src/Provers/clasimp.ML
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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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simplifier.ML, 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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infix 4 addSss addss;
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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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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 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 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 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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(* 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.addSaltern (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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(* 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) = 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 (Classical.claset(), Simplifier.simpset()) 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 (Classical.claset(), Simplifier.simpset()) 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 (Classical.claset(), Simplifier.simpset()) 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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(* change 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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(* methods *)
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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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val clasimp_modifiers =
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  Simplifier.simp_modifiers @ Splitter.split_modifiers @ Classical.cla_modifiers;
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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 (get_local_clasimpset 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 (get_local_clasimpset 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 o auto_tac)
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  | auto_meth (Some (m, n)) = clasimp_meth (CHANGED 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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 [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 oo clarsimp_tac), "clarify simplified goal")]];
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end;