1 (* Title: HOLCF/Tools/pcpodef_package.ML |
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2 Author: Brian Huffman |
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3 |
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4 Primitive domain definitions for HOLCF, similar to Gordon/HOL-style |
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5 typedef (see also ~~/src/HOL/Tools/typedef_package.ML). |
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6 *) |
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7 |
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8 signature PCPODEF_PACKAGE = |
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9 sig |
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10 val pcpodef_proof: (bool * binding) * (binding * string list * mixfix) * term |
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11 * (binding * binding) option -> theory -> Proof.state |
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12 val pcpodef_proof_cmd: (bool * binding) * (binding * string list * mixfix) * string |
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13 * (binding * binding) option -> theory -> Proof.state |
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14 val cpodef_proof: (bool * binding) * (binding * string list * mixfix) * term |
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15 * (binding * binding) option -> theory -> Proof.state |
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16 val cpodef_proof_cmd: (bool * binding) * (binding * string list * mixfix) * string |
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17 * (binding * binding) option -> theory -> Proof.state |
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18 end; |
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19 |
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20 structure PcpodefPackage :> PCPODEF_PACKAGE = |
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21 struct |
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22 |
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23 (** type definitions **) |
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24 |
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25 (* prepare_cpodef *) |
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26 |
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27 fun declare_type_name a = Variable.declare_constraints (Logic.mk_type (TFree (a, dummyS))); |
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28 |
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29 fun adm_const T = Const (@{const_name adm}, (T --> HOLogic.boolT) --> HOLogic.boolT); |
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30 fun mk_adm (x, T, P) = adm_const T $ absfree (x, T, P); |
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31 |
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32 fun prepare_pcpodef prep_term pcpo def name (t, vs, mx) raw_set opt_morphs thy = |
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33 let |
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34 val _ = Theory.requires thy "Pcpodef" "pcpodefs"; |
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35 val ctxt = ProofContext.init thy; |
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36 |
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37 val full = Sign.full_name thy; |
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38 val full_name = full name; |
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39 val bname = Binding.name_of name; |
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40 |
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41 (*rhs*) |
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42 val set = prep_term (ctxt |> fold declare_type_name vs) raw_set; |
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43 val setT = Term.fastype_of set; |
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44 val rhs_tfrees = Term.add_tfrees set []; |
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45 val oldT = HOLogic.dest_setT setT handle TYPE _ => |
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46 error ("Not a set type: " ^ quote (Syntax.string_of_typ ctxt setT)); |
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47 |
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48 (*goal*) |
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49 val goal_UU_mem = HOLogic.mk_Trueprop (HOLogic.mk_mem (Const (@{const_name UU}, oldT), set)); |
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50 val goal_nonempty = |
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51 HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), set))); |
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52 val goal_admissible = |
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53 HOLogic.mk_Trueprop (mk_adm ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), set))); |
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54 |
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55 (*lhs*) |
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56 val defS = Sign.defaultS thy; |
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57 val lhs_tfrees = map (fn v => (v, the_default defS (AList.lookup (op =) rhs_tfrees v))) vs; |
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58 val lhs_sorts = map snd lhs_tfrees; |
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59 |
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60 val tname = Binding.map_name (Syntax.type_name mx) t; |
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61 val full_tname = full tname; |
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62 val newT = Type (full_tname, map TFree lhs_tfrees); |
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63 |
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64 val (Rep_name, Abs_name) = |
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65 (case opt_morphs of |
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66 NONE => (Binding.prefix_name "Rep_" name, Binding.prefix_name "Abs_" name) |
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67 | SOME morphs => morphs); |
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68 val RepC = Const (full Rep_name, newT --> oldT); |
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69 fun belowC T = Const (@{const_name below}, T --> T --> HOLogic.boolT); |
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70 val below_def = Logic.mk_equals (belowC newT, |
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71 Abs ("x", newT, Abs ("y", newT, belowC oldT $ (RepC $ Bound 1) $ (RepC $ Bound 0)))); |
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72 |
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73 fun make_po tac thy1 = |
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74 let |
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75 val ((_, {type_definition, set_def, ...}), thy2) = thy1 |
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76 |> Typedef.add_typedef def (SOME name) (t, vs, mx) set opt_morphs tac; |
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77 val lthy3 = thy2 |
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78 |> TheoryTarget.instantiation ([full_tname], lhs_tfrees, @{sort po}); |
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79 val below_def' = Syntax.check_term lthy3 below_def; |
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80 val ((_, (_, below_definition')), lthy4) = lthy3 |
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81 |> Specification.definition (NONE, |
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82 ((Binding.prefix_name "below_" (Binding.suffix_name "_def" name), []), below_def')); |
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83 val ctxt_thy = ProofContext.init (ProofContext.theory_of lthy4); |
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84 val below_definition = singleton (ProofContext.export lthy4 ctxt_thy) below_definition'; |
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85 val thy5 = lthy4 |
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86 |> Class.prove_instantiation_instance |
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87 (K (Tactic.rtac (@{thm typedef_po} OF [type_definition, below_definition]) 1)) |
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88 |> LocalTheory.exit_global; |
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89 in ((type_definition, below_definition, set_def), thy5) end; |
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90 |
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91 fun make_cpo admissible (type_def, below_def, set_def) theory = |
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92 let |
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93 val admissible' = fold_rule (the_list set_def) admissible; |
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94 val cpo_thms = map (Thm.transfer theory) [type_def, below_def, admissible']; |
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95 val theory' = theory |
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96 |> AxClass.prove_arity (full_tname, lhs_sorts, @{sort cpo}) |
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97 (Tactic.rtac (@{thm typedef_cpo} OF cpo_thms) 1); |
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98 val cpo_thms' = map (Thm.transfer theory') cpo_thms; |
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99 in |
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100 theory' |
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101 |> Sign.add_path (Binding.name_of name) |
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102 |> PureThy.add_thms |
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103 ([((Binding.prefix_name "adm_" name, admissible'), []), |
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104 ((Binding.prefix_name "cont_" Rep_name, @{thm typedef_cont_Rep} OF cpo_thms'), []), |
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105 ((Binding.prefix_name "cont_" Abs_name, @{thm typedef_cont_Abs} OF cpo_thms'), []), |
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106 ((Binding.prefix_name "lub_" name, @{thm typedef_lub} OF cpo_thms'), []), |
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107 ((Binding.prefix_name "thelub_" name, @{thm typedef_thelub} OF cpo_thms'), []), |
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108 ((Binding.prefix_name "compact_" name, @{thm typedef_compact} OF cpo_thms'), [])]) |
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109 |> snd |
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110 |> Sign.parent_path |
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111 end; |
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112 |
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113 fun make_pcpo UU_mem (type_def, below_def, set_def) theory = |
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114 let |
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115 val UU_mem' = fold_rule (the_list set_def) UU_mem; |
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116 val pcpo_thms = map (Thm.transfer theory) [type_def, below_def, UU_mem']; |
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117 val theory' = theory |
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118 |> AxClass.prove_arity (full_tname, lhs_sorts, @{sort pcpo}) |
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119 (Tactic.rtac (@{thm typedef_pcpo} OF pcpo_thms) 1); |
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120 val pcpo_thms' = map (Thm.transfer theory') pcpo_thms; |
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121 in |
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122 theory' |
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123 |> Sign.add_path (Binding.name_of name) |
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124 |> PureThy.add_thms |
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125 ([((Binding.suffix_name "_strict" Rep_name, @{thm typedef_Rep_strict} OF pcpo_thms'), []), |
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126 ((Binding.suffix_name "_strict" Abs_name, @{thm typedef_Abs_strict} OF pcpo_thms'), []), |
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127 ((Binding.suffix_name "_strict_iff" Rep_name, @{thm typedef_Rep_strict_iff} OF pcpo_thms'), []), |
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128 ((Binding.suffix_name "_strict_iff" Abs_name, @{thm typedef_Abs_strict_iff} OF pcpo_thms'), []), |
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129 ((Binding.suffix_name "_defined" Rep_name, @{thm typedef_Rep_defined} OF pcpo_thms'), []), |
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130 ((Binding.suffix_name "_defined" Abs_name, @{thm typedef_Abs_defined} OF pcpo_thms'), [])]) |
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131 |> snd |
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132 |> Sign.parent_path |
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133 end; |
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134 |
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135 fun pcpodef_result UU_mem admissible = |
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136 make_po (Tactic.rtac exI 1 THEN Tactic.rtac UU_mem 1) |
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137 #-> (fn defs => make_cpo admissible defs #> make_pcpo UU_mem defs); |
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138 |
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139 fun cpodef_result nonempty admissible = |
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140 make_po (Tactic.rtac nonempty 1) |
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141 #-> make_cpo admissible; |
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142 in |
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143 if pcpo |
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144 then (goal_UU_mem, goal_admissible, pcpodef_result) |
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145 else (goal_nonempty, goal_admissible, cpodef_result) |
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146 end |
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147 handle ERROR msg => |
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148 cat_error msg ("The error(s) above occurred in cpodef " ^ quote (Binding.str_of name)); |
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149 |
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150 |
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151 (* proof interface *) |
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152 |
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153 local |
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154 |
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155 fun gen_pcpodef_proof prep_term pcpo ((def, name), typ, set, opt_morphs) thy = |
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156 let |
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157 val (goal1, goal2, make_result) = |
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158 prepare_pcpodef prep_term pcpo def name typ set opt_morphs thy; |
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159 fun after_qed [[th1, th2]] = ProofContext.theory (make_result th1 th2); |
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160 in Proof.theorem_i NONE after_qed [[(goal1, []), (goal2, [])]] (ProofContext.init thy) end; |
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161 |
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162 in |
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163 |
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164 fun pcpodef_proof x = gen_pcpodef_proof Syntax.check_term true x; |
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165 fun pcpodef_proof_cmd x = gen_pcpodef_proof Syntax.read_term true x; |
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166 |
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167 fun cpodef_proof x = gen_pcpodef_proof Syntax.check_term false x; |
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168 fun cpodef_proof_cmd x = gen_pcpodef_proof Syntax.read_term false x; |
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169 |
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170 end; |
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171 |
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172 |
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173 |
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174 (** outer syntax **) |
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175 |
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176 local structure P = OuterParse and K = OuterKeyword in |
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177 |
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178 val typedef_proof_decl = |
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179 Scan.optional (P.$$$ "(" |-- |
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180 ((P.$$$ "open" >> K false) -- Scan.option P.binding || P.binding >> (fn s => (true, SOME s))) |
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181 --| P.$$$ ")") (true, NONE) -- |
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182 (P.type_args -- P.binding) -- P.opt_infix -- (P.$$$ "=" |-- P.term) -- |
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183 Scan.option (P.$$$ "morphisms" |-- P.!!! (P.binding -- P.binding)); |
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184 |
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185 fun mk_pcpodef_proof pcpo ((((((def, opt_name), (vs, t)), mx), A), morphs)) = |
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186 (if pcpo then pcpodef_proof_cmd else cpodef_proof_cmd) |
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187 ((def, the_default (Binding.map_name (Syntax.type_name mx) t) opt_name), (t, vs, mx), A, morphs); |
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188 |
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189 val _ = |
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190 OuterSyntax.command "pcpodef" "HOLCF type definition (requires admissibility proof)" K.thy_goal |
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191 (typedef_proof_decl >> |
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192 (Toplevel.print oo (Toplevel.theory_to_proof o mk_pcpodef_proof true))); |
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193 |
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194 val _ = |
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195 OuterSyntax.command "cpodef" "HOLCF type definition (requires admissibility proof)" K.thy_goal |
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196 (typedef_proof_decl >> |
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197 (Toplevel.print oo (Toplevel.theory_to_proof o mk_pcpodef_proof false))); |
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198 |
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199 end; |
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200 |
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201 end; |
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