(*  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

  val print_simpset: theory -> unit

  val change_simpset_of: theory -> (simpset -> simpset) -> unit

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

  val simpset_of: theory -> simpset

  val simpset: unit -> simpset

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

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

  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 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               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 clear_ss: simpset -> simpset

  val debug_bounds: bool ref

  val inherit_context: simpset -> simpset -> simpset

  val the_context: simpset -> Proof.context

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

  val theory_context: theory  -> 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 -> 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 get_simpset: theory -> simpset

  val print_local_simpset: Proof.context -> unit

  val get_local_simpset: Proof.context -> simpset

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

  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 get_simproc: Proof.context -> 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: (Args.T list -> (Method.modifier * Args.T list)) list

  val simp_modifiers': (Args.T list -> (Method.modifier * Args.T list)) list

  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

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

end;

structure Simplifier: SIMPLIFIER =

struct

open MetaSimplifier;

(** simpset data **)

(* global simpsets *)

structure GlobalSimpset = TheoryDataFun

(struct

  val name = "Pure/simpset";

  type T = simpset ref;

  val empty = ref empty_ss;

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

  fun extend (ref ss) = ref (MetaSimplifier.inherit_context empty_ss ss);

  fun merge _ (ref ss1, ref ss2) = ref (merge_ss (ss1, ss2));

  fun print _ (ref ss) = print_ss ss;

end);

val _ = Context.add_setup GlobalSimpset.init;

val print_simpset = GlobalSimpset.print;

val get_simpset = ! o GlobalSimpset.get;

val change_simpset_of = change o GlobalSimpset.get;

fun change_simpset f = change_simpset_of (ML_Context.the_context ()) f;

fun simpset_of thy = MetaSimplifier.context (ProofContext.init thy) (get_simpset thy);

val simpset = simpset_of o ML_Context.the_context;

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

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

fun Addsimps args = change_simpset (fn ss => ss addsimps args);

fun Delsimps args = change_simpset (fn ss => ss delsimps args);

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

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

fun Addcongs args = change_simpset (fn ss => ss addcongs args);

fun Delcongs args = change_simpset (fn ss => ss delcongs args);

(* local simpsets *)

structure LocalSimpset = ProofDataFun

(struct

  val name = "Pure/simpset";

  type T = simpset;

  val init = get_simpset;

  fun print _ ss = print_ss ss;

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 local_simpset_of ctxt = MetaSimplifier.context ctxt (get_local_simpset ctxt);

val _ = ML_Context.value_antiq "simpset"

  (Scan.succeed ("simpset", "Simplifier.local_simpset_of (ML_Context.the_local_context ())"));

(* generic simpsets *)

fun get_ss (Context.Theory thy) = simpset_of thy

  | get_ss (Context.Proof ctxt) = local_simpset_of ctxt;

fun map_ss f (Context.Theory thy) = (change_simpset_of thy f; Context.Theory thy)

  | map_ss f (Context.Proof ctxt) = Context.Proof (LocalSimpset.map f ctxt);

(* 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);

(** named simprocs **)

fun err_dup_simprocs ds =

  error ("Duplicate simproc(s): " ^ commas_quote ds);

(* data *)

structure Simprocs = GenericDataFun

(

  val name = "Pure/simprocs";

  type T = simproc NameSpace.table;

  val empty = NameSpace.empty_table;

  val extend = I;

  fun merge _ simprocs = NameSpace.merge_tables eq_simproc simprocs

    handle Symtab.DUPS ds => err_dup_simprocs ds;

  fun print _ _ = ();

);

val _ = Context.add_setup Simprocs.init;

(* get simprocs *)

fun get_simproc ctxt xname =

  let

    val (space, tab) = Simprocs.get (Context.Proof ctxt);

    val name = NameSpace.intern space xname;

  in

    (case Symtab.lookup tab name of

      SOME proc => proc

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

  end;

val _ = ML_Context.value_antiq "simproc" (Scan.lift Args.name >> (fn name =>

  ("simproc",

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

(* define simprocs *)

local

(* FIXME *)

fun read_terms ctxt ts =

  #1 (ProofContext.read_termTs ctxt (K false) (K NONE) (K NONE) []

    (map (rpair dummyT) ts));

(* FIXME *)

fun cert_terms ctxt ts = map (ProofContext.cert_term ctxt) ts;

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

  let

    val naming = LocalTheory.full_naming lthy;

    val simproc = make_simproc

      {name = LocalTheory.full_name lthy name,

       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}

      |> morph_simproc (LocalTheory.target_morphism lthy);

  in

    lthy |> LocalTheory.declaration (fn phi => fn context =>

      let

        val name' = Morphism.name phi name;

        val simproc' = morph_simproc phi simproc;

      in

        context

        |> Simprocs.map (fn simprocs =>

            NameSpace.extend_table naming (simprocs, [(name', simproc')])

              handle Symtab.DUPS ds => err_dup_simprocs ds)

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

      end)

  end;

in

val def_simproc = gen_simproc read_terms;

val def_simproc_i = gen_simproc cert_terms;

end;

(** simplification tactics and rules **)

fun solve_all_tac solvers ss =

  let

    val (_, {subgoal_tac, ...}) = MetaSimplifier.rep_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.rep_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 =

      Goal.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.rep_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);

(*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";

(* 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 =

  Attrib.syntax (conv_mode -- Attrib.thms >> (fn (f, ths) => Thm.rule_attribute (fn x =>

    f ((if null ths then I else MetaSimplifier.clear_ss) (get_ss x) addsimps ths))));

end;

(* setup attributes *)

val _ = Context.add_setup

 (Attrib.add_attributes

   [(simpN, Attrib.add_del_args simp_add simp_del, "declaration of Simplifier rule"),

    (congN, Attrib.add_del_args cong_add cong_del, "declaration of Simplifier congruence rule"),

    ("simplified", simplified, "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): 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 (LocalSimpset.map 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 (LocalSimpset.map MetaSimplifier.clear_ss, simp_add)]

   @ 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 **)

fun method_setup 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 easy_setup reflect trivs = method_setup [] #> (fn thy =>

  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 (Drule.forall_elim_vars (#maxidx (Thm.rep_thm thm) + 1) thm);

  in

    GlobalSimpset.get thy :=

      empty_ss setsubgoaler asm_simp_tac

      setSSolver safe_solver

      setSolver unsafe_solver

      setmksimps mksimps;

    thy

  end);

end;

structure BasicSimplifier: BASIC_SIMPLIFIER = Simplifier;

open BasicSimplifier;