src/HOL/Decision_Procs/ferrack_tac.ML
author haftmann
Wed May 05 18:25:34 2010 +0200 (2010-05-05)
changeset 36692 54b64d4ad524
parent 35625 9c818cab0dd0
child 36853 c8e4102b08aa
permissions -rw-r--r--
farewell to old-style mem infixes -- type inference in situations with mem_int and mem_string should provide enough information to resolve the type of (op =)
     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 Unsynchronized.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 = Unsynchronized.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 member (op =) (loose_bnos P) 0 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) =  List.foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n)))
    62       (List.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 = List.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 =
    76     Object_Logic.atomize_prems_tac
    77         THEN' (REPEAT_DETERM o split_tac [@{thm split_min}, @{thm split_max}, @{thm abs_split}])
    78         THEN' SUBGOAL (fn (g, i) =>
    79   let
    80     val thy = ProofContext.theory_of ctxt
    81     (* Transform the term*)
    82     val (t,np,nh) = prepare_for_linr thy q g
    83     (* Some simpsets for dealing with mod div abs and nat*)
    84     val simpset0 = Simplifier.context ctxt HOL_basic_ss addsimps comp_arith
    85     val ct = cterm_of thy (HOLogic.mk_Trueprop t)
    86     (* Theorem for the nat --> int transformation *)
    87    val pre_thm = Seq.hd (EVERY
    88       [simp_tac simpset0 1,
    89        TRY (simp_tac (Simplifier.context ctxt ferrack_ss) 1)]
    90       (trivial ct))
    91     fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i)
    92     (* The result of the quantifier elimination *)
    93     val (th, tac) = case prop_of pre_thm of
    94         Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ =>
    95     let val pth = linr_oracle (cterm_of thy (Pattern.eta_long [] t1))
    96     in 
    97           (trace_msg ("calling procedure with term:\n" ^
    98              Syntax.string_of_term ctxt t1);
    99            ((pth RS iffD2) RS pre_thm,
   100             assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i)))
   101     end
   102       | _ => (pre_thm, assm_tac i)
   103   in rtac ((mp_step nh o spec_step np) th) i THEN tac end);
   104 
   105 val setup =
   106   Method.setup @{binding rferrack}
   107     (Args.mode "no_quantify" >> (fn q => fn ctxt =>
   108       SIMPLE_METHOD' (linr_tac ctxt (not q))))
   109     "decision procedure for linear real arithmetic";
   110 
   111 end