src/Provers/simplifier.ML
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(*  Title:      Provers/simplifier.ML
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    ID:         $Id$
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    Author:     Tobias Nipkow
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    Copyright   1993  TU Munich
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Generic simplifier, suitable for most logics.
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TODO:
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  - stamps to identify funs / tacs
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  - merge: fail if incompatible funs
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  - improve merge
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*)
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infix 4 addsimps addeqcongs addsimprocs delsimprocs addsolver delsimps
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  setsolver setloop setmksimps settermless setsubgoaler;
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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 name_of_simproc: simproc -> string
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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	(* FIXME move?, rename? *)
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  type simpset
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  val empty_ss: simpset
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  val rep_ss: simpset -> {simps: thm list, procs: string list, congs: thm list}
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  val prems_of_ss: simpset -> thm list
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  val setloop: simpset * (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 setsubgoaler: simpset * (simpset -> 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 addsimprocs: simpset * simproc list -> simpset
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  val delsimprocs: simpset * simproc list -> simpset
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  val addeqcongs: simpset * thm list -> simpset
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  val merge_ss: simpset * simpset -> simpset
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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          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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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 {
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    name: string,
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    procs: (Sign.sg * term * (Sign.sg -> term -> thm option) * stamp) list}
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(* FIXME stamps!? *)
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fun eq_simproc (Simproc {name = name1, ...}, Simproc {name = name2, ...}) =
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  (name1 = name2);
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fun mk_simproc name lhss proc =
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  let
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    fun mk_proc lhs =
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      (#sign (Thm.rep_cterm lhs), Logic.varify (term_of lhs), proc, stamp ());
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  in
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    Simproc {name = name, procs = map mk_proc lhss}
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  end;
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fun name_of_simproc (Simproc {name, ...}) = name;
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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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    simps: thm list,
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    procs: simproc list,
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    congs: thm list,
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    subgoal_tac: simpset -> int -> tactic,
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    finish_tac: thm list -> int -> tactic,
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    loop_tac: int -> tactic};
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fun make_ss (mss, simps, procs, congs, subgoal_tac, finish_tac, loop_tac) =
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  Simpset {mss = mss, simps = simps, procs = procs, congs = congs,
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    subgoal_tac = subgoal_tac, finish_tac = finish_tac,
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    loop_tac = loop_tac};
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val empty_ss =
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  make_ss (Thm.empty_mss, [], [], [], K (K no_tac), K (K no_tac), K no_tac);
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fun rep_ss (Simpset {simps, procs, congs, ...}) =
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  {simps = simps, procs = map name_of_simproc procs, congs = congs};
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fun prems_of_ss (Simpset {mss, ...}) = Thm.prems_of_mss mss;
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(* extend simpsets *)
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fun (Simpset {mss, simps, procs, congs, subgoal_tac, finish_tac, loop_tac = _})
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    setloop loop_tac =
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  make_ss (mss, simps, procs, congs, subgoal_tac, finish_tac, DETERM o loop_tac);
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fun (Simpset {mss, simps, procs, congs, subgoal_tac, finish_tac = _, loop_tac})
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    setsolver finish_tac =
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  make_ss (mss, simps, procs, congs, subgoal_tac, finish_tac, loop_tac);
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fun (Simpset {mss, simps, procs, congs, subgoal_tac, loop_tac, finish_tac})
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    addsolver tac =
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  make_ss (mss, simps, procs, congs, subgoal_tac,
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    fn hyps => finish_tac hyps ORELSE' tac hyps, loop_tac);
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fun (Simpset {mss, simps, procs, congs, subgoal_tac = _, finish_tac, loop_tac})
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    setsubgoaler subgoal_tac =
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  make_ss (mss, simps, procs, congs, subgoal_tac, finish_tac, loop_tac);
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fun (Simpset {mss, simps, procs, congs, subgoal_tac, finish_tac, loop_tac})
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    setmksimps mk_simps =
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  make_ss (Thm.set_mk_rews (mss, mk_simps), simps, procs, congs,
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    subgoal_tac, finish_tac, loop_tac);
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fun (Simpset {mss, simps, procs, congs, subgoal_tac, finish_tac, loop_tac})
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    settermless termless =
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  make_ss (Thm.set_termless (mss, termless), simps, procs, congs,
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    subgoal_tac, finish_tac, loop_tac);
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fun (Simpset {mss, simps, procs, congs, subgoal_tac, finish_tac, loop_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'), gen_union eq_thm (rews', simps),
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      procs, congs, subgoal_tac, finish_tac, loop_tac)
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  end;
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fun (Simpset {mss, simps, procs, congs, subgoal_tac, finish_tac, loop_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'),
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      foldl (gen_rem eq_thm) (simps, rews'),
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      procs, congs, subgoal_tac, finish_tac, loop_tac)
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  end;
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fun (Simpset {mss, simps, procs, congs, subgoal_tac, finish_tac, loop_tac})
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    addeqcongs newcongs =
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  make_ss (Thm.add_congs (mss, newcongs),
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    simps, procs, gen_union eq_thm (newcongs, congs),
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    subgoal_tac, finish_tac, loop_tac);
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fun addsimproc ((Simpset {mss, simps, procs, congs, subgoal_tac, finish_tac, loop_tac}),
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      simproc as Simproc {name = _, procs = procs'}) =
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  make_ss (Thm.add_simprocs (mss, procs'),
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    simps, gen_ins eq_simproc (simproc, procs),
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    congs, subgoal_tac, finish_tac, loop_tac);
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val op addsimprocs = foldl addsimproc;
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fun delsimproc ((Simpset {mss, simps, procs, congs, subgoal_tac, finish_tac, loop_tac}),
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      simproc as Simproc {name = _, procs = procs'}) =
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  make_ss (Thm.del_simprocs (mss, procs'),
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    simps, gen_rem eq_simproc (procs, simproc),
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    congs, subgoal_tac, finish_tac, loop_tac);
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val op delsimprocs = foldl delsimproc;
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(* merge simpsets *)
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(*prefers first simpset (FIXME improve?)*)
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fun merge_ss (Simpset {mss, simps, procs, congs, subgoal_tac, finish_tac, loop_tac},
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    Simpset {simps = simps2, procs = procs2, congs = congs2, ...}) =
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  let
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    val simps' = gen_union eq_thm (simps, simps2);
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    val procs' = gen_union eq_simproc (procs, procs2);
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    val congs' = gen_union eq_thm (congs, congs2);
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    val mss' = Thm.set_mk_rews (empty_mss, Thm.mk_rews_of_mss mss);
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    val mss' = Thm.add_simps (mss', simps');
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    val mss' = Thm.add_congs (mss', congs');
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  in
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    make_ss (mss', simps', procs', congs', subgoal_tac, finish_tac, loop_tac)
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  end;
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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 =
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  STATE (fn state0 =>
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    tac THEN STATE (fn state1 => tacf (nprems_of state1 - nprems_of state0)));
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fun gen_simp_tac mode =
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  fn (Simpset {mss, simps, procs, congs, subgoal_tac, finish_tac, loop_tac}) =>
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  let fun solve_all_tac mss =
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        let val ss =
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              make_ss (mss, simps, procs, congs, subgoal_tac, finish_tac, loop_tac);
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            val solve1_tac =
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              NEWSUBGOALS (subgoal_tac ss 1)
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                          (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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      fun simp_loop_tac i thm =
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          (asm_rewrite_goal_tac mode solve_all_tac mss i THEN
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           (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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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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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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end;