src/HOL/ex/coopertac.ML
author huffman
Wed Jun 13 03:28:21 2007 +0200 (2007-06-13)
changeset 23364 1f3b832c90c1
parent 23318 6d68b07ab5cf
child 23469 3f309f885d0b
permissions -rw-r--r--
thm antiquotations
     1 structure LinZTac =
     2 struct
     3 
     4 val trace = ref false;
     5 fun trace_msg s = if !trace then tracing s else ();
     6 
     7 val cooper_ss = @{simpset};
     8 
     9 val nT = HOLogic.natT;
    10 val binarith = map thm
    11   ["Pls_0_eq", "Min_1_eq"];
    12 val comp_arith = binarith @ simp_thms
    13 
    14 val zdvd_int = thm "zdvd_int";
    15 val zdiff_int_split = thm "zdiff_int_split";
    16 val all_nat = thm "all_nat";
    17 val ex_nat = thm "ex_nat";
    18 val number_of1 = thm "number_of1";
    19 val number_of2 = thm "number_of2";
    20 val split_zdiv = thm "split_zdiv";
    21 val split_zmod = thm "split_zmod";
    22 val mod_div_equality' = thm "mod_div_equality'";
    23 val split_div' = thm "split_div'";
    24 val Suc_plus1 = thm "Suc_plus1";
    25 val imp_le_cong = thm "imp_le_cong";
    26 val conj_le_cong = thm "conj_le_cong";
    27 val nat_mod_add_eq = mod_add1_eq RS sym;
    28 val nat_mod_add_left_eq = mod_add_left_eq RS sym;
    29 val nat_mod_add_right_eq = mod_add_right_eq RS sym;
    30 val int_mod_add_eq = @{thm "zmod_zadd1_eq"} RS sym;
    31 val int_mod_add_left_eq = @{thm "zmod_zadd_left_eq"} RS sym;
    32 val int_mod_add_right_eq = @{thm "zmod_zadd_right_eq"} RS sym;
    33 val nat_div_add_eq = @{thm "div_add1_eq"} RS sym;
    34 val int_div_add_eq = @{thm "zdiv_zadd1_eq"} RS sym;
    35 val ZDIVISION_BY_ZERO_MOD = @{thm "DIVISION_BY_ZERO"} RS conjunct2;
    36 val ZDIVISION_BY_ZERO_DIV = @{thm "DIVISION_BY_ZERO"} RS conjunct1;
    37 
    38 (*
    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"]);
    40 *)
    41 fun prepare_for_linz q fm = 
    42   let
    43     val ps = Logic.strip_params fm
    44     val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm)
    45     val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm)
    46     fun mk_all ((s, T), (P,n)) =
    47       if 0 mem loose_bnos P then
    48         (HOLogic.all_const T $ Abs (s, T, P), n)
    49       else (incr_boundvars ~1 P, n-1)
    50     fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t;
    51       val rhs = hs
    52 (*    val (rhs,irhs) = List.partition (relevant (rev ps)) hs *)
    53     val np = length ps
    54     val (fm',np) =  foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n)))
    55       (foldr HOLogic.mk_imp c rhs, np) ps
    56     val (vs, _) = List.partition (fn t => q orelse (type_of t) = nT)
    57       (term_frees fm' @ term_vars fm');
    58     val fm2 = foldr mk_all2 fm' vs
    59   in (fm2, np + length vs, length rhs) end;
    60 
    61 (*Object quantifier to meta --*)
    62 fun spec_step n th = if (n=0) then th else (spec_step (n-1) th) RS spec ;
    63 
    64 (* object implication to meta---*)
    65 fun mp_step n th = if (n=0) then th else (mp_step (n-1) th) RS mp;
    66 
    67 
    68 fun linz_tac ctxt q i = ObjectLogic.atomize_tac i THEN (fn st =>
    69   let
    70     val g = List.nth (prems_of st, i - 1)
    71     val thy = ProofContext.theory_of ctxt
    72     (* Transform the term*)
    73     val (t,np,nh) = prepare_for_linz q g
    74     (* Some simpsets for dealing with mod div abs and nat*)
    75     val mod_div_simpset = HOL_basic_ss 
    76 			addsimps [refl,nat_mod_add_eq, nat_mod_add_left_eq, 
    77 				  nat_mod_add_right_eq, int_mod_add_eq, 
    78 				  int_mod_add_right_eq, int_mod_add_left_eq,
    79 				  nat_div_add_eq, int_div_add_eq,
    80 				  mod_self, @{thm "zmod_self"},
    81 				  DIVISION_BY_ZERO_MOD,DIVISION_BY_ZERO_DIV,
    82 				  ZDIVISION_BY_ZERO_MOD,ZDIVISION_BY_ZERO_DIV,
    83 				  @{thm "zdiv_zero"}, @{thm "zmod_zero"}, @{thm "div_0"}, @{thm "mod_0"},
    84 				  @{thm "zdiv_1"}, @{thm "zmod_1"}, @{thm "div_1"}, @{thm "mod_1"},
    85 				  Suc_plus1]
    86 			addsimps add_ac
    87 			addsimprocs [cancel_div_mod_proc]
    88     val simpset0 = HOL_basic_ss
    89       addsimps [mod_div_equality', Suc_plus1]
    90       addsimps comp_arith
    91       addsplits [split_zdiv, split_zmod, split_div', @{thm "split_min"}, @{thm "split_max"}]
    92     (* Simp rules for changing (n::int) to int n *)
    93     val simpset1 = HOL_basic_ss
    94       addsimps [nat_number_of_def, zdvd_int] @ map (fn r => r RS sym)
    95         [@{thm int_int_eq}, @{thm zle_int}, @{thm zless_int}, @{thm zadd_int}, @{thm zmult_int}]
    96       addsplits [zdiff_int_split]
    97     (*simp rules for elimination of int n*)
    98 
    99     val simpset2 = HOL_basic_ss
   100       addsimps [@{thm nat_0_le}, @{thm all_nat}, @{thm ex_nat}, @{thm number_of1}, @{thm number_of2}, @{thm int_0}, @{thm int_1}]
   101       addcongs [@{thm conj_le_cong}, @{thm imp_le_cong}]
   102     (* simp rules for elimination of abs *)
   103     val simpset3 = HOL_basic_ss addsplits [@{thm abs_split}]
   104     val ct = cterm_of thy (HOLogic.mk_Trueprop t)
   105     (* Theorem for the nat --> int transformation *)
   106     val pre_thm = Seq.hd (EVERY
   107       [simp_tac mod_div_simpset 1, simp_tac simpset0 1,
   108        TRY (simp_tac simpset1 1), TRY (simp_tac simpset2 1),
   109        TRY (simp_tac simpset3 1), TRY (simp_tac cooper_ss 1)]
   110       (trivial ct))
   111     fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i)
   112     (* The result of the quantifier elimination *)
   113     val (th, tac) = case (prop_of pre_thm) of
   114         Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ =>
   115     let val pth = linzqe_oracle thy (Pattern.eta_long [] t1)
   116     in 
   117           ((pth RS iffD2) RS pre_thm,
   118             assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i))
   119     end
   120       | _ => (pre_thm, assm_tac i)
   121   in (rtac (((mp_step nh) o (spec_step np)) th) i 
   122       THEN tac) st
   123   end handle Subscript => no_tac st);
   124 
   125 fun linz_args meth =
   126  let val parse_flag = 
   127          Args.$$$ "no_quantify" >> (K (K false));
   128  in
   129    Method.simple_args 
   130   (Scan.optional (Args.$$$ "(" |-- Scan.repeat1 parse_flag --| Args.$$$ ")") [] >>
   131     curry (Library.foldl op |>) true)
   132     (fn q => fn ctxt => meth ctxt q 1)
   133   end;
   134 
   135 fun linz_method ctxt q i = Method.METHOD (fn facts =>
   136   Method.insert_tac facts 1 THEN linz_tac ctxt q i);
   137 
   138 val setup =
   139   Method.add_method ("cooper",
   140      linz_args linz_method,
   141      "decision procedure for linear integer arithmetic");
   142 
   143 end