(*  Title:      Pure/simplifier.ML

    ID:         $Id$

    Author:     Tobias Nipkow and Markus Wenzel, TU Muenchen

Generic simplifier, suitable for most logics (see also

meta_simplifier.ML for the actual meta-level rewriting engine).

*)

signature BASIC_SIMPLIFIER =

sig

  include BASIC_META_SIMPLIFIER

  type context_solver

  val mk_context_solver: string -> (Proof.context -> thm list -> int -> tactic)

    -> context_solver

  type context_simproc

  val mk_context_simproc: string -> cterm list ->

    (Proof.context -> simpset -> term -> thm option) -> context_simproc

  val print_simpset: theory -> unit

  val simpset_ref_of_sg: theory -> simpset ref    (*obsolete*)

  val simpset_ref_of: theory -> simpset ref

  val simpset_of_sg: theory -> simpset            (*obsolete*)

  val simpset_of: theory -> simpset

  val SIMPSET: (simpset -> tactic) -> tactic

  val SIMPSET': (simpset -> 'a -> tactic) -> 'a -> tactic

  val simpset: unit -> simpset

  val simpset_ref: unit -> simpset ref

  val Addsimps: thm list -> unit

  val Delsimps: thm list -> unit

  val Addsimprocs: simproc list -> unit

  val Delsimprocs: simproc list -> unit

  val Addcongs: thm list -> unit

  val Delcongs: thm list -> unit

  val local_simpset_of: Proof.context -> simpset

  val safe_asm_full_simp_tac: simpset -> int -> tactic

  val               simp_tac: simpset -> int -> tactic

  val           asm_simp_tac: simpset -> int -> tactic

  val          full_simp_tac: simpset -> int -> tactic

  val        asm_lr_simp_tac: simpset -> int -> tactic

  val      asm_full_simp_tac: simpset -> int -> tactic

  val               Simp_tac:            int -> tactic

  val           Asm_simp_tac:            int -> tactic

  val          Full_simp_tac:            int -> tactic

  val        Asm_lr_simp_tac:            int -> tactic

  val      Asm_full_simp_tac:            int -> tactic

  val          simplify: simpset -> thm -> thm

  val      asm_simplify: simpset -> thm -> thm

  val     full_simplify: simpset -> thm -> thm

  val   asm_lr_simplify: simpset -> thm -> thm

  val asm_full_simplify: simpset -> thm -> thm

end;

signature SIMPLIFIER =

sig

  include BASIC_SIMPLIFIER

  val simproc_i: theory -> string -> term list

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

  val simproc: theory -> string -> string list

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

  val context_simproc_i: theory -> string -> term list

    -> (Proof.context -> simpset -> term -> thm option) -> context_simproc

  val context_simproc: theory -> string -> string list

    -> (Proof.context -> simpset -> term -> thm option) -> context_simproc

  val          rewrite: simpset -> cterm -> thm

  val      asm_rewrite: simpset -> cterm -> thm

  val     full_rewrite: simpset -> cterm -> thm

  val   asm_lr_rewrite: simpset -> cterm -> thm

  val asm_full_rewrite: simpset -> cterm -> thm

  val add_context_simprocs: context_simproc list -> theory -> theory

  val del_context_simprocs: context_simproc list -> theory -> theory

  val set_context_subgoaler: (Proof.context -> simpset -> int -> tactic) -> theory -> theory

  val reset_context_subgoaler: theory -> theory

  val add_context_looper: string * (Proof.context -> int -> Tactical.tactic) ->

    theory -> theory

  val del_context_looper: string -> theory -> theory

  val add_context_unsafe_solver: context_solver -> theory -> theory

  val add_context_safe_solver: context_solver -> theory -> theory

  val print_local_simpset: Proof.context -> unit

  val get_local_simpset: Proof.context -> simpset

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

  val change_global_ss: (simpset * thm list -> simpset) -> theory attribute

  val change_local_ss: (simpset * thm list -> simpset) -> Proof.context attribute

  val simp_add_global: theory attribute

  val simp_del_global: theory attribute

  val simp_add_local: Proof.context attribute

  val simp_del_local: Proof.context attribute

  val cong_add_global: theory attribute

  val cong_del_global: theory attribute

  val cong_add_local: Proof.context attribute

  val cong_del_local: Proof.context attribute

  val change_simpset_of: (simpset * 'a -> simpset) -> 'a -> theory -> theory

  val simp_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list

  val method_setup: (Args.T list -> (Method.modifier * Args.T list)) list

    -> (theory -> theory) list

  val easy_setup: thm -> thm list -> (theory -> theory) list

end;

structure Simplifier: SIMPLIFIER =

struct

open MetaSimplifier;

(** context dependent simpset components **)

(* datatype context_solver *)

datatype context_solver =

  ContextSolver of (string * (Proof.context -> thm list -> int -> tactic)) * stamp;

fun mk_context_solver name f = ContextSolver ((name, f), stamp ());

fun eq_context_solver (ContextSolver (_, id1), ContextSolver (_, id2)) = (id1 = id2);

val merge_context_solvers = gen_merge_lists eq_context_solver;

(* datatype context_simproc *)

datatype context_simproc = ContextSimproc of

  (string * cterm list * (Proof.context -> simpset -> term -> thm option)) * stamp;

fun mk_context_simproc name lhss f = ContextSimproc ((name, lhss, f), stamp ());

fun eq_context_simproc (ContextSimproc (_, id1), ContextSimproc (_, id2)) = (id1 = id2);

val merge_context_simprocs = gen_merge_lists eq_context_simproc;

fun context_simproc_i thy name =

  mk_context_simproc name o map (Thm.cterm_of thy o Logic.varify);

fun context_simproc thy name =

  context_simproc_i thy name o map (Sign.read_term thy);

(* datatype context_ss *)

datatype context_ss = ContextSS of

 {simprocs: context_simproc list,

  subgoal_tac: (Proof.context -> simpset -> int -> tactic) option,

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

  unsafe_solvers: context_solver list,

  solvers: context_solver list};

fun context_ss ctxt ss ctxt_ss =

  let

    val ContextSS {simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers} = ctxt_ss;

    fun prep_simproc (ContextSimproc ((name, lhss, f), _)) =

      mk_simproc name lhss (K (f ctxt));

    fun add_loop (name, f) simpset = simpset addloop (name, f ctxt);

    fun add_solver add (ContextSolver ((name, f), _)) simpset =

      add (simpset, mk_solver name (f ctxt));

  in

    ((case subgoal_tac of NONE => ss | SOME tac => ss setsubgoaler tac ctxt)

      addsimprocs map prep_simproc simprocs)

    |> fold_rev add_loop loop_tacs

    |> fold_rev (add_solver (op addSolver)) unsafe_solvers

    |> fold_rev (add_solver (op addSSolver)) solvers

  end;

fun make_context_ss (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =

  ContextSS {simprocs = simprocs, subgoal_tac = subgoal_tac, loop_tacs = loop_tacs,

    unsafe_solvers = unsafe_solvers, solvers = solvers};

val empty_context_ss = make_context_ss ([], NONE, [], [], []);

fun merge_context_ss (ctxt_ss1, ctxt_ss2) =

  let

    val ContextSS {simprocs = simprocs1, subgoal_tac = subgoal_tac1, loop_tacs = loop_tacs1,

      unsafe_solvers = unsafe_solvers1, solvers = solvers1} = ctxt_ss1;

    val ContextSS {simprocs = simprocs2, subgoal_tac = subgoal_tac2, loop_tacs = loop_tacs2,

      unsafe_solvers = unsafe_solvers2, solvers = solvers2} = ctxt_ss2;

    val simprocs' = merge_context_simprocs simprocs1 simprocs2;

    val subgoal_tac' = (case subgoal_tac1 of NONE => subgoal_tac2 | some => some);

    val loop_tacs' = merge_alists loop_tacs1 loop_tacs2;

    val unsafe_solvers' = merge_context_solvers unsafe_solvers1 unsafe_solvers2;

    val solvers' = merge_context_solvers solvers1 solvers2;

  in make_context_ss (simprocs', subgoal_tac', loop_tacs', unsafe_solvers', solvers') end;

(** global and local simpset data **)

(* theory data kind 'Pure/simpset' *)

structure GlobalSimpset = TheoryDataFun

(struct

  val name = "Pure/simpset";

  type T = simpset ref * context_ss;

  val empty = (ref empty_ss, empty_context_ss);

  fun copy (ref ss, ctxt_ss) = (ref ss, ctxt_ss): T;            (*create new reference!*)

  val extend = copy;

  fun merge _ ((ref ss1, ctxt_ss1), (ref ss2, ctxt_ss2)) =

    (ref (merge_ss (ss1, ss2)), merge_context_ss (ctxt_ss1, ctxt_ss2));

  fun print _ (ref ss, _) = print_ss ss;

end);

val _ = Context.add_setup [GlobalSimpset.init];

val print_simpset = GlobalSimpset.print;

val simpset_ref_of = #1 o GlobalSimpset.get;

val simpset_ref_of_sg = simpset_ref_of;

val get_context_ss = #2 o GlobalSimpset.get o ProofContext.theory_of;

fun map_context_ss f = GlobalSimpset.map (apsnd

  (fn ContextSS {simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers} =>

    make_context_ss (f (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers))));

(* access global simpset *)

val simpset_of = ! o simpset_ref_of;

val simpset_of_sg = simpset_of;

fun SIMPSET tacf state = tacf (simpset_of (Thm.theory_of_thm state)) state;

fun SIMPSET' tacf i state = tacf (simpset_of (Thm.theory_of_thm state)) i state;

val simpset = simpset_of o Context.the_context;

val simpset_ref = simpset_ref_of o Context.the_context;

(* change global simpset *)

fun change_simpset_of f x thy =

  let val r = simpset_ref_of thy

  in r := f (! r, x); thy end;

fun change_simpset f x = (change_simpset_of f x (Context.the_context ()); ());

val Addsimps = change_simpset (op addsimps);

val Delsimps = change_simpset (op delsimps);

val Addsimprocs = change_simpset (op addsimprocs);

val Delsimprocs = change_simpset (op delsimprocs);

val Addcongs = change_simpset (op addcongs);

val Delcongs = change_simpset (op delcongs);

(* change context dependent components *)

fun add_context_simprocs procs =

  map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =>

    (merge_context_simprocs procs simprocs, subgoal_tac, loop_tacs,

      unsafe_solvers, solvers));

fun del_context_simprocs procs =

  map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =>

    (gen_rems eq_context_simproc (simprocs, procs), subgoal_tac, loop_tacs,

      unsafe_solvers, solvers));

fun set_context_subgoaler tac =

  map_context_ss (fn (simprocs, _, loop_tacs, unsafe_solvers, solvers) =>

    (simprocs, SOME tac, loop_tacs, unsafe_solvers, solvers));

val reset_context_subgoaler =

  map_context_ss (fn (simprocs, _, loop_tacs, unsafe_solvers, solvers) =>

    (simprocs, NONE, loop_tacs, unsafe_solvers, solvers));

fun add_context_looper (name, tac) =

  map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =>

    (simprocs, subgoal_tac, merge_alists [(name, tac)] loop_tacs,

      unsafe_solvers, solvers));

fun del_context_looper name =

  map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =>

    (simprocs, subgoal_tac, filter_out (equal name o #1) loop_tacs,

      unsafe_solvers, solvers));

fun add_context_unsafe_solver solver =

  map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =>

    (simprocs, subgoal_tac, loop_tacs,

      merge_context_solvers [solver] unsafe_solvers, solvers));

fun add_context_safe_solver solver =

  map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =>

    (simprocs, subgoal_tac, loop_tacs, unsafe_solvers,

      merge_context_solvers [solver] solvers));

(* proof data kind 'Pure/simpset' *)

structure LocalSimpset = ProofDataFun

(struct

  val name = "Pure/simpset";

  type T = simpset;

  val init = simpset_of;

  fun print ctxt ss = print_ss (context_ss ctxt ss (get_context_ss ctxt));

end);

val _ = Context.add_setup [LocalSimpset.init];

val print_local_simpset = LocalSimpset.print;

val get_local_simpset = LocalSimpset.get;

val put_local_simpset = LocalSimpset.put;

fun map_local_simpset f ctxt = put_local_simpset (f (get_local_simpset ctxt)) ctxt;

fun local_simpset_of ctxt =

  context_ss ctxt (get_local_simpset ctxt) (get_context_ss ctxt);

(* attributes *)

fun change_global_ss f (thy, th) =

  let val r = simpset_ref_of thy

  in r := f (! r, [th]); (thy, th) end;

fun change_local_ss f (ctxt, th) =

  let val ss = f (get_local_simpset ctxt, [th])

  in (put_local_simpset ss ctxt, th) end;

val simp_add_global = change_global_ss (op addsimps);

val simp_del_global = change_global_ss (op delsimps);

val simp_add_local = change_local_ss (op addsimps);

val simp_del_local = change_local_ss (op delsimps);

val cong_add_global = change_global_ss (op addcongs);

val cong_del_global = change_global_ss (op delcongs);

val cong_add_local = change_local_ss (op addcongs);

val cong_del_local = change_local_ss (op delcongs);

(* tactics *)

val simp_tac = generic_simp_tac false (false, false, false);

val asm_simp_tac = generic_simp_tac false (false, true, false);

val full_simp_tac = generic_simp_tac false (true, false, false);

val asm_lr_simp_tac = generic_simp_tac false (true, true, false);

val asm_full_simp_tac = generic_simp_tac false (true, true, true);

val safe_asm_full_simp_tac = generic_simp_tac true (true, true, true);

(*the abstraction over the proof state delays the dereferencing*)

fun          Simp_tac i st =          simp_tac (simpset ()) i st;

fun      Asm_simp_tac i st =      asm_simp_tac (simpset ()) i st;

fun     Full_simp_tac i st =     full_simp_tac (simpset ()) i st;

fun   Asm_lr_simp_tac i st =   asm_lr_simp_tac (simpset ()) i st;

fun Asm_full_simp_tac i st = asm_full_simp_tac (simpset ()) i st;

(* conversions *)

val          simplify = simp_thm (false, false, false);

val      asm_simplify = simp_thm (false, true, false);

val     full_simplify = simp_thm (true, false, false);

val   asm_lr_simplify = simp_thm (true, true, false);

val asm_full_simplify = simp_thm (true, true, true);

val          rewrite = simp_cterm (false, false, false);

val      asm_rewrite = simp_cterm (false, true, false);

val     full_rewrite = simp_cterm (true, false, false);

val   asm_lr_rewrite = simp_cterm (true, true, false);

val asm_full_rewrite = simp_cterm (true, true, true);

(** concrete syntax of attributes **)

(* add / del *)

val simpN = "simp";

val congN = "cong";

val addN = "add";

val delN = "del";

val onlyN = "only";

val no_asmN = "no_asm";

val no_asm_useN = "no_asm_use";

val no_asm_simpN = "no_asm_simp";

val asm_lrN = "asm_lr";

val simp_attr =

 (Attrib.add_del_args simp_add_global simp_del_global,

  Attrib.add_del_args simp_add_local simp_del_local);

val cong_attr =

 (Attrib.add_del_args cong_add_global cong_del_global,

  Attrib.add_del_args cong_add_local cong_del_local);

(* conversions *)

local

fun conv_mode x =

  ((Args.parens (Args.$$$ no_asmN) >> K simplify ||

    Args.parens (Args.$$$ no_asm_simpN) >> K asm_simplify ||

    Args.parens (Args.$$$ no_asm_useN) >> K full_simplify ||

    Scan.succeed asm_full_simplify) |> Scan.lift) x;

fun simplified_att get args =

  Attrib.syntax (conv_mode -- args >> (fn (f, ths) =>

    Drule.rule_attribute (fn x => f ((if null ths then I else clear_ss) (get x) addsimps ths))));

in

val simplified_attr =

 (simplified_att simpset_of Attrib.global_thmss,

  simplified_att local_simpset_of Attrib.local_thmss);

end;

(* setup attributes *)

val _ = Context.add_setup

 [Attrib.add_attributes

   [(simpN, simp_attr, "declaration of simplification rule"),

    (congN, cong_attr, "declaration of Simplifier congruence rule"),

    ("simplified", simplified_attr, "simplified rule")]];

(** proof methods **)

(* simplification *)

val simp_options =

 (Args.parens (Args.$$$ no_asmN) >> K simp_tac ||

  Args.parens (Args.$$$ no_asm_simpN) >> K asm_simp_tac ||

  Args.parens (Args.$$$ no_asm_useN) >> K full_simp_tac ||

  Args.parens (Args.$$$ asm_lrN) >> K asm_lr_simp_tac ||

  Scan.succeed asm_full_simp_tac);

fun simp_flags x = (Scan.repeat

  (Args.parens (Args.$$$ "depth_limit" -- Args.colon |-- Args.nat)

    >> setmp MetaSimplifier.simp_depth_limit)

  >> (curry (Library.foldl op o) I o rev)) x;

val cong_modifiers =

 [Args.$$$ congN -- Args.colon >> K ((I, cong_add_local):Method.modifier),

  Args.$$$ congN -- Args.add -- Args.colon >> K (I, cong_add_local),

  Args.$$$ congN -- Args.del -- Args.colon >> K (I, cong_del_local)];

val simp_modifiers =

 [Args.$$$ simpN -- Args.colon >> K (I, simp_add_local),

  Args.$$$ simpN -- Args.add -- Args.colon >> K (I, simp_add_local),

  Args.$$$ simpN -- Args.del -- Args.colon >> K (I, simp_del_local),

  Args.$$$ simpN -- Args.$$$ onlyN -- Args.colon >> K (map_local_simpset clear_ss, simp_add_local)]

   @ cong_modifiers;

val simp_modifiers' =

 [Args.add -- Args.colon >> K (I, simp_add_local),

  Args.del -- Args.colon >> K (I, simp_del_local),

  Args.$$$ onlyN -- Args.colon >> K (map_local_simpset clear_ss, simp_add_local)]

   @ cong_modifiers;

fun simp_args more_mods =

  Method.sectioned_args (Args.bang_facts -- Scan.lift simp_options -- Scan.lift simp_flags)

    (more_mods @ simp_modifiers');

fun simp_method ((prems, tac), FLAGS) ctxt = Method.METHOD (fn facts =>

  ALLGOALS (Method.insert_tac (prems @ facts)) THEN

    (FLAGS o CHANGED_PROP o ALLGOALS o tac) (local_simpset_of ctxt));

fun simp_method' ((prems, tac), FLAGS) ctxt = Method.METHOD (fn facts =>

  HEADGOAL (Method.insert_tac (prems @ facts) THEN'

      ((FLAGS o CHANGED_PROP) oo tac) (local_simpset_of ctxt)));

(* setup methods *)

fun setup_methods more_mods = Method.add_methods

 [(simpN, simp_args more_mods simp_method', "simplification"),

  ("simp_all", simp_args more_mods simp_method, "simplification (all goals)")];

fun method_setup mods = [setup_methods mods];

(** easy_setup **)

fun easy_setup reflect trivs =

  let

    val trivialities = Drule.reflexive_thm :: trivs;

    fun unsafe_solver_tac prems = FIRST' [resolve_tac (trivialities @ prems), assume_tac];

    val unsafe_solver = mk_solver "easy unsafe" unsafe_solver_tac;

    (*no premature instantiation of variables during simplification*)

    fun safe_solver_tac prems = FIRST' [match_tac (trivialities @ prems), eq_assume_tac];

    val safe_solver = mk_solver "easy safe" safe_solver_tac;

    fun mk_eq thm =

      if Logic.is_equals (Thm.concl_of thm) then [thm]

      else [thm RS reflect] handle THM _ => [];

    fun mksimps thm = mk_eq (Drule.forall_elim_vars (#maxidx (Thm.rep_thm thm) + 1) thm);

    fun init_ss thy =

      (simpset_ref_of thy :=

        empty_ss setsubgoaler asm_simp_tac

        setSSolver safe_solver

        setSolver unsafe_solver

        setmksimps mksimps; thy);

  in method_setup [] @ [init_ss] end;

end;

structure BasicSimplifier: BASIC_SIMPLIFIER = Simplifier;

open BasicSimplifier;