src/HOL/Decision_Procs/cooper_tac.ML
author nipkow
Tue Mar 03 17:05:18 2009 +0100 (2009-03-03)
changeset 30224 79136ce06bdb
parent 30034 60f64f112174
child 30242 aea5d7fa7ef5
permissions -rw-r--r--
removed and renamed redundant lemmas
     1 (*  Title:      HOL/Reflection/cooper_tac.ML
     2     Author:     Amine Chaieb, TU Muenchen
     3 *)
     4 
     5 structure Cooper_Tac =
     6 struct
     7 
     8 val trace = ref false;
     9 fun trace_msg s = if !trace then tracing s else ();
    10 
    11 val cooper_ss = @{simpset};
    12 
    13 val nT = HOLogic.natT;
    14 val binarith = @{thms normalize_bin_simps};
    15 val comp_arith = binarith @ simp_thms
    16 
    17 val zdvd_int = @{thm zdvd_int};
    18 val zdiff_int_split = @{thm zdiff_int_split};
    19 val all_nat = @{thm all_nat};
    20 val ex_nat = @{thm ex_nat};
    21 val number_of1 = @{thm number_of1};
    22 val number_of2 = @{thm number_of2};
    23 val split_zdiv = @{thm split_zdiv};
    24 val split_zmod = @{thm split_zmod};
    25 val mod_div_equality' = @{thm mod_div_equality'};
    26 val split_div' = @{thm split_div'};
    27 val Suc_plus1 = @{thm Suc_plus1};
    28 val imp_le_cong = @{thm imp_le_cong};
    29 val conj_le_cong = @{thm conj_le_cong};
    30 val mod_add_left_eq = @{thm mod_add_left_eq} RS sym;
    31 val mod_add_right_eq = @{thm mod_add_right_eq} RS sym;
    32 val mod_add_eq = @{thm mod_add_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 
    36 fun prepare_for_linz q fm = 
    37   let
    38     val ps = Logic.strip_params fm
    39     val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm)
    40     val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm)
    41     fun mk_all ((s, T), (P,n)) =
    42       if 0 mem loose_bnos P then
    43         (HOLogic.all_const T $ Abs (s, T, P), n)
    44       else (incr_boundvars ~1 P, n-1)
    45     fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t;
    46     val rhs = hs
    47     val np = length ps
    48     val (fm',np) =  foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n)))
    49       (foldr HOLogic.mk_imp c rhs, np) ps
    50     val (vs, _) = List.partition (fn t => q orelse (type_of t) = nT)
    51       (OldTerm.term_frees fm' @ OldTerm.term_vars fm');
    52     val fm2 = foldr mk_all2 fm' vs
    53   in (fm2, np + length vs, length rhs) end;
    54 
    55 (*Object quantifier to meta --*)
    56 fun spec_step n th = if (n=0) then th else (spec_step (n-1) th) RS spec ;
    57 
    58 (* object implication to meta---*)
    59 fun mp_step n th = if (n=0) then th else (mp_step (n-1) th) RS mp;
    60 
    61 
    62 fun linz_tac ctxt q i = ObjectLogic.atomize_prems_tac i THEN (fn st =>
    63   let
    64     val g = List.nth (prems_of st, i - 1)
    65     val thy = ProofContext.theory_of ctxt
    66     (* Transform the term*)
    67     val (t,np,nh) = prepare_for_linz q g
    68     (* Some simpsets for dealing with mod div abs and nat*)
    69     val mod_div_simpset = HOL_basic_ss 
    70 			addsimps [refl,mod_add_eq, mod_add_left_eq, 
    71 				  mod_add_right_eq,
    72 				  nat_div_add_eq, int_div_add_eq,
    73 				  @{thm mod_self}, @{thm "zmod_self"},
    74 				  @{thm mod_by_0}, @{thm div_by_0},
    75 				  @{thm "zdiv_zero"}, @{thm "zmod_zero"}, @{thm "div_0"}, @{thm "mod_0"},
    76 				  @{thm "div_by_1"}, @{thm "mod_by_1"}, @{thm "div_1"}, @{thm "mod_1"},
    77 				  Suc_plus1]
    78 			addsimps @{thms add_ac}
    79 			addsimprocs [cancel_div_mod_proc]
    80     val simpset0 = HOL_basic_ss
    81       addsimps [mod_div_equality', Suc_plus1]
    82       addsimps comp_arith
    83       addsplits [split_zdiv, split_zmod, split_div', @{thm "split_min"}, @{thm "split_max"}]
    84     (* Simp rules for changing (n::int) to int n *)
    85     val simpset1 = HOL_basic_ss
    86       addsimps [nat_number_of_def, zdvd_int] @ map (fn r => r RS sym)
    87         [@{thm int_int_eq}, @{thm zle_int}, @{thm zless_int}, @{thm zadd_int}, @{thm zmult_int}]
    88       addsplits [zdiff_int_split]
    89     (*simp rules for elimination of int n*)
    90 
    91     val simpset2 = HOL_basic_ss
    92       addsimps [@{thm nat_0_le}, @{thm all_nat}, @{thm ex_nat}, @{thm number_of1}, @{thm number_of2}, @{thm int_0}, @{thm int_1}]
    93       addcongs [@{thm conj_le_cong}, @{thm imp_le_cong}]
    94     (* simp rules for elimination of abs *)
    95     val simpset3 = HOL_basic_ss addsplits [@{thm abs_split}]
    96     val ct = cterm_of thy (HOLogic.mk_Trueprop t)
    97     (* Theorem for the nat --> int transformation *)
    98     val pre_thm = Seq.hd (EVERY
    99       [simp_tac mod_div_simpset 1, simp_tac simpset0 1,
   100        TRY (simp_tac simpset1 1), TRY (simp_tac simpset2 1),
   101        TRY (simp_tac simpset3 1), TRY (simp_tac cooper_ss 1)]
   102       (trivial ct))
   103     fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i)
   104     (* The result of the quantifier elimination *)
   105     val (th, tac) = case (prop_of pre_thm) of
   106         Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ =>
   107     let val pth = linzqe_oracle (cterm_of thy (Pattern.eta_long [] t1))
   108     in 
   109           ((pth RS iffD2) RS pre_thm,
   110             assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i))
   111     end
   112       | _ => (pre_thm, assm_tac i)
   113   in (rtac (((mp_step nh) o (spec_step np)) th) i 
   114       THEN tac) st
   115   end handle Subscript => no_tac st);
   116 
   117 fun linz_args meth =
   118  let val parse_flag = 
   119          Args.$$$ "no_quantify" >> (K (K false));
   120  in
   121    Method.simple_args 
   122   (Scan.optional (Args.$$$ "(" |-- Scan.repeat1 parse_flag --| Args.$$$ ")") [] >>
   123     curry (Library.foldl op |>) true)
   124     (fn q => fn ctxt => meth ctxt q 1)
   125   end;
   126 
   127 fun linz_method ctxt q i = Method.METHOD (fn facts =>
   128   Method.insert_tac facts 1 THEN linz_tac ctxt q i);
   129 
   130 val setup =
   131   Method.add_method ("cooper",
   132      linz_args linz_method,
   133      "decision procedure for linear integer arithmetic");
   134 
   135 end