(*  Title:      Provers/clasimp.ML

     ID:         $Id$

     Author:     David von Oheimb, TU Muenchen

 Combination of classical reasoner and simplifier (depends on

 simplifier.ML, splitter.ML classical.ML, blast.ML).

 *)

 infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2 addsimps2 delsimps2

   addSss addss addIffs delIffs;

 signature CLASIMP_DATA =

 sig

   structure Simplifier: SIMPLIFIER

   structure Splitter: SPLITTER

   structure Classical: CLASSICAL

   structure Blast: BLAST

   sharing type Classical.claset = Blast.claset

   val dest_Trueprop: term -> term

   val not_const: term

   val iff_const: term

   val notE: thm

   val iffD1: thm

   val iffD2: thm

   val cla_make_elim: thm -> thm

 end

 signature CLASIMP =

 sig

   include CLASIMP_DATA

   type claset

   type simpset

   type clasimpset

   val addSIs2: clasimpset * thm list -> clasimpset

   val addSEs2: clasimpset * thm list -> clasimpset

   val addSDs2: clasimpset * thm list -> clasimpset

   val addIs2: clasimpset * thm list -> clasimpset

   val addEs2: clasimpset * thm list -> clasimpset

   val addDs2: clasimpset * thm list -> clasimpset

   val addsimps2: clasimpset * thm list -> clasimpset

   val delsimps2: clasimpset * thm list -> clasimpset

   val addSss: claset * simpset -> claset

   val addss: claset * simpset -> claset

   val addIffs: clasimpset * thm list -> clasimpset

   val delIffs: clasimpset * thm list -> clasimpset

   val AddIffs: thm list -> unit

   val DelIffs: thm list -> unit

   val CLASIMPSET: (clasimpset -> tactic) -> tactic

   val CLASIMPSET': (clasimpset -> 'a -> tactic) -> 'a -> tactic

   val clarsimp_tac: clasimpset -> int -> tactic

   val Clarsimp_tac: int -> tactic

   val mk_auto_tac: clasimpset -> int -> int -> tactic

   val auto_tac: clasimpset -> tactic

   val Auto_tac: tactic

   val auto: unit -> unit

   val force_tac: clasimpset  -> int -> tactic

   val Force_tac: int -> tactic

   val force: int -> unit

   val fast_simp_tac: clasimpset -> int -> tactic

   val slow_simp_tac: clasimpset -> int -> tactic

   val best_simp_tac: clasimpset -> int -> tactic

   val change_global_css: (clasimpset * thm list -> clasimpset) -> theory attribute

   val change_local_css: (clasimpset * thm list -> clasimpset) -> Proof.context attribute

   val get_local_clasimpset: Proof.context -> clasimpset

   val iff_add_global: theory attribute

   val iff_del_global: theory attribute

   val iff_add_local: Proof.context attribute

   val iff_del_local: Proof.context attribute

   val iff_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list

   val clasimp_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list

   val setup: (theory -> theory) list

 end;

 functor ClasimpFun(Data: CLASIMP_DATA): CLASIMP =

 struct

 open Data;

 type claset = Classical.claset;

 type simpset = Simplifier.simpset;

 type clasimpset = claset * simpset;

 (* clasimpset operations *)

 (*this interface for updating a clasimpset is rudimentary and just for

   convenience for the most common cases*)

 fun pair_upd1 f ((a,b),x) = (f(a,x), b);

 fun pair_upd2 f ((a,b),x) = (a, f(b,x));

 fun op addSIs2   arg = pair_upd1 Classical.addSIs arg;

 fun op addSEs2   arg = pair_upd1 Classical.addSEs arg;

 fun op addSDs2   arg = pair_upd1 Classical.addSDs arg;

 fun op addIs2    arg = pair_upd1 Classical.addIs arg;

 fun op addEs2    arg = pair_upd1 Classical.addEs arg;

 fun op addDs2    arg = pair_upd1 Classical.addDs arg;

 fun op addsimps2 arg = pair_upd2 Simplifier.addsimps arg;

 fun op delsimps2 arg = pair_upd2 Simplifier.delsimps arg;

 (*not totally safe: may instantiate unknowns that appear also in other subgoals*)

 val safe_asm_full_simp_tac = Simplifier.generic_simp_tac true (true,true,true);

 (*Add a simpset to a classical set!*)

 (*Caution: only one simpset added can be added by each of addSss and addss*)

 fun cs addSss ss = Classical.addSaltern (cs, ("safe_asm_full_simp_tac",

                             CHANGED o safe_asm_full_simp_tac ss));

 fun cs addss  ss = Classical.addbefore  (cs, ("asm_full_simp_tac",

                             CHANGED o Simplifier.asm_full_simp_tac ss));

 (* iffs: addition of rules to simpsets and clasets simultaneously *)

 (*Takes UNCONDITIONAL theorems of the form A<->B to

         the Safe Intr     rule B==>A and

         the Safe Destruct rule A==>B.

   Also ~A goes to the Safe Elim rule A ==> ?R

   Failing other cases, A is added as a Safe Intr rule*)

 local

 fun addIff ((cla, simp), th) =

   (case dest_Trueprop (#prop (rep_thm th)) of

     con $ _ $ _ =>

       if con = Data.iff_const then

         Classical.addSDs (Classical.addSIs (cla, [zero_var_indexes (th RS Data.iffD2)]),

           [zero_var_indexes (th RS Data.iffD1)])

       else Classical.addSIs (cla, [th])

   | con $ A =>

       if con = Data.not_const then Classical.addSEs (cla, [zero_var_indexes (th RS Data.notE)])

       else Classical.addSIs (cla, [th])

   | _ => Classical.addSIs (cla, [th]), Simplifier.addsimps (simp, [th]))

   handle TERM _ => error ("iff add: theorem must be unconditional\n" ^ Display.string_of_thm th);

 fun delIff ((cla, simp), th) =

   (case dest_Trueprop (#prop (rep_thm th)) of

     con $ _ $ _ =>

       if con = Data.iff_const then

         Classical.delrules (cla, [zero_var_indexes (th RS Data.iffD2),

           Data.cla_make_elim (zero_var_indexes (th RS Data.iffD1))])

       else Classical.delrules (cla, [th])

   | con $ A =>

       if con = Data.not_const then Classical.delrules (cla, [zero_var_indexes (th RS Data.notE)])

       else Classical.delrules (cla, [th])

   | _ => Classical.delrules (cla, [th]), Simplifier.delsimps (simp, [th]))

   handle TERM _ =>

     (warning ("iff del: ignoring conditional theorem\n" ^ string_of_thm th); (cla, simp));

 fun store_clasimp (cla, simp) =

   (Classical.claset_ref () := cla; Simplifier.simpset_ref () := simp);

 in

 val op addIffs = foldl addIff;

 val op delIffs = foldl delIff;

 fun AddIffs thms = store_clasimp ((Classical.claset (), Simplifier.simpset ()) addIffs thms);

 fun DelIffs thms = store_clasimp ((Classical.claset (), Simplifier.simpset ()) delIffs thms);

 end;

 (* tacticals *)

 fun CLASIMPSET tacf state =

   Classical.CLASET (fn cs => Simplifier.SIMPSET (fn ss => tacf (cs, ss))) state;

 fun CLASIMPSET' tacf i state =

   Classical.CLASET (fn cs => Simplifier.SIMPSET (fn ss => tacf (cs, ss) i)) state;

 fun clarsimp_tac (cs, ss) = safe_asm_full_simp_tac ss THEN_ALL_NEW

                             Classical.clarify_tac (cs addSss ss);

 fun Clarsimp_tac i = clarsimp_tac (Classical.claset(), Simplifier.simpset()) i;

 (* auto_tac *)

 fun blast_depth_tac cs m i thm =

     Blast.depth_tac cs m i thm

       handle Blast.TRANS s => (warning ("Blast_tac: " ^ s); Seq.empty);

 (* a variant of depth_tac that avoids interference of the simplifier

    with dup_step_tac when they are combined by auto_tac *)

 local

 fun slow_step_tac' cs = Classical.appWrappers cs

         (Classical.instp_step_tac cs APPEND' Classical.haz_step_tac cs);

 in fun nodup_depth_tac cs m i state = SELECT_GOAL

    (Classical.safe_steps_tac cs 1 THEN_ELSE

         (DEPTH_SOLVE (nodup_depth_tac cs m 1),

          Classical.inst0_step_tac cs 1 APPEND COND (K (m=0)) no_tac

              (slow_step_tac' cs 1 THEN DEPTH_SOLVE (nodup_depth_tac cs (m-1) 1))

         )) i state;

 end;

 (*Designed to be idempotent, except if blast_depth_tac instantiates variables

   in some of the subgoals*)

 fun mk_auto_tac (cs, ss) m n =

     let val cs' = cs addss ss

         val maintac =

           blast_depth_tac cs m               (* fast but can't use wrappers *)

           ORELSE'

           (CHANGED o nodup_depth_tac cs' n); (* slower but more general *)

     in  EVERY [ALLGOALS (Simplifier.asm_full_simp_tac ss),

                TRY (Classical.safe_tac cs),

                REPEAT (FIRSTGOAL maintac),

                TRY (Classical.safe_tac (cs addSss ss)),

                prune_params_tac]

     end;

 fun auto_tac css = mk_auto_tac css 4 2;

 fun Auto_tac st = auto_tac (Classical.claset(), Simplifier.simpset()) st;

 fun auto () = by Auto_tac;

 (* force_tac *)

 (* aimed to solve the given subgoal totally, using whatever tools possible *)

 fun force_tac (cs,ss) = let val cs' = cs addss ss in SELECT_GOAL (EVERY [

         Classical.clarify_tac cs' 1,

         IF_UNSOLVED (Simplifier.asm_full_simp_tac ss 1),

         ALLGOALS (Classical.first_best_tac cs')]) end;

 fun Force_tac i = force_tac (Classical.claset(), Simplifier.simpset()) i;

 fun force i = by (Force_tac i);

 (* basic combinations *)

 fun ADDSS tac (cs, ss) = let val cs' = cs addss ss in tac cs' end;

 val fast_simp_tac = ADDSS Classical.fast_tac;

 val slow_simp_tac = ADDSS Classical.slow_tac;

 val best_simp_tac = ADDSS Classical.best_tac;

 (* access clasimpset *)

 fun change_global_css f (thy, th) =

   let

     val cs_ref = Classical.claset_ref_of thy;

     val ss_ref = Simplifier.simpset_ref_of thy;

     val (cs', ss') = f ((! cs_ref, ! ss_ref), [th]);

   in cs_ref := cs'; ss_ref := ss'; (thy, th) end;

 fun change_local_css f (ctxt, th) =

   let

     val cs = Classical.get_local_claset ctxt;

     val ss = Simplifier.get_local_simpset ctxt;

     val (cs', ss') = f ((cs, ss), [th]);

     val ctxt' =

       ctxt

       |> Classical.put_local_claset cs'

       |> Simplifier.put_local_simpset ss';

   in (ctxt', th) end;

 fun get_local_clasimpset ctxt =

   (Classical.get_local_claset ctxt, Simplifier.get_local_simpset ctxt);

 (* attributes *)

 val iff_add_global = change_global_css (op addIffs);

 val iff_del_global = change_global_css (op delIffs);

 val iff_add_local = change_local_css (op addIffs);

 val iff_del_local = change_local_css (op delIffs);

 val iff_attr =

  (Attrib.add_del_args iff_add_global iff_del_global,

   Attrib.add_del_args iff_add_local iff_del_local);

 (* method modifiers *)

 val iffN = "iff";

 val iff_modifiers =

  [Args.$$$ iffN -- Args.colon >> K ((I, iff_add_local): Method.modifier),

   Args.$$$ iffN -- Args.$$$ Args.addN -- Args.colon >> K (I, iff_add_local),

   Args.$$$ iffN -- Args.$$$ Args.delN -- Args.colon >> K (I, iff_del_local)];

 val clasimp_modifiers =

   Simplifier.simp_modifiers @ Splitter.split_modifiers @

   Classical.cla_modifiers @ iff_modifiers;

 (* methods *)

 fun clasimp_meth tac prems ctxt = Method.METHOD (fn facts =>

   ALLGOALS (Method.insert_tac (prems @ facts)) THEN tac (get_local_clasimpset ctxt));

 fun clasimp_meth' tac prems ctxt = Method.METHOD (fn facts =>

   HEADGOAL (Method.insert_tac (prems @ facts) THEN' tac (get_local_clasimpset ctxt)));

 val clasimp_method = Method.bang_sectioned_args clasimp_modifiers o clasimp_meth;

 val clasimp_method' = Method.bang_sectioned_args clasimp_modifiers o clasimp_meth';

 fun auto_args m =

   Method.bang_sectioned_args' clasimp_modifiers (Scan.lift (Scan.option (Args.nat -- Args.nat))) m;

 fun auto_meth None = clasimp_meth (CHANGED o auto_tac)

   | auto_meth (Some (m, n)) = clasimp_meth (CHANGED o (fn css => mk_auto_tac css m n));

 (* theory setup *)

 val setup =

  [Attrib.add_attributes

   [("iff", iff_attr, "declaration of Simplifier / Classical rules")],

   Method.add_methods

    [("fastsimp", clasimp_method' fast_simp_tac, "combined fast and simp"),

     ("slowsimp", clasimp_method' slow_simp_tac, "combined slow and simp"),

     ("bestsimp", clasimp_method' best_simp_tac, "combined best and simp"),

     ("force", clasimp_method' force_tac, "force"),

     ("auto", auto_args auto_meth, "auto"),

     ("clarsimp", clasimp_method' (CHANGED oo clarsimp_tac), "clarify simplified goal")]];

 end;