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1 signature SIMPLE_INDUCTIVE_PACKAGE = |
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2 sig |
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3 val add_inductive_i: |
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4 ((binding * typ) * mixfix) list -> |
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5 (binding * typ) list -> |
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6 (Attrib.binding * term) list -> |
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7 local_theory -> (thm list * thm list) * local_theory |
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8 val add_inductive: |
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9 (binding * string option * mixfix) list -> |
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10 (binding * string option * mixfix) list -> |
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11 (Attrib.binding * string) list -> |
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12 local_theory -> (thm list * thm list) * local_theory |
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13 end; |
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14 |
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15 structure SimpleInductivePackage: SIMPLE_INDUCTIVE_PACKAGE = |
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16 struct |
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17 |
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18 fun add_inductive_i preds_syn params intrs lthy = |
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19 let |
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20 val params' = map (fn (p, T) => Free (Binding.name_of p, T)) params; |
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21 val preds = map (fn ((R, T), _) => |
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22 list_comb (Free (Binding.name_of R, T), params')) preds_syn; |
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23 val Tss = map (binder_types o fastype_of) preds; |
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24 |
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25 (* making the definition *) |
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26 |
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27 val intrs' = map |
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28 (ObjectLogic.atomize_term (ProofContext.theory_of lthy) o snd) intrs; |
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29 |
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30 fun mk_all x P = HOLogic.all_const (fastype_of x) $ lambda x P; |
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31 |
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32 val (defs, lthy1) = fold_map (fn ((((R, _), syn), pred), Ts) => |
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33 let val zs = map Free (Variable.variant_frees lthy intrs' |
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34 (map (pair "z") Ts)) |
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35 in |
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36 LocalTheory.define Thm.internalK |
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37 ((R, syn), (Attrib.empty_binding, fold_rev lambda (params' @ zs) |
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38 (fold_rev mk_all preds (fold_rev (curry HOLogic.mk_imp) |
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39 intrs' (list_comb (pred, zs)))))) #>> snd #>> snd |
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40 end) (preds_syn ~~ preds ~~ Tss) lthy; |
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41 |
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42 val (_, lthy2) = Variable.add_fixes (map (Binding.name_of o fst) params) lthy1; |
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43 |
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44 |
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45 (* proving the induction rules *) |
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46 |
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47 val (Pnames, lthy3) = |
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48 Variable.variant_fixes (replicate (length preds) "P") lthy2; |
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49 val Ps = map (fn (s, Ts) => Free (s, Ts ---> HOLogic.boolT)) |
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50 (Pnames ~~ Tss); |
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51 val cPs = map (cterm_of (ProofContext.theory_of lthy3)) Ps; |
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52 val intrs'' = map (subst_free (preds ~~ Ps) o snd) intrs; |
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53 |
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54 fun inst_spec ct = Drule.instantiate' |
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55 [SOME (ctyp_of_term ct)] [NONE, SOME ct] spec; |
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56 |
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57 fun prove_indrule ((R, P), Ts) = |
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58 let |
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59 val (znames, lthy4) = |
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60 Variable.variant_fixes (replicate (length Ts) "z") lthy3; |
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61 val zs = map Free (znames ~~ Ts) |
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62 in |
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63 Goal.prove lthy4 [] |
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64 [HOLogic.mk_Trueprop (list_comb (R, zs))] |
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65 (Logic.list_implies (intrs'', |
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66 HOLogic.mk_Trueprop (list_comb (P, zs)))) |
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67 (fn {prems, ...} => EVERY |
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68 ([ObjectLogic.full_atomize_tac 1, |
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69 cut_facts_tac prems 1, |
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70 rewrite_goals_tac defs] @ |
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71 map (fn ct => dtac (inst_spec ct) 1) cPs @ |
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72 [assume_tac 1])) |> |
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73 singleton (ProofContext.export lthy4 lthy1) |
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74 end; |
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75 |
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76 val indrules = map prove_indrule (preds ~~ Ps ~~ Tss); |
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77 |
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78 |
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79 (* proving the introduction rules *) |
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80 |
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81 val all_elims = fold (fn ct => fn th => th RS inst_spec ct); |
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82 val imp_elims = fold (fn th => fn th' => [th', th] MRS mp); |
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83 |
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84 fun prove_intr (i, (_, r)) = |
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85 Goal.prove lthy2 [] [] r |
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86 (fn {prems, context = ctxt} => EVERY |
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87 [ObjectLogic.rulify_tac 1, |
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88 rewrite_goals_tac defs, |
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89 REPEAT (resolve_tac [allI, impI] 1), |
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90 SUBPROOF (fn {params, prems, context = ctxt', ...} => |
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91 let |
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92 val (prems1, prems2) = |
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93 chop (length prems - length intrs) prems; |
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94 val (params1, params2) = |
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95 chop (length params - length preds) (map snd params) |
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96 in |
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97 rtac (ObjectLogic.rulify |
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98 (all_elims params1 (nth prems2 i))) 1 THEN |
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99 EVERY (map (fn prem => |
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100 SUBPROOF (fn {prems = prems', concl, ...} => |
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101 let |
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102 val prem' = prems' MRS prem; |
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103 val prem'' = case prop_of prem' of |
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104 _ $ (Const (@{const_name All}, _) $ _) => |
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105 prem' |> all_elims params2 |> |
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106 imp_elims prems2 |
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107 | _ => prem' |
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108 in rtac prem'' 1 end) ctxt' 1) prems1) |
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109 end) ctxt 1]) |> |
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110 singleton (ProofContext.export lthy2 lthy1); |
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111 |
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112 val intr_ths = map_index prove_intr intrs; |
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113 |
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114 |
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115 (* storing the theorems *) |
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116 |
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117 val mut_name = space_implode "_" (map (Binding.name_of o fst o fst) preds_syn); |
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118 val case_names = map (Binding.name_of o fst o fst) intrs |
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119 in |
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120 lthy1 |> |
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121 LocalTheory.notes Thm.theoremK (map (fn (((a, atts), _), th) => |
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122 ((Binding.qualify false mut_name a, atts), [([th], [])])) |
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123 (intrs ~~ intr_ths)) |-> |
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124 (fn intr_thss => LocalTheory.note Thm.theoremK |
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125 ((Binding.qualify false mut_name (Binding.name "intros"), []), maps snd intr_thss)) |>> |
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126 snd ||>> |
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127 (LocalTheory.notes Thm.theoremK (map (fn (((R, _), _), th) => |
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128 ((Binding.qualify false (Binding.name_of R) (Binding.name "induct"), |
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129 [Attrib.internal (K (RuleCases.case_names case_names)), |
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130 Attrib.internal (K (RuleCases.consumes 1)), |
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131 Attrib.internal (K (Induct.induct_pred ""))]), [([th], [])])) |
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132 (preds_syn ~~ indrules)) #>> maps snd) |
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133 end; |
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134 |
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135 fun add_inductive preds_syn params_syn intro_srcs lthy = |
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136 let |
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137 val ((vars, intrs), _) = Specification.read_spec |
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138 (preds_syn @ params_syn) intro_srcs lthy; |
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139 val (preds_syn', params_syn') = chop (length preds_syn) vars |
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140 in |
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141 add_inductive_i preds_syn' (map fst params_syn') intrs lthy |
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142 end; |
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143 |
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144 |
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145 (* outer syntax *) |
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146 |
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147 local structure P = OuterParse and K = OuterKeyword in |
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148 |
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149 val ind_decl = |
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150 P.fixes -- P.for_fixes -- |
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151 Scan.optional (P.$$$ "where" |-- |
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152 P.!!! (P.enum1 "|" (SpecParse.opt_thm_name ":" -- P.prop))) [] >> |
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153 (fn ((preds, params), specs) => |
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154 add_inductive preds params specs #> snd); |
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155 |
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156 val _ = OuterSyntax.local_theory "simple_inductive" "define inductive predicates" |
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157 K.thy_decl ind_decl; |
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158 |
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159 end; |
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160 |
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161 end; |