(*  Title:      Provers/clasimp.ML

    ID:         $Id$

    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 Simplifier: SIMPLIFIER

  structure Splitter: SPLITTER

  structure Classical: CLASSICAL

  structure Blast: BLAST

  sharing type Classical.claset = Blast.claset

  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 clasimpset: unit -> 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 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 local_clasimpset_of: Proof.context -> clasimpset

  val iff_add_global: theory attribute

  val iff_add_global': theory attribute

  val iff_del_global: theory attribute

  val iff_add_local: Proof.context 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;

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

(*Attach a suffix, provided we have a name to start with.*)

fun suffix_thm "" _ th = th

  | suffix_thm a b th = Thm.name_thm (a^b, th);

(* 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 name = Thm.name_of_thm th;

    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, [suffix_thm name "_iff2" (zero_rotate (th RS Data.iffD2))]),

           [suffix_thm name "_iff1" (Data.cla_make_elim (zero_rotate (th RS Data.iffD1)))])

      handle THM _ => (elim (cs, [suffix_thm name "_iff" (zero_rotate (th RS Data.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 Data.iffD2),

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

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

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

     delss (ss, [th]))

  end;

fun store_clasimp (cs, ss) =

  (Classical.claset_ref () := cs; Simplifier.simpset_ref () := ss);

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 = store_clasimp (clasimpset () addIffs thms);

fun DelIffs thms = store_clasimp (clasimpset () delIffs thms);

fun addIffs_global (thy, ths) =

  Library.foldl (addIff

    (ContextRules.addXEs_global, ContextRules.addXIs_global)

    (ContextRules.addXEs_global, ContextRules.addXIs_global) #1)

  ((thy, ()), ths) |> #1;

fun addIffs_local (ctxt, ths) =

  Library.foldl (addIff

    (ContextRules.addXEs_local, ContextRules.addXIs_local)

    (ContextRules.addXEs_local, ContextRules.addXIs_local) #1)

  ((ctxt, ()), ths) |> #1;

fun delIffs_global (thy, ths) =

  Library.foldl (delIff ContextRules.delrules_global #1) ((thy, ()), ths) |> #1;

fun delIffs_local (ctxt, ths) =

  Library.foldl (delIff ContextRules.delrules_local #1) ((ctxt, ()), 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 *)

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);

fun local_clasimpset_of ctxt =

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

(* attributes *)

fun change_rules f (x, th) = (f (x, [th]), th);

val iff_add_global = change_global_css (op addIffs);

val iff_add_global' = change_rules addIffs_global;

val iff_del_global = change_global_css (op delIffs) o change_rules delIffs_global;

val iff_add_local = change_local_css (op addIffs);

val iff_add_local' = change_rules addIffs_local;

val iff_del_local = change_local_css (op delIffs) o change_rules delIffs_local;

fun iff_att add add' del = Attrib.syntax (Scan.lift

 (Args.del >> K del ||

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

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

val iff_attr =

 (iff_att iff_add_global iff_add_global' iff_del_global,

  iff_att iff_add_local iff_add_local' iff_del_local);

(* method modifiers *)

val iffN = "iff";

val iff_modifiers =

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

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

  Args.$$$ iffN -- Args.del -- 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 (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 (Args.nat -- Args.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 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_PROP oo clarsimp_tac), "clarify simplified goal")]];

end;