers2);

      val solvers' = merge eq_solver (solvers1, solvers2);

    in

      make_simpset ((rules', prems', bounds', depth', NONE), ((congs', weak'), procs',

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

    end;

(* dest_ss *)

fun dest_ss (Simpset ({rules, ...}, {congs, procs, loop_tacs, solvers, ...})) =

 {simps = Net.entries rules

    |> map (fn {name, thm, ...} => (name, thm)),

  procs = Net.entries procs

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

    |> partition_eq (eq_snd eq_procid)

    |> map (fn ps => (fst (fst (hd ps)), map (snd o fst) ps)),

  congs = #1 congs,

  weak_congs = #2 congs,

  loopers = map fst loop_tacs,

  unsafe_solvers = map solver_name (#1 solvers),

  safe_solvers = map solver_name (#2 solvers)};

(** rewriting **)

(*

  Uses conversions, see:

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

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

*)

fun check_conv msg ss thm thm' =

  let

    val thm'' = Thm.transitive thm thm' handle THM _ =>

     Thm.transitive thm (Thm.transitive

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

  in if msg then trace_thm (fn () => "SUCCEEDED") ss thm' else (); SOME thm'' end

  handle THM _ =>

    let

      val _ $ _ $ prop0 = Thm.prop_of thm;

    in

      trace_thm (fn () => "Proved wrong thm (Check subgoaler?)") ss thm';

      trace_term false (fn () => "Should have proved:") ss prop0;

      NONE

    end;

(* mk_procrule *)

fun mk_procrule ss thm =

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

    if rewrite_rule_extra_vars prems lhs rhs

    then (cond_warn_thm "Extra vars on rhs:" ss 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 (member (op =) weak o #1) 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 (_, (lhs, rhs))) =

  if subset (op =) (Term.add_vars rhs [], Term.add_vars lhs []) then uncond_skel args

  else skel0;

(*

  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, thyt, maxt) ss t =

  let

    val ctxt = the_context ss;

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

    val eta_thm = Thm.eta_conversion t;

    val eta_t' = Thm.rhs_of eta_thm;

    val eta_t = term_of eta_t';

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

      let

        val prop = Thm.prop_of thm;

        val (rthm, elhs') =

          if maxt = ~1 orelse not extra then (thm, elhs)

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

        val insts =

          if fo then Thm.first_order_match (elhs', eta_t')

          else Thm.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);

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

      in

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

        then (trace_named_thm (fn () => "Cannot apply permutative rewrite rule") ss (thm, name);

              trace_thm (fn () => "Term does not become smaller:") ss thm'; NONE)

        else (trace_named_thm (fn () => "Applying instance of rewrite rule") ss (thm, name);

           if unconditional

           then

             (trace_thm (fn () => "Rewriting:") ss thm';

              let

                val lr = Logic.dest_equals prop;

                val SOME thm'' = check_conv false ss eta_thm thm';

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

           else

             (trace_thm (fn () => "Trying to rewrite:") ss thm';

              if simp_depth ss > Config.get ctxt simp_depth_limit

              then

                let

                  val s = "simp_depth_limit exceeded - giving up";

                  val _ = trace false (fn () => s) ss;

                  val _ = if_visible ss warning s;

                in NONE end

              else

              case prover ss thm' of

                NONE => (trace_thm (fn () => "FAILED") ss thm'; NONE)

              | SOME thm2 =>

                  (case check_conv true ss 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 thyt (Thm.term_of lhs, Thm.term_of t) then

            (debug_term false (fn () => "Trying procedure " ^ quote name ^ " on:") ss eta_t;

             case proc ss eta_t' of

               NONE => (debug false (fn () => "FAILED") ss; proc_rews ps)

             | SOME raw_thm =>

                 (trace_thm (fn () => "Procedure " ^ quote name ^ " produced rewrite rule:")

                   ss raw_thm;

                  (case rews (mk_procrule ss raw_thm) of

                    NONE => (trace_cterm true (fn () => "IGNORED result of simproc " ^ quote name ^

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

                  | some => some)))

          else proc_rews ps;

  in

    (case eta_t of

      Abs _ $ _ => SOME (Thm.transitive eta_thm (Thm.beta_conversion false eta_t'), skel0)

    | _ =>

      (case rews (sort_rrules (Net.match_term rules eta_t)) of