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1 (* Title: HOL/Reflection/ferrack_tac.ML |
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2 Author: Amine Chaieb, TU Muenchen |
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3 *) |
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4 |
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5 structure Ferrack_Tac = |
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6 struct |
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7 |
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8 val trace = ref false; |
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9 fun trace_msg s = if !trace then tracing s else (); |
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10 |
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11 val ferrack_ss = let val ths = [@{thm real_of_int_inject}, @{thm real_of_int_less_iff}, |
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12 @{thm real_of_int_le_iff}] |
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13 in @{simpset} delsimps ths addsimps (map (fn th => th RS sym) ths) |
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14 end; |
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15 |
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16 val binarith = |
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17 @{thms normalize_bin_simps} @ @{thms pred_bin_simps} @ @{thms succ_bin_simps} @ |
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18 @{thms add_bin_simps} @ @{thms minus_bin_simps} @ @{thms mult_bin_simps}; |
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19 val comp_arith = binarith @ simp_thms |
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20 |
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21 val zdvd_int = @{thm zdvd_int}; |
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22 val zdiff_int_split = @{thm zdiff_int_split}; |
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23 val all_nat = @{thm all_nat}; |
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24 val ex_nat = @{thm ex_nat}; |
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25 val number_of1 = @{thm number_of1}; |
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26 val number_of2 = @{thm number_of2}; |
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27 val split_zdiv = @{thm split_zdiv}; |
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28 val split_zmod = @{thm split_zmod}; |
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29 val mod_div_equality' = @{thm mod_div_equality'}; |
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30 val split_div' = @{thm split_div'}; |
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31 val Suc_plus1 = @{thm Suc_plus1}; |
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32 val imp_le_cong = @{thm imp_le_cong}; |
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33 val conj_le_cong = @{thm conj_le_cong}; |
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34 val nat_mod_add_eq = @{thm mod_add1_eq} RS sym; |
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35 val nat_mod_add_left_eq = @{thm mod_add_left_eq} RS sym; |
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36 val nat_mod_add_right_eq = @{thm mod_add_right_eq} RS sym; |
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37 val int_mod_add_eq = @{thm zmod_zadd1_eq} RS sym; |
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38 val int_mod_add_left_eq = @{thm zmod_zadd_left_eq} RS sym; |
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39 val int_mod_add_right_eq = @{thm zmod_zadd_right_eq} RS sym; |
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40 val nat_div_add_eq = @{thm div_add1_eq} RS sym; |
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41 val int_div_add_eq = @{thm zdiv_zadd1_eq} RS sym; |
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42 val ZDIVISION_BY_ZERO_MOD = @{thm DIVISION_BY_ZERO} RS conjunct2; |
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43 val ZDIVISION_BY_ZERO_DIV = @{thm DIVISION_BY_ZERO} RS conjunct1; |
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44 |
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45 fun prepare_for_linr sg q fm = |
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46 let |
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47 val ps = Logic.strip_params fm |
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48 val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm) |
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49 val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm) |
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50 fun mk_all ((s, T), (P,n)) = |
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51 if 0 mem loose_bnos P then |
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52 (HOLogic.all_const T $ Abs (s, T, P), n) |
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53 else (incr_boundvars ~1 P, n-1) |
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54 fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t; |
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55 val rhs = hs |
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56 (* val (rhs,irhs) = List.partition (relevant (rev ps)) hs *) |
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57 val np = length ps |
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58 val (fm',np) = foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n))) |
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59 (foldr HOLogic.mk_imp c rhs, np) ps |
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60 val (vs, _) = List.partition (fn t => q orelse (type_of t) = HOLogic.natT) |
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61 (OldTerm.term_frees fm' @ OldTerm.term_vars fm'); |
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62 val fm2 = foldr mk_all2 fm' vs |
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63 in (fm2, np + length vs, length rhs) end; |
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64 |
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65 (*Object quantifier to meta --*) |
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66 fun spec_step n th = if (n=0) then th else (spec_step (n-1) th) RS spec ; |
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67 |
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68 (* object implication to meta---*) |
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69 fun mp_step n th = if (n=0) then th else (mp_step (n-1) th) RS mp; |
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70 |
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71 |
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72 fun linr_tac ctxt q i = |
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73 (ObjectLogic.atomize_prems_tac i) |
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74 THEN (REPEAT_DETERM (split_tac [@{thm split_min}, @{thm split_max}, @{thm abs_split}] i)) |
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75 THEN (fn st => |
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76 let |
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77 val g = List.nth (prems_of st, i - 1) |
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78 val thy = ProofContext.theory_of ctxt |
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79 (* Transform the term*) |
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80 val (t,np,nh) = prepare_for_linr thy q g |
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81 (* Some simpsets for dealing with mod div abs and nat*) |
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82 val simpset0 = Simplifier.theory_context thy HOL_basic_ss addsimps comp_arith |
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83 val ct = cterm_of thy (HOLogic.mk_Trueprop t) |
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84 (* Theorem for the nat --> int transformation *) |
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85 val pre_thm = Seq.hd (EVERY |
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86 [simp_tac simpset0 1, |
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87 TRY (simp_tac (Simplifier.theory_context thy ferrack_ss) 1)] |
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88 (trivial ct)) |
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89 fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i) |
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90 (* The result of the quantifier elimination *) |
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91 val (th, tac) = case (prop_of pre_thm) of |
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92 Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ => |
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93 let val pth = linr_oracle (cterm_of thy (Pattern.eta_long [] t1)) |
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94 in |
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95 (trace_msg ("calling procedure with term:\n" ^ |
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96 Syntax.string_of_term ctxt t1); |
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97 ((pth RS iffD2) RS pre_thm, |
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98 assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i))) |
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99 end |
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100 | _ => (pre_thm, assm_tac i) |
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101 in (rtac (((mp_step nh) o (spec_step np)) th) i |
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102 THEN tac) st |
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103 end handle Subscript => no_tac st); |
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104 |
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105 fun linr_meth src = |
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106 Method.syntax (Args.mode "no_quantify") src |
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107 #> (fn (q, ctxt) => Method.SIMPLE_METHOD' (linr_tac ctxt (not q))); |
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108 |
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109 val setup = |
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110 Method.add_method ("rferrack", linr_meth, |
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111 "decision procedure for linear real arithmetic"); |
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112 |
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113 end |