src/HOL/Tools/Groebner_Basis/normalizer.ML
author wenzelm
Wed Dec 31 15:30:10 2008 +0100 (2008-12-31)
changeset 29269 5c25a2012975
parent 27222 b08abdb8f499
child 30866 dd5117e2d73e
permissions -rw-r--r--
moved term order operations to structure TermOrd (cf. Pure/term_ord.ML);
tuned signature of structure Term;
wenzelm@23252
     1
(*  Title:      HOL/Tools/Groebner_Basis/normalizer.ML
wenzelm@23252
     2
    Author:     Amine Chaieb, TU Muenchen
wenzelm@23252
     3
*)
wenzelm@23252
     4
wenzelm@23252
     5
signature NORMALIZER = 
wenzelm@23252
     6
sig
wenzelm@23485
     7
 val semiring_normalize_conv : Proof.context -> conv
wenzelm@23485
     8
 val semiring_normalize_ord_conv : Proof.context -> (cterm -> cterm -> bool) -> conv
wenzelm@23252
     9
 val semiring_normalize_tac : Proof.context -> int -> tactic
wenzelm@23485
    10
 val semiring_normalize_wrapper :  Proof.context -> NormalizerData.entry -> conv
chaieb@27222
    11
 val semiring_normalizers_ord_wrapper :  
chaieb@27222
    12
     Proof.context -> NormalizerData.entry -> (cterm -> cterm -> bool) ->
chaieb@27222
    13
      {add: conv, mul: conv, neg: conv, main: conv, pow: conv, sub: conv}
wenzelm@23485
    14
 val semiring_normalize_ord_wrapper :  Proof.context -> NormalizerData.entry ->
wenzelm@23485
    15
   (cterm -> cterm -> bool) -> conv
wenzelm@23252
    16
 val semiring_normalizers_conv :
wenzelm@23252
    17
     cterm list -> cterm list * thm list -> cterm list * thm list ->
wenzelm@23485
    18
     (cterm -> bool) * conv * conv * conv -> (cterm -> cterm -> bool) ->
wenzelm@23485
    19
       {add: conv, mul: conv, neg: conv, main: conv, pow: conv, sub: conv}
wenzelm@23252
    20
end
wenzelm@23252
    21
wenzelm@23252
    22
structure Normalizer: NORMALIZER = 
wenzelm@23252
    23
struct
wenzelm@23559
    24
chaieb@25253
    25
open Conv;
wenzelm@23252
    26
wenzelm@23252
    27
(* Very basic stuff for terms *)
chaieb@25253
    28
chaieb@25253
    29
fun is_comb ct =
chaieb@25253
    30
  (case Thm.term_of ct of
chaieb@25253
    31
    _ $ _ => true
chaieb@25253
    32
  | _ => false);
chaieb@25253
    33
chaieb@25253
    34
val concl = Thm.cprop_of #> Thm.dest_arg;
chaieb@25253
    35
chaieb@25253
    36
fun is_binop ct ct' =
chaieb@25253
    37
  (case Thm.term_of ct' of
chaieb@25253
    38
    c $ _ $ _ => term_of ct aconv c
chaieb@25253
    39
  | _ => false);
chaieb@25253
    40
chaieb@25253
    41
fun dest_binop ct ct' =
chaieb@25253
    42
  if is_binop ct ct' then Thm.dest_binop ct'
chaieb@25253
    43
  else raise CTERM ("dest_binop: bad binop", [ct, ct'])
chaieb@25253
    44
chaieb@25253
    45
fun inst_thm inst = Thm.instantiate ([], inst);
chaieb@25253
    46
wenzelm@23252
    47
val dest_numeral = term_of #> HOLogic.dest_number #> snd;
wenzelm@23252
    48
val is_numeral = can dest_numeral;
wenzelm@23252
    49
wenzelm@23252
    50
val numeral01_conv = Simplifier.rewrite
haftmann@25481
    51
                         (HOL_basic_ss addsimps [@{thm numeral_1_eq_1}, @{thm numeral_0_eq_0}]);
wenzelm@23252
    52
val zero1_numeral_conv = 
haftmann@25481
    53
 Simplifier.rewrite (HOL_basic_ss addsimps [@{thm numeral_1_eq_1} RS sym, @{thm numeral_0_eq_0} RS sym]);
wenzelm@23580
    54
fun zerone_conv cv = zero1_numeral_conv then_conv cv then_conv numeral01_conv;
wenzelm@23252
    55
val natarith = [@{thm "add_nat_number_of"}, @{thm "diff_nat_number_of"},
wenzelm@23252
    56
                @{thm "mult_nat_number_of"}, @{thm "eq_nat_number_of"}, 
wenzelm@23252
    57
                @{thm "less_nat_number_of"}];
wenzelm@23252
    58
val nat_add_conv = 
wenzelm@23252
    59
 zerone_conv 
wenzelm@23252
    60
  (Simplifier.rewrite 
wenzelm@23252
    61
    (HOL_basic_ss 
haftmann@25481
    62
       addsimps @{thms arith_simps} @ natarith @ @{thms rel_simps}
haftmann@25481
    63
             @ [if_False, if_True, @{thm add_0}, @{thm add_Suc},
haftmann@25481
    64
                 @{thm add_number_of_left}, @{thm Suc_eq_add_numeral_1}]
haftmann@25481
    65
             @ map (fn th => th RS sym) @{thms numerals}));
wenzelm@23252
    66
wenzelm@23252
    67
val nat_mul_conv = nat_add_conv;
wenzelm@23252
    68
val zeron_tm = @{cterm "0::nat"};
wenzelm@23252
    69
val onen_tm  = @{cterm "1::nat"};
wenzelm@23252
    70
val true_tm = @{cterm "True"};
wenzelm@23252
    71
wenzelm@23252
    72
wenzelm@23252
    73
(* The main function! *)
wenzelm@23252
    74
fun semiring_normalizers_conv vars (sr_ops, sr_rules) (r_ops, r_rules)
wenzelm@23252
    75
  (is_semiring_constant, semiring_add_conv, semiring_mul_conv, semiring_pow_conv) =
wenzelm@23252
    76
let
wenzelm@23252
    77
wenzelm@23252
    78
val [pthm_02, pthm_03, pthm_04, pthm_05, pthm_07, pthm_08,
wenzelm@23252
    79
     pthm_09, pthm_10, pthm_11, pthm_12, pthm_13, pthm_14, pthm_15, pthm_16,
wenzelm@23252
    80
     pthm_17, pthm_18, pthm_19, pthm_21, pthm_22, pthm_23, pthm_24,
wenzelm@23252
    81
     pthm_25, pthm_26, pthm_27, pthm_28, pthm_29, pthm_30, pthm_31, pthm_32,
wenzelm@23252
    82
     pthm_33, pthm_34, pthm_35, pthm_36, pthm_37, pthm_38,pthm_39,pthm_40] = sr_rules;
wenzelm@23252
    83
wenzelm@23252
    84
val [ca, cb, cc, cd, cm, cn, cp, cq, cx, cy, cz, clx, crx, cly, cry] = vars;
wenzelm@23252
    85
val [add_pat, mul_pat, pow_pat, zero_tm, one_tm] = sr_ops;
wenzelm@23252
    86
val [add_tm, mul_tm, pow_tm] = map (Thm.dest_fun o Thm.dest_fun) [add_pat, mul_pat, pow_pat];
wenzelm@23252
    87
wenzelm@23252
    88
val dest_add = dest_binop add_tm
wenzelm@23252
    89
val dest_mul = dest_binop mul_tm
wenzelm@23252
    90
fun dest_pow tm =
wenzelm@23252
    91
 let val (l,r) = dest_binop pow_tm tm
wenzelm@23252
    92
 in if is_numeral r then (l,r) else raise CTERM ("dest_pow",[tm])
wenzelm@23252
    93
 end;
wenzelm@23252
    94
val is_add = is_binop add_tm
wenzelm@23252
    95
val is_mul = is_binop mul_tm
wenzelm@23252
    96
fun is_pow tm = is_binop pow_tm tm andalso is_numeral(Thm.dest_arg tm);
wenzelm@23252
    97
wenzelm@23252
    98
val (neg_mul,sub_add,sub_tm,neg_tm,dest_sub,is_sub,cx',cy') =
wenzelm@23252
    99
  (case (r_ops, r_rules) of
wenzelm@23252
   100
    ([], []) => (TrueI, TrueI, true_tm, true_tm, (fn t => (t,t)), K false, true_tm, true_tm)
wenzelm@23252
   101
  | ([sub_pat, neg_pat], [neg_mul, sub_add]) =>
wenzelm@23252
   102
      let
wenzelm@23252
   103
        val sub_tm = Thm.dest_fun (Thm.dest_fun sub_pat)
wenzelm@23252
   104
        val neg_tm = Thm.dest_fun neg_pat
wenzelm@23252
   105
        val dest_sub = dest_binop sub_tm
wenzelm@23252
   106
        val is_sub = is_binop sub_tm
wenzelm@23252
   107
      in (neg_mul,sub_add,sub_tm,neg_tm,dest_sub,is_sub, neg_mul |> concl |> Thm.dest_arg,
wenzelm@23252
   108
          sub_add |> concl |> Thm.dest_arg |> Thm.dest_arg)
wenzelm@23252
   109
      end);
wenzelm@23252
   110
in fn variable_order =>
wenzelm@23252
   111
 let
wenzelm@23252
   112
wenzelm@23252
   113
(* Conversion for "x^n * x^m", with either x^n = x and/or x^m = x possible.  *)
wenzelm@23252
   114
(* Also deals with "const * const", but both terms must involve powers of    *)
wenzelm@23252
   115
(* the same variable, or both be constants, or behaviour may be incorrect.   *)
wenzelm@23252
   116
wenzelm@23252
   117
 fun powvar_mul_conv tm =
wenzelm@23252
   118
  let
wenzelm@23252
   119
  val (l,r) = dest_mul tm
wenzelm@23252
   120
  in if is_semiring_constant l andalso is_semiring_constant r
wenzelm@23252
   121
     then semiring_mul_conv tm
wenzelm@23252
   122
     else
wenzelm@23252
   123
      ((let
wenzelm@23252
   124
         val (lx,ln) = dest_pow l
wenzelm@23252
   125
        in
wenzelm@23252
   126
         ((let val (rx,rn) = dest_pow r
wenzelm@23252
   127
               val th1 = inst_thm [(cx,lx),(cp,ln),(cq,rn)] pthm_29
wenzelm@23252
   128
                val (tm1,tm2) = Thm.dest_comb(concl th1) in
wenzelm@23252
   129
               transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv tm2)) end)
wenzelm@23252
   130
           handle CTERM _ =>
wenzelm@23252
   131
            (let val th1 = inst_thm [(cx,lx),(cq,ln)] pthm_31
wenzelm@23252
   132
                 val (tm1,tm2) = Thm.dest_comb(concl th1) in
wenzelm@23252
   133
               transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv tm2)) end)) end)
wenzelm@23252
   134
       handle CTERM _ =>
wenzelm@23252
   135
           ((let val (rx,rn) = dest_pow r
wenzelm@23252
   136
                val th1 = inst_thm [(cx,rx),(cq,rn)] pthm_30
wenzelm@23252
   137
                val (tm1,tm2) = Thm.dest_comb(concl th1) in
wenzelm@23252
   138
               transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv tm2)) end)
wenzelm@23252
   139
           handle CTERM _ => inst_thm [(cx,l)] pthm_32
wenzelm@23252
   140
wenzelm@23252
   141
))
wenzelm@23252
   142
 end;
wenzelm@23252
   143
wenzelm@23252
   144
(* Remove "1 * m" from a monomial, and just leave m.                         *)
wenzelm@23252
   145
wenzelm@23252
   146
 fun monomial_deone th =
wenzelm@23252
   147
       (let val (l,r) = dest_mul(concl th) in
wenzelm@23252
   148
           if l aconvc one_tm
wenzelm@23252
   149
          then transitive th (inst_thm [(ca,r)] pthm_13)  else th end)
wenzelm@23252
   150
       handle CTERM _ => th;
wenzelm@23252
   151
wenzelm@23252
   152
(* Conversion for "(monomial)^n", where n is a numeral.                      *)
wenzelm@23252
   153
wenzelm@23252
   154
 val monomial_pow_conv =
wenzelm@23252
   155
  let
wenzelm@23252
   156
   fun monomial_pow tm bod ntm =
wenzelm@23252
   157
    if not(is_comb bod)
wenzelm@23252
   158
    then reflexive tm
wenzelm@23252
   159
    else
wenzelm@23252
   160
     if is_semiring_constant bod
wenzelm@23252
   161
     then semiring_pow_conv tm
wenzelm@23252
   162
     else
wenzelm@23252
   163
      let
wenzelm@23252
   164
      val (lopr,r) = Thm.dest_comb bod
wenzelm@23252
   165
      in if not(is_comb lopr)
wenzelm@23252
   166
         then reflexive tm
wenzelm@23252
   167
        else
wenzelm@23252
   168
          let
wenzelm@23252
   169
          val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   170
         in
wenzelm@23252
   171
           if opr aconvc pow_tm andalso is_numeral r
wenzelm@23252
   172
          then
wenzelm@23252
   173
            let val th1 = inst_thm [(cx,l),(cp,r),(cq,ntm)] pthm_34
wenzelm@23252
   174
                val (l,r) = Thm.dest_comb(concl th1)
wenzelm@23252
   175
           in transitive th1 (Drule.arg_cong_rule l (nat_mul_conv r))
wenzelm@23252
   176
           end
wenzelm@23252
   177
           else
wenzelm@23252
   178
            if opr aconvc mul_tm
wenzelm@23252
   179
            then
wenzelm@23252
   180
             let
wenzelm@23252
   181
              val th1 = inst_thm [(cx,l),(cy,r),(cq,ntm)] pthm_33
wenzelm@23252
   182
             val (xy,z) = Thm.dest_comb(concl th1)
wenzelm@23252
   183
              val (x,y) = Thm.dest_comb xy
wenzelm@23252
   184
              val thl = monomial_pow y l ntm
wenzelm@23252
   185
              val thr = monomial_pow z r ntm
wenzelm@23252
   186
             in transitive th1 (combination (Drule.arg_cong_rule x thl) thr)
wenzelm@23252
   187
             end
wenzelm@23252
   188
             else reflexive tm
wenzelm@23252
   189
          end
wenzelm@23252
   190
      end
wenzelm@23252
   191
  in fn tm =>
wenzelm@23252
   192
   let
wenzelm@23252
   193
    val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   194
    val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   195
   in if not (opr aconvc pow_tm) orelse not(is_numeral r)
wenzelm@23252
   196
      then raise CTERM ("monomial_pow_conv", [tm])
wenzelm@23252
   197
      else if r aconvc zeron_tm
wenzelm@23252
   198
      then inst_thm [(cx,l)] pthm_35
wenzelm@23252
   199
      else if r aconvc onen_tm
wenzelm@23252
   200
      then inst_thm [(cx,l)] pthm_36
wenzelm@23252
   201
      else monomial_deone(monomial_pow tm l r)
wenzelm@23252
   202
   end
wenzelm@23252
   203
  end;
wenzelm@23252
   204
wenzelm@23252
   205
(* Multiplication of canonical monomials.                                    *)
wenzelm@23252
   206
 val monomial_mul_conv =
wenzelm@23252
   207
  let
wenzelm@23252
   208
   fun powvar tm =
wenzelm@23252
   209
    if is_semiring_constant tm then one_tm
wenzelm@23252
   210
    else
wenzelm@23252
   211
     ((let val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   212
           val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   213
       in if opr aconvc pow_tm andalso is_numeral r then l 
wenzelm@23252
   214
          else raise CTERM ("monomial_mul_conv",[tm]) end)
wenzelm@23252
   215
     handle CTERM _ => tm)   (* FIXME !? *)
wenzelm@23252
   216
   fun  vorder x y =
wenzelm@23252
   217
    if x aconvc y then 0
wenzelm@23252
   218
    else
wenzelm@23252
   219
     if x aconvc one_tm then ~1
wenzelm@23252
   220
     else if y aconvc one_tm then 1
wenzelm@23252
   221
      else if variable_order x y then ~1 else 1
wenzelm@23252
   222
   fun monomial_mul tm l r =
wenzelm@23252
   223
    ((let val (lx,ly) = dest_mul l val vl = powvar lx
wenzelm@23252
   224
      in
wenzelm@23252
   225
      ((let
wenzelm@23252
   226
        val (rx,ry) = dest_mul r
wenzelm@23252
   227
         val vr = powvar rx
wenzelm@23252
   228
         val ord = vorder vl vr
wenzelm@23252
   229
        in
wenzelm@23252
   230
         if ord = 0
wenzelm@23252
   231
        then
wenzelm@23252
   232
          let
wenzelm@23252
   233
             val th1 = inst_thm [(clx,lx),(cly,ly),(crx,rx),(cry,ry)] pthm_15
wenzelm@23252
   234
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   235
             val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   236
             val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv tm4)) tm2
wenzelm@23252
   237
             val th3 = transitive th1 th2
wenzelm@23252
   238
              val  (tm5,tm6) = Thm.dest_comb(concl th3)
wenzelm@23252
   239
              val  (tm7,tm8) = Thm.dest_comb tm6
wenzelm@23252
   240
             val  th4 = monomial_mul tm6 (Thm.dest_arg tm7) tm8
wenzelm@23252
   241
         in  transitive th3 (Drule.arg_cong_rule tm5 th4)
wenzelm@23252
   242
         end
wenzelm@23252
   243
         else
wenzelm@23252
   244
          let val th0 = if ord < 0 then pthm_16 else pthm_17
wenzelm@23252
   245
             val th1 = inst_thm [(clx,lx),(cly,ly),(crx,rx),(cry,ry)] th0
wenzelm@23252
   246
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   247
             val (tm3,tm4) = Thm.dest_comb tm2
wenzelm@23252
   248
         in transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4))
wenzelm@23252
   249
         end
wenzelm@23252
   250
        end)
wenzelm@23252
   251
       handle CTERM _ =>
wenzelm@23252
   252
        (let val vr = powvar r val ord = vorder vl vr
wenzelm@23252
   253
        in
wenzelm@23252
   254
          if ord = 0 then
wenzelm@23252
   255
           let
wenzelm@23252
   256
           val th1 = inst_thm [(clx,lx),(cly,ly),(crx,r)] pthm_18
wenzelm@23252
   257
                 val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   258
           val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   259
           val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv tm4)) tm2
wenzelm@23252
   260
          in transitive th1 th2
wenzelm@23252
   261
          end
wenzelm@23252
   262
          else
wenzelm@23252
   263
          if ord < 0 then
wenzelm@23252
   264
            let val th1 = inst_thm [(clx,lx),(cly,ly),(crx,r)] pthm_19
wenzelm@23252
   265
                val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   266
                val (tm3,tm4) = Thm.dest_comb tm2
wenzelm@23252
   267
           in transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4))
wenzelm@23252
   268
           end
wenzelm@23252
   269
           else inst_thm [(ca,l),(cb,r)] pthm_09
wenzelm@23252
   270
        end)) end)
wenzelm@23252
   271
     handle CTERM _ =>
wenzelm@23252
   272
      (let val vl = powvar l in
wenzelm@23252
   273
        ((let
wenzelm@23252
   274
          val (rx,ry) = dest_mul r
wenzelm@23252
   275
          val vr = powvar rx
wenzelm@23252
   276
           val ord = vorder vl vr
wenzelm@23252
   277
         in if ord = 0 then
wenzelm@23252
   278
              let val th1 = inst_thm [(clx,l),(crx,rx),(cry,ry)] pthm_21
wenzelm@23252
   279
                 val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   280
                 val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   281
             in transitive th1 (Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv tm4)) tm2)
wenzelm@23252
   282
             end
wenzelm@23252
   283
             else if ord > 0 then
wenzelm@23252
   284
                 let val th1 = inst_thm [(clx,l),(crx,rx),(cry,ry)] pthm_22
wenzelm@23252
   285
                     val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   286
                    val (tm3,tm4) = Thm.dest_comb tm2
wenzelm@23252
   287
                in transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4))
wenzelm@23252
   288
                end
wenzelm@23252
   289
             else reflexive tm
wenzelm@23252
   290
         end)
wenzelm@23252
   291
        handle CTERM _ =>
wenzelm@23252
   292
          (let val vr = powvar r
wenzelm@23252
   293
               val  ord = vorder vl vr
wenzelm@23252
   294
          in if ord = 0 then powvar_mul_conv tm
wenzelm@23252
   295
              else if ord > 0 then inst_thm [(ca,l),(cb,r)] pthm_09
wenzelm@23252
   296
              else reflexive tm
wenzelm@23252
   297
          end)) end))
wenzelm@23252
   298
  in fn tm => let val (l,r) = dest_mul tm in monomial_deone(monomial_mul tm l r)
wenzelm@23252
   299
             end
wenzelm@23252
   300
  end;
wenzelm@23252
   301
(* Multiplication by monomial of a polynomial.                               *)
wenzelm@23252
   302
wenzelm@23252
   303
 val polynomial_monomial_mul_conv =
wenzelm@23252
   304
  let
wenzelm@23252
   305
   fun pmm_conv tm =
wenzelm@23252
   306
    let val (l,r) = dest_mul tm
wenzelm@23252
   307
    in
wenzelm@23252
   308
    ((let val (y,z) = dest_add r
wenzelm@23252
   309
          val th1 = inst_thm [(cx,l),(cy,y),(cz,z)] pthm_37
wenzelm@23252
   310
          val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   311
          val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   312
          val th2 = combination (Drule.arg_cong_rule tm3 (monomial_mul_conv tm4)) (pmm_conv tm2)
wenzelm@23252
   313
      in transitive th1 th2
wenzelm@23252
   314
      end)
wenzelm@23252
   315
     handle CTERM _ => monomial_mul_conv tm)
wenzelm@23252
   316
   end
wenzelm@23252
   317
 in pmm_conv
wenzelm@23252
   318
 end;
wenzelm@23252
   319
wenzelm@23252
   320
(* Addition of two monomials identical except for constant multiples.        *)
wenzelm@23252
   321
wenzelm@23252
   322
fun monomial_add_conv tm =
wenzelm@23252
   323
 let val (l,r) = dest_add tm
wenzelm@23252
   324
 in if is_semiring_constant l andalso is_semiring_constant r
wenzelm@23252
   325
    then semiring_add_conv tm
wenzelm@23252
   326
    else
wenzelm@23252
   327
     let val th1 =
wenzelm@23252
   328
           if is_mul l andalso is_semiring_constant(Thm.dest_arg1 l)
wenzelm@23252
   329
           then if is_mul r andalso is_semiring_constant(Thm.dest_arg1 r) then
wenzelm@23252
   330
                    inst_thm [(ca,Thm.dest_arg1 l),(cm,Thm.dest_arg r), (cb,Thm.dest_arg1 r)] pthm_02
wenzelm@23252
   331
                else inst_thm [(ca,Thm.dest_arg1 l),(cm,r)] pthm_03
wenzelm@23252
   332
           else if is_mul r andalso is_semiring_constant(Thm.dest_arg1 r)
wenzelm@23252
   333
           then inst_thm [(cm,l),(ca,Thm.dest_arg1 r)] pthm_04
wenzelm@23252
   334
           else inst_thm [(cm,r)] pthm_05
wenzelm@23252
   335
         val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   336
         val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   337
         val th2 = Drule.arg_cong_rule tm3 (semiring_add_conv tm4)
wenzelm@23252
   338
         val th3 = transitive th1 (Drule.fun_cong_rule th2 tm2)
wenzelm@23252
   339
         val tm5 = concl th3
wenzelm@23252
   340
      in
wenzelm@23252
   341
      if (Thm.dest_arg1 tm5) aconvc zero_tm
wenzelm@23252
   342
      then transitive th3 (inst_thm [(ca,Thm.dest_arg tm5)] pthm_11)
wenzelm@23252
   343
      else monomial_deone th3
wenzelm@23252
   344
     end
wenzelm@23252
   345
 end;
wenzelm@23252
   346
wenzelm@23252
   347
(* Ordering on monomials.                                                    *)
wenzelm@23252
   348
wenzelm@23252
   349
fun striplist dest =
wenzelm@23252
   350
 let fun strip x acc =
wenzelm@23252
   351
   ((let val (l,r) = dest x in
wenzelm@23252
   352
        strip l (strip r acc) end)
wenzelm@23252
   353
    handle CTERM _ => x::acc)    (* FIXME !? *)
wenzelm@23252
   354
 in fn x => strip x []
wenzelm@23252
   355
 end;
wenzelm@23252
   356
wenzelm@23252
   357
wenzelm@23252
   358
fun powervars tm =
wenzelm@23252
   359
 let val ptms = striplist dest_mul tm
wenzelm@23252
   360
 in if is_semiring_constant (hd ptms) then tl ptms else ptms
wenzelm@23252
   361
 end;
wenzelm@23252
   362
val num_0 = 0;
wenzelm@23252
   363
val num_1 = 1;
wenzelm@23252
   364
fun dest_varpow tm =
wenzelm@23252
   365
 ((let val (x,n) = dest_pow tm in (x,dest_numeral n) end)
wenzelm@23252
   366
   handle CTERM _ =>
wenzelm@23252
   367
   (tm,(if is_semiring_constant tm then num_0 else num_1)));
wenzelm@23252
   368
wenzelm@23252
   369
val morder =
wenzelm@23252
   370
 let fun lexorder l1 l2 =
wenzelm@23252
   371
  case (l1,l2) of
wenzelm@23252
   372
    ([],[]) => 0
wenzelm@23252
   373
  | (vps,[]) => ~1
wenzelm@23252
   374
  | ([],vps) => 1
wenzelm@23252
   375
  | (((x1,n1)::vs1),((x2,n2)::vs2)) =>
wenzelm@23252
   376
     if variable_order x1 x2 then 1
wenzelm@23252
   377
     else if variable_order x2 x1 then ~1
wenzelm@23252
   378
     else if n1 < n2 then ~1
wenzelm@23252
   379
     else if n2 < n1 then 1
wenzelm@23252
   380
     else lexorder vs1 vs2
wenzelm@23252
   381
 in fn tm1 => fn tm2 =>
wenzelm@23252
   382
  let val vdegs1 = map dest_varpow (powervars tm1)
wenzelm@23252
   383
      val vdegs2 = map dest_varpow (powervars tm2)
wenzelm@23252
   384
      val deg1 = fold_rev ((curry (op +)) o snd) vdegs1 num_0
wenzelm@23252
   385
      val deg2 = fold_rev ((curry (op +)) o snd) vdegs2 num_0
wenzelm@23252
   386
  in if deg1 < deg2 then ~1 else if deg1 > deg2 then 1
wenzelm@23252
   387
                            else lexorder vdegs1 vdegs2
wenzelm@23252
   388
  end
wenzelm@23252
   389
 end;
wenzelm@23252
   390
wenzelm@23252
   391
(* Addition of two polynomials.                                              *)
wenzelm@23252
   392
wenzelm@23252
   393
val polynomial_add_conv =
wenzelm@23252
   394
 let
wenzelm@23252
   395
 fun dezero_rule th =
wenzelm@23252
   396
  let
wenzelm@23252
   397
   val tm = concl th
wenzelm@23252
   398
  in
wenzelm@23252
   399
   if not(is_add tm) then th else
wenzelm@23252
   400
   let val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   401
       val l = Thm.dest_arg lopr
wenzelm@23252
   402
   in
wenzelm@23252
   403
    if l aconvc zero_tm
wenzelm@23252
   404
    then transitive th (inst_thm [(ca,r)] pthm_07)   else
wenzelm@23252
   405
        if r aconvc zero_tm
wenzelm@23252
   406
        then transitive th (inst_thm [(ca,l)] pthm_08)  else th
wenzelm@23252
   407
   end
wenzelm@23252
   408
  end
wenzelm@23252
   409
 fun padd tm =
wenzelm@23252
   410
  let
wenzelm@23252
   411
   val (l,r) = dest_add tm
wenzelm@23252
   412
  in
wenzelm@23252
   413
   if l aconvc zero_tm then inst_thm [(ca,r)] pthm_07
wenzelm@23252
   414
   else if r aconvc zero_tm then inst_thm [(ca,l)] pthm_08
wenzelm@23252
   415
   else
wenzelm@23252
   416
    if is_add l
wenzelm@23252
   417
    then
wenzelm@23252
   418
     let val (a,b) = dest_add l
wenzelm@23252
   419
     in
wenzelm@23252
   420
     if is_add r then
wenzelm@23252
   421
      let val (c,d) = dest_add r
wenzelm@23252
   422
          val ord = morder a c
wenzelm@23252
   423
      in
wenzelm@23252
   424
       if ord = 0 then
wenzelm@23252
   425
        let val th1 = inst_thm [(ca,a),(cb,b),(cc,c),(cd,d)] pthm_23
wenzelm@23252
   426
            val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   427
            val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   428
            val th2 = Drule.arg_cong_rule tm3 (monomial_add_conv tm4)
wenzelm@23252
   429
        in dezero_rule (transitive th1 (combination th2 (padd tm2)))
wenzelm@23252
   430
        end
wenzelm@23252
   431
       else (* ord <> 0*)
wenzelm@23252
   432
        let val th1 =
wenzelm@23252
   433
                if ord > 0 then inst_thm [(ca,a),(cb,b),(cc,r)] pthm_24
wenzelm@23252
   434
                else inst_thm [(ca,l),(cc,c),(cd,d)] pthm_25
wenzelm@23252
   435
            val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   436
        in dezero_rule (transitive th1 (Drule.arg_cong_rule tm1 (padd tm2)))
wenzelm@23252
   437
        end
wenzelm@23252
   438
      end
wenzelm@23252
   439
     else (* not (is_add r)*)
wenzelm@23252
   440
      let val ord = morder a r
wenzelm@23252
   441
      in
wenzelm@23252
   442
       if ord = 0 then
wenzelm@23252
   443
        let val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_26
wenzelm@23252
   444
            val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   445
            val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   446
            val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (monomial_add_conv tm4)) tm2
wenzelm@23252
   447
        in dezero_rule (transitive th1 th2)
wenzelm@23252
   448
        end
wenzelm@23252
   449
       else (* ord <> 0*)
wenzelm@23252
   450
        if ord > 0 then
wenzelm@23252
   451
          let val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_24
wenzelm@23252
   452
              val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   453
          in dezero_rule (transitive th1 (Drule.arg_cong_rule tm1 (padd tm2)))
wenzelm@23252
   454
          end
wenzelm@23252
   455
        else dezero_rule (inst_thm [(ca,l),(cc,r)] pthm_27)
wenzelm@23252
   456
      end
wenzelm@23252
   457
    end
wenzelm@23252
   458
   else (* not (is_add l)*)
wenzelm@23252
   459
    if is_add r then
wenzelm@23252
   460
      let val (c,d) = dest_add r
wenzelm@23252
   461
          val  ord = morder l c
wenzelm@23252
   462
      in
wenzelm@23252
   463
       if ord = 0 then
wenzelm@23252
   464
         let val th1 = inst_thm [(ca,l),(cc,c),(cd,d)] pthm_28
wenzelm@23252
   465
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   466
             val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   467
             val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (monomial_add_conv tm4)) tm2
wenzelm@23252
   468
         in dezero_rule (transitive th1 th2)
wenzelm@23252
   469
         end
wenzelm@23252
   470
       else
wenzelm@23252
   471
        if ord > 0 then reflexive tm
wenzelm@23252
   472
        else
wenzelm@23252
   473
         let val th1 = inst_thm [(ca,l),(cc,c),(cd,d)] pthm_25
wenzelm@23252
   474
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   475
         in dezero_rule (transitive th1 (Drule.arg_cong_rule tm1 (padd tm2)))
wenzelm@23252
   476
         end
wenzelm@23252
   477
      end
wenzelm@23252
   478
    else
wenzelm@23252
   479
     let val ord = morder l r
wenzelm@23252
   480
     in
wenzelm@23252
   481
      if ord = 0 then monomial_add_conv tm
wenzelm@23252
   482
      else if ord > 0 then dezero_rule(reflexive tm)
wenzelm@23252
   483
      else dezero_rule (inst_thm [(ca,l),(cc,r)] pthm_27)
wenzelm@23252
   484
     end
wenzelm@23252
   485
  end
wenzelm@23252
   486
 in padd
wenzelm@23252
   487
 end;
wenzelm@23252
   488
wenzelm@23252
   489
(* Multiplication of two polynomials.                                        *)
wenzelm@23252
   490
wenzelm@23252
   491
val polynomial_mul_conv =
wenzelm@23252
   492
 let
wenzelm@23252
   493
  fun pmul tm =
wenzelm@23252
   494
   let val (l,r) = dest_mul tm
wenzelm@23252
   495
   in
wenzelm@23252
   496
    if not(is_add l) then polynomial_monomial_mul_conv tm
wenzelm@23252
   497
    else
wenzelm@23252
   498
     if not(is_add r) then
wenzelm@23252
   499
      let val th1 = inst_thm [(ca,l),(cb,r)] pthm_09
wenzelm@23252
   500
      in transitive th1 (polynomial_monomial_mul_conv(concl th1))
wenzelm@23252
   501
      end
wenzelm@23252
   502
     else
wenzelm@23252
   503
       let val (a,b) = dest_add l
wenzelm@23252
   504
           val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_10
wenzelm@23252
   505
           val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   506
           val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   507
           val th2 = Drule.arg_cong_rule tm3 (polynomial_monomial_mul_conv tm4)
wenzelm@23252
   508
           val th3 = transitive th1 (combination th2 (pmul tm2))
wenzelm@23252
   509
       in transitive th3 (polynomial_add_conv (concl th3))
wenzelm@23252
   510
       end
wenzelm@23252
   511
   end
wenzelm@23252
   512
 in fn tm =>
wenzelm@23252
   513
   let val (l,r) = dest_mul tm
wenzelm@23252
   514
   in
wenzelm@23252
   515
    if l aconvc zero_tm then inst_thm [(ca,r)] pthm_11
wenzelm@23252
   516
    else if r aconvc zero_tm then inst_thm [(ca,l)] pthm_12
wenzelm@23252
   517
    else if l aconvc one_tm then inst_thm [(ca,r)] pthm_13
wenzelm@23252
   518
    else if r aconvc one_tm then inst_thm [(ca,l)] pthm_14
wenzelm@23252
   519
    else pmul tm
wenzelm@23252
   520
   end
wenzelm@23252
   521
 end;
wenzelm@23252
   522
wenzelm@23252
   523
(* Power of polynomial (optimized for the monomial and trivial cases).       *)
wenzelm@23252
   524
wenzelm@23580
   525
fun num_conv n =
wenzelm@23580
   526
  nat_add_conv (Thm.capply @{cterm Suc} (Numeral.mk_cnumber @{ctyp nat} (dest_numeral n - 1)))
wenzelm@23580
   527
  |> Thm.symmetric;
wenzelm@23252
   528
wenzelm@23252
   529
wenzelm@23252
   530
val polynomial_pow_conv =
wenzelm@23252
   531
 let
wenzelm@23252
   532
  fun ppow tm =
wenzelm@23252
   533
    let val (l,n) = dest_pow tm
wenzelm@23252
   534
    in
wenzelm@23252
   535
     if n aconvc zeron_tm then inst_thm [(cx,l)] pthm_35
wenzelm@23252
   536
     else if n aconvc onen_tm then inst_thm [(cx,l)] pthm_36
wenzelm@23252
   537
     else
wenzelm@23252
   538
         let val th1 = num_conv n
wenzelm@23252
   539
             val th2 = inst_thm [(cx,l),(cq,Thm.dest_arg (concl th1))] pthm_38
wenzelm@23252
   540
             val (tm1,tm2) = Thm.dest_comb(concl th2)
wenzelm@23252
   541
             val th3 = transitive th2 (Drule.arg_cong_rule tm1 (ppow tm2))
wenzelm@23252
   542
             val th4 = transitive (Drule.arg_cong_rule (Thm.dest_fun tm) th1) th3
wenzelm@23252
   543
         in transitive th4 (polynomial_mul_conv (concl th4))
wenzelm@23252
   544
         end
wenzelm@23252
   545
    end
wenzelm@23252
   546
 in fn tm =>
wenzelm@23252
   547
       if is_add(Thm.dest_arg1 tm) then ppow tm else monomial_pow_conv tm
wenzelm@23252
   548
 end;
wenzelm@23252
   549
wenzelm@23252
   550
(* Negation.                                                                 *)
wenzelm@23252
   551
wenzelm@23580
   552
fun polynomial_neg_conv tm =
wenzelm@23252
   553
   let val (l,r) = Thm.dest_comb tm in
wenzelm@23252
   554
        if not (l aconvc neg_tm) then raise CTERM ("polynomial_neg_conv",[tm]) else
wenzelm@23252
   555
        let val th1 = inst_thm [(cx',r)] neg_mul
wenzelm@23252
   556
            val th2 = transitive th1 (arg1_conv semiring_mul_conv (concl th1))
wenzelm@23252
   557
        in transitive th2 (polynomial_monomial_mul_conv (concl th2))
wenzelm@23252
   558
        end
wenzelm@23252
   559
   end;
wenzelm@23252
   560
wenzelm@23252
   561
wenzelm@23252
   562
(* Subtraction.                                                              *)
wenzelm@23580
   563
fun polynomial_sub_conv tm =
wenzelm@23252
   564
  let val (l,r) = dest_sub tm
wenzelm@23252
   565
      val th1 = inst_thm [(cx',l),(cy',r)] sub_add
wenzelm@23252
   566
      val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   567
      val th2 = Drule.arg_cong_rule tm1 (polynomial_neg_conv tm2)
wenzelm@23252
   568
  in transitive th1 (transitive th2 (polynomial_add_conv (concl th2)))
wenzelm@23252
   569
  end;
wenzelm@23252
   570
wenzelm@23252
   571
(* Conversion from HOL term.                                                 *)
wenzelm@23252
   572
wenzelm@23252
   573
fun polynomial_conv tm =
chaieb@23407
   574
 if is_semiring_constant tm then semiring_add_conv tm
chaieb@23407
   575
 else if not(is_comb tm) then reflexive tm
wenzelm@23252
   576
 else
wenzelm@23252
   577
  let val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   578
  in if lopr aconvc neg_tm then
wenzelm@23252
   579
       let val th1 = Drule.arg_cong_rule lopr (polynomial_conv r)
wenzelm@23252
   580
       in transitive th1 (polynomial_neg_conv (concl th1))
wenzelm@23252
   581
       end
wenzelm@23252
   582
     else
wenzelm@23252
   583
       if not(is_comb lopr) then reflexive tm
wenzelm@23252
   584
       else
wenzelm@23252
   585
         let val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   586
         in if opr aconvc pow_tm andalso is_numeral r
wenzelm@23252
   587
            then
wenzelm@23252
   588
              let val th1 = Drule.fun_cong_rule (Drule.arg_cong_rule opr (polynomial_conv l)) r
wenzelm@23252
   589
              in transitive th1 (polynomial_pow_conv (concl th1))
wenzelm@23252
   590
              end
wenzelm@23252
   591
            else
wenzelm@23252
   592
              if opr aconvc add_tm orelse opr aconvc mul_tm orelse opr aconvc sub_tm
wenzelm@23252
   593
              then
wenzelm@23252
   594
               let val th1 = combination (Drule.arg_cong_rule opr (polynomial_conv l)) (polynomial_conv r)
wenzelm@23252
   595
                   val f = if opr aconvc add_tm then polynomial_add_conv
wenzelm@23252
   596
                      else if opr aconvc mul_tm then polynomial_mul_conv
wenzelm@23252
   597
                      else polynomial_sub_conv
wenzelm@23252
   598
               in transitive th1 (f (concl th1))
wenzelm@23252
   599
               end
wenzelm@23252
   600
              else reflexive tm
wenzelm@23252
   601
         end
wenzelm@23252
   602
  end;
wenzelm@23252
   603
 in
wenzelm@23252
   604
   {main = polynomial_conv,
wenzelm@23252
   605
    add = polynomial_add_conv,
wenzelm@23252
   606
    mul = polynomial_mul_conv,
wenzelm@23252
   607
    pow = polynomial_pow_conv,
wenzelm@23252
   608
    neg = polynomial_neg_conv,
wenzelm@23252
   609
    sub = polynomial_sub_conv}
wenzelm@23252
   610
 end
wenzelm@23252
   611
end;
wenzelm@23252
   612
wenzelm@23252
   613
val nat_arith = @{thms "nat_arith"};
haftmann@25481
   614
val nat_exp_ss = HOL_basic_ss addsimps (@{thms nat_number} @ nat_arith @ @{thms arith_simps} @ @{thms rel_simps})
haftmann@23880
   615
                              addsimps [Let_def, if_False, if_True, @{thm add_0}, @{thm add_Suc}];
wenzelm@23252
   616
wenzelm@29269
   617
fun simple_cterm_ord t u = TermOrd.term_ord (term_of t, term_of u) = LESS;
chaieb@27222
   618
chaieb@27222
   619
fun semiring_normalizers_ord_wrapper ctxt ({vars, semiring, ring, idom, ideal}, 
chaieb@23407
   620
                                     {conv, dest_const, mk_const, is_const}) ord =
wenzelm@23252
   621
  let
wenzelm@23252
   622
    val pow_conv =
wenzelm@23252
   623
      arg_conv (Simplifier.rewrite nat_exp_ss)
wenzelm@23252
   624
      then_conv Simplifier.rewrite
wenzelm@23252
   625
        (HOL_basic_ss addsimps [nth (snd semiring) 31, nth (snd semiring) 34])
chaieb@23330
   626
      then_conv conv ctxt
chaieb@23330
   627
    val dat = (is_const, conv ctxt, conv ctxt, pow_conv)
chaieb@27222
   628
  in semiring_normalizers_conv vars semiring ring dat ord end;
chaieb@27222
   629
chaieb@27222
   630
fun semiring_normalize_ord_wrapper ctxt ({vars, semiring, ring, idom, ideal}, {conv, dest_const, mk_const, is_const}) ord =
chaieb@27222
   631
 #main (semiring_normalizers_ord_wrapper ctxt ({vars = vars, semiring = semiring, ring = ring, idom = idom, ideal = ideal},{conv = conv, dest_const = dest_const, mk_const = mk_const, is_const = is_const}) ord);
wenzelm@23252
   632
chaieb@23407
   633
fun semiring_normalize_wrapper ctxt data = 
chaieb@23407
   634
  semiring_normalize_ord_wrapper ctxt data simple_cterm_ord;
chaieb@23407
   635
chaieb@23407
   636
fun semiring_normalize_ord_conv ctxt ord tm =
wenzelm@23252
   637
  (case NormalizerData.match ctxt tm of
wenzelm@23252
   638
    NONE => reflexive tm
chaieb@23407
   639
  | SOME res => semiring_normalize_ord_wrapper ctxt res ord tm);
chaieb@23407
   640
 
wenzelm@23252
   641
chaieb@23407
   642
fun semiring_normalize_conv ctxt = semiring_normalize_ord_conv ctxt simple_cterm_ord;
wenzelm@23252
   643
wenzelm@23252
   644
fun semiring_normalize_tac ctxt = SUBGOAL (fn (goal, i) =>
wenzelm@23252
   645
  rtac (semiring_normalize_conv ctxt
wenzelm@23252
   646
    (cterm_of (ProofContext.theory_of ctxt) (fst (Logic.dest_equals goal)))) i);
wenzelm@23252
   647
end;