1 (* Title: Tools/code/code_wellsorted.ML |
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2 Author: Florian Haftmann, TU Muenchen |
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3 |
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4 Producing well-sorted systems of code equations in a graph |
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5 with explicit dependencies -- the Waisenhaus algorithm. |
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6 *) |
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7 |
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8 signature CODE_WELLSORTED = |
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9 sig |
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10 type code_algebra |
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11 type code_graph |
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12 val eqns: code_graph -> string -> (thm * bool) list |
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13 val typ: code_graph -> string -> (string * sort) list * typ |
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14 val all: code_graph -> string list |
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15 val pretty: theory -> code_graph -> Pretty.T |
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16 val obtain: theory -> string list -> term list -> code_algebra * code_graph |
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17 val eval_conv: theory -> (sort -> sort) |
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18 -> (code_algebra -> code_graph -> (string * sort) list -> term -> cterm -> thm) -> cterm -> thm |
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19 val eval: theory -> (sort -> sort) -> ((term -> term) -> 'a -> 'a) |
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20 -> (code_algebra -> code_graph -> (string * sort) list -> term -> 'a) -> term -> 'a |
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21 end |
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22 |
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23 structure Code_Wellsorted : CODE_WELLSORTED = |
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24 struct |
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25 |
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26 (** the algebra and code equation graph types **) |
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27 |
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28 type code_algebra = (sort -> sort) * Sorts.algebra; |
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29 type code_graph = (((string * sort) list * typ) * (thm * bool) list) Graph.T; |
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30 |
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31 fun eqns eqngr = these o Option.map snd o try (Graph.get_node eqngr); |
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32 fun typ eqngr = fst o Graph.get_node eqngr; |
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33 fun all eqngr = Graph.keys eqngr; |
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34 |
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35 fun pretty thy eqngr = |
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36 AList.make (snd o Graph.get_node eqngr) (Graph.keys eqngr) |
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37 |> (map o apfst) (Code_Unit.string_of_const thy) |
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38 |> sort (string_ord o pairself fst) |
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39 |> map (fn (s, thms) => |
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40 (Pretty.block o Pretty.fbreaks) ( |
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41 Pretty.str s |
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42 :: map (Display.pretty_thm o fst) thms |
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43 )) |
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44 |> Pretty.chunks; |
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45 |
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46 |
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47 (** the Waisenhaus algorithm **) |
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48 |
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49 (* auxiliary *) |
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50 |
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51 fun is_proper_class thy = can (AxClass.get_info thy); |
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52 |
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53 fun complete_proper_sort thy = |
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54 Sign.complete_sort thy #> filter (is_proper_class thy); |
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55 |
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56 fun inst_params thy tyco = |
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57 map (fn (c, _) => AxClass.param_of_inst thy (c, tyco)) |
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58 o maps (#params o AxClass.get_info thy); |
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59 |
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60 fun consts_of thy eqns = [] |> (fold o fold o fold_aterms) |
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61 (fn Const (c, ty) => insert (op =) (c, Sign.const_typargs thy (c, Logic.unvarifyT ty)) | _ => I) |
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62 (map (op :: o swap o apfst (snd o strip_comb) o Logic.dest_equals o Thm.plain_prop_of o fst) eqns); |
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63 |
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64 fun tyscm_rhss_of thy c eqns = |
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65 let |
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66 val tyscm = case eqns of [] => Code.default_typscheme thy c |
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67 | ((thm, _) :: _) => Code_Unit.typscheme_eqn thy thm; |
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68 val rhss = consts_of thy eqns; |
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69 in (tyscm, rhss) end; |
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70 |
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71 |
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72 (* data structures *) |
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73 |
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74 datatype const = Fun of string | Inst of class * string; |
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75 |
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76 fun const_ord (Fun c1, Fun c2) = fast_string_ord (c1, c2) |
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77 | const_ord (Inst class_tyco1, Inst class_tyco2) = |
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78 prod_ord fast_string_ord fast_string_ord (class_tyco1, class_tyco2) |
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79 | const_ord (Fun _, Inst _) = LESS |
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80 | const_ord (Inst _, Fun _) = GREATER; |
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81 |
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82 type var = const * int; |
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83 |
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84 structure Vargraph = |
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85 GraphFun(type key = var val ord = prod_ord const_ord int_ord); |
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86 |
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87 datatype styp = Tyco of string * styp list | Var of var | Free; |
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88 |
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89 fun styp_of c_lhs (Type (tyco, tys)) = Tyco (tyco, map (styp_of c_lhs) tys) |
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90 | styp_of c_lhs (TFree (v, _)) = case c_lhs |
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91 of SOME (c, lhs) => Var (Fun c, find_index (fn (v', _) => v = v') lhs) |
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92 | NONE => Free; |
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93 |
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94 type vardeps_data = ((string * styp list) list * class list) Vargraph.T |
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95 * (((string * sort) list * (thm * bool) list) Symtab.table |
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96 * (class * string) list); |
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97 |
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98 val empty_vardeps_data : vardeps_data = |
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99 (Vargraph.empty, (Symtab.empty, [])); |
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100 |
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101 |
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102 (* retrieving equations and instances from the background context *) |
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103 |
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104 fun obtain_eqns thy eqngr c = |
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105 case try (Graph.get_node eqngr) c |
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106 of SOME ((lhs, _), eqns) => ((lhs, []), []) |
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107 | NONE => let |
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108 val eqns = Code.these_eqns thy c |
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109 |> burrow_fst (Code_Unit.norm_args thy) |
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110 |> burrow_fst (Code_Unit.norm_varnames thy); |
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111 val ((lhs, _), rhss) = tyscm_rhss_of thy c eqns; |
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112 in ((lhs, rhss), eqns) end; |
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113 |
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114 fun obtain_instance thy arities (inst as (class, tyco)) = |
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115 case AList.lookup (op =) arities inst |
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116 of SOME classess => (classess, ([], [])) |
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117 | NONE => let |
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118 val all_classes = complete_proper_sort thy [class]; |
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119 val superclasses = remove (op =) class all_classes |
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120 val classess = map (complete_proper_sort thy) |
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121 (Sign.arity_sorts thy tyco [class]); |
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122 val inst_params = inst_params thy tyco all_classes; |
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123 in (classess, (superclasses, inst_params)) end; |
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124 |
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125 |
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126 (* computing instantiations *) |
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127 |
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128 fun add_classes thy arities eqngr c_k new_classes vardeps_data = |
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129 let |
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130 val (styps, old_classes) = Vargraph.get_node (fst vardeps_data) c_k; |
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131 val diff_classes = new_classes |> subtract (op =) old_classes; |
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132 in if null diff_classes then vardeps_data |
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133 else let |
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134 val c_ks = Vargraph.imm_succs (fst vardeps_data) c_k |> insert (op =) c_k; |
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135 in |
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136 vardeps_data |
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137 |> (apfst o Vargraph.map_node c_k o apsnd) (append diff_classes) |
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138 |> fold (fn styp => fold (assert_typmatch_inst thy arities eqngr styp) new_classes) styps |
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139 |> fold (fn c_k => add_classes thy arities eqngr c_k diff_classes) c_ks |
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140 end end |
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141 and add_styp thy arities eqngr c_k tyco_styps vardeps_data = |
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142 let |
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143 val (old_styps, classes) = Vargraph.get_node (fst vardeps_data) c_k; |
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144 in if member (op =) old_styps tyco_styps then vardeps_data |
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145 else |
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146 vardeps_data |
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147 |> (apfst o Vargraph.map_node c_k o apfst) (cons tyco_styps) |
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148 |> fold (assert_typmatch_inst thy arities eqngr tyco_styps) classes |
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149 end |
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150 and add_dep thy arities eqngr c_k c_k' vardeps_data = |
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151 let |
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152 val (_, classes) = Vargraph.get_node (fst vardeps_data) c_k; |
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153 in |
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154 vardeps_data |
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155 |> add_classes thy arities eqngr c_k' classes |
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156 |> apfst (Vargraph.add_edge (c_k, c_k')) |
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157 end |
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158 and assert_typmatch_inst thy arities eqngr (tyco, styps) class vardeps_data = |
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159 if can (Sign.arity_sorts thy tyco) [class] |
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160 then vardeps_data |
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161 |> assert_inst thy arities eqngr (class, tyco) |
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162 |> fold_index (fn (k, styp) => |
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163 assert_typmatch thy arities eqngr styp (Inst (class, tyco), k)) styps |
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164 else vardeps_data (*permissive!*) |
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165 and assert_inst thy arities eqngr (inst as (class, tyco)) (vardeps_data as (_, (_, insts))) = |
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166 if member (op =) insts inst then vardeps_data |
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167 else let |
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168 val (classess, (superclasses, inst_params)) = |
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169 obtain_instance thy arities inst; |
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170 in |
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171 vardeps_data |
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172 |> (apsnd o apsnd) (insert (op =) inst) |
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173 |> fold_index (fn (k, _) => |
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174 apfst (Vargraph.new_node ((Inst (class, tyco), k), ([] ,[])))) classess |
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175 |> fold (fn superclass => assert_inst thy arities eqngr (superclass, tyco)) superclasses |
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176 |> fold (assert_fun thy arities eqngr) inst_params |
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177 |> fold_index (fn (k, classes) => |
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178 add_classes thy arities eqngr (Inst (class, tyco), k) classes |
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179 #> fold (fn superclass => |
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180 add_dep thy arities eqngr (Inst (superclass, tyco), k) |
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181 (Inst (class, tyco), k)) superclasses |
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182 #> fold (fn inst_param => |
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183 add_dep thy arities eqngr (Fun inst_param, k) |
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184 (Inst (class, tyco), k) |
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185 ) inst_params |
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186 ) classess |
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187 end |
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188 and assert_typmatch thy arities eqngr (Tyco tyco_styps) c_k vardeps_data = |
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189 vardeps_data |
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190 |> add_styp thy arities eqngr c_k tyco_styps |
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191 | assert_typmatch thy arities eqngr (Var c_k') c_k vardeps_data = |
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192 vardeps_data |
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193 |> add_dep thy arities eqngr c_k c_k' |
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194 | assert_typmatch thy arities eqngr Free c_k vardeps_data = |
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195 vardeps_data |
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196 and assert_rhs thy arities eqngr (c', styps) vardeps_data = |
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197 vardeps_data |
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198 |> assert_fun thy arities eqngr c' |
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199 |> fold_index (fn (k, styp) => |
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200 assert_typmatch thy arities eqngr styp (Fun c', k)) styps |
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201 and assert_fun thy arities eqngr c (vardeps_data as (_, (eqntab, _))) = |
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202 if Symtab.defined eqntab c then vardeps_data |
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203 else let |
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204 val ((lhs, rhss), eqns) = obtain_eqns thy eqngr c; |
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205 val rhss' = (map o apsnd o map) (styp_of (SOME (c, lhs))) rhss; |
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206 in |
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207 vardeps_data |
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208 |> (apsnd o apfst) (Symtab.update_new (c, (lhs, eqns))) |
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209 |> fold_index (fn (k, _) => |
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210 apfst (Vargraph.new_node ((Fun c, k), ([] ,[])))) lhs |
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211 |> fold_index (fn (k, (_, sort)) => |
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212 add_classes thy arities eqngr (Fun c, k) (complete_proper_sort thy sort)) lhs |
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213 |> fold (assert_rhs thy arities eqngr) rhss' |
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214 end; |
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215 |
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216 |
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217 (* applying instantiations *) |
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218 |
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219 fun dicts_of thy (proj_sort, algebra) (T, sort) = |
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220 let |
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221 fun class_relation (x, _) _ = x; |
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222 fun type_constructor tyco xs class = |
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223 inst_params thy tyco (Sorts.complete_sort algebra [class]) |
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224 @ (maps o maps) fst xs; |
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225 fun type_variable (TFree (_, sort)) = map (pair []) (proj_sort sort); |
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226 in |
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227 flat (Sorts.of_sort_derivation (Syntax.pp_global thy) algebra |
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228 { class_relation = class_relation, type_constructor = type_constructor, |
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229 type_variable = type_variable } (T, proj_sort sort) |
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230 handle Sorts.CLASS_ERROR _ => [] (*permissive!*)) |
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231 end; |
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232 |
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233 fun add_arity thy vardeps (class, tyco) = |
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234 AList.default (op =) |
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235 ((class, tyco), map (fn k => (snd o Vargraph.get_node vardeps) (Inst (class, tyco), k)) |
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236 (0 upto Sign.arity_number thy tyco - 1)); |
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237 |
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238 fun add_eqs thy vardeps (c, (proto_lhs, proto_eqns)) (rhss, eqngr) = |
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239 if can (Graph.get_node eqngr) c then (rhss, eqngr) |
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240 else let |
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241 val lhs = map_index (fn (k, (v, _)) => |
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242 (v, snd (Vargraph.get_node vardeps (Fun c, k)))) proto_lhs; |
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243 val inst_tab = Vartab.empty |> fold (fn (v, sort) => |
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244 Vartab.update ((v, 0), sort)) lhs; |
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245 val eqns = proto_eqns |
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246 |> (map o apfst) (Code_Unit.inst_thm thy inst_tab); |
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247 val (tyscm, rhss') = tyscm_rhss_of thy c eqns; |
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248 val eqngr' = Graph.new_node (c, (tyscm, eqns)) eqngr; |
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249 in (map (pair c) rhss' @ rhss, eqngr') end; |
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250 |
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251 fun extend_arities_eqngr thy cs ts (arities, eqngr) = |
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252 let |
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253 val cs_rhss = (fold o fold_aterms) (fn Const (c_ty as (c, _)) => |
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254 insert (op =) (c, (map (styp_of NONE) o Sign.const_typargs thy) c_ty) | _ => I) ts []; |
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255 val (vardeps, (eqntab, insts)) = empty_vardeps_data |
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256 |> fold (assert_fun thy arities eqngr) cs |
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257 |> fold (assert_rhs thy arities eqngr) cs_rhss; |
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258 val arities' = fold (add_arity thy vardeps) insts arities; |
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259 val pp = Syntax.pp_global thy; |
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260 val algebra = Sorts.subalgebra pp (is_proper_class thy) |
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261 (AList.lookup (op =) arities') (Sign.classes_of thy); |
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262 val (rhss, eqngr') = Symtab.fold (add_eqs thy vardeps) eqntab ([], eqngr); |
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263 fun deps_of (c, rhs) = c :: maps (dicts_of thy algebra) |
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264 (rhs ~~ (map snd o fst o fst o Graph.get_node eqngr') c); |
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265 val eqngr'' = fold (fn (c, rhs) => fold |
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266 (curry Graph.add_edge c) (deps_of rhs)) rhss eqngr'; |
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267 in (algebra, (arities', eqngr'')) end; |
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268 |
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269 |
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270 (** store **) |
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271 |
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272 structure Wellsorted = CodeDataFun |
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273 ( |
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274 type T = ((string * class) * sort list) list * code_graph; |
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275 val empty = ([], Graph.empty); |
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276 fun purge thy cs (arities, eqngr) = |
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277 let |
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278 val del_cs = ((Graph.all_preds eqngr |
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279 o filter (can (Graph.get_node eqngr))) cs); |
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280 val del_arities = del_cs |
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281 |> map_filter (AxClass.inst_of_param thy) |
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282 |> maps (fn (c, tyco) => |
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283 (map (rpair tyco) o Sign.complete_sort thy o the_list |
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284 o AxClass.class_of_param thy) c); |
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285 val arities' = fold (AList.delete (op =)) del_arities arities; |
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286 val eqngr' = Graph.del_nodes del_cs eqngr; |
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287 in (arities', eqngr') end; |
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288 ); |
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289 |
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290 |
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291 (** retrieval interfaces **) |
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292 |
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293 fun obtain thy cs ts = apsnd snd |
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294 (Wellsorted.change_yield thy (extend_arities_eqngr thy cs ts)); |
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295 |
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296 fun prepare_sorts_typ prep_sort |
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297 = map_type_tfree (fn (v, sort) => TFree (v, prep_sort sort)); |
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298 |
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299 fun prepare_sorts prep_sort (Const (c, ty)) = |
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300 Const (c, prepare_sorts_typ prep_sort ty) |
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301 | prepare_sorts prep_sort (t1 $ t2) = |
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302 prepare_sorts prep_sort t1 $ prepare_sorts prep_sort t2 |
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303 | prepare_sorts prep_sort (Abs (v, ty, t)) = |
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304 Abs (v, prepare_sorts_typ prep_sort ty, prepare_sorts prep_sort t) |
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305 | prepare_sorts _ (t as Bound _) = t; |
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306 |
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307 fun gen_eval thy cterm_of conclude_evaluation prep_sort evaluator proto_ct = |
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308 let |
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309 val pp = Syntax.pp_global thy; |
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310 val ct = cterm_of proto_ct; |
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311 val _ = (Sign.no_frees pp o map_types (K dummyT) o Sign.no_vars pp) |
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312 (Thm.term_of ct); |
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313 val thm = Code.preprocess_conv thy ct; |
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314 val ct' = Thm.rhs_of thm; |
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315 val t' = Thm.term_of ct'; |
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316 val vs = Term.add_tfrees t' []; |
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317 val consts = fold_aterms |
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318 (fn Const (c, _) => insert (op =) c | _ => I) t' []; |
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319 |
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320 val t'' = prepare_sorts prep_sort t'; |
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321 val (algebra', eqngr') = obtain thy consts [t'']; |
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322 in conclude_evaluation (evaluator algebra' eqngr' vs t'' ct') thm end; |
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323 |
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324 fun simple_evaluator evaluator algebra eqngr vs t ct = |
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325 evaluator algebra eqngr vs t; |
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326 |
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327 fun eval_conv thy = |
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328 let |
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329 fun conclude_evaluation thm2 thm1 = |
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330 let |
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331 val thm3 = Code.postprocess_conv thy (Thm.rhs_of thm2); |
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332 in |
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333 Thm.transitive thm1 (Thm.transitive thm2 thm3) handle THM _ => |
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334 error ("could not construct evaluation proof:\n" |
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335 ^ (cat_lines o map Display.string_of_thm) [thm1, thm2, thm3]) |
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336 end; |
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337 in gen_eval thy I conclude_evaluation end; |
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338 |
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339 fun eval thy prep_sort postproc evaluator = gen_eval thy (Thm.cterm_of thy) |
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340 (K o postproc (Code.postprocess_term thy)) prep_sort (simple_evaluator evaluator); |
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341 |
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342 end; (*struct*) |
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