(*  Title:      Pure/simplifier.ML

    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

  val change_simpset: (simpset -> simpset) -> unit

  val global_simpset_of: theory -> simpset

  val Addsimprocs: simproc list -> unit

  val Delsimprocs: simproc list -> unit

  val simpset_of: Proof.context -> simpset

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

  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 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 pretty_ss: Proof.context -> simpset -> Pretty.T

  val clear_ss: simpset -> simpset

  val debug_bounds: bool Unsynchronized.ref

  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 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 rewrite: simpset -> conv

  val asm_rewrite: simpset -> conv

  val full_rewrite: simpset -> conv

  val asm_lr_rewrite: simpset -> conv

  val asm_full_rewrite: simpset -> conv

  val get_ss: Context.generic -> simpset

  val map_ss: (simpset -> simpset) -> Context.generic -> Context.generic

  val attrib: (simpset * thm list -> simpset) -> attribute

  val simp_add: attribute

  val simp_del: attribute

  val cong_add: attribute

  val cong_del: attribute

  val map_simpset: (simpset -> simpset) -> theory -> theory

  val get_simproc: Context.generic -> xstring -> simproc

  val def_simproc: {name: string, lhss: string list,

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

    local_theory -> local_theory

  val def_simproc_i: {name: string, lhss: term list,

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

    local_theory -> local_theory

  val cong_modifiers: Method.modifier parser list

  val simp_modifiers': Method.modifier parser list

  val simp_modifiers: Method.modifier parser list

  val method_setup: Method.modifier parser list -> theory -> theory

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

end;

structure Simplifier: SIMPLIFIER =

struct

open MetaSimplifier;

(** pretty printing **)

fun pretty_ss ctxt ss =

  let

    val pretty_cterm = Syntax.pretty_term ctxt o Thm.term_of;

    val pretty_thm = Display.pretty_thm ctxt;

    fun pretty_proc (name, lhss) = Pretty.big_list (name ^ ":") (map pretty_cterm lhss);

    fun pretty_cong (name, thm) =

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

    val {simps, procs, congs, loopers, unsafe_solvers, safe_solvers, ...} = dest_ss ss;

  in

    [Pretty.big_list "simplification rules:" (map (pretty_thm o #2) simps),

      Pretty.big_list "simplification procedures:" (map pretty_proc (sort_wrt #1 procs)),

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

      Pretty.strs ("loopers:" :: map quote loopers),

      Pretty.strs ("unsafe solvers:" :: map quote unsafe_solvers),

      Pretty.strs ("safe solvers:" :: map quote safe_solvers)]

    |> Pretty.chunks

  end;

(** simpset data **)

structure Simpset = Generic_Data

(

  type T = simpset;

  val empty = empty_ss;

  fun extend ss = MetaSimplifier.inherit_context empty_ss ss;

  val merge = merge_ss;

);

val get_ss = Simpset.get;

fun map_ss f context = Simpset.map (with_context (Context.proof_of context) f) context;

(* attributes *)

fun attrib f = Thm.declaration_attribute (fn th => map_ss (fn ss => f (ss, [th])));

val simp_add = attrib (op addsimps);

val simp_del = attrib (op delsimps);

val cong_add = attrib (op addcongs);

val cong_del = attrib (op delcongs);

(* global simpset *)

fun map_simpset f = Context.theory_map (map_ss f);

fun change_simpset f = Context.>> (Context.map_theory (map_simpset f));

fun global_simpset_of thy =

  MetaSimplifier.context (ProofContext.init_global thy) (get_ss (Context.Theory thy));

fun Addsimprocs args = change_simpset (fn ss => ss addsimprocs args);

fun Delsimprocs args = change_simpset (fn ss => ss delsimprocs args);

(* local simpset *)

fun simpset_of ctxt = MetaSimplifier.context ctxt (get_ss (Context.Proof ctxt));

val _ = ML_Antiquote.value "simpset"

  (Scan.succeed "Simplifier.simpset_of (ML_Context.the_local_context ())");

(** named simprocs **)

(* data *)

structure Simprocs = Generic_Data

(

  type T = simproc Name_Space.table;

  val empty : T = Name_Space.empty_table "simproc";

  val extend = I;

  fun merge simprocs = Name_Space.merge_tables simprocs;

);

(* get simprocs *)

fun get_simproc context xname =

  let

    val (space, tab) = Simprocs.get context;

    val name = Name_Space.intern space xname;

  in

    (case Symtab.lookup tab name of

      SOME proc => proc

    | NONE => error ("Undefined simplification procedure: " ^ quote name))

  end;

val _ = ML_Antiquote.value "simproc" (Scan.lift Args.name >> (fn name =>

  "Simplifier.get_simproc (ML_Context.the_generic_context ()) " ^ ML_Syntax.print_string name));

(* define simprocs *)

local

fun gen_simproc prep {name, lhss, proc, identifier} lthy =

  let

    val b = Binding.name name;

    val naming = Local_Theory.naming_of lthy;

    val simproc = make_simproc

      {name = Name_Space.full_name naming b,

       lhss =

        let

          val lhss' = prep lthy lhss;

          val ctxt' = lthy

            |> fold Variable.declare_term lhss'

            |> fold Variable.auto_fixes lhss';

        in Variable.export_terms ctxt' lthy lhss' end

        |> map (Thm.cterm_of (ProofContext.theory_of lthy)),

       proc = proc,

       identifier = identifier};

  in

    lthy |> Local_Theory.declaration false (fn phi =>

      let

        val b' = Morphism.binding phi b;

        val simproc' = morph_simproc phi simproc;

      in

        Simprocs.map (#2 o Name_Space.define true naming (b', simproc'))

        #> map_ss (fn ss => ss addsimprocs [simproc'])

      end)

  end;

in

val def_simproc = gen_simproc Syntax.read_terms;

val def_simproc_i = gen_simproc Syntax.check_terms;

end;

(** simplification tactics and rules **)

fun solve_all_tac solvers ss =

  let

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

    val solve_tac = subgoal_tac (MetaSimplifier.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 (_, {loop_tacs, solvers = (unsafe_solvers, solvers), ...}) = MetaSimplifier.internal_ss ss;

    val loop_tac = FIRST' (map (fn (_, tac) => tac ss) (rev loop_tacs));

    val solve_tac = FIRST' (map (MetaSimplifier.solver ss)

      (rev (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;

local

fun simp rew mode ss thm =

  let

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

    val tacf = solve_all_tac (rev unsafe_solvers);

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

  in rew mode prover ss thm end;

in

val simp_thm = simp MetaSimplifier.rewrite_thm;

val simp_cterm = simp MetaSimplifier.rewrite_cterm;

end;

(* 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);

(* 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 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";

(* simprocs *)

local

val add_del =

  (Args.del -- Args.colon >> K (op delsimprocs) ||

    Scan.option (Args.add -- Args.colon) >> K (op addsimprocs))

  >> (fn f => fn simproc => fn phi => Thm.declaration_attribute

      (K (map_ss (fn ss => f (ss, [morph_simproc phi simproc])))));

in

val simproc_att =

  Scan.peek (fn context =>

    add_del :|-- (fn decl =>

      Scan.repeat1 (Args.named_attribute (decl o get_simproc context))

      >> (Library.apply o map Morphism.form)));

end;

(* 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;

in

val simplified = conv_mode -- Attrib.thms >>

  (fn (f, ths) => Thm.rule_attribute (fn context =>

    f ((if null ths then I else MetaSimplifier.clear_ss)

        (simpset_of (Context.proof_of context)) addsimps ths)));

end;

(* setup attributes *)

val _ = Context.>> (Context.map_theory

 (Attrib.setup (Binding.name simpN) (Attrib.add_del simp_add simp_del)

    "declaration of Simplifier rewrite rule" #>

  Attrib.setup (Binding.name congN) (Attrib.add_del cong_add cong_del)

    "declaration of Simplifier congruence rule" #>

  Attrib.setup (Binding.name "simproc") simproc_att

    "declaration of simplification procedures" #>

  Attrib.setup (Binding.name "simplified") simplified "simplified rule"));

(** method syntax **)

val cong_modifiers =

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

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

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

val simp_modifiers =

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

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

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

  Args.$$$ simpN -- Args.$$$ onlyN -- Args.colon

    >> K (Context.proof_map (map_ss MetaSimplifier.clear_ss), simp_add)]

   @ cong_modifiers;

val simp_modifiers' =

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

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

  Args.$$$ onlyN -- Args.colon

    >> K (Context.proof_map (map_ss MetaSimplifier.clear_ss), simp_add)]

   @ cong_modifiers;

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_method more_mods meth =

  Scan.lift simp_options --|

    Method.sections (more_mods @ simp_modifiers') >>

    (fn tac => fn ctxt => METHOD (fn facts => meth ctxt tac facts));

(** setup **)

fun method_setup more_mods =

  Method.setup (Binding.name simpN)

    (simp_method more_mods (fn ctxt => fn tac => fn facts =>

      HEADGOAL (Method.insert_tac facts THEN'

        (CHANGED_PROP oo tac) (simpset_of ctxt))))

    "simplification" #>

  Method.setup (Binding.name "simp_all")

    (simp_method more_mods (fn ctxt => fn tac => fn facts =>

      ALLGOALS (Method.insert_tac facts) THEN

        (CHANGED_PROP o ALLGOALS o tac) (simpset_of ctxt)))

    "simplification (all goals)";

fun easy_setup reflect trivs = method_setup [] #> Context.theory_map (map_ss (fn _ =>

  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 can Logic.dest_equals (Thm.concl_of thm) then [thm]

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

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

  in

    empty_ss setsubgoaler asm_simp_tac

    setSSolver safe_solver

    setSolver unsafe_solver

    setmksimps (K mksimps)

  end));

end;

structure Basic_Simplifier: BASIC_SIMPLIFIER = Simplifier;

open Basic_Simplifier;