src/HOL/Decision_Procs/cooper_tac.ML
author wenzelm
Sun Mar 07 12:19:47 2010 +0100 (2010-03-07)
changeset 35625 9c818cab0dd0
parent 33004 715566791eb0
child 36692 54b64d4ad524
permissions -rw-r--r--
modernized structure Object_Logic;
     1 (*  Title:      HOL/Decision_Procs/cooper_tac.ML
     2     Author:     Amine Chaieb, TU Muenchen
     3 *)
     4 
     5 signature COOPER_TAC =
     6 sig
     7   val trace: bool Unsynchronized.ref
     8   val linz_tac: Proof.context -> bool -> int -> tactic
     9   val setup: theory -> theory
    10 end
    11 
    12 structure Cooper_Tac: COOPER_TAC =
    13 struct
    14 
    15 val trace = Unsynchronized.ref false;
    16 fun trace_msg s = if !trace then tracing s else ();
    17 
    18 val cooper_ss = @{simpset};
    19 
    20 val nT = HOLogic.natT;
    21 val binarith = @{thms normalize_bin_simps};
    22 val comp_arith = binarith @ simp_thms
    23 
    24 val zdvd_int = @{thm zdvd_int};
    25 val zdiff_int_split = @{thm zdiff_int_split};
    26 val all_nat = @{thm all_nat};
    27 val ex_nat = @{thm ex_nat};
    28 val number_of1 = @{thm number_of1};
    29 val number_of2 = @{thm number_of2};
    30 val split_zdiv = @{thm split_zdiv};
    31 val split_zmod = @{thm split_zmod};
    32 val mod_div_equality' = @{thm mod_div_equality'};
    33 val split_div' = @{thm split_div'};
    34 val Suc_eq_plus1 = @{thm Suc_eq_plus1};
    35 val imp_le_cong = @{thm imp_le_cong};
    36 val conj_le_cong = @{thm conj_le_cong};
    37 val mod_add_left_eq = @{thm mod_add_left_eq} RS sym;
    38 val mod_add_right_eq = @{thm mod_add_right_eq} RS sym;
    39 val mod_add_eq = @{thm mod_add_eq} RS sym;
    40 val nat_div_add_eq = @{thm div_add1_eq} RS sym;
    41 val int_div_add_eq = @{thm zdiv_zadd1_eq} RS sym;
    42 
    43 fun prepare_for_linz q fm =
    44   let
    45     val ps = Logic.strip_params fm
    46     val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm)
    47     val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm)
    48     fun mk_all ((s, T), (P,n)) =
    49       if 0 mem loose_bnos P then
    50         (HOLogic.all_const T $ Abs (s, T, P), n)
    51       else (incr_boundvars ~1 P, n-1)
    52     fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t;
    53     val rhs = hs
    54     val np = length ps
    55     val (fm',np) = List.foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n)))
    56       (List.foldr HOLogic.mk_imp c rhs, np) ps
    57     val (vs, _) = List.partition (fn t => q orelse (type_of t) = nT)
    58       (OldTerm.term_frees fm' @ OldTerm.term_vars fm');
    59     val fm2 = List.foldr mk_all2 fm' vs
    60   in (fm2, np + length vs, length rhs) end;
    61 
    62 (*Object quantifier to meta --*)
    63 fun spec_step n th = if (n=0) then th else (spec_step (n-1) th) RS spec ;
    64 
    65 (* object implication to meta---*)
    66 fun mp_step n th = if (n=0) then th else (mp_step (n-1) th) RS mp;
    67 
    68 
    69 fun linz_tac ctxt q i = Object_Logic.atomize_prems_tac i THEN (fn st =>
    70   let
    71     val g = List.nth (prems_of st, i - 1)
    72     val thy = ProofContext.theory_of ctxt
    73     (* Transform the term*)
    74     val (t,np,nh) = prepare_for_linz q g
    75     (* Some simpsets for dealing with mod div abs and nat*)
    76     val mod_div_simpset = HOL_basic_ss
    77       addsimps [refl,mod_add_eq, mod_add_left_eq,
    78           mod_add_right_eq,
    79           nat_div_add_eq, int_div_add_eq,
    80           @{thm mod_self}, @{thm "zmod_self"},
    81           @{thm mod_by_0}, @{thm div_by_0},
    82           @{thm "zdiv_zero"}, @{thm "zmod_zero"}, @{thm "div_0"}, @{thm "mod_0"},
    83           @{thm "div_by_1"}, @{thm "mod_by_1"}, @{thm "div_1"}, @{thm "mod_1"},
    84           Suc_eq_plus1]
    85       addsimps @{thms add_ac}
    86       addsimprocs [cancel_div_mod_nat_proc, cancel_div_mod_int_proc]
    87     val simpset0 = HOL_basic_ss
    88       addsimps [mod_div_equality', Suc_eq_plus1]
    89       addsimps comp_arith
    90       addsplits [split_zdiv, split_zmod, split_div', @{thm "split_min"}, @{thm "split_max"}]
    91     (* Simp rules for changing (n::int) to int n *)
    92     val simpset1 = HOL_basic_ss
    93       addsimps [@{thm nat_number_of_def}, zdvd_int] @ map (fn r => r RS sym)
    94         [@{thm int_int_eq}, @{thm zle_int}, @{thm zless_int}, @{thm zadd_int}, @{thm zmult_int}]
    95       addsplits [zdiff_int_split]
    96     (*simp rules for elimination of int n*)
    97 
    98     val simpset2 = HOL_basic_ss
    99       addsimps [@{thm nat_0_le}, @{thm all_nat}, @{thm ex_nat}, @{thm number_of1}, @{thm number_of2}, @{thm int_0}, @{thm int_1}]
   100       addcongs [@{thm conj_le_cong}, @{thm imp_le_cong}]
   101     (* simp rules for elimination of abs *)
   102     val simpset3 = HOL_basic_ss addsplits [@{thm abs_split}]
   103     val ct = cterm_of thy (HOLogic.mk_Trueprop t)
   104     (* Theorem for the nat --> int transformation *)
   105     val pre_thm = Seq.hd (EVERY
   106       [simp_tac mod_div_simpset 1, simp_tac simpset0 1,
   107        TRY (simp_tac simpset1 1), TRY (simp_tac simpset2 1),
   108        TRY (simp_tac simpset3 1), TRY (simp_tac cooper_ss 1)]
   109       (trivial ct))
   110     fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i)
   111     (* The result of the quantifier elimination *)
   112     val (th, tac) = case (prop_of pre_thm) of
   113         Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ =>
   114     let val pth = linzqe_oracle (cterm_of thy (Pattern.eta_long [] t1))
   115     in
   116           ((pth RS iffD2) RS pre_thm,
   117             assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i))
   118     end
   119       | _ => (pre_thm, assm_tac i)
   120   in (rtac (((mp_step nh) o (spec_step np)) th) i
   121       THEN tac) st
   122   end handle Subscript => no_tac st);
   123 
   124 val setup =
   125   Method.setup @{binding cooper}
   126     let
   127       val parse_flag = Args.$$$ "no_quantify" >> K (K false)
   128     in
   129       Scan.lift (Scan.optional (Args.$$$ "(" |-- Scan.repeat1 parse_flag --| Args.$$$ ")") [] >>
   130         curry (Library.foldl op |>) true) >>
   131       (fn q => fn ctxt => SIMPLE_METHOD' (linz_tac ctxt q))
   132     end
   133     "decision procedure for linear integer arithmetic";
   134 
   135 end