(*  Title:      Pure/simplifier.ML

     Author:     Tobias Nipkow and Markus Wenzel, TU Muenchen

 Generic simplifier, suitable for most logics (see also

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

 *)

 signature BASIC_SIMPLIFIER =

 sig

   include BASIC_RAW_SIMPLIFIER

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

   val simpset_of: Proof.context -> simpset

   val global_simpset_of: theory -> simpset

   val Addsimprocs: simproc list -> unit

   val Delsimprocs: simproc list -> unit

   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 map_simpset_global: (simpset -> simpset) -> theory -> theory

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

   val clear_ss: simpset -> simpset

   val debug_bounds: bool Unsynchronized.ref

   val prems_of: simpset -> thm list

   val add_simp: thm -> simpset -> simpset

   val del_simp: thm -> simpset -> simpset

   val add_eqcong: thm -> simpset -> simpset

   val del_eqcong: thm -> simpset -> simpset

   val add_cong: thm -> simpset -> simpset

   val del_cong: thm -> simpset -> simpset

   val add_prems: thm list -> simpset -> simpset

   val mksimps: simpset -> thm -> thm list

   val set_mksimps: (simpset -> thm -> thm list) -> simpset -> simpset

   val set_mkcong: (simpset -> thm -> thm) -> simpset -> simpset

   val set_mksym: (simpset -> thm -> thm option) -> simpset -> simpset

   val set_mkeqTrue: (simpset -> thm -> thm option) -> simpset -> simpset

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

   val set_subgoaler: (simpset -> int -> tactic) -> 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 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 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: (thm -> simpset -> simpset) -> attribute

   val simp_add: attribute

   val simp_del: attribute

   val cong_add: attribute

   val cong_del: attribute

   val check_simproc: Proof.context -> xstring * Position.T -> string

   val the_simproc: Proof.context -> string -> simproc

   val def_simproc: {name: binding, lhss: term list,

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

     local_theory -> local_theory

   val def_simproc_cmd: {name: binding, lhss: string 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 Raw_Simplifier;

 (** data **)

 structure Data = Generic_Data

 (

   type T = simpset * simproc Name_Space.table;

   val empty : T = (empty_ss, Name_Space.empty_table "simproc");

   fun extend (ss, tab) = (Raw_Simplifier.inherit_context empty_ss ss, tab);

   fun merge ((ss1, tab1), (ss2, tab2)) =

     (merge_ss (ss1, ss2), Name_Space.merge_tables (tab1, tab2));

 );

 val get_ss = fst o Data.get;

 fun map_ss f context =

   Data.map (apfst ((Raw_Simplifier.with_context (Context.proof_of context) f))) context;

 val get_simprocs = snd o Data.get o Context.Proof;

 (** 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 **)

 (* attributes *)

 fun attrib f = Thm.declaration_attribute (map_ss o f);

 val simp_add = attrib add_simp;

 val simp_del = attrib del_simp;

 val cong_add = attrib add_cong;

 val cong_del = attrib del_cong;

 (* local simpset *)

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

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

 val _ = Context.>> (Context.map_theory

   (ML_Antiquote.value (Binding.name "simpset")

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

 (* global simpset *)

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

 fun global_simpset_of thy =

   Raw_Simplifier.context (Proof_Context.init_global thy) (get_ss (Context.Theory thy));

 fun Addsimprocs args = Context.>> (map_ss (fn ss => ss addsimprocs args));

 fun Delsimprocs args = Context.>> (map_ss (fn ss => ss delsimprocs args));

 (** named simprocs **)

 (* get simprocs *)

 fun check_simproc ctxt = Name_Space.check ctxt (get_simprocs ctxt) #> #1;

 val the_simproc = Name_Space.get o get_simprocs;

 val _ =

   Context.>> (Context.map_theory

    (ML_Antiquote.value (Binding.name "simproc")

       (Args.context -- Scan.lift (Parse.position Args.name)

         >> (fn (ctxt, name) =>

           "Simplifier.the_simproc (ML_Context.the_local_context ()) " ^

             ML_Syntax.print_string (check_simproc ctxt name)))));

 (* define simprocs *)

 local

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

   let

     val simproc = make_simproc

       {name = Local_Theory.full_name lthy b,

        lhss =

         let

           val lhss' = prep lthy lhss;

           val ctxt' = fold Variable.auto_fixes lhss' lthy;

         in Variable.export_terms ctxt' lthy lhss' end

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

        proc = proc,

        identifier = identifier};

   in

     lthy |> Local_Theory.declaration {syntax = false, pervasive = true} (fn phi => fn context =>

       let

         val naming = Proof_Context.target_naming_of context;

         val b' = Morphism.binding phi b;

         val simproc' = transform_simproc phi simproc;

       in

         context

         |> Data.map (fn (ss, tab) =>

           (ss addsimprocs [simproc'],

             #2 (Name_Space.define (Context.proof_of context) true naming (b', simproc') tab)))

       end)

   end;

 in

 val def_simproc = gen_simproc Syntax.check_terms;

 val def_simproc_cmd = gen_simproc Syntax.read_terms;

 end;

 (** simplification tactics and rules **)

 fun solve_all_tac solvers ss =

   let

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

     val solve_tac = subgoal_tac (Raw_Simplifier.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), ...}) = Raw_Simplifier.internal_ss ss;

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

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

       (rev (if safe then solvers else unsafe_solvers)));

     fun simp_loop_tac i =

       Raw_Simplifier.generic_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, _), ...}) = Raw_Simplifier.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 Raw_Simplifier.rewrite_thm;

 val simp_cterm = simp Raw_Simplifier.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, [transform_simproc phi simproc])))));

 in

 val simproc_att =

   (Args.context -- Scan.lift add_del) :|-- (fn (ctxt, decl) =>

     Scan.repeat1 (Scan.lift (Args.named_attribute (decl o the_simproc ctxt o check_simproc ctxt))))

   >> (fn atts => Thm.declaration_attribute (fn th =>

         fold (fn att => Thm.attribute_declaration (Morphism.form att) th) atts));

 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 Raw_Simplifier.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 Raw_Simplifier.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 Raw_Simplifier.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 PARALLEL_GOALS 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 ss =

       FIRST' [resolve_tac (trivialities @ Raw_Simplifier.prems_of ss), assume_tac];

     val unsafe_solver = mk_solver "easy unsafe" unsafe_solver_tac;

     (*no premature instantiation of variables during simplification*)

     fun safe_solver_tac ss =

       FIRST' [match_tac (trivialities @ Raw_Simplifier.prems_of ss), 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 (Thm.maxidx_of thm + 1) thm);

   in

     empty_ss

     setSSolver safe_solver

     setSolver unsafe_solver

     |> set_subgoaler asm_simp_tac

     |> set_mksimps (K mksimps)

   end));

 end;

 structure Basic_Simplifier: BASIC_SIMPLIFIER = Simplifier;

 open Basic_Simplifier;