src/HOL/Decision_Procs/ferrack_tac.ML
author nipkow
Wed Jun 24 09:41:14 2009 +0200 (2009-06-24)
changeset 31790 05c92381363c
parent 31302 12677a808d43
child 32740 9dd0a2f83429
permissions -rw-r--r--
corrected and unified thm names
     1 (*  Title:      HOL/Decision_Procs/ferrack_tac.ML
     2     Author:     Amine Chaieb, TU Muenchen
     3 *)
     4 
     5 signature FERRACK_TAC =
     6 sig
     7   val trace: bool ref
     8   val linr_tac: Proof.context -> bool -> int -> tactic
     9   val setup: theory -> theory
    10 end
    11 
    12 structure Ferrack_Tac =
    13 struct
    14 
    15 val trace = ref false;
    16 fun trace_msg s = if !trace then tracing s else ();
    17 
    18 val ferrack_ss = let val ths = [@{thm real_of_int_inject}, @{thm real_of_int_less_iff}, 
    19 				@{thm real_of_int_le_iff}]
    20 	     in @{simpset} delsimps ths addsimps (map (fn th => th RS sym) ths)
    21 	     end;
    22 
    23 val binarith =
    24   @{thms normalize_bin_simps} @ @{thms pred_bin_simps} @ @{thms succ_bin_simps} @
    25   @{thms add_bin_simps} @ @{thms minus_bin_simps} @  @{thms mult_bin_simps};
    26 val comp_arith = binarith @ simp_thms
    27 
    28 val zdvd_int = @{thm zdvd_int};
    29 val zdiff_int_split = @{thm zdiff_int_split};
    30 val all_nat = @{thm all_nat};
    31 val ex_nat = @{thm ex_nat};
    32 val number_of1 = @{thm number_of1};
    33 val number_of2 = @{thm number_of2};
    34 val split_zdiv = @{thm split_zdiv};
    35 val split_zmod = @{thm split_zmod};
    36 val mod_div_equality' = @{thm mod_div_equality'};
    37 val split_div' = @{thm split_div'};
    38 val Suc_eq_plus1 = @{thm Suc_eq_plus1};
    39 val imp_le_cong = @{thm imp_le_cong};
    40 val conj_le_cong = @{thm conj_le_cong};
    41 val mod_add_left_eq = @{thm mod_add_left_eq} RS sym;
    42 val mod_add_right_eq = @{thm mod_add_right_eq} RS sym;
    43 val nat_div_add_eq = @{thm div_add1_eq} RS sym;
    44 val int_div_add_eq = @{thm zdiv_zadd1_eq} RS sym;
    45 val ZDIVISION_BY_ZERO_MOD = @{thm DIVISION_BY_ZERO} RS conjunct2;
    46 val ZDIVISION_BY_ZERO_DIV = @{thm DIVISION_BY_ZERO} RS conjunct1;
    47 
    48 fun prepare_for_linr sg q fm = 
    49   let
    50     val ps = Logic.strip_params fm
    51     val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm)
    52     val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm)
    53     fun mk_all ((s, T), (P,n)) =
    54       if 0 mem loose_bnos P then
    55         (HOLogic.all_const T $ Abs (s, T, P), n)
    56       else (incr_boundvars ~1 P, n-1)
    57     fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t;
    58       val rhs = hs
    59 (*    val (rhs,irhs) = List.partition (relevant (rev ps)) hs *)
    60     val np = length ps
    61     val (fm',np) =  foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n)))
    62       (foldr HOLogic.mk_imp c rhs, np) ps
    63     val (vs, _) = List.partition (fn t => q orelse (type_of t) = HOLogic.natT)
    64       (OldTerm.term_frees fm' @ OldTerm.term_vars fm');
    65     val fm2 = foldr mk_all2 fm' vs
    66   in (fm2, np + length vs, length rhs) end;
    67 
    68 (*Object quantifier to meta --*)
    69 fun spec_step n th = if (n=0) then th else (spec_step (n-1) th) RS spec ;
    70 
    71 (* object implication to meta---*)
    72 fun mp_step n th = if (n=0) then th else (mp_step (n-1) th) RS mp;
    73 
    74 
    75 fun linr_tac ctxt q i = 
    76     (ObjectLogic.atomize_prems_tac i) 
    77 	THEN (REPEAT_DETERM (split_tac [@{thm split_min}, @{thm split_max}, @{thm abs_split}] i))
    78 	THEN (fn st =>
    79   let
    80     val g = List.nth (prems_of st, i - 1)
    81     val thy = ProofContext.theory_of ctxt
    82     (* Transform the term*)
    83     val (t,np,nh) = prepare_for_linr thy q g
    84     (* Some simpsets for dealing with mod div abs and nat*)
    85     val simpset0 = Simplifier.theory_context thy HOL_basic_ss addsimps comp_arith
    86     val ct = cterm_of thy (HOLogic.mk_Trueprop t)
    87     (* Theorem for the nat --> int transformation *)
    88    val pre_thm = Seq.hd (EVERY
    89       [simp_tac simpset0 1,
    90        TRY (simp_tac (Simplifier.theory_context thy ferrack_ss) 1)]
    91       (trivial ct))
    92     fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i)
    93     (* The result of the quantifier elimination *)
    94     val (th, tac) = case (prop_of pre_thm) of
    95         Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ =>
    96     let val pth = linr_oracle (cterm_of thy (Pattern.eta_long [] t1))
    97     in 
    98           (trace_msg ("calling procedure with term:\n" ^
    99              Syntax.string_of_term ctxt t1);
   100            ((pth RS iffD2) RS pre_thm,
   101             assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i)))
   102     end
   103       | _ => (pre_thm, assm_tac i)
   104   in (rtac (((mp_step nh) o (spec_step np)) th) i 
   105       THEN tac) st
   106   end handle Subscript => no_tac st);
   107 
   108 val setup =
   109   Method.setup @{binding rferrack}
   110     (Args.mode "no_quantify" >> (fn q => fn ctxt =>
   111       SIMPLE_METHOD' (linr_tac ctxt (not q))))
   112     "decision procedure for linear real arithmetic";
   113 
   114 end