src/Provers/clasimp.ML
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Simplifier already setup in Pure;
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(*  Title:      Provers/clasimp.ML
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    ID:         $Id$
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    Author:     David von Oheimb, TU Muenchen
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Combination of classical reasoner and simplifier (depends on
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splitter.ML, classical.ML, blast.ML).
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*)
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infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2 addsimps2 delsimps2
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  addSss addss addss' addIffs delIffs;
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signature CLASIMP_DATA =
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sig
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  structure Simplifier: SIMPLIFIER
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  structure Splitter: SPLITTER
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  structure Classical: CLASSICAL
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  structure Blast: BLAST
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  sharing type Classical.claset = Blast.claset
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  val notE: thm
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  val iffD1: thm
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  val iffD2: thm
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  val cla_make_elim: thm -> thm
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end
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signature CLASIMP =
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sig
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  include CLASIMP_DATA
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  type claset
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  type simpset
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  type clasimpset
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  val clasimpset: unit -> clasimpset
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  val addSIs2: clasimpset * thm list -> clasimpset
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  val addSEs2: clasimpset * thm list -> clasimpset
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  val addSDs2: clasimpset * thm list -> clasimpset
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  val addIs2: clasimpset * thm list -> clasimpset
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  val addEs2: clasimpset * thm list -> clasimpset
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  val addDs2: clasimpset * thm list -> clasimpset
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  val addsimps2: clasimpset * thm list -> clasimpset
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  val delsimps2: clasimpset * thm list -> clasimpset
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  val addSss: claset * simpset -> claset
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  val addss: claset * simpset -> claset
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  val addss': claset * simpset -> claset
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  val addIffs: clasimpset * thm list -> clasimpset
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  val delIffs: clasimpset * thm list -> clasimpset
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  val AddIffs: thm list -> unit
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  val DelIffs: thm list -> unit
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  val CLASIMPSET: (clasimpset -> tactic) -> tactic
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  val CLASIMPSET': (clasimpset -> 'a -> tactic) -> 'a -> tactic
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  val clarsimp_tac: clasimpset -> int -> tactic
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  val Clarsimp_tac: int -> tactic
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  val mk_auto_tac: clasimpset -> int -> int -> tactic
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  val auto_tac: clasimpset -> tactic
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  val Auto_tac: tactic
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  val auto: unit -> unit
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  val force_tac: clasimpset  -> int -> tactic
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  val Force_tac: int -> tactic
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  val force: int -> unit
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  val fast_simp_tac: clasimpset -> int -> tactic
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  val slow_simp_tac: clasimpset -> int -> tactic
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  val best_simp_tac: clasimpset -> int -> tactic
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  val change_global_css: (clasimpset * thm list -> clasimpset) -> theory attribute
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  val change_local_css: (clasimpset * thm list -> clasimpset) -> Proof.context attribute
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  val get_local_clasimpset: Proof.context -> clasimpset
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  val local_clasimpset_of: Proof.context -> clasimpset
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  val iff_add_global: theory attribute
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  val iff_add_global': theory attribute
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  val iff_del_global: theory attribute
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  val iff_add_local: Proof.context attribute
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  val iff_add_local': Proof.context attribute
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  val iff_del_local: Proof.context attribute
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  val iff_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list
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  val clasimp_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list
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  val setup: (theory -> theory) list
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end;
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functor ClasimpFun(Data: CLASIMP_DATA): CLASIMP =
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struct
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open Data;
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type claset = Classical.claset;
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type simpset = Simplifier.simpset;
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type clasimpset = claset * simpset;
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fun clasimpset () = (Classical.claset (), Simplifier.simpset ());
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(* clasimpset operations *)
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(*this interface for updating a clasimpset is rudimentary and just for
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  convenience for the most common cases*)
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fun pair_upd1 f ((a,b),x) = (f(a,x), b);
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fun pair_upd2 f ((a,b),x) = (a, f(b,x));
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fun op addSIs2   arg = pair_upd1 Classical.addSIs arg;
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fun op addSEs2   arg = pair_upd1 Classical.addSEs arg;
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fun op addSDs2   arg = pair_upd1 Classical.addSDs arg;
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fun op addIs2    arg = pair_upd1 Classical.addIs arg;
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fun op addEs2    arg = pair_upd1 Classical.addEs arg;
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fun op addDs2    arg = pair_upd1 Classical.addDs arg;
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fun op addsimps2 arg = pair_upd2 Simplifier.addsimps arg;
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fun op delsimps2 arg = pair_upd2 Simplifier.delsimps arg;
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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 = Simplifier.generic_simp_tac true (true,true,true);
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(*Add a simpset to a classical set!*)
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(*Caution: only one simpset added can be added by each of addSss and addss*)
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fun cs addSss ss = Classical.addSafter (cs, ("safe_asm_full_simp_tac",
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                            CHANGED o safe_asm_full_simp_tac ss));
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fun cs addss  ss = Classical.addbefore  (cs, ("asm_full_simp_tac",
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                            CHANGED o Simplifier.asm_full_simp_tac ss));
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fun cs addss' ss = Classical.addbefore  (cs, ("asm_full_simp_tac",
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                            CHANGED o Simplifier.asm_lr_simp_tac ss));
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(* iffs: addition of rules to simpsets and clasets simultaneously *)
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(*Takes (possibly conditional) theorems of the form A<->B to
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        the Safe Intr     rule B==>A and
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        the Safe Destruct rule A==>B.
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  Also ~A goes to the Safe Elim rule A ==> ?R
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  Failing other cases, A is added as a Safe Intr rule*)
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local
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fun addIff decls1 decls2 simp ((cs, ss), th) =
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  let
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    val n = nprems_of th;
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    val (dest, elim, intro) = if n = 0 then decls1 else decls2;
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    val zero_rotate = zero_var_indexes o rotate_prems n;
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  in
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    (dest (intro (cs, [zero_rotate (th RS Data.iffD2)]), [zero_rotate (th RS Data.iffD1)])
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      handle THM _ => (elim (cs, [zero_rotate (th RS Data.notE)])
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        handle THM _ => intro (cs, [th])),
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     simp (ss, [th]))
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  end;
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fun delIff delcs delss ((cs, ss), th) =
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  let val zero_rotate = zero_var_indexes o rotate_prems (nprems_of th) in
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    (delcs (cs, [zero_rotate (th RS Data.iffD2),
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        Data.cla_make_elim (zero_rotate (th RS Data.iffD1))])
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      handle THM _ => (delcs (cs, [zero_rotate (th RS Data.notE)])
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        handle THM _ => delcs (cs, [th])),
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     delss (ss, [th]))
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  end;
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fun store_clasimp (cs, ss) =
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  (Classical.claset_ref () := cs; Simplifier.simpset_ref () := ss);
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in
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val op addIffs =
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  Library.foldl (addIff (Classical.addSDs, Classical.addSEs, Classical.addSIs)
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    (Classical.addDs, Classical.addEs, Classical.addIs) Simplifier.addsimps);
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val op delIffs = Library.foldl (delIff Classical.delrules Simplifier.delsimps);
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fun AddIffs thms = store_clasimp (clasimpset () addIffs thms);
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fun DelIffs thms = store_clasimp (clasimpset () delIffs thms);
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fun addIffs_global (thy, ths) =
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  Library.foldl (addIff
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    (ContextRules.addXDs_global, ContextRules.addXEs_global, ContextRules.addXIs_global)
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    (ContextRules.addXDs_global, ContextRules.addXEs_global, ContextRules.addXIs_global) #1)
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  ((thy, ()), ths) |> #1;
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fun addIffs_local (ctxt, ths) =
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  Library.foldl (addIff
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    (ContextRules.addXDs_local, ContextRules.addXEs_local, ContextRules.addXIs_local)
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    (ContextRules.addXDs_local, ContextRules.addXEs_local, ContextRules.addXIs_local) #1)
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  ((ctxt, ()), ths) |> #1;
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fun delIffs_global (thy, ths) =
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  Library.foldl (delIff ContextRules.delrules_global #1) ((thy, ()), ths) |> #1;
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fun delIffs_local (ctxt, ths) =
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  Library.foldl (delIff ContextRules.delrules_local #1) ((ctxt, ()), ths) |> #1;
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end;
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(* tacticals *)
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fun CLASIMPSET tacf state =
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  Classical.CLASET (fn cs => Simplifier.SIMPSET (fn ss => tacf (cs, ss))) state;
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fun CLASIMPSET' tacf i state =
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  Classical.CLASET (fn cs => Simplifier.SIMPSET (fn ss => tacf (cs, ss) i)) state;
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fun clarsimp_tac (cs, ss) =
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  safe_asm_full_simp_tac ss THEN_ALL_NEW
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  Classical.clarify_tac (cs addSss ss);
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fun Clarsimp_tac i = clarsimp_tac (clasimpset ()) i;
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(* auto_tac *)
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fun blast_depth_tac cs m i thm =
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    Blast.depth_tac cs m i thm
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      handle Blast.TRANS s => (warning ("Blast_tac: " ^ s); Seq.empty);
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(* a variant of depth_tac that avoids interference of the simplifier
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   with dup_step_tac when they are combined by auto_tac *)
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local
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fun slow_step_tac' cs = Classical.appWrappers cs
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        (Classical.instp_step_tac cs APPEND' Classical.haz_step_tac cs);
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in fun nodup_depth_tac cs m i state = SELECT_GOAL
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   (Classical.safe_steps_tac cs 1 THEN_ELSE
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        (DEPTH_SOLVE (nodup_depth_tac cs m 1),
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         Classical.inst0_step_tac cs 1 APPEND COND (K (m=0)) no_tac
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             (slow_step_tac' cs 1 THEN DEPTH_SOLVE (nodup_depth_tac cs (m-1) 1))
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        )) i state;
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end;
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(*Designed to be idempotent, except if blast_depth_tac instantiates variables
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  in some of the subgoals*)
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fun mk_auto_tac (cs, ss) m n =
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    let val cs' = cs addss ss
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        val maintac =
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          blast_depth_tac cs m               (* fast but can't use wrappers *)
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          ORELSE'
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          (CHANGED o nodup_depth_tac cs' n); (* slower but more general *)
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    in  EVERY [ALLGOALS (Simplifier.asm_full_simp_tac ss),
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               TRY (Classical.safe_tac cs),
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               REPEAT (FIRSTGOAL maintac),
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               TRY (Classical.safe_tac (cs addSss ss)),
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               prune_params_tac]
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    end;
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fun auto_tac css = mk_auto_tac css 4 2;
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fun Auto_tac st = auto_tac (clasimpset ()) st;
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fun auto () = by Auto_tac;
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(* force_tac *)
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(* aimed to solve the given subgoal totally, using whatever tools possible *)
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fun force_tac (cs,ss) = let val cs' = cs addss ss in SELECT_GOAL (EVERY [
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        Classical.clarify_tac cs' 1,
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        IF_UNSOLVED (Simplifier.asm_full_simp_tac ss 1),
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        ALLGOALS (Classical.first_best_tac cs')]) end;
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fun Force_tac i = force_tac (clasimpset ()) i;
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fun force i = by (Force_tac i);
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(* basic combinations *)
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fun ADDSS tac (cs, ss) = let val cs' = cs addss ss in tac cs' end;
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val fast_simp_tac = ADDSS Classical.fast_tac;
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val slow_simp_tac = ADDSS Classical.slow_tac;
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val best_simp_tac = ADDSS Classical.best_tac;
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(* access clasimpset *)
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fun change_global_css f (thy, th) =
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  let
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    val cs_ref = Classical.claset_ref_of thy;
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    val ss_ref = Simplifier.simpset_ref_of thy;
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    val (cs', ss') = f ((! cs_ref, ! ss_ref), [th]);
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  in cs_ref := cs'; ss_ref := ss'; (thy, th) end;
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fun change_local_css f (ctxt, th) =
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  let
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    val cs = Classical.get_local_claset ctxt;
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    val ss = Simplifier.get_local_simpset ctxt;
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    val (cs', ss') = f ((cs, ss), [th]);
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    val ctxt' =
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      ctxt
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      |> Classical.put_local_claset cs'
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      |> Simplifier.put_local_simpset ss';
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  in (ctxt', th) end;
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fun get_local_clasimpset ctxt =
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  (Classical.get_local_claset ctxt, Simplifier.get_local_simpset ctxt);
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fun local_clasimpset_of ctxt =
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  (Classical.local_claset_of ctxt, Simplifier.local_simpset_of ctxt);
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(* attributes *)
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fun change_rules f (x, th) = (f (x, [th]), th);
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val iff_add_global = change_global_css (op addIffs);
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val iff_add_global' = change_rules addIffs_global;
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val iff_del_global = change_global_css (op delIffs) o change_rules delIffs_global;
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val iff_add_local = change_local_css (op addIffs);
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val iff_add_local' = change_rules addIffs_local;
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val iff_del_local = change_local_css (op delIffs) o change_rules delIffs_local;
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fun iff_att add add' del = Attrib.syntax (Scan.lift
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 (Args.del >> K del ||
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  Scan.option Args.add -- Args.query >> K add' ||
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  Scan.option Args.add >> K add));
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val iff_attr =
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 (iff_att iff_add_global iff_add_global' iff_del_global,
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  iff_att iff_add_local iff_add_local' iff_del_local);
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(* method modifiers *)
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val iffN = "iff";
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val iff_modifiers =
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 [Args.$$$ iffN -- Scan.option Args.add -- Args.colon >> K ((I, iff_add_local): Method.modifier),
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  Args.$$$ iffN -- Scan.option Args.add -- Args.query_colon >> K (I, iff_add_local'),
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  Args.$$$ iffN -- Args.del -- Args.colon >> K (I, iff_del_local)];
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val clasimp_modifiers =
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  Simplifier.simp_modifiers @ Splitter.split_modifiers @
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  Classical.cla_modifiers @ iff_modifiers;
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(* methods *)
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fun clasimp_meth tac prems ctxt = Method.METHOD (fn facts =>
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  ALLGOALS (Method.insert_tac (prems @ facts)) THEN tac (local_clasimpset_of ctxt));
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fun clasimp_meth' tac prems ctxt = Method.METHOD (fn facts =>
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  HEADGOAL (Method.insert_tac (prems @ facts) THEN' tac (local_clasimpset_of ctxt)));
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val clasimp_method = Method.bang_sectioned_args clasimp_modifiers o clasimp_meth;
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val clasimp_method' = Method.bang_sectioned_args clasimp_modifiers o clasimp_meth';
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fun auto_args m =
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  Method.bang_sectioned_args' clasimp_modifiers (Scan.lift (Scan.option (Args.nat -- Args.nat))) m;
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fun auto_meth NONE = clasimp_meth (CHANGED_PROP o auto_tac)
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  | auto_meth (SOME (m, n)) = clasimp_meth (CHANGED_PROP o (fn css => mk_auto_tac css m n));
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(* theory setup *)
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val setup =
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 [Attrib.add_attributes
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  [("iff", iff_attr, "declaration of Simplifier / Classical rules")],
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  Method.add_methods
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   [("fastsimp", clasimp_method' fast_simp_tac, "combined fast and simp"),
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    ("slowsimp", clasimp_method' slow_simp_tac, "combined slow and simp"),
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    ("bestsimp", clasimp_method' best_simp_tac, "combined best and simp"),
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    ("force", clasimp_method' force_tac, "force"),
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    ("auto", auto_args auto_meth, "auto"),
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    ("clarsimp", clasimp_method' (CHANGED_PROP oo clarsimp_tac), "clarify simplified goal")]];
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end;