(*  Title:      Provers/clasimp.ML

     Author:     David von Oheimb, TU Muenchen

 Combination of classical reasoner and simplifier (depends on

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

 *)

 infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2 addsimps2 delsimps2

   addSss addss addss' addIffs delIffs;

 signature CLASIMP_DATA =

 sig

   structure Splitter: SPLITTER

   structure Classical: CLASSICAL

   structure Blast: BLAST

   sharing type Classical.claset = Blast.claset

   val notE: thm

   val iffD1: thm

   val iffD2: thm

 end

 signature CLASIMP =

 sig

   include CLASIMP_DATA

   type claset

   type clasimpset

   val get_css: Context.generic -> clasimpset

   val map_css: (clasimpset -> clasimpset) -> Context.generic -> Context.generic

   val change_clasimpset: (clasimpset -> clasimpset) -> unit

   val clasimpset: unit -> clasimpset

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

   val iff_add: attribute

   val iff_add': attribute

   val iff_del: 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 clasimp_setup: theory -> theory

 end;

 functor ClasimpFun(Data: CLASIMP_DATA): CLASIMP =

 struct

 open Data;

 (* type clasimpset *)

 type claset = Classical.claset;

 type clasimpset = claset * simpset;

 fun get_css context = (Classical.get_cs context, Simplifier.get_ss context);

 fun map_css f context =

   let val (cs', ss') = f (get_css context)

   in context |> Classical.map_cs (K cs') |> Simplifier.map_ss (K ss') end;

 fun change_clasimpset f = Context.>> (fn context => (Context.the_theory context; map_css f context));

 fun clasimpset () = (Classical.claset (), Simplifier.simpset ());

 fun local_clasimpset_of ctxt =

   (Classical.local_claset_of ctxt, Simplifier.local_simpset_of ctxt);

 (* 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.addSafter (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));

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

                             CHANGED o Simplifier.asm_lr_simp_tac ss));

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

 (*Takes (possibly conditional) 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 decls1 decls2 simp ((cs, ss), th) =

   let

     val n = nprems_of th;

     val (elim, intro) = if n = 0 then decls1 else decls2;

     val zero_rotate = zero_var_indexes o rotate_prems n;

   in

     (elim (intro (cs, [zero_rotate (th RS iffD2)]),

            [Tactic.make_elim (zero_rotate (th RS iffD1))])

       handle THM _ => (elim (cs, [zero_rotate (th RS notE)])

         handle THM _ => intro (cs, [th])),

      simp (ss, [th]))

   end;

 fun delIff delcs delss ((cs, ss), th) =

   let val zero_rotate = zero_var_indexes o rotate_prems (nprems_of th) in

     (delcs (cs, [zero_rotate (th RS iffD2),

         Tactic.make_elim (zero_rotate (th RS iffD1))])

       handle THM _ => (delcs (cs, [zero_rotate (th RS notE)])

         handle THM _ => delcs (cs, [th])),

      delss (ss, [th]))

   end;

 fun modifier att (x, ths) =

   fst (Library.foldl_map (Library.apply [att]) (x, rev ths));

 val addXIs = modifier (ContextRules.intro_query NONE);

 val addXEs = modifier (ContextRules.elim_query NONE);

 val addXDs = modifier (ContextRules.dest_query NONE);

 val delXs = modifier ContextRules.rule_del;

 in

 val op addIffs =

   Library.foldl

       (addIff (Classical.addSEs, Classical.addSIs)

               (Classical.addEs, Classical.addIs)

               Simplifier.addsimps);

 val op delIffs = Library.foldl (delIff Classical.delrules Simplifier.delsimps);

 fun AddIffs thms = change_clasimpset (fn css => css addIffs thms);

 fun DelIffs thms = change_clasimpset (fn css => css delIffs thms);

 fun addIffs_generic (x, ths) =

   Library.foldl (addIff (addXEs, addXIs) (addXEs, addXIs) #1) ((x, ()), ths) |> #1;

 fun delIffs_generic (x, ths) =

   Library.foldl (delIff delXs #1) ((x, ()), ths) |> #1;

 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 (clasimpset ()) 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 (clasimpset ()) 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 (clasimpset ()) 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 *)

 (* attributes *)

 fun attrib f = Thm.declaration_attribute (fn th => map_css (fn css => f (css, [th])));

 fun attrib' f (x, th) = (f (x, [th]), th);

 val iff_add = attrib (op addIffs);

 val iff_add' = attrib' addIffs_generic;

 val iff_del = attrib (op delIffs) o attrib' delIffs_generic;

 val iff_att = Attrib.syntax (Scan.lift

  (Args.del >> K iff_del ||

   Scan.option Args.add -- Args.query >> K iff_add' ||

   Scan.option Args.add >> K iff_add));

 (* method modifiers *)

 val iffN = "iff";

 val iff_modifiers =

  [Args.$$$ iffN -- Scan.option Args.add -- Args.colon >> K ((I, iff_add): Method.modifier),

   Args.$$$ iffN -- Scan.option Args.add -- Args.query_colon >> K (I, iff_add'),

   Args.$$$ iffN -- Args.del -- Args.colon >> K (I, iff_del)];

 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 (local_clasimpset_of ctxt));

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

   HEADGOAL (Method.insert_tac (prems @ facts) THEN' tac (local_clasimpset_of 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 (OuterParse.nat -- OuterParse.nat))) m;

 fun auto_meth NONE = clasimp_meth (CHANGED_PROP o auto_tac)

   | auto_meth (SOME (m, n)) = clasimp_meth (CHANGED_PROP o (fn css => mk_auto_tac css m n));

 (* theory setup *)

 val clasimp_setup =

  (Attrib.add_attributes

    [("iff", iff_att, "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_PROP oo clarsimp_tac), "clarify simplified goal")]);

 end;