src/Provers/simplifier.ML
author wenzelm
Mon, 16 Nov 1998 11:10:00 +0100
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all modifiers turned into attributes; realistic method syntax; smart_simp method;
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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.  See Pure/thm.ML for the
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actual meta-level rewriting engine.
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*)
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infix 4
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  setsubgoaler setloop addloop delloop setSSolver addSSolver setSolver
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  addSolver addsimps delsimps addeqcongs deleqcongs
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  setmksimps setmkeqTrue setmksym settermless addsimprocs delsimprocs;
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signature BASIC_SIMPLIFIER =
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sig
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  type simproc
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  val mk_simproc: string -> cterm list
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    -> (Sign.sg -> thm list -> term -> thm option) -> simproc
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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_tacs:          (string * (int -> tactic))list,
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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 print_simpset: theory -> 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 *  (string * (int -> tactic)) -> simpset
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  val delloop:      simpset *   string                    -> 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 setmkeqTrue:  simpset * (thm -> thm option) -> simpset
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  val setmksym:     simpset * (thm -> thm option) -> 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_ref_of_sg: Sign.sg -> simpset ref
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  val simpset_ref_of: theory -> simpset ref
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  val simpset_of_sg: Sign.sg -> simpset
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  val simpset_of: theory -> simpset
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  val SIMPSET: (simpset -> tactic) -> tactic
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  val SIMPSET': (simpset -> 'a -> tactic) -> 'a -> tactic
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  val simpset: unit -> simpset
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  val simpset_ref: unit -> 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_lr_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_lr_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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signature SIMPLIFIER =
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sig
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  include BASIC_SIMPLIFIER
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  val          rewrite: simpset -> cterm -> thm
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  val      asm_rewrite: simpset -> cterm -> thm
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  val     full_rewrite: simpset -> cterm -> thm
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  val asm_full_rewrite: simpset -> cterm -> thm
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  val print_local_simpset: Proof.context -> unit
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  val get_local_simpset: Proof.context -> simpset
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  val put_local_simpset: simpset -> Proof.context -> Proof.context
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  val simp_add_global: theory attribute
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  val simp_del_global: theory attribute
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  val simp_add_local: Proof.context attribute
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  val simp_del_local: Proof.context attribute
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  val setup: (theory -> theory) list
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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 -> thm list -> 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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(** 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_tacs:          (string * (int -> tactic))list,
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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_tacs, finish_tac, unsafe_finish_tac) =
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  Simpset {mss = mss, subgoal_tac = subgoal_tac, loop_tacs = loop_tacs,
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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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  let val mss = Thm.set_mk_sym(Thm.empty_mss, Some o symmetric_fun)
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  in make_ss (mss, K (K no_tac), [], K (K no_tac), K (K no_tac)) end;
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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_tacs, finish_tac, unsafe_finish_tac})
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    setsubgoaler subgoal_tac =
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  make_ss (mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs = _, finish_tac, unsafe_finish_tac})
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    setloop tac =
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  make_ss (mss, subgoal_tac, [("",tac)], finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    addloop tac = make_ss (mss, subgoal_tac, 
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        (case assoc_string (loop_tacs,(fst tac)) of None => () | Some x => 
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         warning ("overwriting looper "^fst tac); overwrite(loop_tacs,tac)),
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           finish_tac, unsafe_finish_tac);
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fun (ss as Simpset {mss,subgoal_tac,loop_tacs,finish_tac,unsafe_finish_tac})
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    delloop name =
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  let val (del,rest) = partition (fn (n,_) => n=name) loop_tacs
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  in if null del then (warning ("No such looper in simpset: " ^ name); ss)
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     else make_ss (mss, subgoal_tac, rest, finish_tac, unsafe_finish_tac)
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  end;
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac = _, unsafe_finish_tac})
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    setSSolver finish_tac =
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  make_ss (mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    addSSolver tac =
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  make_ss (mss, subgoal_tac, loop_tacs, 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_tacs, finish_tac, unsafe_finish_tac = _})
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    setSolver unsafe_finish_tac =
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  make_ss (mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    addSolver tac =
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  make_ss (mss, subgoal_tac, loop_tacs, 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_tacs, 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_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    setmkeqTrue mk_eq_True =
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  make_ss (Thm.set_mk_eq_True (mss, mk_eq_True),
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    subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    setmksym mksym =
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  make_ss (Thm.set_mk_sym (mss, mksym),
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    subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs,  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_tacs,
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    finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    addsimps rews =
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  make_ss (Thm.add_simps (mss, rews), subgoal_tac, loop_tacs,
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           finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    delsimps rews =
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  make_ss (Thm.del_simps (mss, rews), subgoal_tac, loop_tacs,
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           finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, 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_tacs,
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    finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, 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_tacs,
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    finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, 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_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, 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_tacs, finish_tac, unsafe_finish_tac);
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(* merge simpsets *)    (*NOTE: ignores tactics of 2nd simpset (except loopers)*)
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fun merge_ss
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   (Simpset {mss = mss1, loop_tacs = loop_tacs1, subgoal_tac, finish_tac, unsafe_finish_tac},
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    Simpset {mss = mss2, loop_tacs = loop_tacs2, ...}) =
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  make_ss (Thm.merge_mss (mss1, mss2), subgoal_tac,
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    merge_alists loop_tacs1 loop_tacs2, finish_tac, unsafe_finish_tac);
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(** global and local simpset data **)
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(* theory data kind 'Provers/simpset' *)
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structure GlobalSimpsetArgs =
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struct
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  val name = "Provers/simpset";
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  type T = simpset ref;
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  val empty = ref empty_ss;
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  fun prep_ext (ref ss) = (ref ss): T;            (*create new reference!*)
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  fun merge (ref ss1, ref ss2) = ref (merge_ss (ss1, ss2));
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  fun print _ (ref ss) = print_ss ss;
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end;
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structure GlobalSimpset = TheoryDataFun(GlobalSimpsetArgs);
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val print_simpset = GlobalSimpset.print;
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val simpset_ref_of_sg = GlobalSimpset.get_sg;
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val simpset_ref_of = GlobalSimpset.get;
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(* access global simpset *)
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val simpset_of_sg = ! o simpset_ref_of_sg;
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val simpset_of = simpset_of_sg o sign_of;
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fun SIMPSET tacf state = tacf (simpset_of_sg (sign_of_thm state)) state;
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fun SIMPSET' tacf i state = tacf (simpset_of_sg (sign_of_thm state)) i state;
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val simpset = simpset_of o Context.the_context;
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val simpset_ref = simpset_ref_of_sg o sign_of o Context.the_context;
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(* change global simpset *)
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fun change_simpset f x = simpset_ref () := (f (simpset (), x));
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val Addsimps = change_simpset (op addsimps);
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val Delsimps = change_simpset (op delsimps);
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val Addsimprocs = change_simpset (op addsimprocs);
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val Delsimprocs = change_simpset (op delsimprocs);
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(* proof data kind 'Provers/simpset' *)
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structure LocalSimpsetArgs =
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struct
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  val name = "Provers/simpset";
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  type T = simpset;
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  val init = simpset_of;
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  fun print _ ss = print_ss ss;
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end;
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structure LocalSimpset = ProofDataFun(LocalSimpsetArgs);
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val print_local_simpset = LocalSimpset.print;
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val get_local_simpset = LocalSimpset.get;
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val put_local_simpset = LocalSimpset.put;
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(* attributes *)
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fun change_global_ss f (thy, th) =
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  let val r = simpset_ref_of thy
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  in r := f (! r, [Attribute.thm_of th]); (thy, th) end;
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fun change_local_ss f (ctxt, th) =
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  let val ss = f (get_local_simpset ctxt, [Attribute.thm_of th])
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  in (put_local_simpset ss ctxt, th) end;
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val simp_add_global = change_global_ss (op addsimps);
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val simp_del_global = change_global_ss (op delsimps);
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val simp_add_local = change_local_ss (op addsimps);
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val simp_del_local = change_local_ss (op delsimps);
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(** simplification tactics **)
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fun solve_all_tac (subgoal_tac, loop_tacs, 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_tacs, unsafe_finish_tac, unsafe_finish_tac);
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    val solve1_tac = (subgoal_tac ss THEN_ALL_NEW (K no_tac)) 1
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  in DEPTH_SOLVE solve1_tac end;
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fun loop_tac loop_tacs = FIRST'(map snd loop_tacs);
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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_tacs, finish_tac, unsafe_finish_tac}) =>
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    let
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      fun simp_loop_tac i =
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        asm_rewrite_goal_tac mode
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          (solve_all_tac (subgoal_tac,loop_tacs,finish_tac,unsafe_finish_tac))
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          mss i
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        THEN (finish_tac (prems_of_mss mss) i ORELSE
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              TRY ((loop_tac loop_tacs THEN_ALL_NEW simp_loop_tac) 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, false);
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val      asm_simp_tac = gen_simp_tac (false, true, false);
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val     full_simp_tac = gen_simp_tac (true,  false, false);
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val   asm_lr_simp_tac = gen_simp_tac (true,  true, false);
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val asm_full_simp_tac = gen_simp_tac (true,  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, false);
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(*the abstraction over the proof state delays the dereferencing*)
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fun          Simp_tac i st =          simp_tac (simpset ()) i st;
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fun      Asm_simp_tac i st =      asm_simp_tac (simpset ()) i st;
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fun     Full_simp_tac i st =     full_simp_tac (simpset ()) i st;
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fun   Asm_lr_simp_tac i st =   asm_lr_simp_tac (simpset ()) i st;
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fun Asm_full_simp_tac i st = asm_full_simp_tac (simpset ()) i st;
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(** simplification rules and conversions **)
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fun simp rew mode (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) thm =
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  let
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    val tacf = solve_all_tac (subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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    fun prover m th = apsome fst (Seq.pull (tacf m th));
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  in rew mode prover mss thm end;
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val simp_thm = simp Drule.rewrite_thm;
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val simp_cterm = simp Drule.rewrite_cterm;
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val          simplify = simp_thm (false, false, false);
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val      asm_simplify = simp_thm (false, true, false);
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val     full_simplify = simp_thm (true, false, false);
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val asm_full_simplify = simp_thm (true, true, false);
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val          rewrite = simp_cterm (false, false, false);
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val      asm_rewrite = simp_cterm (false, true, false);
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val     full_rewrite = simp_cterm (true, false, false);
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val asm_full_rewrite = simp_cterm (true, true, false);
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9546f8185c43 added simplification meta rules;
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(** concrete syntax of attributes **)
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(* add / del *)
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   404
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   405
val simp_addN = "add";
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   406
val simp_delN = "del";
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val simp_ignoreN = "other";
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   408
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   409
fun simp_att change =
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   410
  (Args.$$$ simp_addN >> K (op addsimps) ||
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   411
    Args.$$$ simp_delN >> K (op delsimps) ||
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   412
    Scan.succeed (op addsimps))
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   413
  >> change
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   414
  |> Scan.lift
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   415
  |> Attrib.syntax;
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val simp_attr = (simp_att change_global_ss, simp_att change_local_ss);
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1a708aa63ff0 local simpset theory data;
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   420
(* conversions *)
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   421
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   422
fun conv_attr f =
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   423
  (Attrib.no_args (Attribute.rule (f o simpset_of)),
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   424
    Attrib.no_args (Attribute.rule (f o get_local_simpset)));
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1a708aa63ff0 local simpset theory data;
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(* setup_attrs *)
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   428
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   429
val setup_attrs = Attrib.add_attributes
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   430
 [("simp",              simp_attr, "simplification rule"),
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   431
  ("simplify",          conv_attr simplify, "simplify rule"),
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   432
  ("asm_simplify",      conv_attr asm_simplify, "simplify rule, using assumptions"),
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   433
  ("full_simplify",     conv_attr full_simplify, "fully simplify rule"),
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   434
  ("asm_full_simplify", conv_attr asm_full_simplify, "fully simplify rule, using assumptions")];
1a708aa63ff0 local simpset theory data;
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1a708aa63ff0 local simpset theory data;
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diff changeset
   436
1a708aa63ff0 local simpset theory data;
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   437
1a708aa63ff0 local simpset theory data;
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   438
(** proof methods **)
1a708aa63ff0 local simpset theory data;
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diff changeset
   439
1a708aa63ff0 local simpset theory data;
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   440
(* simplification *)
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   441
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   442
val simp_args =
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   443
  Method.only_sectioned_args
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   444
   [Args.$$$ simp_addN >> K simp_add_local,
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   445
    Args.$$$ simp_delN >> K simp_del_local,
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   446
    Args.$$$ simp_ignoreN >> K I];
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   447
5886
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   448
fun simp_meth tac ctxt = Method.METHOD (fn facts =>
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   449
  FIRSTGOAL (REPEAT_DETERM o etac Drule.thin_rl THEN'
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diff changeset
   450
    metacuts_tac (Attribute.thms_of facts) THEN'
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   451
    tac (get_local_simpset ctxt)));
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   452
5886
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val simp_method = simp_args o simp_meth;
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1a708aa63ff0 local simpset theory data;
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(* setup_methods *)
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val setup_methods = Method.add_methods
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 [("simp",              simp_method asm_full_simp_tac, "simplification"),
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  ("simp_tac",          simp_method simp_tac, "simp_tac"),
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  ("asm_simp_tac",      simp_method asm_simp_tac, "asm_simp_tac"),
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   462
  ("full_simp_tac",     simp_method full_simp_tac, "full_simp_tac"),
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  ("asm_full_simp_tac", simp_method asm_full_simp_tac, "asm_full_simp_tac"),
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  ("asm_lr_simp_tac",   simp_method asm_lr_simp_tac, "asm_lr_simp_tac")];
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1a708aa63ff0 local simpset theory data;
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4795
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(** theory setup **)
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val setup = [GlobalSimpset.init, LocalSimpset.init, setup_attrs, setup_methods];
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end;
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structure BasicSimplifier: BASIC_SIMPLIFIER = Simplifier;
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open BasicSimplifier;