src/HOL/simpdata.ML
author wenzelm
Sun Jan 21 16:43:46 2007 +0100 (2007-01-21)
changeset 22147 f4ed4d940d44
parent 22128 cdd92316dd31
child 22838 466599ecf610
permissions -rw-r--r--
simplified ML setup;
haftmann@21163
     1
(*  Title:      HOL/simpdata.ML
haftmann@21163
     2
    ID:         $Id$
haftmann@21163
     3
    Author:     Tobias Nipkow
haftmann@21163
     4
    Copyright   1991  University of Cambridge
haftmann@21163
     5
haftmann@21163
     6
Instantiation of the generic simplifier for HOL.
haftmann@21163
     7
*)
haftmann@21163
     8
haftmann@21163
     9
(** tools setup **)
haftmann@21163
    10
haftmann@21163
    11
structure Quantifier1 = Quantifier1Fun
haftmann@21163
    12
(struct
haftmann@21163
    13
  (*abstract syntax*)
haftmann@21163
    14
  fun dest_eq ((c as Const("op =",_)) $ s $ t) = SOME (c, s, t)
haftmann@21163
    15
    | dest_eq _ = NONE;
haftmann@21163
    16
  fun dest_conj ((c as Const("op &",_)) $ s $ t) = SOME (c, s, t)
haftmann@21163
    17
    | dest_conj _ = NONE;
haftmann@21163
    18
  fun dest_imp ((c as Const("op -->",_)) $ s $ t) = SOME (c, s, t)
haftmann@21163
    19
    | dest_imp _ = NONE;
haftmann@21163
    20
  val conj = HOLogic.conj
haftmann@21163
    21
  val imp  = HOLogic.imp
haftmann@21163
    22
  (*rules*)
wenzelm@22147
    23
  val iff_reflection = @{thm eq_reflection}
wenzelm@22147
    24
  val iffI = @{thm iffI}
wenzelm@22147
    25
  val iff_trans = @{thm trans}
wenzelm@22147
    26
  val conjI= @{thm conjI}
wenzelm@22147
    27
  val conjE= @{thm conjE}
wenzelm@22147
    28
  val impI = @{thm impI}
wenzelm@22147
    29
  val mp   = @{thm mp}
wenzelm@22147
    30
  val uncurry = @{thm uncurry}
wenzelm@22147
    31
  val exI  = @{thm exI}
wenzelm@22147
    32
  val exE  = @{thm exE}
wenzelm@22147
    33
  val iff_allI = @{thm iff_allI}
wenzelm@22147
    34
  val iff_exI = @{thm iff_exI}
wenzelm@22147
    35
  val all_comm = @{thm all_comm}
wenzelm@22147
    36
  val ex_comm = @{thm ex_comm}
haftmann@21163
    37
end);
haftmann@21163
    38
haftmann@21551
    39
structure Simpdata =
haftmann@21163
    40
struct
haftmann@21163
    41
wenzelm@22147
    42
fun mk_meta_eq r = r RS @{thm eq_reflection};
haftmann@21163
    43
fun safe_mk_meta_eq r = mk_meta_eq r handle Thm.THM _ => r;
haftmann@21163
    44
wenzelm@22147
    45
fun mk_eq th = case concl_of th
haftmann@21163
    46
  (*expects Trueprop if not == *)
haftmann@21551
    47
  of Const ("==",_) $ _ $ _ => th
haftmann@21551
    48
   | _ $ (Const ("op =", _) $ _ $ _) => mk_meta_eq th
wenzelm@22147
    49
   | _ $ (Const ("Not", _) $ _) => th RS @{thm Eq_FalseI}
wenzelm@22147
    50
   | _ => th RS @{thm Eq_TrueI}
haftmann@21163
    51
wenzelm@22147
    52
fun mk_eq_True r =
wenzelm@22147
    53
  SOME (r RS @{thm meta_eq_to_obj_eq} RS @{thm Eq_TrueI}) handle Thm.THM _ => NONE;
haftmann@21163
    54
haftmann@21163
    55
(* Produce theorems of the form
haftmann@21163
    56
  (P1 =simp=> ... =simp=> Pn => x == y) ==> (P1 =simp=> ... =simp=> Pn => x = y)
haftmann@21163
    57
*)
wenzelm@22147
    58
fun lift_meta_eq_to_obj_eq i st =
haftmann@21163
    59
  let
haftmann@21163
    60
    fun count_imp (Const ("HOL.simp_implies", _) $ P $ Q) = 1 + count_imp Q
haftmann@21163
    61
      | count_imp _ = 0;
haftmann@21163
    62
    val j = count_imp (Logic.strip_assums_concl (List.nth (prems_of st, i - 1)))
wenzelm@22147
    63
  in if j = 0 then @{thm meta_eq_to_obj_eq}
haftmann@21163
    64
    else
haftmann@21163
    65
      let
haftmann@21163
    66
        val Ps = map (fn k => Free ("P" ^ string_of_int k, propT)) (1 upto j);
haftmann@21163
    67
        fun mk_simp_implies Q = foldr (fn (R, S) =>
haftmann@21163
    68
          Const ("HOL.simp_implies", propT --> propT --> propT) $ R $ S) Q Ps
haftmann@21163
    69
        val aT = TFree ("'a", HOLogic.typeS);
haftmann@21163
    70
        val x = Free ("x", aT);
haftmann@21163
    71
        val y = Free ("y", aT)
haftmann@21163
    72
      in Goal.prove_global (Thm.theory_of_thm st) []
haftmann@21163
    73
        [mk_simp_implies (Logic.mk_equals (x, y))]
haftmann@21163
    74
        (mk_simp_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (x, y))))
haftmann@21163
    75
        (fn prems => EVERY
wenzelm@22147
    76
         [rewrite_goals_tac @{thms simp_implies_def},
wenzelm@22147
    77
          REPEAT (ares_tac (@{thm meta_eq_to_obj_eq} ::
wenzelm@22147
    78
            map (rewrite_rule @{thms simp_implies_def}) prems) 1)])
haftmann@21163
    79
      end
haftmann@21163
    80
  end;
haftmann@21163
    81
haftmann@21163
    82
(*Congruence rules for = (instead of ==)*)
haftmann@21163
    83
fun mk_meta_cong rl = zero_var_indexes
haftmann@21163
    84
  (let val rl' = Seq.hd (TRYALL (fn i => fn st =>
haftmann@21163
    85
     rtac (lift_meta_eq_to_obj_eq i st) i st) rl)
haftmann@21163
    86
   in mk_meta_eq rl' handle THM _ =>
haftmann@21163
    87
     if can Logic.dest_equals (concl_of rl') then rl'
haftmann@21163
    88
     else error "Conclusion of congruence rules must be =-equality"
haftmann@21163
    89
   end);
haftmann@21163
    90
haftmann@21163
    91
fun mk_atomize pairs =
haftmann@21163
    92
  let
wenzelm@21313
    93
    fun atoms thm =
wenzelm@21313
    94
      let
wenzelm@21313
    95
        fun res th = map (fn rl => th RS rl);   (*exception THM*)
wenzelm@21313
    96
        fun res_fixed rls =
wenzelm@21313
    97
          if Thm.maxidx_of (Thm.adjust_maxidx_thm ~1 thm) = ~1 then res thm rls
wenzelm@21313
    98
          else Variable.trade (K (fn [thm'] => res thm' rls)) (Variable.thm_context thm) [thm];
wenzelm@21313
    99
      in
wenzelm@21313
   100
        case concl_of thm
wenzelm@21313
   101
          of Const ("Trueprop", _) $ p => (case head_of p
wenzelm@21313
   102
            of Const (a, _) => (case AList.lookup (op =) pairs a
wenzelm@21313
   103
              of SOME rls => (maps atoms (res_fixed rls) handle THM _ => [thm])
wenzelm@21313
   104
              | NONE => [thm])
wenzelm@21313
   105
            | _ => [thm])
wenzelm@21313
   106
          | _ => [thm]
wenzelm@21313
   107
      end;
haftmann@21163
   108
  in atoms end;
haftmann@21163
   109
haftmann@21163
   110
fun mksimps pairs =
wenzelm@21313
   111
  map_filter (try mk_eq) o mk_atomize pairs o gen_all;
haftmann@21163
   112
wenzelm@22147
   113
fun unsafe_solver_tac prems =
wenzelm@22147
   114
  (fn i => REPEAT_DETERM (match_tac @{thms simp_impliesI} i)) THEN'
wenzelm@22147
   115
  FIRST' [resolve_tac (reflexive_thm :: @{thm TrueI} :: @{thm refl} :: prems), atac,
wenzelm@22147
   116
    etac @{thm FalseE}];
wenzelm@22147
   117
haftmann@21163
   118
val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac;
haftmann@21163
   119
haftmann@21163
   120
(*No premature instantiation of variables during simplification*)
wenzelm@22147
   121
fun safe_solver_tac prems =
wenzelm@22147
   122
  (fn i => REPEAT_DETERM (match_tac @{thms simp_impliesI} i)) THEN'
wenzelm@22147
   123
  FIRST' [match_tac (reflexive_thm :: @{thm TrueI} :: @{thm refl} :: prems),
wenzelm@22147
   124
         eq_assume_tac, ematch_tac @{thms FalseE}];
wenzelm@22147
   125
haftmann@21163
   126
val safe_solver = mk_solver "HOL safe" safe_solver_tac;
haftmann@21163
   127
haftmann@21163
   128
structure SplitterData =
haftmann@21163
   129
struct
haftmann@21163
   130
  structure Simplifier = Simplifier
haftmann@21551
   131
  val mk_eq           = mk_eq
wenzelm@22147
   132
  val meta_eq_to_iff  = @{thm meta_eq_to_obj_eq}
wenzelm@22147
   133
  val iffD            = @{thm iffD2}
wenzelm@22147
   134
  val disjE           = @{thm disjE}
wenzelm@22147
   135
  val conjE           = @{thm conjE}
wenzelm@22147
   136
  val exE             = @{thm exE}
wenzelm@22147
   137
  val contrapos       = @{thm contrapos_nn}
wenzelm@22147
   138
  val contrapos2      = @{thm contrapos_pp}
wenzelm@22147
   139
  val notnotD         = @{thm notnotD}
haftmann@21163
   140
end;
haftmann@21163
   141
haftmann@21163
   142
structure Splitter = SplitterFun(SplitterData);
haftmann@21163
   143
wenzelm@21674
   144
val split_tac        = Splitter.split_tac;
wenzelm@21674
   145
val split_inside_tac = Splitter.split_inside_tac;
wenzelm@21674
   146
wenzelm@21674
   147
val op addsplits     = Splitter.addsplits;
wenzelm@21674
   148
val op delsplits     = Splitter.delsplits;
wenzelm@21674
   149
val Addsplits        = Splitter.Addsplits;
wenzelm@21674
   150
val Delsplits        = Splitter.Delsplits;
wenzelm@21674
   151
wenzelm@21674
   152
haftmann@21163
   153
(* integration of simplifier with classical reasoner *)
haftmann@21163
   154
haftmann@21163
   155
structure Clasimp = ClasimpFun
haftmann@21163
   156
 (structure Simplifier = Simplifier and Splitter = Splitter
haftmann@21163
   157
  and Classical  = Classical and Blast = Blast
wenzelm@22147
   158
  val iffD1 = @{thm iffD1} val iffD2 = @{thm iffD2} val notE = @{thm notE});
wenzelm@21674
   159
open Clasimp;
haftmann@21163
   160
wenzelm@22128
   161
val _ = ML_Context.value_antiq "clasimpset"
wenzelm@22128
   162
  (Scan.succeed ("clasimpset", "Clasimp.local_clasimpset_of (ML_Context.the_local_context ())"));
wenzelm@22128
   163
haftmann@21163
   164
val mksimps_pairs =
wenzelm@22147
   165
  [("op -->", [@{thm mp}]), ("op &", [@{thm conjunct1}, @{thm conjunct2}]),
wenzelm@22147
   166
   ("All", [@{thm spec}]), ("True", []), ("False", []),
wenzelm@22147
   167
   ("HOL.If", [@{thm if_bool_eq_conj} RS @{thm iffD1}])];
haftmann@21163
   168
wenzelm@21674
   169
val HOL_basic_ss =
wenzelm@22147
   170
  Simplifier.theory_context @{theory} empty_ss
haftmann@21163
   171
    setsubgoaler asm_simp_tac
haftmann@21163
   172
    setSSolver safe_solver
haftmann@21163
   173
    setSolver unsafe_solver
haftmann@21163
   174
    setmksimps (mksimps mksimps_pairs)
haftmann@21163
   175
    setmkeqTrue mk_eq_True
haftmann@21163
   176
    setmkcong mk_meta_cong;
haftmann@21163
   177
wenzelm@21674
   178
fun hol_simplify rews = Simplifier.full_simplify (HOL_basic_ss addsimps rews);
haftmann@21163
   179
haftmann@21163
   180
fun unfold_tac ths =
wenzelm@21674
   181
  let val ss0 = Simplifier.clear_ss HOL_basic_ss addsimps ths
haftmann@21163
   182
  in fn ss => ALLGOALS (full_simp_tac (Simplifier.inherit_context ss ss0)) end;
haftmann@21163
   183
wenzelm@21313
   184
wenzelm@21313
   185
haftmann@21163
   186
(** simprocs **)
haftmann@21163
   187
haftmann@21163
   188
(* simproc for proving "(y = x) == False" from premise "~(x = y)" *)
haftmann@21163
   189
haftmann@21163
   190
val use_neq_simproc = ref true;
haftmann@21163
   191
haftmann@21163
   192
local
wenzelm@22147
   193
  val neq_to_EQ_False = @{thm not_sym} RS @{thm Eq_FalseI};
haftmann@21163
   194
  fun neq_prover sg ss (eq $ lhs $ rhs) =
haftmann@21163
   195
    let
haftmann@21163
   196
      fun test thm = (case #prop (rep_thm thm) of
haftmann@21163
   197
                    _ $ (Not $ (eq' $ l' $ r')) =>
haftmann@21163
   198
                      Not = HOLogic.Not andalso eq' = eq andalso
haftmann@21163
   199
                      r' aconv lhs andalso l' aconv rhs
haftmann@21163
   200
                  | _ => false)
haftmann@21163
   201
    in if !use_neq_simproc then case find_first test (prems_of_ss ss)
haftmann@21163
   202
     of NONE => NONE
haftmann@21163
   203
      | SOME thm => SOME (thm RS neq_to_EQ_False)
haftmann@21163
   204
     else NONE
haftmann@21163
   205
    end
haftmann@21163
   206
in
haftmann@21163
   207
wenzelm@22147
   208
val neq_simproc = Simplifier.simproc @{theory} "neq_simproc" ["x = y"] neq_prover;
haftmann@21163
   209
wenzelm@21313
   210
end;
haftmann@21163
   211
haftmann@21163
   212
haftmann@21163
   213
(* simproc for Let *)
haftmann@21163
   214
haftmann@21163
   215
val use_let_simproc = ref true;
haftmann@21163
   216
haftmann@21163
   217
local
haftmann@21163
   218
  val (f_Let_unfold, x_Let_unfold) =
wenzelm@22147
   219
      let val [(_$(f$x)$_)] = prems_of @{thm Let_unfold}
wenzelm@22147
   220
      in (cterm_of @{theory} f, cterm_of @{theory} x) end
haftmann@21163
   221
  val (f_Let_folded, x_Let_folded) =
wenzelm@22147
   222
      let val [(_$(f$x)$_)] = prems_of @{thm Let_folded}
wenzelm@22147
   223
      in (cterm_of @{theory} f, cterm_of @{theory} x) end;
haftmann@21163
   224
  val g_Let_folded =
wenzelm@22147
   225
      let val [(_$_$(g$_))] = prems_of @{thm Let_folded} in cterm_of @{theory} g end;
haftmann@21163
   226
in
haftmann@21163
   227
haftmann@21163
   228
val let_simproc =
wenzelm@22147
   229
  Simplifier.simproc @{theory} "let_simp" ["Let x f"]
haftmann@21163
   230
   (fn sg => fn ss => fn t =>
haftmann@21163
   231
     let val ctxt = Simplifier.the_context ss;
haftmann@21163
   232
         val ([t'], ctxt') = Variable.import_terms false [t] ctxt;
haftmann@21163
   233
     in Option.map (hd o Variable.export ctxt' ctxt o single)
haftmann@21163
   234
      (case t' of (Const ("Let",_)$x$f) => (* x and f are already in normal form *)
haftmann@21163
   235
         if not (!use_let_simproc) then NONE
haftmann@21163
   236
         else if is_Free x orelse is_Bound x orelse is_Const x
wenzelm@22147
   237
         then SOME @{thm Let_def}
haftmann@21163
   238
         else
haftmann@21163
   239
          let
haftmann@21163
   240
             val n = case f of (Abs (x,_,_)) => x | _ => "x";
haftmann@21163
   241
             val cx = cterm_of sg x;
haftmann@21163
   242
             val {T=xT,...} = rep_cterm cx;
haftmann@21163
   243
             val cf = cterm_of sg f;
haftmann@21163
   244
             val fx_g = Simplifier.rewrite ss (Thm.capply cf cx);
haftmann@21163
   245
             val (_$_$g) = prop_of fx_g;
haftmann@21163
   246
             val g' = abstract_over (x,g);
haftmann@21163
   247
           in (if (g aconv g')
haftmann@21163
   248
               then
haftmann@21163
   249
                  let
wenzelm@22147
   250
                    val rl =
wenzelm@22147
   251
                      cterm_instantiate [(f_Let_unfold,cf),(x_Let_unfold,cx)] @{thm Let_unfold};
haftmann@21163
   252
                  in SOME (rl OF [fx_g]) end
haftmann@21163
   253
               else if Term.betapply (f,x) aconv g then NONE (*avoid identity conversion*)
haftmann@21163
   254
               else let
haftmann@21163
   255
                     val abs_g'= Abs (n,xT,g');
haftmann@21163
   256
                     val g'x = abs_g'$x;
haftmann@21163
   257
                     val g_g'x = symmetric (beta_conversion false (cterm_of sg g'x));
haftmann@21163
   258
                     val rl = cterm_instantiate
haftmann@21163
   259
                               [(f_Let_folded,cterm_of sg f),(x_Let_folded,cx),
haftmann@21163
   260
                                (g_Let_folded,cterm_of sg abs_g')]
wenzelm@22147
   261
                               @{thm Let_folded};
haftmann@21163
   262
                   in SOME (rl OF [transitive fx_g g_g'x])
haftmann@21163
   263
                   end)
haftmann@21163
   264
           end
haftmann@21163
   265
        | _ => NONE)
haftmann@21163
   266
     end)
haftmann@21163
   267
wenzelm@21313
   268
end;
wenzelm@21313
   269
haftmann@21163
   270
haftmann@21163
   271
(* generic refutation procedure *)
haftmann@21163
   272
haftmann@21163
   273
(* parameters:
haftmann@21163
   274
haftmann@21163
   275
   test: term -> bool
haftmann@21163
   276
   tests if a term is at all relevant to the refutation proof;
haftmann@21163
   277
   if not, then it can be discarded. Can improve performance,
haftmann@21163
   278
   esp. if disjunctions can be discarded (no case distinction needed!).
haftmann@21163
   279
haftmann@21163
   280
   prep_tac: int -> tactic
haftmann@21163
   281
   A preparation tactic to be applied to the goal once all relevant premises
haftmann@21163
   282
   have been moved to the conclusion.
haftmann@21163
   283
haftmann@21163
   284
   ref_tac: int -> tactic
haftmann@21163
   285
   the actual refutation tactic. Should be able to deal with goals
haftmann@21163
   286
   [| A1; ...; An |] ==> False
haftmann@21163
   287
   where the Ai are atomic, i.e. no top-level &, | or EX
haftmann@21163
   288
*)
haftmann@21163
   289
haftmann@21163
   290
local
haftmann@21163
   291
  val nnf_simpset =
haftmann@21163
   292
    empty_ss setmkeqTrue mk_eq_True
haftmann@21163
   293
    setmksimps (mksimps mksimps_pairs)
wenzelm@22147
   294
    addsimps [@{thm imp_conv_disj}, @{thm iff_conv_conj_imp}, @{thm de_Morgan_disj},
wenzelm@22147
   295
      @{thm de_Morgan_conj}, @{thm not_all}, @{thm not_ex}, @{thm not_not}];
haftmann@21163
   296
  fun prem_nnf_tac i st =
haftmann@21163
   297
    full_simp_tac (Simplifier.theory_context (Thm.theory_of_thm st) nnf_simpset) i st;
haftmann@21163
   298
in
haftmann@21163
   299
fun refute_tac test prep_tac ref_tac =
haftmann@21163
   300
  let val refute_prems_tac =
haftmann@21163
   301
        REPEAT_DETERM
wenzelm@22147
   302
              (eresolve_tac [@{thm conjE}, @{thm exE}] 1 ORELSE
haftmann@21163
   303
               filter_prems_tac test 1 ORELSE
wenzelm@22147
   304
               etac @{thm disjE} 1) THEN
wenzelm@22147
   305
        ((etac @{thm notE} 1 THEN eq_assume_tac 1) ORELSE
haftmann@21163
   306
         ref_tac 1);
haftmann@21163
   307
  in EVERY'[TRY o filter_prems_tac test,
wenzelm@22147
   308
            REPEAT_DETERM o etac @{thm rev_mp}, prep_tac, rtac @{thm ccontr}, prem_nnf_tac,
haftmann@21163
   309
            SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
haftmann@21163
   310
  end;
wenzelm@21313
   311
end;
haftmann@21163
   312
haftmann@21163
   313
val defALL_regroup =
wenzelm@22147
   314
  Simplifier.simproc @{theory}
haftmann@21163
   315
    "defined ALL" ["ALL x. P x"] Quantifier1.rearrange_all;
haftmann@21163
   316
haftmann@21163
   317
val defEX_regroup =
wenzelm@22147
   318
  Simplifier.simproc @{theory}
haftmann@21163
   319
    "defined EX" ["EX x. P x"] Quantifier1.rearrange_ex;
haftmann@21163
   320
haftmann@21163
   321
wenzelm@21674
   322
val simpset_simprocs = HOL_basic_ss
haftmann@21163
   323
  addsimprocs [defALL_regroup, defEX_regroup, neq_simproc, let_simproc]
haftmann@21163
   324
wenzelm@21313
   325
end;
haftmann@21551
   326
haftmann@21551
   327
structure Splitter = Simpdata.Splitter;
haftmann@21551
   328
structure Clasimp = Simpdata.Clasimp;