src/HOL/Tools/Groebner_Basis/normalizer.ML
author haftmann
Fri Jul 20 14:28:05 2007 +0200 (2007-07-20)
changeset 23880 64b9806e160b
parent 23580 998a6fda9bb6
child 25253 c642b36f2bec
permissions -rw-r--r--
dropped Nat.ML legacy bindings
wenzelm@23252
     1
(*  Title:      HOL/Tools/Groebner_Basis/normalizer.ML
wenzelm@23252
     2
    ID:         $Id$
wenzelm@23252
     3
    Author:     Amine Chaieb, TU Muenchen
wenzelm@23252
     4
*)
wenzelm@23252
     5
wenzelm@23252
     6
signature NORMALIZER = 
wenzelm@23252
     7
sig
wenzelm@23485
     8
 val semiring_normalize_conv : Proof.context -> conv
wenzelm@23485
     9
 val semiring_normalize_ord_conv : Proof.context -> (cterm -> cterm -> bool) -> conv
wenzelm@23252
    10
 val semiring_normalize_tac : Proof.context -> int -> tactic
wenzelm@23485
    11
 val semiring_normalize_wrapper :  Proof.context -> NormalizerData.entry -> conv
wenzelm@23485
    12
 val semiring_normalize_ord_wrapper :  Proof.context -> NormalizerData.entry ->
wenzelm@23485
    13
   (cterm -> cterm -> bool) -> conv
wenzelm@23252
    14
 val semiring_normalizers_conv :
wenzelm@23252
    15
     cterm list -> cterm list * thm list -> cterm list * thm list ->
wenzelm@23485
    16
     (cterm -> bool) * conv * conv * conv -> (cterm -> cterm -> bool) ->
wenzelm@23485
    17
       {add: conv, mul: conv, neg: conv, main: conv, pow: conv, sub: conv}
wenzelm@23252
    18
end
wenzelm@23252
    19
wenzelm@23252
    20
structure Normalizer: NORMALIZER = 
wenzelm@23252
    21
struct
wenzelm@23559
    22
wenzelm@23559
    23
open Conv Misc;
wenzelm@23252
    24
wenzelm@23252
    25
(* Very basic stuff for terms *)
wenzelm@23252
    26
val dest_numeral = term_of #> HOLogic.dest_number #> snd;
wenzelm@23252
    27
val is_numeral = can dest_numeral;
wenzelm@23252
    28
wenzelm@23252
    29
val numeral01_conv = Simplifier.rewrite
wenzelm@23252
    30
                         (HOL_basic_ss addsimps [numeral_1_eq_1, numeral_0_eq_0]);
wenzelm@23252
    31
val zero1_numeral_conv = 
wenzelm@23252
    32
 Simplifier.rewrite (HOL_basic_ss addsimps [numeral_1_eq_1 RS sym, numeral_0_eq_0 RS sym]);
wenzelm@23580
    33
fun zerone_conv cv = zero1_numeral_conv then_conv cv then_conv numeral01_conv;
wenzelm@23252
    34
val natarith = [@{thm "add_nat_number_of"}, @{thm "diff_nat_number_of"},
wenzelm@23252
    35
                @{thm "mult_nat_number_of"}, @{thm "eq_nat_number_of"}, 
wenzelm@23252
    36
                @{thm "less_nat_number_of"}];
wenzelm@23252
    37
val nat_add_conv = 
wenzelm@23252
    38
 zerone_conv 
wenzelm@23252
    39
  (Simplifier.rewrite 
wenzelm@23252
    40
    (HOL_basic_ss 
wenzelm@23252
    41
       addsimps arith_simps @ natarith @ rel_simps
haftmann@23880
    42
             @ [if_False, if_True, @{thm add_0}, @{thm add_Suc}, add_number_of_left, Suc_eq_add_numeral_1]
wenzelm@23252
    43
             @ map (fn th => th RS sym) numerals));
wenzelm@23252
    44
wenzelm@23252
    45
val nat_mul_conv = nat_add_conv;
wenzelm@23252
    46
val zeron_tm = @{cterm "0::nat"};
wenzelm@23252
    47
val onen_tm  = @{cterm "1::nat"};
wenzelm@23252
    48
val true_tm = @{cterm "True"};
wenzelm@23252
    49
wenzelm@23252
    50
wenzelm@23252
    51
(* The main function! *)
wenzelm@23252
    52
fun semiring_normalizers_conv vars (sr_ops, sr_rules) (r_ops, r_rules)
wenzelm@23252
    53
  (is_semiring_constant, semiring_add_conv, semiring_mul_conv, semiring_pow_conv) =
wenzelm@23252
    54
let
wenzelm@23252
    55
wenzelm@23252
    56
val [pthm_02, pthm_03, pthm_04, pthm_05, pthm_07, pthm_08,
wenzelm@23252
    57
     pthm_09, pthm_10, pthm_11, pthm_12, pthm_13, pthm_14, pthm_15, pthm_16,
wenzelm@23252
    58
     pthm_17, pthm_18, pthm_19, pthm_21, pthm_22, pthm_23, pthm_24,
wenzelm@23252
    59
     pthm_25, pthm_26, pthm_27, pthm_28, pthm_29, pthm_30, pthm_31, pthm_32,
wenzelm@23252
    60
     pthm_33, pthm_34, pthm_35, pthm_36, pthm_37, pthm_38,pthm_39,pthm_40] = sr_rules;
wenzelm@23252
    61
wenzelm@23252
    62
val [ca, cb, cc, cd, cm, cn, cp, cq, cx, cy, cz, clx, crx, cly, cry] = vars;
wenzelm@23252
    63
val [add_pat, mul_pat, pow_pat, zero_tm, one_tm] = sr_ops;
wenzelm@23252
    64
val [add_tm, mul_tm, pow_tm] = map (Thm.dest_fun o Thm.dest_fun) [add_pat, mul_pat, pow_pat];
wenzelm@23252
    65
wenzelm@23252
    66
val dest_add = dest_binop add_tm
wenzelm@23252
    67
val dest_mul = dest_binop mul_tm
wenzelm@23252
    68
fun dest_pow tm =
wenzelm@23252
    69
 let val (l,r) = dest_binop pow_tm tm
wenzelm@23252
    70
 in if is_numeral r then (l,r) else raise CTERM ("dest_pow",[tm])
wenzelm@23252
    71
 end;
wenzelm@23252
    72
val is_add = is_binop add_tm
wenzelm@23252
    73
val is_mul = is_binop mul_tm
wenzelm@23252
    74
fun is_pow tm = is_binop pow_tm tm andalso is_numeral(Thm.dest_arg tm);
wenzelm@23252
    75
wenzelm@23252
    76
val (neg_mul,sub_add,sub_tm,neg_tm,dest_sub,is_sub,cx',cy') =
wenzelm@23252
    77
  (case (r_ops, r_rules) of
wenzelm@23252
    78
    ([], []) => (TrueI, TrueI, true_tm, true_tm, (fn t => (t,t)), K false, true_tm, true_tm)
wenzelm@23252
    79
  | ([sub_pat, neg_pat], [neg_mul, sub_add]) =>
wenzelm@23252
    80
      let
wenzelm@23252
    81
        val sub_tm = Thm.dest_fun (Thm.dest_fun sub_pat)
wenzelm@23252
    82
        val neg_tm = Thm.dest_fun neg_pat
wenzelm@23252
    83
        val dest_sub = dest_binop sub_tm
wenzelm@23252
    84
        val is_sub = is_binop sub_tm
wenzelm@23252
    85
      in (neg_mul,sub_add,sub_tm,neg_tm,dest_sub,is_sub, neg_mul |> concl |> Thm.dest_arg,
wenzelm@23252
    86
          sub_add |> concl |> Thm.dest_arg |> Thm.dest_arg)
wenzelm@23252
    87
      end);
wenzelm@23252
    88
in fn variable_order =>
wenzelm@23252
    89
 let
wenzelm@23252
    90
wenzelm@23252
    91
(* Conversion for "x^n * x^m", with either x^n = x and/or x^m = x possible.  *)
wenzelm@23252
    92
(* Also deals with "const * const", but both terms must involve powers of    *)
wenzelm@23252
    93
(* the same variable, or both be constants, or behaviour may be incorrect.   *)
wenzelm@23252
    94
wenzelm@23252
    95
 fun powvar_mul_conv tm =
wenzelm@23252
    96
  let
wenzelm@23252
    97
  val (l,r) = dest_mul tm
wenzelm@23252
    98
  in if is_semiring_constant l andalso is_semiring_constant r
wenzelm@23252
    99
     then semiring_mul_conv tm
wenzelm@23252
   100
     else
wenzelm@23252
   101
      ((let
wenzelm@23252
   102
         val (lx,ln) = dest_pow l
wenzelm@23252
   103
        in
wenzelm@23252
   104
         ((let val (rx,rn) = dest_pow r
wenzelm@23252
   105
               val th1 = inst_thm [(cx,lx),(cp,ln),(cq,rn)] pthm_29
wenzelm@23252
   106
                val (tm1,tm2) = Thm.dest_comb(concl th1) in
wenzelm@23252
   107
               transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv tm2)) end)
wenzelm@23252
   108
           handle CTERM _ =>
wenzelm@23252
   109
            (let val th1 = inst_thm [(cx,lx),(cq,ln)] pthm_31
wenzelm@23252
   110
                 val (tm1,tm2) = Thm.dest_comb(concl th1) in
wenzelm@23252
   111
               transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv tm2)) end)) end)
wenzelm@23252
   112
       handle CTERM _ =>
wenzelm@23252
   113
           ((let val (rx,rn) = dest_pow r
wenzelm@23252
   114
                val th1 = inst_thm [(cx,rx),(cq,rn)] pthm_30
wenzelm@23252
   115
                val (tm1,tm2) = Thm.dest_comb(concl th1) in
wenzelm@23252
   116
               transitive th1 (Drule.arg_cong_rule tm1 (nat_add_conv tm2)) end)
wenzelm@23252
   117
           handle CTERM _ => inst_thm [(cx,l)] pthm_32
wenzelm@23252
   118
wenzelm@23252
   119
))
wenzelm@23252
   120
 end;
wenzelm@23252
   121
wenzelm@23252
   122
(* Remove "1 * m" from a monomial, and just leave m.                         *)
wenzelm@23252
   123
wenzelm@23252
   124
 fun monomial_deone th =
wenzelm@23252
   125
       (let val (l,r) = dest_mul(concl th) in
wenzelm@23252
   126
           if l aconvc one_tm
wenzelm@23252
   127
          then transitive th (inst_thm [(ca,r)] pthm_13)  else th end)
wenzelm@23252
   128
       handle CTERM _ => th;
wenzelm@23252
   129
wenzelm@23252
   130
(* Conversion for "(monomial)^n", where n is a numeral.                      *)
wenzelm@23252
   131
wenzelm@23252
   132
 val monomial_pow_conv =
wenzelm@23252
   133
  let
wenzelm@23252
   134
   fun monomial_pow tm bod ntm =
wenzelm@23252
   135
    if not(is_comb bod)
wenzelm@23252
   136
    then reflexive tm
wenzelm@23252
   137
    else
wenzelm@23252
   138
     if is_semiring_constant bod
wenzelm@23252
   139
     then semiring_pow_conv tm
wenzelm@23252
   140
     else
wenzelm@23252
   141
      let
wenzelm@23252
   142
      val (lopr,r) = Thm.dest_comb bod
wenzelm@23252
   143
      in if not(is_comb lopr)
wenzelm@23252
   144
         then reflexive tm
wenzelm@23252
   145
        else
wenzelm@23252
   146
          let
wenzelm@23252
   147
          val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   148
         in
wenzelm@23252
   149
           if opr aconvc pow_tm andalso is_numeral r
wenzelm@23252
   150
          then
wenzelm@23252
   151
            let val th1 = inst_thm [(cx,l),(cp,r),(cq,ntm)] pthm_34
wenzelm@23252
   152
                val (l,r) = Thm.dest_comb(concl th1)
wenzelm@23252
   153
           in transitive th1 (Drule.arg_cong_rule l (nat_mul_conv r))
wenzelm@23252
   154
           end
wenzelm@23252
   155
           else
wenzelm@23252
   156
            if opr aconvc mul_tm
wenzelm@23252
   157
            then
wenzelm@23252
   158
             let
wenzelm@23252
   159
              val th1 = inst_thm [(cx,l),(cy,r),(cq,ntm)] pthm_33
wenzelm@23252
   160
             val (xy,z) = Thm.dest_comb(concl th1)
wenzelm@23252
   161
              val (x,y) = Thm.dest_comb xy
wenzelm@23252
   162
              val thl = monomial_pow y l ntm
wenzelm@23252
   163
              val thr = monomial_pow z r ntm
wenzelm@23252
   164
             in transitive th1 (combination (Drule.arg_cong_rule x thl) thr)
wenzelm@23252
   165
             end
wenzelm@23252
   166
             else reflexive tm
wenzelm@23252
   167
          end
wenzelm@23252
   168
      end
wenzelm@23252
   169
  in fn tm =>
wenzelm@23252
   170
   let
wenzelm@23252
   171
    val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   172
    val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   173
   in if not (opr aconvc pow_tm) orelse not(is_numeral r)
wenzelm@23252
   174
      then raise CTERM ("monomial_pow_conv", [tm])
wenzelm@23252
   175
      else if r aconvc zeron_tm
wenzelm@23252
   176
      then inst_thm [(cx,l)] pthm_35
wenzelm@23252
   177
      else if r aconvc onen_tm
wenzelm@23252
   178
      then inst_thm [(cx,l)] pthm_36
wenzelm@23252
   179
      else monomial_deone(monomial_pow tm l r)
wenzelm@23252
   180
   end
wenzelm@23252
   181
  end;
wenzelm@23252
   182
wenzelm@23252
   183
(* Multiplication of canonical monomials.                                    *)
wenzelm@23252
   184
 val monomial_mul_conv =
wenzelm@23252
   185
  let
wenzelm@23252
   186
   fun powvar tm =
wenzelm@23252
   187
    if is_semiring_constant tm then one_tm
wenzelm@23252
   188
    else
wenzelm@23252
   189
     ((let val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   190
           val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   191
       in if opr aconvc pow_tm andalso is_numeral r then l 
wenzelm@23252
   192
          else raise CTERM ("monomial_mul_conv",[tm]) end)
wenzelm@23252
   193
     handle CTERM _ => tm)   (* FIXME !? *)
wenzelm@23252
   194
   fun  vorder x y =
wenzelm@23252
   195
    if x aconvc y then 0
wenzelm@23252
   196
    else
wenzelm@23252
   197
     if x aconvc one_tm then ~1
wenzelm@23252
   198
     else if y aconvc one_tm then 1
wenzelm@23252
   199
      else if variable_order x y then ~1 else 1
wenzelm@23252
   200
   fun monomial_mul tm l r =
wenzelm@23252
   201
    ((let val (lx,ly) = dest_mul l val vl = powvar lx
wenzelm@23252
   202
      in
wenzelm@23252
   203
      ((let
wenzelm@23252
   204
        val (rx,ry) = dest_mul r
wenzelm@23252
   205
         val vr = powvar rx
wenzelm@23252
   206
         val ord = vorder vl vr
wenzelm@23252
   207
        in
wenzelm@23252
   208
         if ord = 0
wenzelm@23252
   209
        then
wenzelm@23252
   210
          let
wenzelm@23252
   211
             val th1 = inst_thm [(clx,lx),(cly,ly),(crx,rx),(cry,ry)] pthm_15
wenzelm@23252
   212
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   213
             val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   214
             val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv tm4)) tm2
wenzelm@23252
   215
             val th3 = transitive th1 th2
wenzelm@23252
   216
              val  (tm5,tm6) = Thm.dest_comb(concl th3)
wenzelm@23252
   217
              val  (tm7,tm8) = Thm.dest_comb tm6
wenzelm@23252
   218
             val  th4 = monomial_mul tm6 (Thm.dest_arg tm7) tm8
wenzelm@23252
   219
         in  transitive th3 (Drule.arg_cong_rule tm5 th4)
wenzelm@23252
   220
         end
wenzelm@23252
   221
         else
wenzelm@23252
   222
          let val th0 = if ord < 0 then pthm_16 else pthm_17
wenzelm@23252
   223
             val th1 = inst_thm [(clx,lx),(cly,ly),(crx,rx),(cry,ry)] th0
wenzelm@23252
   224
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   225
             val (tm3,tm4) = Thm.dest_comb tm2
wenzelm@23252
   226
         in transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4))
wenzelm@23252
   227
         end
wenzelm@23252
   228
        end)
wenzelm@23252
   229
       handle CTERM _ =>
wenzelm@23252
   230
        (let val vr = powvar r val ord = vorder vl vr
wenzelm@23252
   231
        in
wenzelm@23252
   232
          if ord = 0 then
wenzelm@23252
   233
           let
wenzelm@23252
   234
           val th1 = inst_thm [(clx,lx),(cly,ly),(crx,r)] pthm_18
wenzelm@23252
   235
                 val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   236
           val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   237
           val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv tm4)) tm2
wenzelm@23252
   238
          in transitive th1 th2
wenzelm@23252
   239
          end
wenzelm@23252
   240
          else
wenzelm@23252
   241
          if ord < 0 then
wenzelm@23252
   242
            let val th1 = inst_thm [(clx,lx),(cly,ly),(crx,r)] pthm_19
wenzelm@23252
   243
                val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   244
                val (tm3,tm4) = Thm.dest_comb tm2
wenzelm@23252
   245
           in transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4))
wenzelm@23252
   246
           end
wenzelm@23252
   247
           else inst_thm [(ca,l),(cb,r)] pthm_09
wenzelm@23252
   248
        end)) end)
wenzelm@23252
   249
     handle CTERM _ =>
wenzelm@23252
   250
      (let val vl = powvar l in
wenzelm@23252
   251
        ((let
wenzelm@23252
   252
          val (rx,ry) = dest_mul r
wenzelm@23252
   253
          val vr = powvar rx
wenzelm@23252
   254
           val ord = vorder vl vr
wenzelm@23252
   255
         in if ord = 0 then
wenzelm@23252
   256
              let val th1 = inst_thm [(clx,l),(crx,rx),(cry,ry)] pthm_21
wenzelm@23252
   257
                 val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   258
                 val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   259
             in transitive th1 (Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (powvar_mul_conv tm4)) tm2)
wenzelm@23252
   260
             end
wenzelm@23252
   261
             else if ord > 0 then
wenzelm@23252
   262
                 let val th1 = inst_thm [(clx,l),(crx,rx),(cry,ry)] pthm_22
wenzelm@23252
   263
                     val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   264
                    val (tm3,tm4) = Thm.dest_comb tm2
wenzelm@23252
   265
                in transitive th1 (Drule.arg_cong_rule tm1 (monomial_mul tm2 (Thm.dest_arg tm3) tm4))
wenzelm@23252
   266
                end
wenzelm@23252
   267
             else reflexive tm
wenzelm@23252
   268
         end)
wenzelm@23252
   269
        handle CTERM _ =>
wenzelm@23252
   270
          (let val vr = powvar r
wenzelm@23252
   271
               val  ord = vorder vl vr
wenzelm@23252
   272
          in if ord = 0 then powvar_mul_conv tm
wenzelm@23252
   273
              else if ord > 0 then inst_thm [(ca,l),(cb,r)] pthm_09
wenzelm@23252
   274
              else reflexive tm
wenzelm@23252
   275
          end)) end))
wenzelm@23252
   276
  in fn tm => let val (l,r) = dest_mul tm in monomial_deone(monomial_mul tm l r)
wenzelm@23252
   277
             end
wenzelm@23252
   278
  end;
wenzelm@23252
   279
(* Multiplication by monomial of a polynomial.                               *)
wenzelm@23252
   280
wenzelm@23252
   281
 val polynomial_monomial_mul_conv =
wenzelm@23252
   282
  let
wenzelm@23252
   283
   fun pmm_conv tm =
wenzelm@23252
   284
    let val (l,r) = dest_mul tm
wenzelm@23252
   285
    in
wenzelm@23252
   286
    ((let val (y,z) = dest_add r
wenzelm@23252
   287
          val th1 = inst_thm [(cx,l),(cy,y),(cz,z)] pthm_37
wenzelm@23252
   288
          val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   289
          val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   290
          val th2 = combination (Drule.arg_cong_rule tm3 (monomial_mul_conv tm4)) (pmm_conv tm2)
wenzelm@23252
   291
      in transitive th1 th2
wenzelm@23252
   292
      end)
wenzelm@23252
   293
     handle CTERM _ => monomial_mul_conv tm)
wenzelm@23252
   294
   end
wenzelm@23252
   295
 in pmm_conv
wenzelm@23252
   296
 end;
wenzelm@23252
   297
wenzelm@23252
   298
(* Addition of two monomials identical except for constant multiples.        *)
wenzelm@23252
   299
wenzelm@23252
   300
fun monomial_add_conv tm =
wenzelm@23252
   301
 let val (l,r) = dest_add tm
wenzelm@23252
   302
 in if is_semiring_constant l andalso is_semiring_constant r
wenzelm@23252
   303
    then semiring_add_conv tm
wenzelm@23252
   304
    else
wenzelm@23252
   305
     let val th1 =
wenzelm@23252
   306
           if is_mul l andalso is_semiring_constant(Thm.dest_arg1 l)
wenzelm@23252
   307
           then if is_mul r andalso is_semiring_constant(Thm.dest_arg1 r) then
wenzelm@23252
   308
                    inst_thm [(ca,Thm.dest_arg1 l),(cm,Thm.dest_arg r), (cb,Thm.dest_arg1 r)] pthm_02
wenzelm@23252
   309
                else inst_thm [(ca,Thm.dest_arg1 l),(cm,r)] pthm_03
wenzelm@23252
   310
           else if is_mul r andalso is_semiring_constant(Thm.dest_arg1 r)
wenzelm@23252
   311
           then inst_thm [(cm,l),(ca,Thm.dest_arg1 r)] pthm_04
wenzelm@23252
   312
           else inst_thm [(cm,r)] pthm_05
wenzelm@23252
   313
         val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   314
         val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   315
         val th2 = Drule.arg_cong_rule tm3 (semiring_add_conv tm4)
wenzelm@23252
   316
         val th3 = transitive th1 (Drule.fun_cong_rule th2 tm2)
wenzelm@23252
   317
         val tm5 = concl th3
wenzelm@23252
   318
      in
wenzelm@23252
   319
      if (Thm.dest_arg1 tm5) aconvc zero_tm
wenzelm@23252
   320
      then transitive th3 (inst_thm [(ca,Thm.dest_arg tm5)] pthm_11)
wenzelm@23252
   321
      else monomial_deone th3
wenzelm@23252
   322
     end
wenzelm@23252
   323
 end;
wenzelm@23252
   324
wenzelm@23252
   325
(* Ordering on monomials.                                                    *)
wenzelm@23252
   326
wenzelm@23252
   327
fun striplist dest =
wenzelm@23252
   328
 let fun strip x acc =
wenzelm@23252
   329
   ((let val (l,r) = dest x in
wenzelm@23252
   330
        strip l (strip r acc) end)
wenzelm@23252
   331
    handle CTERM _ => x::acc)    (* FIXME !? *)
wenzelm@23252
   332
 in fn x => strip x []
wenzelm@23252
   333
 end;
wenzelm@23252
   334
wenzelm@23252
   335
wenzelm@23252
   336
fun powervars tm =
wenzelm@23252
   337
 let val ptms = striplist dest_mul tm
wenzelm@23252
   338
 in if is_semiring_constant (hd ptms) then tl ptms else ptms
wenzelm@23252
   339
 end;
wenzelm@23252
   340
val num_0 = 0;
wenzelm@23252
   341
val num_1 = 1;
wenzelm@23252
   342
fun dest_varpow tm =
wenzelm@23252
   343
 ((let val (x,n) = dest_pow tm in (x,dest_numeral n) end)
wenzelm@23252
   344
   handle CTERM _ =>
wenzelm@23252
   345
   (tm,(if is_semiring_constant tm then num_0 else num_1)));
wenzelm@23252
   346
wenzelm@23252
   347
val morder =
wenzelm@23252
   348
 let fun lexorder l1 l2 =
wenzelm@23252
   349
  case (l1,l2) of
wenzelm@23252
   350
    ([],[]) => 0
wenzelm@23252
   351
  | (vps,[]) => ~1
wenzelm@23252
   352
  | ([],vps) => 1
wenzelm@23252
   353
  | (((x1,n1)::vs1),((x2,n2)::vs2)) =>
wenzelm@23252
   354
     if variable_order x1 x2 then 1
wenzelm@23252
   355
     else if variable_order x2 x1 then ~1
wenzelm@23252
   356
     else if n1 < n2 then ~1
wenzelm@23252
   357
     else if n2 < n1 then 1
wenzelm@23252
   358
     else lexorder vs1 vs2
wenzelm@23252
   359
 in fn tm1 => fn tm2 =>
wenzelm@23252
   360
  let val vdegs1 = map dest_varpow (powervars tm1)
wenzelm@23252
   361
      val vdegs2 = map dest_varpow (powervars tm2)
wenzelm@23252
   362
      val deg1 = fold_rev ((curry (op +)) o snd) vdegs1 num_0
wenzelm@23252
   363
      val deg2 = fold_rev ((curry (op +)) o snd) vdegs2 num_0
wenzelm@23252
   364
  in if deg1 < deg2 then ~1 else if deg1 > deg2 then 1
wenzelm@23252
   365
                            else lexorder vdegs1 vdegs2
wenzelm@23252
   366
  end
wenzelm@23252
   367
 end;
wenzelm@23252
   368
wenzelm@23252
   369
(* Addition of two polynomials.                                              *)
wenzelm@23252
   370
wenzelm@23252
   371
val polynomial_add_conv =
wenzelm@23252
   372
 let
wenzelm@23252
   373
 fun dezero_rule th =
wenzelm@23252
   374
  let
wenzelm@23252
   375
   val tm = concl th
wenzelm@23252
   376
  in
wenzelm@23252
   377
   if not(is_add tm) then th else
wenzelm@23252
   378
   let val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   379
       val l = Thm.dest_arg lopr
wenzelm@23252
   380
   in
wenzelm@23252
   381
    if l aconvc zero_tm
wenzelm@23252
   382
    then transitive th (inst_thm [(ca,r)] pthm_07)   else
wenzelm@23252
   383
        if r aconvc zero_tm
wenzelm@23252
   384
        then transitive th (inst_thm [(ca,l)] pthm_08)  else th
wenzelm@23252
   385
   end
wenzelm@23252
   386
  end
wenzelm@23252
   387
 fun padd tm =
wenzelm@23252
   388
  let
wenzelm@23252
   389
   val (l,r) = dest_add tm
wenzelm@23252
   390
  in
wenzelm@23252
   391
   if l aconvc zero_tm then inst_thm [(ca,r)] pthm_07
wenzelm@23252
   392
   else if r aconvc zero_tm then inst_thm [(ca,l)] pthm_08
wenzelm@23252
   393
   else
wenzelm@23252
   394
    if is_add l
wenzelm@23252
   395
    then
wenzelm@23252
   396
     let val (a,b) = dest_add l
wenzelm@23252
   397
     in
wenzelm@23252
   398
     if is_add r then
wenzelm@23252
   399
      let val (c,d) = dest_add r
wenzelm@23252
   400
          val ord = morder a c
wenzelm@23252
   401
      in
wenzelm@23252
   402
       if ord = 0 then
wenzelm@23252
   403
        let val th1 = inst_thm [(ca,a),(cb,b),(cc,c),(cd,d)] pthm_23
wenzelm@23252
   404
            val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   405
            val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   406
            val th2 = Drule.arg_cong_rule tm3 (monomial_add_conv tm4)
wenzelm@23252
   407
        in dezero_rule (transitive th1 (combination th2 (padd tm2)))
wenzelm@23252
   408
        end
wenzelm@23252
   409
       else (* ord <> 0*)
wenzelm@23252
   410
        let val th1 =
wenzelm@23252
   411
                if ord > 0 then inst_thm [(ca,a),(cb,b),(cc,r)] pthm_24
wenzelm@23252
   412
                else inst_thm [(ca,l),(cc,c),(cd,d)] pthm_25
wenzelm@23252
   413
            val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   414
        in dezero_rule (transitive th1 (Drule.arg_cong_rule tm1 (padd tm2)))
wenzelm@23252
   415
        end
wenzelm@23252
   416
      end
wenzelm@23252
   417
     else (* not (is_add r)*)
wenzelm@23252
   418
      let val ord = morder a r
wenzelm@23252
   419
      in
wenzelm@23252
   420
       if ord = 0 then
wenzelm@23252
   421
        let val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_26
wenzelm@23252
   422
            val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   423
            val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   424
            val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (monomial_add_conv tm4)) tm2
wenzelm@23252
   425
        in dezero_rule (transitive th1 th2)
wenzelm@23252
   426
        end
wenzelm@23252
   427
       else (* ord <> 0*)
wenzelm@23252
   428
        if ord > 0 then
wenzelm@23252
   429
          let val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_24
wenzelm@23252
   430
              val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   431
          in dezero_rule (transitive th1 (Drule.arg_cong_rule tm1 (padd tm2)))
wenzelm@23252
   432
          end
wenzelm@23252
   433
        else dezero_rule (inst_thm [(ca,l),(cc,r)] pthm_27)
wenzelm@23252
   434
      end
wenzelm@23252
   435
    end
wenzelm@23252
   436
   else (* not (is_add l)*)
wenzelm@23252
   437
    if is_add r then
wenzelm@23252
   438
      let val (c,d) = dest_add r
wenzelm@23252
   439
          val  ord = morder l c
wenzelm@23252
   440
      in
wenzelm@23252
   441
       if ord = 0 then
wenzelm@23252
   442
         let val th1 = inst_thm [(ca,l),(cc,c),(cd,d)] pthm_28
wenzelm@23252
   443
             val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   444
             val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   445
             val th2 = Drule.fun_cong_rule (Drule.arg_cong_rule tm3 (monomial_add_conv tm4)) tm2
wenzelm@23252
   446
         in dezero_rule (transitive th1 th2)
wenzelm@23252
   447
         end
wenzelm@23252
   448
       else
wenzelm@23252
   449
        if ord > 0 then reflexive tm
wenzelm@23252
   450
        else
wenzelm@23252
   451
         let val th1 = inst_thm [(ca,l),(cc,c),(cd,d)] pthm_25
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
      end
wenzelm@23252
   456
    else
wenzelm@23252
   457
     let val ord = morder l r
wenzelm@23252
   458
     in
wenzelm@23252
   459
      if ord = 0 then monomial_add_conv tm
wenzelm@23252
   460
      else if ord > 0 then dezero_rule(reflexive tm)
wenzelm@23252
   461
      else dezero_rule (inst_thm [(ca,l),(cc,r)] pthm_27)
wenzelm@23252
   462
     end
wenzelm@23252
   463
  end
wenzelm@23252
   464
 in padd
wenzelm@23252
   465
 end;
wenzelm@23252
   466
wenzelm@23252
   467
(* Multiplication of two polynomials.                                        *)
wenzelm@23252
   468
wenzelm@23252
   469
val polynomial_mul_conv =
wenzelm@23252
   470
 let
wenzelm@23252
   471
  fun pmul tm =
wenzelm@23252
   472
   let val (l,r) = dest_mul tm
wenzelm@23252
   473
   in
wenzelm@23252
   474
    if not(is_add l) then polynomial_monomial_mul_conv tm
wenzelm@23252
   475
    else
wenzelm@23252
   476
     if not(is_add r) then
wenzelm@23252
   477
      let val th1 = inst_thm [(ca,l),(cb,r)] pthm_09
wenzelm@23252
   478
      in transitive th1 (polynomial_monomial_mul_conv(concl th1))
wenzelm@23252
   479
      end
wenzelm@23252
   480
     else
wenzelm@23252
   481
       let val (a,b) = dest_add l
wenzelm@23252
   482
           val th1 = inst_thm [(ca,a),(cb,b),(cc,r)] pthm_10
wenzelm@23252
   483
           val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   484
           val (tm3,tm4) = Thm.dest_comb tm1
wenzelm@23252
   485
           val th2 = Drule.arg_cong_rule tm3 (polynomial_monomial_mul_conv tm4)
wenzelm@23252
   486
           val th3 = transitive th1 (combination th2 (pmul tm2))
wenzelm@23252
   487
       in transitive th3 (polynomial_add_conv (concl th3))
wenzelm@23252
   488
       end
wenzelm@23252
   489
   end
wenzelm@23252
   490
 in fn tm =>
wenzelm@23252
   491
   let val (l,r) = dest_mul tm
wenzelm@23252
   492
   in
wenzelm@23252
   493
    if l aconvc zero_tm then inst_thm [(ca,r)] pthm_11
wenzelm@23252
   494
    else if r aconvc zero_tm then inst_thm [(ca,l)] pthm_12
wenzelm@23252
   495
    else if l aconvc one_tm then inst_thm [(ca,r)] pthm_13
wenzelm@23252
   496
    else if r aconvc one_tm then inst_thm [(ca,l)] pthm_14
wenzelm@23252
   497
    else pmul tm
wenzelm@23252
   498
   end
wenzelm@23252
   499
 end;
wenzelm@23252
   500
wenzelm@23252
   501
(* Power of polynomial (optimized for the monomial and trivial cases).       *)
wenzelm@23252
   502
wenzelm@23580
   503
fun num_conv n =
wenzelm@23580
   504
  nat_add_conv (Thm.capply @{cterm Suc} (Numeral.mk_cnumber @{ctyp nat} (dest_numeral n - 1)))
wenzelm@23580
   505
  |> Thm.symmetric;
wenzelm@23252
   506
wenzelm@23252
   507
wenzelm@23252
   508
val polynomial_pow_conv =
wenzelm@23252
   509
 let
wenzelm@23252
   510
  fun ppow tm =
wenzelm@23252
   511
    let val (l,n) = dest_pow tm
wenzelm@23252
   512
    in
wenzelm@23252
   513
     if n aconvc zeron_tm then inst_thm [(cx,l)] pthm_35
wenzelm@23252
   514
     else if n aconvc onen_tm then inst_thm [(cx,l)] pthm_36
wenzelm@23252
   515
     else
wenzelm@23252
   516
         let val th1 = num_conv n
wenzelm@23252
   517
             val th2 = inst_thm [(cx,l),(cq,Thm.dest_arg (concl th1))] pthm_38
wenzelm@23252
   518
             val (tm1,tm2) = Thm.dest_comb(concl th2)
wenzelm@23252
   519
             val th3 = transitive th2 (Drule.arg_cong_rule tm1 (ppow tm2))
wenzelm@23252
   520
             val th4 = transitive (Drule.arg_cong_rule (Thm.dest_fun tm) th1) th3
wenzelm@23252
   521
         in transitive th4 (polynomial_mul_conv (concl th4))
wenzelm@23252
   522
         end
wenzelm@23252
   523
    end
wenzelm@23252
   524
 in fn tm =>
wenzelm@23252
   525
       if is_add(Thm.dest_arg1 tm) then ppow tm else monomial_pow_conv tm
wenzelm@23252
   526
 end;
wenzelm@23252
   527
wenzelm@23252
   528
(* Negation.                                                                 *)
wenzelm@23252
   529
wenzelm@23580
   530
fun polynomial_neg_conv tm =
wenzelm@23252
   531
   let val (l,r) = Thm.dest_comb tm in
wenzelm@23252
   532
        if not (l aconvc neg_tm) then raise CTERM ("polynomial_neg_conv",[tm]) else
wenzelm@23252
   533
        let val th1 = inst_thm [(cx',r)] neg_mul
wenzelm@23252
   534
            val th2 = transitive th1 (arg1_conv semiring_mul_conv (concl th1))
wenzelm@23252
   535
        in transitive th2 (polynomial_monomial_mul_conv (concl th2))
wenzelm@23252
   536
        end
wenzelm@23252
   537
   end;
wenzelm@23252
   538
wenzelm@23252
   539
wenzelm@23252
   540
(* Subtraction.                                                              *)
wenzelm@23580
   541
fun polynomial_sub_conv tm =
wenzelm@23252
   542
  let val (l,r) = dest_sub tm
wenzelm@23252
   543
      val th1 = inst_thm [(cx',l),(cy',r)] sub_add
wenzelm@23252
   544
      val (tm1,tm2) = Thm.dest_comb(concl th1)
wenzelm@23252
   545
      val th2 = Drule.arg_cong_rule tm1 (polynomial_neg_conv tm2)
wenzelm@23252
   546
  in transitive th1 (transitive th2 (polynomial_add_conv (concl th2)))
wenzelm@23252
   547
  end;
wenzelm@23252
   548
wenzelm@23252
   549
(* Conversion from HOL term.                                                 *)
wenzelm@23252
   550
wenzelm@23252
   551
fun polynomial_conv tm =
chaieb@23407
   552
 if is_semiring_constant tm then semiring_add_conv tm
chaieb@23407
   553
 else if not(is_comb tm) then reflexive tm
wenzelm@23252
   554
 else
wenzelm@23252
   555
  let val (lopr,r) = Thm.dest_comb tm
wenzelm@23252
   556
  in if lopr aconvc neg_tm then
wenzelm@23252
   557
       let val th1 = Drule.arg_cong_rule lopr (polynomial_conv r)
wenzelm@23252
   558
       in transitive th1 (polynomial_neg_conv (concl th1))
wenzelm@23252
   559
       end
wenzelm@23252
   560
     else
wenzelm@23252
   561
       if not(is_comb lopr) then reflexive tm
wenzelm@23252
   562
       else
wenzelm@23252
   563
         let val (opr,l) = Thm.dest_comb lopr
wenzelm@23252
   564
         in if opr aconvc pow_tm andalso is_numeral r
wenzelm@23252
   565
            then
wenzelm@23252
   566
              let val th1 = Drule.fun_cong_rule (Drule.arg_cong_rule opr (polynomial_conv l)) r
wenzelm@23252
   567
              in transitive th1 (polynomial_pow_conv (concl th1))
wenzelm@23252
   568
              end
wenzelm@23252
   569
            else
wenzelm@23252
   570
              if opr aconvc add_tm orelse opr aconvc mul_tm orelse opr aconvc sub_tm
wenzelm@23252
   571
              then
wenzelm@23252
   572
               let val th1 = combination (Drule.arg_cong_rule opr (polynomial_conv l)) (polynomial_conv r)
wenzelm@23252
   573
                   val f = if opr aconvc add_tm then polynomial_add_conv
wenzelm@23252
   574
                      else if opr aconvc mul_tm then polynomial_mul_conv
wenzelm@23252
   575
                      else polynomial_sub_conv
wenzelm@23252
   576
               in transitive th1 (f (concl th1))
wenzelm@23252
   577
               end
wenzelm@23252
   578
              else reflexive tm
wenzelm@23252
   579
         end
wenzelm@23252
   580
  end;
wenzelm@23252
   581
 in
wenzelm@23252
   582
   {main = polynomial_conv,
wenzelm@23252
   583
    add = polynomial_add_conv,
wenzelm@23252
   584
    mul = polynomial_mul_conv,
wenzelm@23252
   585
    pow = polynomial_pow_conv,
wenzelm@23252
   586
    neg = polynomial_neg_conv,
wenzelm@23252
   587
    sub = polynomial_sub_conv}
wenzelm@23252
   588
 end
wenzelm@23252
   589
end;
wenzelm@23252
   590
wenzelm@23252
   591
val nat_arith = @{thms "nat_arith"};
wenzelm@23252
   592
val nat_exp_ss = HOL_basic_ss addsimps (nat_number @ nat_arith @ arith_simps @ rel_simps)
haftmann@23880
   593
                              addsimps [Let_def, if_False, if_True, @{thm add_0}, @{thm add_Suc}];
wenzelm@23252
   594
chaieb@23407
   595
fun simple_cterm_ord t u = Term.term_ord (term_of t, term_of u) = LESS;
chaieb@23407
   596
fun semiring_normalize_ord_wrapper ctxt ({vars, semiring, ring, idom}, 
chaieb@23407
   597
                                     {conv, dest_const, mk_const, is_const}) ord =
wenzelm@23252
   598
  let
wenzelm@23252
   599
    val pow_conv =
wenzelm@23252
   600
      arg_conv (Simplifier.rewrite nat_exp_ss)
wenzelm@23252
   601
      then_conv Simplifier.rewrite
wenzelm@23252
   602
        (HOL_basic_ss addsimps [nth (snd semiring) 31, nth (snd semiring) 34])
chaieb@23330
   603
      then_conv conv ctxt
chaieb@23330
   604
    val dat = (is_const, conv ctxt, conv ctxt, pow_conv)
wenzelm@23252
   605
    val {main, ...} = semiring_normalizers_conv vars semiring ring dat ord
wenzelm@23252
   606
  in main end;
wenzelm@23252
   607
chaieb@23407
   608
fun semiring_normalize_wrapper ctxt data = 
chaieb@23407
   609
  semiring_normalize_ord_wrapper ctxt data simple_cterm_ord;
chaieb@23407
   610
chaieb@23407
   611
fun semiring_normalize_ord_conv ctxt ord tm =
wenzelm@23252
   612
  (case NormalizerData.match ctxt tm of
wenzelm@23252
   613
    NONE => reflexive tm
chaieb@23407
   614
  | SOME res => semiring_normalize_ord_wrapper ctxt res ord tm);
chaieb@23407
   615
 
wenzelm@23252
   616
chaieb@23407
   617
fun semiring_normalize_conv ctxt = semiring_normalize_ord_conv ctxt simple_cterm_ord;
wenzelm@23252
   618
wenzelm@23252
   619
fun semiring_normalize_tac ctxt = SUBGOAL (fn (goal, i) =>
wenzelm@23252
   620
  rtac (semiring_normalize_conv ctxt
wenzelm@23252
   621
    (cterm_of (ProofContext.theory_of ctxt) (fst (Logic.dest_equals goal)))) i);
wenzelm@23252
   622
end;