1 (* Title: HOL/BNF/Tools/bnf_fp_rec_sugar.ML |
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2 Author: Lorenz Panny, TU Muenchen |
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3 Copyright 2013 |
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4 |
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5 Recursor and corecursor sugar. |
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6 *) |
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7 |
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8 signature BNF_FP_REC_SUGAR = |
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9 sig |
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10 val add_primrec: (binding * typ option * mixfix) list -> |
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11 (Attrib.binding * term) list -> local_theory -> (term list * thm list list) * local_theory |
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12 val add_primrec_cmd: (binding * string option * mixfix) list -> |
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13 (Attrib.binding * string) list -> local_theory -> (term list * thm list list) * local_theory |
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14 val add_primrec_global: (binding * typ option * mixfix) list -> |
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15 (Attrib.binding * term) list -> theory -> (term list * thm list list) * theory |
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16 val add_primrec_overloaded: (string * (string * typ) * bool) list -> |
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17 (binding * typ option * mixfix) list -> |
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18 (Attrib.binding * term) list -> theory -> (term list * thm list list) * theory |
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19 val add_primrec_simple: ((binding * typ) * mixfix) list -> term list -> |
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20 local_theory -> (string list * (term list * (int list list * thm list list))) * local_theory |
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21 val add_primcorecursive_cmd: bool -> |
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22 (binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list -> |
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23 Proof.context -> Proof.state |
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24 val add_primcorec_cmd: bool -> |
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25 (binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list -> |
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26 local_theory -> local_theory |
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27 end; |
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28 |
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29 structure BNF_FP_Rec_Sugar : BNF_FP_REC_SUGAR = |
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30 struct |
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31 |
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32 open BNF_Util |
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33 open BNF_FP_Util |
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34 open BNF_FP_Rec_Sugar_Util |
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35 open BNF_FP_Rec_Sugar_Tactics |
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36 |
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37 val codeN = "code" |
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38 val ctrN = "ctr" |
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39 val discN = "disc" |
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40 val selN = "sel" |
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41 |
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42 val nitpick_attrs = @{attributes [nitpick_simp]}; |
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43 val simp_attrs = @{attributes [simp]}; |
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44 val code_nitpick_attrs = Code.add_default_eqn_attrib :: nitpick_attrs; |
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45 val code_nitpick_simp_attrs = Code.add_default_eqn_attrib :: nitpick_attrs @ simp_attrs; |
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46 |
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47 exception Primrec_Error of string * term list; |
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48 |
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49 fun primrec_error str = raise Primrec_Error (str, []); |
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50 fun primrec_error_eqn str eqn = raise Primrec_Error (str, [eqn]); |
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51 fun primrec_error_eqns str eqns = raise Primrec_Error (str, eqns); |
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52 |
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53 fun finds eq = fold_map (fn x => List.partition (curry eq x) #>> pair x); |
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54 |
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55 val free_name = try (fn Free (v, _) => v); |
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56 val const_name = try (fn Const (v, _) => v); |
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57 val undef_const = Const (@{const_name undefined}, dummyT); |
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58 |
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59 fun permute_args n t = list_comb (t, map Bound (0 :: (n downto 1))) |
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60 |> fold (K (Term.abs (Name.uu, dummyT))) (0 upto n); |
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61 val abs_tuple = HOLogic.tupled_lambda o HOLogic.mk_tuple; |
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62 fun drop_All t = subst_bounds (strip_qnt_vars @{const_name all} t |> map Free |> rev, |
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63 strip_qnt_body @{const_name all} t) |
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64 fun abstract vs = |
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65 let fun a n (t $ u) = a n t $ a n u |
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66 | a n (Abs (v, T, b)) = Abs (v, T, a (n + 1) b) |
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67 | a n t = let val idx = find_index (equal t) vs in |
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68 if idx < 0 then t else Bound (n + idx) end |
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69 in a 0 end; |
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70 fun mk_prod1 Ts (t, u) = HOLogic.pair_const (fastype_of1 (Ts, t)) (fastype_of1 (Ts, u)) $ t $ u; |
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71 fun mk_tuple1 Ts = the_default HOLogic.unit o try (foldr1 (mk_prod1 Ts)); |
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72 |
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73 fun get_indices fixes t = map (fst #>> Binding.name_of #> Free) fixes |
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74 |> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE) |
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75 |> map_filter I; |
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76 |
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77 |
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78 (* Primrec *) |
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79 |
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80 type eqn_data = { |
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81 fun_name: string, |
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82 rec_type: typ, |
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83 ctr: term, |
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84 ctr_args: term list, |
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85 left_args: term list, |
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86 right_args: term list, |
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87 res_type: typ, |
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88 rhs_term: term, |
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89 user_eqn: term |
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90 }; |
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91 |
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92 fun dissect_eqn lthy fun_names eqn' = |
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93 let |
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94 val eqn = drop_All eqn' |> HOLogic.dest_Trueprop |
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95 handle TERM _ => |
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96 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn'; |
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97 val (lhs, rhs) = HOLogic.dest_eq eqn |
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98 handle TERM _ => |
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99 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn'; |
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100 val (fun_name, args) = strip_comb lhs |
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101 |>> (fn x => if is_Free x then fst (dest_Free x) |
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102 else primrec_error_eqn "malformed function equation (does not start with free)" eqn); |
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103 val (left_args, rest) = take_prefix is_Free args; |
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104 val (nonfrees, right_args) = take_suffix is_Free rest; |
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105 val num_nonfrees = length nonfrees; |
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106 val _ = num_nonfrees = 1 orelse if num_nonfrees = 0 then |
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107 primrec_error_eqn "constructor pattern missing in left-hand side" eqn else |
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108 primrec_error_eqn "more than one non-variable argument in left-hand side" eqn; |
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109 val _ = member (op =) fun_names fun_name orelse |
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110 primrec_error_eqn "malformed function equation (does not start with function name)" eqn |
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111 |
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112 val (ctr, ctr_args) = strip_comb (the_single nonfrees); |
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113 val _ = try (num_binder_types o fastype_of) ctr = SOME (length ctr_args) orelse |
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114 primrec_error_eqn "partially applied constructor in pattern" eqn; |
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115 val _ = let val d = duplicates (op =) (left_args @ ctr_args @ right_args) in null d orelse |
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116 primrec_error_eqn ("duplicate variable \"" ^ Syntax.string_of_term lthy (hd d) ^ |
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117 "\" in left-hand side") eqn end; |
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118 val _ = forall is_Free ctr_args orelse |
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119 primrec_error_eqn "non-primitive pattern in left-hand side" eqn; |
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120 val _ = |
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121 let val b = fold_aterms (fn x as Free (v, _) => |
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122 if (not (member (op =) (left_args @ ctr_args @ right_args) x) andalso |
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123 not (member (op =) fun_names v) andalso |
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124 not (Variable.is_fixed lthy v)) then cons x else I | _ => I) rhs [] |
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125 in |
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126 null b orelse |
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127 primrec_error_eqn ("extra variable(s) in right-hand side: " ^ |
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128 commas (map (Syntax.string_of_term lthy) b)) eqn |
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129 end; |
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130 in |
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131 {fun_name = fun_name, |
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132 rec_type = body_type (type_of ctr), |
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133 ctr = ctr, |
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134 ctr_args = ctr_args, |
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135 left_args = left_args, |
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136 right_args = right_args, |
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137 res_type = map fastype_of (left_args @ right_args) ---> fastype_of rhs, |
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138 rhs_term = rhs, |
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139 user_eqn = eqn'} |
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140 end; |
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141 |
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142 fun rewrite_map_arg get_ctr_pos rec_type res_type = |
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143 let |
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144 val pT = HOLogic.mk_prodT (rec_type, res_type); |
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145 |
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146 val maybe_suc = Option.map (fn x => x + 1); |
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147 fun subst d (t as Bound d') = t |> d = SOME d' ? curry (op $) (fst_const pT) |
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148 | subst d (Abs (v, T, b)) = Abs (v, if d = SOME ~1 then pT else T, subst (maybe_suc d) b) |
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149 | subst d t = |
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150 let |
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151 val (u, vs) = strip_comb t; |
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152 val ctr_pos = try (get_ctr_pos o the) (free_name u) |> the_default ~1; |
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153 in |
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154 if ctr_pos >= 0 then |
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155 if d = SOME ~1 andalso length vs = ctr_pos then |
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156 list_comb (permute_args ctr_pos (snd_const pT), vs) |
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157 else if length vs > ctr_pos andalso is_some d |
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158 andalso d = try (fn Bound n => n) (nth vs ctr_pos) then |
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159 list_comb (snd_const pT $ nth vs ctr_pos, map (subst d) (nth_drop ctr_pos vs)) |
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160 else |
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161 primrec_error_eqn ("recursive call not directly applied to constructor argument") t |
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162 else if d = SOME ~1 andalso const_name u = SOME @{const_name comp} then |
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163 list_comb (map_types (K dummyT) u, map2 subst [NONE, d] vs) |
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164 else |
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165 list_comb (u, map (subst (d |> d = SOME ~1 ? K NONE)) vs) |
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166 end |
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167 in |
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168 subst (SOME ~1) |
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169 end; |
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170 |
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171 fun subst_rec_calls lthy get_ctr_pos has_call ctr_args direct_calls indirect_calls t = |
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172 let |
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173 fun subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b) |
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174 | subst bound_Ts (t as g' $ y) = |
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175 let |
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176 val maybe_direct_y' = AList.lookup (op =) direct_calls y; |
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177 val maybe_indirect_y' = AList.lookup (op =) indirect_calls y; |
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178 val (g, g_args) = strip_comb g'; |
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179 val ctr_pos = try (get_ctr_pos o the) (free_name g) |> the_default ~1; |
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180 val _ = ctr_pos < 0 orelse length g_args >= ctr_pos orelse |
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181 primrec_error_eqn "too few arguments in recursive call" t; |
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182 in |
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183 if not (member (op =) ctr_args y) then |
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184 pairself (subst bound_Ts) (g', y) |> (op $) |
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185 else if ctr_pos >= 0 then |
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186 list_comb (the maybe_direct_y', g_args) |
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187 else if is_some maybe_indirect_y' then |
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188 (if has_call g' then t else y) |
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189 |> massage_indirect_rec_call lthy has_call |
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190 (rewrite_map_arg get_ctr_pos) bound_Ts y (the maybe_indirect_y') |
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191 |> (if has_call g' then I else curry (op $) g') |
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192 else |
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193 t |
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194 end |
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195 | subst _ t = t |
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196 in |
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197 subst [] t |
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198 |> tap (fn u => has_call u andalso (* FIXME detect this case earlier *) |
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199 primrec_error_eqn "recursive call not directly applied to constructor argument" t) |
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200 end; |
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201 |
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202 fun build_rec_arg lthy (funs_data : eqn_data list list) has_call (ctr_spec : rec_ctr_spec) |
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203 (maybe_eqn_data : eqn_data option) = |
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204 if is_none maybe_eqn_data then undef_const else |
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205 let |
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206 val eqn_data = the maybe_eqn_data; |
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207 val t = #rhs_term eqn_data; |
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208 val ctr_args = #ctr_args eqn_data; |
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209 |
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210 val calls = #calls ctr_spec; |
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211 val n_args = fold (curry (op +) o (fn Direct_Rec _ => 2 | _ => 1)) calls 0; |
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212 |
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213 val no_calls' = tag_list 0 calls |
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214 |> map_filter (try (apsnd (fn No_Rec n => n | Direct_Rec (n, _) => n))); |
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215 val direct_calls' = tag_list 0 calls |
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216 |> map_filter (try (apsnd (fn Direct_Rec (_, n) => n))); |
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217 val indirect_calls' = tag_list 0 calls |
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218 |> map_filter (try (apsnd (fn Indirect_Rec n => n))); |
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219 |
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220 fun make_direct_type _ = dummyT; (* FIXME? *) |
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221 |
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222 val rec_res_type_list = map (fn (x :: _) => (#rec_type x, #res_type x)) funs_data; |
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223 |
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224 fun make_indirect_type (Type (Tname, Ts)) = Type (Tname, Ts |> map (fn T => |
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225 let val maybe_res_type = AList.lookup (op =) rec_res_type_list T in |
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226 if is_some maybe_res_type |
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227 then HOLogic.mk_prodT (T, the maybe_res_type) |
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228 else make_indirect_type T end)) |
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229 | make_indirect_type T = T; |
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230 |
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231 val args = replicate n_args ("", dummyT) |
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232 |> Term.rename_wrt_term t |
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233 |> map Free |
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234 |> fold (fn (ctr_arg_idx, arg_idx) => |
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235 nth_map arg_idx (K (nth ctr_args ctr_arg_idx))) |
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236 no_calls' |
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237 |> fold (fn (ctr_arg_idx, arg_idx) => |
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238 nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_direct_type))) |
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239 direct_calls' |
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240 |> fold (fn (ctr_arg_idx, arg_idx) => |
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241 nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_indirect_type))) |
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242 indirect_calls'; |
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243 |
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244 val fun_name_ctr_pos_list = |
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245 map (fn (x :: _) => (#fun_name x, length (#left_args x))) funs_data; |
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246 val get_ctr_pos = try (the o AList.lookup (op =) fun_name_ctr_pos_list) #> the_default ~1; |
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247 val direct_calls = map (apfst (nth ctr_args) o apsnd (nth args)) direct_calls'; |
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248 val indirect_calls = map (apfst (nth ctr_args) o apsnd (nth args)) indirect_calls'; |
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249 |
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250 val abstractions = args @ #left_args eqn_data @ #right_args eqn_data; |
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251 in |
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252 t |
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253 |> subst_rec_calls lthy get_ctr_pos has_call ctr_args direct_calls indirect_calls |
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254 |> fold_rev lambda abstractions |
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255 end; |
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256 |
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257 fun build_defs lthy bs mxs (funs_data : eqn_data list list) (rec_specs : rec_spec list) has_call = |
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258 let |
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259 val n_funs = length funs_data; |
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260 |
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261 val ctr_spec_eqn_data_list' = |
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262 (take n_funs rec_specs |> map #ctr_specs) ~~ funs_data |
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263 |> maps (uncurry (finds (fn (x, y) => #ctr x = #ctr y)) |
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264 ##> (fn x => null x orelse |
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265 primrec_error_eqns "excess equations in definition" (map #rhs_term x)) #> fst); |
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266 val _ = ctr_spec_eqn_data_list' |> map (fn (_, x) => length x <= 1 orelse |
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267 primrec_error_eqns ("multiple equations for constructor") (map #user_eqn x)); |
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268 |
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269 val ctr_spec_eqn_data_list = |
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270 ctr_spec_eqn_data_list' @ (drop n_funs rec_specs |> maps #ctr_specs |> map (rpair [])); |
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271 |
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272 val recs = take n_funs rec_specs |> map #recx; |
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273 val rec_args = ctr_spec_eqn_data_list |
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274 |> sort ((op <) o pairself (#offset o fst) |> make_ord) |
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275 |> map (uncurry (build_rec_arg lthy funs_data has_call) o apsnd (try the_single)); |
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276 val ctr_poss = map (fn x => |
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277 if length (distinct ((op =) o pairself (length o #left_args)) x) <> 1 then |
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278 primrec_error ("inconstant constructor pattern position for function " ^ |
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279 quote (#fun_name (hd x))) |
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280 else |
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281 hd x |> #left_args |> length) funs_data; |
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282 in |
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283 (recs, ctr_poss) |
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284 |-> map2 (fn recx => fn ctr_pos => list_comb (recx, rec_args) |> permute_args ctr_pos) |
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285 |> Syntax.check_terms lthy |
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286 |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs |
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287 end; |
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288 |
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289 fun find_rec_calls has_call (eqn_data : eqn_data) = |
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290 let |
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291 fun find (Abs (_, _, b)) ctr_arg = find b ctr_arg |
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292 | find (t as _ $ _) ctr_arg = |
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293 let |
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294 val (f', args') = strip_comb t; |
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295 val n = find_index (equal ctr_arg) args'; |
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296 in |
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297 if n < 0 then |
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298 find f' ctr_arg @ maps (fn x => find x ctr_arg) args' |
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299 else |
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300 let val (f, args) = chop n args' |>> curry list_comb f' in |
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301 if has_call f then |
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302 f :: maps (fn x => find x ctr_arg) args |
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303 else |
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304 find f ctr_arg @ maps (fn x => find x ctr_arg) args |
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305 end |
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306 end |
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307 | find _ _ = []; |
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308 in |
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309 map (find (#rhs_term eqn_data)) (#ctr_args eqn_data) |
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310 |> (fn [] => NONE | callss => SOME (#ctr eqn_data, callss)) |
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311 end; |
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312 |
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313 fun prepare_primrec fixes specs lthy = |
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314 let |
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315 val (bs, mxs) = map_split (apfst fst) fixes; |
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316 val fun_names = map Binding.name_of bs; |
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317 val eqns_data = map (dissect_eqn lthy fun_names) specs; |
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318 val funs_data = eqns_data |
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319 |> partition_eq ((op =) o pairself #fun_name) |
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320 |> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst |
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321 |> map (fn (x, y) => the_single y handle List.Empty => |
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322 primrec_error ("missing equations for function " ^ quote x)); |
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323 |
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324 val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =)); |
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325 val arg_Ts = map (#rec_type o hd) funs_data; |
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326 val res_Ts = map (#res_type o hd) funs_data; |
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327 val callssss = funs_data |
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328 |> map (partition_eq ((op =) o pairself #ctr)) |
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329 |> map (maps (map_filter (find_rec_calls has_call))); |
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330 |
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331 val ((n2m, rec_specs, _, induct_thm, induct_thms), lthy') = |
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332 rec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy; |
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333 |
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334 val actual_nn = length funs_data; |
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335 |
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336 val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in |
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337 map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse |
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338 primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^ |
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339 " is not a constructor in left-hand side") user_eqn) eqns_data end; |
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340 |
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341 val defs = build_defs lthy' bs mxs funs_data rec_specs has_call; |
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342 |
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343 fun prove lthy def_thms' ({ctr_specs, nested_map_idents, nested_map_comps, ...} : rec_spec) |
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344 (fun_data : eqn_data list) = |
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345 let |
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346 val def_thms = map (snd o snd) def_thms'; |
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347 val simp_thmss = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs |
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348 |> fst |
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349 |> map_filter (try (fn (x, [y]) => |
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350 (#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y))) |
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351 |> map (fn (user_eqn, num_extra_args, rec_thm) => |
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352 mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm |
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353 |> K |> Goal.prove lthy [] [] user_eqn); |
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354 val poss = find_indices (fn (x, y) => #ctr x = #ctr y) fun_data eqns_data; |
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355 in |
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356 (poss, simp_thmss) |
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357 end; |
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358 |
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359 val notes = |
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360 (if n2m then map2 (fn name => fn thm => |
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361 (name, inductN, [thm], [])) fun_names (take actual_nn induct_thms) else []) |
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362 |> map (fn (prefix, thmN, thms, attrs) => |
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363 ((Binding.qualify true prefix (Binding.name thmN), attrs), [(thms, [])])); |
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364 |
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365 val common_name = mk_common_name fun_names; |
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366 |
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367 val common_notes = |
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368 (if n2m then [(inductN, [induct_thm], [])] else []) |
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369 |> map (fn (thmN, thms, attrs) => |
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370 ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])])); |
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371 in |
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372 (((fun_names, defs), |
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373 fn lthy => fn defs => |
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374 split_list (map2 (prove lthy defs) (take actual_nn rec_specs) funs_data)), |
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375 lthy' |> Local_Theory.notes (notes @ common_notes) |> snd) |
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376 end; |
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377 |
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378 (* primrec definition *) |
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379 |
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380 fun add_primrec_simple fixes ts lthy = |
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381 let |
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382 val (((names, defs), prove), lthy) = prepare_primrec fixes ts lthy |
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383 handle ERROR str => primrec_error str; |
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384 in |
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385 lthy |
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386 |> fold_map Local_Theory.define defs |
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387 |-> (fn defs => `(fn lthy => (names, (map fst defs, prove lthy defs)))) |
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388 end |
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389 handle Primrec_Error (str, eqns) => |
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390 if null eqns |
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391 then error ("primrec_new error:\n " ^ str) |
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392 else error ("primrec_new error:\n " ^ str ^ "\nin\n " ^ |
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393 space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns)); |
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394 |
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395 local |
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396 |
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397 fun gen_primrec prep_spec (raw_fixes : (binding * 'a option * mixfix) list) raw_spec lthy = |
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398 let |
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399 val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes) |
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400 val _ = null d orelse primrec_error ("duplicate function name(s): " ^ commas d); |
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401 |
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402 val (fixes, specs) = fst (prep_spec raw_fixes raw_spec lthy); |
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403 |
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404 val mk_notes = |
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405 flat ooo map3 (fn poss => fn prefix => fn thms => |
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406 let |
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407 val (bs, attrss) = map_split (fst o nth specs) poss; |
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408 val notes = |
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409 map3 (fn b => fn attrs => fn thm => |
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410 ((Binding.qualify false prefix b, code_nitpick_simp_attrs @ attrs), [([thm], [])])) |
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411 bs attrss thms; |
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412 in |
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413 ((Binding.qualify true prefix (Binding.name simpsN), []), [(thms, [])]) :: notes |
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414 end); |
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415 in |
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416 lthy |
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417 |> add_primrec_simple fixes (map snd specs) |
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418 |-> (fn (names, (ts, (posss, simpss))) => |
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419 Spec_Rules.add Spec_Rules.Equational (ts, flat simpss) |
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420 #> Local_Theory.notes (mk_notes posss names simpss) |
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421 #>> pair ts o map snd) |
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422 end; |
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423 |
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424 in |
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425 |
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426 val add_primrec = gen_primrec Specification.check_spec; |
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427 val add_primrec_cmd = gen_primrec Specification.read_spec; |
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428 |
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429 end; |
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430 |
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431 fun add_primrec_global fixes specs thy = |
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432 let |
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433 val lthy = Named_Target.theory_init thy; |
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434 val ((ts, simps), lthy') = add_primrec fixes specs lthy; |
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435 val simps' = burrow (Proof_Context.export lthy' lthy) simps; |
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436 in ((ts, simps'), Local_Theory.exit_global lthy') end; |
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437 |
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438 fun add_primrec_overloaded ops fixes specs thy = |
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439 let |
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440 val lthy = Overloading.overloading ops thy; |
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441 val ((ts, simps), lthy') = add_primrec fixes specs lthy; |
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442 val simps' = burrow (Proof_Context.export lthy' lthy) simps; |
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443 in ((ts, simps'), Local_Theory.exit_global lthy') end; |
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444 |
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445 |
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446 |
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447 (* Primcorec *) |
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448 |
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449 type co_eqn_data_disc = { |
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450 fun_name: string, |
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451 fun_T: typ, |
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452 fun_args: term list, |
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453 ctr: term, |
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454 ctr_no: int, (*###*) |
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455 disc: term, |
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456 prems: term list, |
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457 auto_gen: bool, |
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458 user_eqn: term |
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459 }; |
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460 |
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461 type co_eqn_data_sel = { |
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462 fun_name: string, |
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463 fun_T: typ, |
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464 fun_args: term list, |
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465 ctr: term, |
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466 sel: term, |
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467 rhs_term: term, |
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468 user_eqn: term |
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469 }; |
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470 |
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471 datatype co_eqn_data = |
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472 Disc of co_eqn_data_disc | |
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473 Sel of co_eqn_data_sel; |
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474 |
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475 fun co_dissect_eqn_disc sequential fun_names (corec_specs : corec_spec list) prems' concl |
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476 matchedsss = |
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477 let |
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478 fun find_subterm p = let (* FIXME \<exists>? *) |
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479 fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v) |
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480 | f t = if p t then SOME t else NONE |
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481 in f end; |
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482 |
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483 val applied_fun = concl |
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484 |> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of)) |
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485 |> the |
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486 handle Option.Option => primrec_error_eqn "malformed discriminator equation" concl; |
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487 val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free; |
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488 val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name); |
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489 |
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490 val discs = map #disc ctr_specs; |
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491 val ctrs = map #ctr ctr_specs; |
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492 val not_disc = head_of concl = @{term Not}; |
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493 val _ = not_disc andalso length ctrs <> 2 andalso |
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494 primrec_error_eqn "\<not>ed discriminator for a type with \<noteq> 2 constructors" concl; |
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495 val disc = find_subterm (member (op =) discs o head_of) concl; |
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496 val eq_ctr0 = concl |> perhaps (try (HOLogic.dest_not)) |> try (HOLogic.dest_eq #> snd) |
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497 |> (fn SOME t => let val n = find_index (equal t) ctrs in |
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498 if n >= 0 then SOME n else NONE end | _ => NONE); |
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499 val _ = is_some disc orelse is_some eq_ctr0 orelse |
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500 primrec_error_eqn "no discriminator in equation" concl; |
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501 val ctr_no' = |
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502 if is_none disc then the eq_ctr0 else find_index (equal (head_of (the disc))) discs; |
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503 val ctr_no = if not_disc then 1 - ctr_no' else ctr_no'; |
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504 val ctr = #ctr (nth ctr_specs ctr_no); |
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505 |
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506 val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_; |
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507 val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default []; |
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508 val prems = map (abstract (List.rev fun_args)) prems'; |
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509 val real_prems = |
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510 (if catch_all orelse sequential then maps negate_disj matchedss else []) @ |
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511 (if catch_all then [] else prems); |
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512 |
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513 val matchedsss' = AList.delete (op =) fun_name matchedsss |
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514 |> cons (fun_name, if sequential then matchedss @ [prems] else matchedss @ [real_prems]); |
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515 |
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516 val user_eqn = |
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517 (real_prems, betapply (#disc (nth ctr_specs ctr_no), applied_fun)) |
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518 |>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop |
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519 |> Logic.list_implies; |
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520 in |
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521 (Disc { |
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522 fun_name = fun_name, |
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523 fun_T = fun_T, |
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524 fun_args = fun_args, |
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525 ctr = ctr, |
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526 ctr_no = ctr_no, |
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527 disc = #disc (nth ctr_specs ctr_no), |
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528 prems = real_prems, |
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529 auto_gen = catch_all, |
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530 user_eqn = user_eqn |
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531 }, matchedsss') |
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532 end; |
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533 |
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534 fun co_dissect_eqn_sel fun_names (corec_specs : corec_spec list) eqn' of_spec eqn = |
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535 let |
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536 val (lhs, rhs) = HOLogic.dest_eq eqn |
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537 handle TERM _ => |
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538 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn; |
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539 val sel = head_of lhs; |
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540 val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free |
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541 handle TERM _ => |
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542 primrec_error_eqn "malformed selector argument in left-hand side" eqn; |
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543 val corec_spec = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name) |
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544 handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn; |
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545 val ctr_spec = |
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546 if is_some of_spec |
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547 then the (find_first (equal (the of_spec) o #ctr) (#ctr_specs corec_spec)) |
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548 else #ctr_specs corec_spec |> filter (exists (equal sel) o #sels) |> the_single |
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549 handle List.Empty => primrec_error_eqn "ambiguous selector - use \"of\"" eqn; |
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550 val user_eqn = drop_All eqn'; |
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551 in |
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552 Sel { |
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553 fun_name = fun_name, |
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554 fun_T = fun_T, |
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555 fun_args = fun_args, |
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556 ctr = #ctr ctr_spec, |
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557 sel = sel, |
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558 rhs_term = rhs, |
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559 user_eqn = user_eqn |
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560 } |
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561 end; |
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562 |
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563 fun co_dissect_eqn_ctr sequential fun_names (corec_specs : corec_spec list) eqn' imp_prems imp_rhs |
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564 matchedsss = |
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565 let |
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566 val (lhs, rhs) = HOLogic.dest_eq imp_rhs; |
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567 val fun_name = head_of lhs |> fst o dest_Free; |
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568 val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name); |
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569 val (ctr, ctr_args) = strip_comb rhs; |
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570 val {disc, sels, ...} = the (find_first (equal ctr o #ctr) ctr_specs) |
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571 handle Option.Option => primrec_error_eqn "not a constructor" ctr; |
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572 |
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573 val disc_imp_rhs = betapply (disc, lhs); |
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574 val (maybe_eqn_data_disc, matchedsss') = if length ctr_specs = 1 |
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575 then (NONE, matchedsss) |
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576 else apfst SOME (co_dissect_eqn_disc |
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577 sequential fun_names corec_specs imp_prems disc_imp_rhs matchedsss); |
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578 |
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579 val sel_imp_rhss = (sels ~~ ctr_args) |
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580 |> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg)); |
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581 |
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582 (* |
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583 val _ = tracing ("reduced\n " ^ Syntax.string_of_term @{context} imp_rhs ^ "\nto\n \<cdot> " ^ |
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584 (is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_imp_rhs ^ "\n \<cdot> ")) "" ^ |
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585 space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) sel_imp_rhss)); |
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586 *) |
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587 |
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588 val eqns_data_sel = |
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589 map (co_dissect_eqn_sel fun_names corec_specs eqn' (SOME ctr)) sel_imp_rhss; |
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590 in |
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591 (the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss') |
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592 end; |
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593 |
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594 fun co_dissect_eqn sequential fun_names (corec_specs : corec_spec list) eqn' of_spec matchedsss = |
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595 let |
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596 val eqn = drop_All eqn' |
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597 handle TERM _ => primrec_error_eqn "malformed function equation" eqn'; |
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598 val (imp_prems, imp_rhs) = Logic.strip_horn eqn |
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599 |> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop; |
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600 |
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601 val head = imp_rhs |
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602 |> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq)) |
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603 |> head_of; |
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604 |
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605 val maybe_rhs = imp_rhs |> perhaps (try (HOLogic.dest_not)) |> try (snd o HOLogic.dest_eq); |
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606 |
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607 val discs = maps #ctr_specs corec_specs |> map #disc; |
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608 val sels = maps #ctr_specs corec_specs |> maps #sels; |
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609 val ctrs = maps #ctr_specs corec_specs |> map #ctr; |
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610 in |
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611 if member (op =) discs head orelse |
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612 is_some maybe_rhs andalso |
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613 member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then |
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614 co_dissect_eqn_disc sequential fun_names corec_specs imp_prems imp_rhs matchedsss |
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615 |>> single |
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616 else if member (op =) sels head then |
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617 ([co_dissect_eqn_sel fun_names corec_specs eqn' of_spec imp_rhs], matchedsss) |
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618 else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) then |
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619 co_dissect_eqn_ctr sequential fun_names corec_specs eqn' imp_prems imp_rhs matchedsss |
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620 else |
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621 primrec_error_eqn "malformed function equation" eqn |
|
622 end; |
|
623 |
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624 fun build_corec_arg_disc (ctr_specs : corec_ctr_spec list) |
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625 ({fun_args, ctr_no, prems, ...} : co_eqn_data_disc) = |
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626 if is_none (#pred (nth ctr_specs ctr_no)) then I else |
|
627 mk_conjs prems |
|
628 |> curry subst_bounds (List.rev fun_args) |
|
629 |> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args) |
|
630 |> K |> nth_map (the (#pred (nth ctr_specs ctr_no))); |
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631 |
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632 fun build_corec_arg_no_call (sel_eqns : co_eqn_data_sel list) sel = |
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633 find_first (equal sel o #sel) sel_eqns |
|
634 |> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term) |
|
635 |> the_default undef_const |
|
636 |> K; |
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637 |
|
638 fun build_corec_args_direct_call lthy has_call (sel_eqns : co_eqn_data_sel list) sel = |
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639 let |
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640 val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns; |
|
641 in |
|
642 if is_none maybe_sel_eqn then (I, I, I) else |
|
643 let |
|
644 val {fun_args, rhs_term, ... } = the maybe_sel_eqn; |
|
645 fun rewrite_q _ t = if has_call t then @{term False} else @{term True}; |
|
646 fun rewrite_g _ t = if has_call t then undef_const else t; |
|
647 fun rewrite_h bound_Ts t = |
|
648 if has_call t then mk_tuple1 bound_Ts (snd (strip_comb t)) else undef_const; |
|
649 fun massage f t = massage_direct_corec_call lthy has_call f [] rhs_term |> abs_tuple fun_args; |
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650 in |
|
651 (massage rewrite_q, |
|
652 massage rewrite_g, |
|
653 massage rewrite_h) |
|
654 end |
|
655 end; |
|
656 |
|
657 fun build_corec_arg_indirect_call lthy has_call (sel_eqns : co_eqn_data_sel list) sel = |
|
658 let |
|
659 val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns; |
|
660 in |
|
661 if is_none maybe_sel_eqn then I else |
|
662 let |
|
663 val {fun_args, rhs_term, ...} = the maybe_sel_eqn; |
|
664 fun rewrite bound_Ts U T (Abs (v, V, b)) = Abs (v, V, rewrite (V :: bound_Ts) U T b) |
|
665 | rewrite bound_Ts U T (t as _ $ _) = |
|
666 let val (u, vs) = strip_comb t in |
|
667 if is_Free u andalso has_call u then |
|
668 Inr_const U T $ mk_tuple1 bound_Ts vs |
|
669 else if try (fst o dest_Const) u = SOME @{const_name prod_case} then |
|
670 map (rewrite bound_Ts U T) vs |> chop 1 |>> HOLogic.mk_split o the_single |> list_comb |
|
671 else |
|
672 list_comb (rewrite bound_Ts U T u, map (rewrite bound_Ts U T) vs) |
|
673 end |
|
674 | rewrite _ U T t = |
|
675 if is_Free t andalso has_call t then Inr_const U T $ HOLogic.unit else t; |
|
676 fun massage t = |
|
677 massage_indirect_corec_call lthy has_call rewrite [] (range_type (fastype_of t)) rhs_term |
|
678 |> abs_tuple fun_args; |
|
679 in |
|
680 massage |
|
681 end |
|
682 end; |
|
683 |
|
684 fun build_corec_args_sel lthy has_call (all_sel_eqns : co_eqn_data_sel list) |
|
685 (ctr_spec : corec_ctr_spec) = |
|
686 let val sel_eqns = filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns in |
|
687 if null sel_eqns then I else |
|
688 let |
|
689 val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec; |
|
690 |
|
691 val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list; |
|
692 val direct_calls' = map_filter (try (apsnd (fn Direct_Corec n => n))) sel_call_list; |
|
693 val indirect_calls' = map_filter (try (apsnd (fn Indirect_Corec n => n))) sel_call_list; |
|
694 in |
|
695 I |
|
696 #> fold (fn (sel, n) => nth_map n (build_corec_arg_no_call sel_eqns sel)) no_calls' |
|
697 #> fold (fn (sel, (q, g, h)) => |
|
698 let val (fq, fg, fh) = build_corec_args_direct_call lthy has_call sel_eqns sel in |
|
699 nth_map q fq o nth_map g fg o nth_map h fh end) direct_calls' |
|
700 #> fold (fn (sel, n) => nth_map n |
|
701 (build_corec_arg_indirect_call lthy has_call sel_eqns sel)) indirect_calls' |
|
702 end |
|
703 end; |
|
704 |
|
705 fun co_build_defs lthy bs mxs has_call arg_Tss (corec_specs : corec_spec list) |
|
706 (disc_eqnss : co_eqn_data_disc list list) (sel_eqnss : co_eqn_data_sel list list) = |
|
707 let |
|
708 val corec_specs' = take (length bs) corec_specs; |
|
709 val corecs = map #corec corec_specs'; |
|
710 val ctr_specss = map #ctr_specs corec_specs'; |
|
711 val corec_args = hd corecs |
|
712 |> fst o split_last o binder_types o fastype_of |
|
713 |> map (Const o pair @{const_name undefined}) |
|
714 |> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss |
|
715 |> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss; |
|
716 fun currys [] t = t |
|
717 | currys Ts t = t $ mk_tuple1 (List.rev Ts) (map Bound (length Ts - 1 downto 0)) |
|
718 |> fold_rev (Term.abs o pair Name.uu) Ts; |
|
719 |
|
720 (* |
|
721 val _ = tracing ("corecursor arguments:\n \<cdot> " ^ |
|
722 space_implode "\n \<cdot> " (map (Syntax.string_of_term lthy) corec_args)); |
|
723 *) |
|
724 |
|
725 val exclss' = |
|
726 disc_eqnss |
|
727 |> map (map (fn x => (#fun_args x, #ctr_no x, #prems x, #auto_gen x)) |
|
728 #> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs []) |
|
729 #> maps (uncurry (map o pair) |
|
730 #> map (fn ((fun_args, c, x, a), (_, c', y, a')) => |
|
731 ((c, c', a orelse a'), (x, s_not (mk_conjs y))) |
|
732 ||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop |
|
733 ||> Logic.list_implies |
|
734 ||> curry Logic.list_all (map dest_Free fun_args)))) |
|
735 in |
|
736 map (list_comb o rpair corec_args) corecs |
|
737 |> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss |
|
738 |> map2 currys arg_Tss |
|
739 |> Syntax.check_terms lthy |
|
740 |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs |
|
741 |> rpair exclss' |
|
742 end; |
|
743 |
|
744 fun mk_real_disc_eqns fun_binding arg_Ts ({ctr_specs, ...} : corec_spec) |
|
745 (sel_eqns : co_eqn_data_sel list) (disc_eqns : co_eqn_data_disc list) = |
|
746 if length disc_eqns <> length ctr_specs - 1 then disc_eqns else |
|
747 let |
|
748 val n = 0 upto length ctr_specs |
|
749 |> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns)); |
|
750 val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns) |
|
751 |> the_default (map (curry Free Name.uu) arg_Ts) o merge_options; |
|
752 val extra_disc_eqn = { |
|
753 fun_name = Binding.name_of fun_binding, |
|
754 fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))), |
|
755 fun_args = fun_args, |
|
756 ctr = #ctr (nth ctr_specs n), |
|
757 ctr_no = n, |
|
758 disc = #disc (nth ctr_specs n), |
|
759 prems = maps (negate_conj o #prems) disc_eqns, |
|
760 auto_gen = true, |
|
761 user_eqn = undef_const}; |
|
762 in |
|
763 chop n disc_eqns ||> cons extra_disc_eqn |> (op @) |
|
764 end; |
|
765 |
|
766 fun add_primcorec simple sequential fixes specs of_specs lthy = |
|
767 let |
|
768 val (bs, mxs) = map_split (apfst fst) fixes; |
|
769 val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list; |
|
770 |
|
771 val callssss = []; (* FIXME *) |
|
772 |
|
773 val ((n2m, corec_specs', _, coinduct_thm, strong_coinduct_thm, coinduct_thms, |
|
774 strong_coinduct_thms), lthy') = |
|
775 corec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy; |
|
776 |
|
777 val actual_nn = length bs; |
|
778 val fun_names = map Binding.name_of bs; |
|
779 val corec_specs = take actual_nn corec_specs'; (*###*) |
|
780 |
|
781 val eqns_data = |
|
782 fold_map2 (co_dissect_eqn sequential fun_names corec_specs) (map snd specs) of_specs [] |
|
783 |> flat o fst; |
|
784 |
|
785 val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data |
|
786 |> partition_eq ((op =) o pairself #fun_name) |
|
787 |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names |
|
788 |> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd); |
|
789 val _ = disc_eqnss' |> map (fn x => |
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790 let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse |
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791 primrec_error_eqns "excess discriminator equations in definition" |
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792 (maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end); |
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793 |
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794 val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data |
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795 |> partition_eq ((op =) o pairself #fun_name) |
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796 |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names |
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797 |> map (flat o snd); |
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798 |
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799 val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =)); |
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800 val arg_Tss = map (binder_types o snd o fst) fixes; |
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801 val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss'; |
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802 val (defs, exclss') = |
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803 co_build_defs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss; |
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804 |
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805 fun excl_tac (c, c', a) = |
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806 if a orelse c = c' orelse sequential then |
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807 SOME (K (HEADGOAL (mk_primcorec_assumption_tac lthy []))) |
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808 else if simple then |
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809 SOME (K (auto_tac lthy)) |
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810 else |
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811 NONE; |
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812 |
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813 (* |
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814 val _ = tracing ("exclusiveness properties:\n \<cdot> " ^ |
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815 space_implode "\n \<cdot> " (maps (map (Syntax.string_of_term lthy o snd)) exclss')); |
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816 *) |
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817 |
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818 val exclss'' = exclss' |> map (map (fn (idx, t) => |
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819 (idx, (Option.map (Goal.prove lthy [] [] t) (excl_tac idx), t)))); |
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820 val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss''; |
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821 val (obligation_idxss, obligationss) = exclss'' |
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822 |> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd)) |
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823 |> split_list o map split_list; |
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824 |
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825 fun prove thmss' def_thms' lthy = |
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826 let |
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827 val def_thms = map (snd o snd) def_thms'; |
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828 |
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829 val exclss' = map (op ~~) (obligation_idxss ~~ thmss'); |
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830 fun mk_exclsss excls n = |
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831 (excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1)) |
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832 |-> fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm]))); |
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833 val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs) |
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834 |-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs)); |
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835 |
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836 fun prove_disc ({ctr_specs, ...} : corec_spec) exclsss |
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837 ({fun_name, fun_T, fun_args, ctr_no, prems, ...} : co_eqn_data_disc) = |
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838 if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then [] else |
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839 let |
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840 val {disc_corec, ...} = nth ctr_specs ctr_no; |
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841 val k = 1 + ctr_no; |
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842 val m = length prems; |
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843 val t = |
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844 list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0)) |
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845 |> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*) |
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846 |> HOLogic.mk_Trueprop |
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847 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems) |
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848 |> curry Logic.list_all (map dest_Free fun_args); |
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849 in |
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850 mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss |
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851 |> K |> Goal.prove lthy [] [] t |
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852 |> pair (#disc (nth ctr_specs ctr_no)) |
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853 |> single |
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854 end; |
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855 |
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856 fun prove_sel ({nested_maps, nested_map_idents, nested_map_comps, ctr_specs, ...} |
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857 : corec_spec) (disc_eqns : co_eqn_data_disc list) exclsss |
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858 ({fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} : co_eqn_data_sel) = |
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859 let |
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860 val SOME ctr_spec = find_first (equal ctr o #ctr) ctr_specs; |
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861 val ctr_no = find_index (equal ctr o #ctr) ctr_specs; |
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862 val prems = the_default (maps (negate_conj o #prems) disc_eqns) |
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863 (find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems); |
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864 val sel_corec = find_index (equal sel) (#sels ctr_spec) |
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865 |> nth (#sel_corecs ctr_spec); |
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866 val k = 1 + ctr_no; |
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867 val m = length prems; |
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868 val t = |
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869 list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0)) |
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870 |> curry betapply sel |
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871 |> rpair (abstract (List.rev fun_args) rhs_term) |
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872 |> HOLogic.mk_Trueprop o HOLogic.mk_eq |
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873 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems) |
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874 |> curry Logic.list_all (map dest_Free fun_args); |
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875 val (distincts, _, sel_splits, sel_split_asms) = case_thms_of_term lthy [] rhs_term; |
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876 in |
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877 mk_primcorec_sel_tac lthy def_thms distincts sel_splits sel_split_asms nested_maps |
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878 nested_map_idents nested_map_comps sel_corec k m exclsss |
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879 |> K |> Goal.prove lthy [] [] t |
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880 |> pair sel |
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881 end; |
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882 |
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883 fun prove_ctr disc_alist sel_alist (disc_eqns : co_eqn_data_disc list) |
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884 (sel_eqns : co_eqn_data_sel list) ({ctr, disc, sels, collapse, ...} : corec_ctr_spec) = |
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885 if not (exists (equal ctr o #ctr) disc_eqns) |
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886 andalso not (exists (equal ctr o #ctr) sel_eqns) |
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887 orelse (* don't try to prove theorems when some sel_eqns are missing *) |
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888 filter (equal ctr o #ctr) sel_eqns |
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889 |> fst o finds ((op =) o apsnd #sel) sels |
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890 |> exists (null o snd) |
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891 then [] else |
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892 let |
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893 val (fun_name, fun_T, fun_args, prems) = |
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894 (find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns) |
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895 |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x)) |
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896 ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, [])) |
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897 |> the o merge_options; |
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898 val m = length prems; |
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899 val t = filter (equal ctr o #ctr) sel_eqns |
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900 |> fst o finds ((op =) o apsnd #sel) sels |
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901 |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract) |
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902 |> curry list_comb ctr |
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903 |> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T), |
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904 map Bound (length fun_args - 1 downto 0))) |
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905 |> HOLogic.mk_Trueprop |
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906 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems) |
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907 |> curry Logic.list_all (map dest_Free fun_args); |
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908 val maybe_disc_thm = AList.lookup (op =) disc_alist disc; |
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909 val sel_thms = map snd (filter (member (op =) sels o fst) sel_alist); |
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910 in |
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911 mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms |
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912 |> K |> Goal.prove lthy [] [] t |
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913 |> single |
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914 end; |
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915 |
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916 val disc_alists = map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss; |
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917 val sel_alists = map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss; |
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918 |
|
919 val disc_thmss = map (map snd) disc_alists; |
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920 val sel_thmss = map (map snd) sel_alists; |
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921 val ctr_thmss = map5 (maps oooo prove_ctr) disc_alists sel_alists disc_eqnss sel_eqnss |
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922 (map #ctr_specs corec_specs); |
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923 |
|
924 val simp_thmss = map2 append disc_thmss sel_thmss |
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925 |
|
926 val common_name = mk_common_name fun_names; |
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927 |
|
928 val notes = |
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929 [(coinductN, map (if n2m then single else K []) coinduct_thms, []), |
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930 (codeN, ctr_thmss(*FIXME*), code_nitpick_attrs), |
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931 (ctrN, ctr_thmss, []), |
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932 (discN, disc_thmss, simp_attrs), |
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933 (selN, sel_thmss, simp_attrs), |
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934 (simpsN, simp_thmss, []), |
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935 (strong_coinductN, map (if n2m then single else K []) strong_coinduct_thms, [])] |
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936 |> maps (fn (thmN, thmss, attrs) => |
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937 map2 (fn fun_name => fn thms => |
|
938 ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])])) |
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939 fun_names (take actual_nn thmss)) |
|
940 |> filter_out (null o fst o hd o snd); |
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941 |
|
942 val common_notes = |
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943 [(coinductN, if n2m then [coinduct_thm] else [], []), |
|
944 (strong_coinductN, if n2m then [strong_coinduct_thm] else [], [])] |
|
945 |> filter_out (null o #2) |
|
946 |> map (fn (thmN, thms, attrs) => |
|
947 ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])])); |
|
948 in |
|
949 lthy |> Local_Theory.notes (notes @ common_notes) |> snd |
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950 end; |
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951 |
|
952 fun after_qed thmss' = fold_map Local_Theory.define defs #-> prove thmss'; |
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953 |
|
954 val _ = if not simple orelse forall null obligationss then () else |
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955 primrec_error "need exclusiveness proofs - use primcorecursive instead of primcorec"; |
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956 in |
|
957 if simple then |
|
958 lthy' |
|
959 |> after_qed (map (fn [] => []) obligationss) |
|
960 |> pair NONE o SOME |
|
961 else |
|
962 lthy' |
|
963 |> Proof.theorem NONE after_qed obligationss |
|
964 |> Proof.refine (Method.primitive_text I) |
|
965 |> Seq.hd |
|
966 |> rpair NONE o SOME |
|
967 end; |
|
968 |
|
969 fun add_primcorec_ursive_cmd simple seq (raw_fixes, raw_specs') lthy = |
|
970 let |
|
971 val (raw_specs, of_specs) = split_list raw_specs' ||> map (Option.map (Syntax.read_term lthy)); |
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972 val ((fixes, specs), _) = Specification.read_spec raw_fixes raw_specs lthy; |
|
973 in |
|
974 add_primcorec simple seq fixes specs of_specs lthy |
|
975 handle ERROR str => primrec_error str |
|
976 end |
|
977 handle Primrec_Error (str, eqns) => |
|
978 if null eqns |
|
979 then error ("primcorec error:\n " ^ str) |
|
980 else error ("primcorec error:\n " ^ str ^ "\nin\n " ^ |
|
981 space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns)); |
|
982 |
|
983 val add_primcorecursive_cmd = (the o fst) ooo add_primcorec_ursive_cmd false; |
|
984 val add_primcorec_cmd = (the o snd) ooo add_primcorec_ursive_cmd true; |
|
985 |
|
986 end; |
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