src/Provers/simplifier.ML
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added simplification meta rules;
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(*  Title:      Provers/simplifier.ML
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    ID:         $Id$
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    Author:     Tobias Nipkow and Markus Wenzel, TU Muenchen
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Generic simplifier, suitable for most logics.
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*)
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infix 4
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  setsubgoaler setloop addloop setSSolver addSSolver setSolver
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  addSolver setmksimps addsimps delsimps addeqcongs deleqcongs
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  settermless addsimprocs delsimprocs;
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signature SIMPLIFIER =
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sig
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  type simproc
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  val mk_simproc: string -> cterm list -> (Sign.sg -> term -> thm option) -> simproc
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  val conv_prover: (term * term -> term) -> thm -> (thm -> thm)
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    -> tactic -> (int -> tactic) -> Sign.sg -> term -> term -> thm
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  type simpset
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  val empty_ss: simpset
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  val rep_ss: simpset ->
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   {mss: meta_simpset,
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    subgoal_tac:        simpset -> int -> tactic,
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    loop_tac:                      int -> tactic,
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           finish_tac: thm list -> int -> tactic,
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    unsafe_finish_tac: thm list -> int -> tactic};
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  val print_ss: simpset -> unit
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  val setsubgoaler: simpset *  (simpset -> int -> tactic) -> simpset
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  val setloop:      simpset *             (int -> tactic) -> simpset
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  val addloop:      simpset *             (int -> tactic) -> simpset
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  val setSSolver:   simpset * (thm list -> int -> tactic) -> simpset
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  val addSSolver:   simpset * (thm list -> int -> tactic) -> simpset
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  val setSolver:    simpset * (thm list -> int -> tactic) -> simpset
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  val addSolver:    simpset * (thm list -> int -> tactic) -> simpset
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  val setmksimps:  simpset * (thm -> thm list) -> simpset
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  val settermless: simpset * (term * term -> bool) -> simpset
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  val addsimps:    simpset * thm list -> simpset
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  val delsimps:    simpset * thm list -> simpset
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  val addeqcongs:  simpset * thm list -> simpset
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  val deleqcongs:  simpset * thm list -> simpset
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  val addsimprocs: simpset * simproc list -> simpset
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  val delsimprocs: simpset * simproc list -> simpset
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  val merge_ss:    simpset * simpset -> simpset
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  val prems_of_ss: simpset -> thm list
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  val simpset:     simpset ref
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  val Addsimps: thm list -> unit
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  val Delsimps: thm list -> unit
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  val Addsimprocs: simproc list -> unit
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  val Delsimprocs: simproc list -> unit
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  val               simp_tac: simpset -> int -> tactic
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  val           asm_simp_tac: simpset -> int -> tactic
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  val          full_simp_tac: simpset -> int -> tactic
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  val      asm_full_simp_tac: simpset -> int -> tactic
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  val safe_asm_full_simp_tac: simpset -> int -> tactic
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  val               Simp_tac:            int -> tactic
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  val           Asm_simp_tac:            int -> tactic
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  val          Full_simp_tac:            int -> tactic
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  val      Asm_full_simp_tac:            int -> tactic
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  val          simplify: simpset -> thm -> thm
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  val      asm_simplify: simpset -> thm -> thm
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  val     full_simplify: simpset -> thm -> thm
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  val asm_full_simplify: simpset -> thm -> thm
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end;
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structure Simplifier: SIMPLIFIER =
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struct
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(** simplification procedures **)
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(* datatype simproc *)
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datatype simproc =
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  Simproc of string * cterm list * (Sign.sg -> term -> thm option) * stamp;
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fun mk_simproc name lhss proc =
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  Simproc (name, map (Thm.cterm_fun Logic.varify) lhss, proc, stamp ());
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fun rep_simproc (Simproc args) = args;
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(* generic conversion prover *)		(* FIXME move?, rename? *)
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fun conv_prover mk_eqv eqv_refl mk_meta_eq expand_tac norm_tac sg t u =
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  let
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    val X = Free (gensym "X.", fastype_of t);
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    val goal = Logic.mk_implies (mk_eqv (X, t), mk_eqv (X, u));
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    val pre_result =
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      prove_goalw_cterm [] (cterm_of sg goal)   (*goal: X=t ==> X=u*)
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        (fn prems => [
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          expand_tac,				(*expand u*)
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          ALLGOALS (cut_facts_tac prems),
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          ALLGOALS norm_tac]);			(*normalize both t and u*)
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  in
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    mk_meta_eq (eqv_refl RS pre_result)         (*final result: t==u*)
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  end
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  handle ERROR => error ("The error(s) above occurred while trying to prove " ^
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    (string_of_cterm (cterm_of sg (mk_eqv (t, u)))));
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(** simplification sets **)
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(* type simpset *)
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datatype simpset =
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  Simpset of {
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    mss: meta_simpset,
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    subgoal_tac:        simpset -> int -> tactic,
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    loop_tac:                      int -> tactic,
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           finish_tac: thm list -> int -> tactic,
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    unsafe_finish_tac: thm list -> int -> tactic};
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fun make_ss (mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac) =
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  Simpset {mss = mss, subgoal_tac = subgoal_tac, loop_tac = loop_tac,
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    finish_tac = finish_tac, unsafe_finish_tac = unsafe_finish_tac};
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val empty_ss =
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  make_ss (Thm.empty_mss, K (K no_tac), K no_tac, K (K no_tac), K (K no_tac));
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fun rep_ss (Simpset args) = args;
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fun prems_of_ss (Simpset {mss, ...}) = Thm.prems_of_mss mss;
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(* print simpsets *)
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fun print_ss ss =
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  let
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    val Simpset {mss, ...} = ss;
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    val {simps, procs, congs} = Thm.dest_mss mss;
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    val pretty_thms = map Display.pretty_thm;
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    fun pretty_proc (name, lhss) =
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      Pretty.big_list (name ^ ":") (map Display.pretty_cterm lhss);
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  in
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    Pretty.writeln (Pretty.big_list "simplification rules:" (pretty_thms simps));
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    Pretty.writeln (Pretty.big_list "simplification procedures:" (map pretty_proc procs));
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    Pretty.writeln (Pretty.big_list "congruences:" (pretty_thms congs))
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  end;
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(* extend simpsets *)
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fun (Simpset {mss, subgoal_tac = _, loop_tac, finish_tac, unsafe_finish_tac})
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    setsubgoaler subgoal_tac =
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  make_ss (mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tac = _, finish_tac, unsafe_finish_tac})
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    setloop loop_tac =
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  make_ss (mss, subgoal_tac, DETERM o loop_tac, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac})
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    addloop tac =
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  make_ss (mss, subgoal_tac, loop_tac ORELSE' (DETERM o tac), finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tac, finish_tac = _, unsafe_finish_tac})
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    setSSolver finish_tac =
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  make_ss (mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac})
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    addSSolver tac =
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  make_ss (mss, subgoal_tac, loop_tac, fn hyps => finish_tac hyps ORELSE' tac hyps,
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    unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac = _})
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    setSolver unsafe_finish_tac =
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  make_ss (mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac})
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    addSolver tac =
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  make_ss (mss, subgoal_tac, loop_tac, finish_tac,
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    fn hyps => unsafe_finish_tac hyps ORELSE' tac hyps);
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fun (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac})
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    setmksimps mk_simps =
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  make_ss (Thm.set_mk_rews (mss, map (Thm.strip_shyps o Drule.zero_var_indexes) o mk_simps),
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    subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tac,  finish_tac, unsafe_finish_tac})
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    settermless termless =
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  make_ss (Thm.set_termless (mss, termless), subgoal_tac, loop_tac,
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    finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac})
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    addsimps rews =
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  let val rews' = flat (map (Thm.mk_rews_of_mss mss) rews) in
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    make_ss (Thm.add_simps (mss, rews'), subgoal_tac, loop_tac,
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      finish_tac, unsafe_finish_tac)
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  end;
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fun (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac})
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    delsimps rews =
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  let val rews' = flat (map (Thm.mk_rews_of_mss mss) rews) in
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    make_ss (Thm.del_simps (mss, rews'), subgoal_tac, loop_tac,
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      finish_tac, unsafe_finish_tac)
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  end;
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fun (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac})
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    addeqcongs newcongs =
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  make_ss (Thm.add_congs (mss, newcongs), subgoal_tac, loop_tac,
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    finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac})
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    deleqcongs oldcongs =
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  make_ss (Thm.del_congs (mss, oldcongs), subgoal_tac, loop_tac,
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    finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac})
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    addsimprocs simprocs =
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  make_ss
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    (Thm.add_simprocs (mss, map rep_simproc simprocs),
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      subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac})
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    delsimprocs simprocs =
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  make_ss
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    (Thm.del_simprocs (mss, map rep_simproc simprocs),
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      subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac);
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(* merge simpsets *)	(*NOTE: ignores tactics of 2nd simpset*)
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fun merge_ss
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   (Simpset {mss = mss1, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac},
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    Simpset {mss = mss2, ...}) =
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  make_ss (Thm.merge_mss (mss1, mss2),
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    subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac);
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(** the current simpset **)
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val simpset = ref empty_ss;
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fun Addsimps rews = (simpset := ! simpset addsimps rews);
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fun Delsimps rews = (simpset := ! simpset delsimps rews);
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fun Addsimprocs procs = (simpset := ! simpset addsimprocs procs);
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fun Delsimprocs procs = (simpset := ! simpset delsimprocs procs);
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(** simplification tactics **)
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fun NEWSUBGOALS tac tacf st0 =
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  st0 |> (tac THEN (fn st1 => tacf (nprems_of st1 - nprems_of st0) st1));
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fun solve_all_tac (subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac) mss =
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  let
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    val ss =
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      make_ss (mss, subgoal_tac, loop_tac, unsafe_finish_tac, unsafe_finish_tac);
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    val solve1_tac =
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      NEWSUBGOALS (subgoal_tac ss 1) (fn n => if n < 0 then all_tac else no_tac);
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  in DEPTH_SOLVE solve1_tac end;
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(*not totally safe: may instantiate unknowns that appear also in other subgoals*)
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fun basic_gen_simp_tac mode =
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  fn (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac}) =>
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    let
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      fun simp_loop_tac i thm =
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        (asm_rewrite_goal_tac mode
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          (solve_all_tac (subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac)) mss i
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        THEN (finish_tac (prems_of_mss mss) i ORELSE looper i)) thm
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      and allsimp i n = EVERY (map (fn j => simp_loop_tac (i + j)) (n downto 0))
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      and looper i = TRY (NEWSUBGOALS (loop_tac i) (allsimp i));
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  in simp_loop_tac end;
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fun gen_simp_tac mode (ss as Simpset {unsafe_finish_tac, ...}) =
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  basic_gen_simp_tac mode (ss setSSolver unsafe_finish_tac);
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val          simp_tac = gen_simp_tac (false, false);
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val      asm_simp_tac = gen_simp_tac (false, true);
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val     full_simp_tac = gen_simp_tac (true,  false);
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val asm_full_simp_tac = gen_simp_tac (true,  true);
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(*not totally safe: may instantiate unknowns that appear also in other subgoals*)
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val safe_asm_full_simp_tac = basic_gen_simp_tac (true, true);
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fun          Simp_tac i =          simp_tac (! simpset) i;
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fun      Asm_simp_tac i =      asm_simp_tac (! simpset) i;
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fun     Full_simp_tac i =     full_simp_tac (! simpset) i;
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fun Asm_full_simp_tac i = asm_full_simp_tac (! simpset) i;
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(** simplification meta rules **)
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fun simp mode (Simpset {mss, subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac}) thm =
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  let
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    val tacf = solve_all_tac (subgoal_tac, loop_tac, finish_tac, unsafe_finish_tac);
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    fun prover m th = apsome fst (Sequence.pull (tacf m th));
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  in
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    Drule.rewrite_thm mode prover mss thm
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  end;
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val          simplify = simp (false, false);
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val      asm_simplify = simp (false, true);
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val     full_simplify = simp (true, false);
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val asm_full_simplify = simp (true, true);
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end;