src/HOL/ex/coopertac.ML
author wenzelm
Thu, 05 Jul 2007 20:01:26 +0200
changeset 23590 ad95084a5c63
parent 23469 3f309f885d0b
child 23880 64b9806e160b
permissions -rw-r--r--
renamed ObjectLogic.atomize_tac to ObjectLogic.atomize_prems_tac;
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
23274
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
     1
structure LinZTac =
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
     2
struct
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
     3
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
     4
val trace = ref false;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
     5
fun trace_msg s = if !trace then tracing s else ();
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
     6
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
     7
val cooper_ss = @{simpset};
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
     8
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
     9
val nT = HOLogic.natT;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    10
val binarith = map thm
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    11
  ["Pls_0_eq", "Min_1_eq"];
23318
6d68b07ab5cf tuned tactic
chaieb
parents: 23274
diff changeset
    12
val comp_arith = binarith @ simp_thms
23274
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    13
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    14
val zdvd_int = thm "zdvd_int";
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    15
val zdiff_int_split = thm "zdiff_int_split";
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    16
val all_nat = thm "all_nat";
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    17
val ex_nat = thm "ex_nat";
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    18
val number_of1 = thm "number_of1";
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    19
val number_of2 = thm "number_of2";
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    20
val split_zdiv = thm "split_zdiv";
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    21
val split_zmod = thm "split_zmod";
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    22
val mod_div_equality' = thm "mod_div_equality'";
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    23
val split_div' = thm "split_div'";
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    24
val Suc_plus1 = thm "Suc_plus1";
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    25
val imp_le_cong = thm "imp_le_cong";
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    26
val conj_le_cong = thm "conj_le_cong";
23469
3f309f885d0b add thm antiquotations
huffman
parents: 23364
diff changeset
    27
val nat_mod_add_eq = @{thm mod_add1_eq} RS sym;
3f309f885d0b add thm antiquotations
huffman
parents: 23364
diff changeset
    28
val nat_mod_add_left_eq = @{thm mod_add_left_eq} RS sym;
3f309f885d0b add thm antiquotations
huffman
parents: 23364
diff changeset
    29
val nat_mod_add_right_eq = @{thm mod_add_right_eq} RS sym;
23274
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    30
val int_mod_add_eq = @{thm "zmod_zadd1_eq"} RS sym;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    31
val int_mod_add_left_eq = @{thm "zmod_zadd_left_eq"} RS sym;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    32
val int_mod_add_right_eq = @{thm "zmod_zadd_right_eq"} RS sym;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    33
val nat_div_add_eq = @{thm "div_add1_eq"} RS sym;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    34
val int_div_add_eq = @{thm "zdiv_zadd1_eq"} RS sym;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    35
val ZDIVISION_BY_ZERO_MOD = @{thm "DIVISION_BY_ZERO"} RS conjunct2;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    36
val ZDIVISION_BY_ZERO_DIV = @{thm "DIVISION_BY_ZERO"} RS conjunct1;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    37
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    38
(*
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    39
val fn_rews = List.concat (map thms ["allpairs.simps","iupt.simps","decr.simps", "decrnum.simps","disjuncts.simps","simpnum.simps", "simpfm.simps","numadd.simps","nummul.simps","numneg_def","numsub","simp_num_pair_def","not.simps","prep.simps","qelim.simps","minusinf.simps","plusinf.simps","rsplit0.simps","rlfm.simps","\\<Upsilon>.simps","\\<upsilon>.simps","linrqe_def", "ferrack_def", "Let_def", "numsub_def", "numneg_def","DJ_def", "imp_def", "evaldjf_def", "djf_def", "split_def", "eq_def", "disj_def", "simp_num_pair_def", "conj_def", "lt_def", "neq_def","gt_def"]);
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    40
*)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    41
fun prepare_for_linz q fm = 
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    42
  let
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    43
    val ps = Logic.strip_params fm
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    44
    val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    45
    val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    46
    fun mk_all ((s, T), (P,n)) =
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    47
      if 0 mem loose_bnos P then
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    48
        (HOLogic.all_const T $ Abs (s, T, P), n)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    49
      else (incr_boundvars ~1 P, n-1)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    50
    fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    51
      val rhs = hs
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    52
(*    val (rhs,irhs) = List.partition (relevant (rev ps)) hs *)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    53
    val np = length ps
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    54
    val (fm',np) =  foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n)))
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    55
      (foldr HOLogic.mk_imp c rhs, np) ps
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    56
    val (vs, _) = List.partition (fn t => q orelse (type_of t) = nT)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    57
      (term_frees fm' @ term_vars fm');
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    58
    val fm2 = foldr mk_all2 fm' vs
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    59
  in (fm2, np + length vs, length rhs) end;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    60
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    61
(*Object quantifier to meta --*)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    62
fun spec_step n th = if (n=0) then th else (spec_step (n-1) th) RS spec ;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    63
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    64
(* object implication to meta---*)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    65
fun mp_step n th = if (n=0) then th else (mp_step (n-1) th) RS mp;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    66
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    67
23590
ad95084a5c63 renamed ObjectLogic.atomize_tac to ObjectLogic.atomize_prems_tac;
wenzelm
parents: 23469
diff changeset
    68
fun linz_tac ctxt q i = ObjectLogic.atomize_prems_tac i THEN (fn st =>
23274
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    69
  let
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    70
    val g = List.nth (prems_of st, i - 1)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    71
    val thy = ProofContext.theory_of ctxt
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    72
    (* Transform the term*)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    73
    val (t,np,nh) = prepare_for_linz q g
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    74
    (* Some simpsets for dealing with mod div abs and nat*)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    75
    val mod_div_simpset = HOL_basic_ss 
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    76
			addsimps [refl,nat_mod_add_eq, nat_mod_add_left_eq, 
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    77
				  nat_mod_add_right_eq, int_mod_add_eq, 
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    78
				  int_mod_add_right_eq, int_mod_add_left_eq,
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    79
				  nat_div_add_eq, int_div_add_eq,
23469
3f309f885d0b add thm antiquotations
huffman
parents: 23364
diff changeset
    80
				  @{thm mod_self}, @{thm "zmod_self"},
3f309f885d0b add thm antiquotations
huffman
parents: 23364
diff changeset
    81
				  @{thm DIVISION_BY_ZERO_MOD}, @{thm DIVISION_BY_ZERO_DIV},
23274
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    82
				  ZDIVISION_BY_ZERO_MOD,ZDIVISION_BY_ZERO_DIV,
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    83
				  @{thm "zdiv_zero"}, @{thm "zmod_zero"}, @{thm "div_0"}, @{thm "mod_0"},
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    84
				  @{thm "zdiv_1"}, @{thm "zmod_1"}, @{thm "div_1"}, @{thm "mod_1"},
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    85
				  Suc_plus1]
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    86
			addsimps add_ac
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    87
			addsimprocs [cancel_div_mod_proc]
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    88
    val simpset0 = HOL_basic_ss
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    89
      addsimps [mod_div_equality', Suc_plus1]
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    90
      addsimps comp_arith
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    91
      addsplits [split_zdiv, split_zmod, split_div', @{thm "split_min"}, @{thm "split_max"}]
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    92
    (* Simp rules for changing (n::int) to int n *)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    93
    val simpset1 = HOL_basic_ss
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    94
      addsimps [nat_number_of_def, zdvd_int] @ map (fn r => r RS sym)
23364
1f3b832c90c1 thm antiquotations
huffman
parents: 23318
diff changeset
    95
        [@{thm int_int_eq}, @{thm zle_int}, @{thm zless_int}, @{thm zadd_int}, @{thm zmult_int}]
23274
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    96
      addsplits [zdiff_int_split]
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    97
    (*simp rules for elimination of int n*)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    98
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
    99
    val simpset2 = HOL_basic_ss
23364
1f3b832c90c1 thm antiquotations
huffman
parents: 23318
diff changeset
   100
      addsimps [@{thm nat_0_le}, @{thm all_nat}, @{thm ex_nat}, @{thm number_of1}, @{thm number_of2}, @{thm int_0}, @{thm int_1}]
1f3b832c90c1 thm antiquotations
huffman
parents: 23318
diff changeset
   101
      addcongs [@{thm conj_le_cong}, @{thm imp_le_cong}]
23274
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   102
    (* simp rules for elimination of abs *)
23364
1f3b832c90c1 thm antiquotations
huffman
parents: 23318
diff changeset
   103
    val simpset3 = HOL_basic_ss addsplits [@{thm abs_split}]
23274
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   104
    val ct = cterm_of thy (HOLogic.mk_Trueprop t)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   105
    (* Theorem for the nat --> int transformation *)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   106
    val pre_thm = Seq.hd (EVERY
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   107
      [simp_tac mod_div_simpset 1, simp_tac simpset0 1,
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   108
       TRY (simp_tac simpset1 1), TRY (simp_tac simpset2 1),
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   109
       TRY (simp_tac simpset3 1), TRY (simp_tac cooper_ss 1)]
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   110
      (trivial ct))
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   111
    fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   112
    (* The result of the quantifier elimination *)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   113
    val (th, tac) = case (prop_of pre_thm) of
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   114
        Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ =>
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   115
    let val pth = linzqe_oracle thy (Pattern.eta_long [] t1)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   116
    in 
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   117
          ((pth RS iffD2) RS pre_thm,
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   118
            assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i))
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   119
    end
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   120
      | _ => (pre_thm, assm_tac i)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   121
  in (rtac (((mp_step nh) o (spec_step np)) th) i 
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   122
      THEN tac) st
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   123
  end handle Subscript => no_tac st);
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   124
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   125
fun linz_args meth =
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   126
 let val parse_flag = 
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   127
         Args.$$$ "no_quantify" >> (K (K false));
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   128
 in
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   129
   Method.simple_args 
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   130
  (Scan.optional (Args.$$$ "(" |-- Scan.repeat1 parse_flag --| Args.$$$ ")") [] >>
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   131
    curry (Library.foldl op |>) true)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   132
    (fn q => fn ctxt => meth ctxt q 1)
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   133
  end;
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   134
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   135
fun linz_method ctxt q i = Method.METHOD (fn facts =>
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   136
  Method.insert_tac facts 1 THEN linz_tac ctxt q i);
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   137
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   138
val setup =
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   139
  Method.add_method ("cooper",
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   140
     linz_args linz_method,
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   141
     "decision procedure for linear integer arithmetic");
f997514ad8f4 New Reflected Presburger added to HOL/ex
chaieb
parents:
diff changeset
   142
23590
ad95084a5c63 renamed ObjectLogic.atomize_tac to ObjectLogic.atomize_prems_tac;
wenzelm
parents: 23469
diff changeset
   143
end