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_N2M_Sugar |
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35 open BNF_FP_Rec_Sugar_Util |
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36 open BNF_FP_Rec_Sugar_Tactics |
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37 |
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38 val codeN = "code"; |
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39 val ctrN = "ctr"; |
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40 val discN = "disc"; |
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41 val selN = "sel"; |
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42 |
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43 val nitpicksimp_attrs = @{attributes [nitpick_simp]}; |
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44 val simp_attrs = @{attributes [simp]}; |
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45 val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs; |
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46 val code_nitpicksimp_simp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs @ simp_attrs; |
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47 |
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48 exception Primrec_Error of string * term list; |
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49 |
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50 fun primrec_error str = raise Primrec_Error (str, []); |
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51 fun primrec_error_eqn str eqn = raise Primrec_Error (str, [eqn]); |
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52 fun primrec_error_eqns str eqns = raise Primrec_Error (str, eqns); |
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53 |
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54 fun finds eq = fold_map (fn x => List.partition (curry eq x) #>> pair x); |
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55 |
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56 val free_name = try (fn Free (v, _) => v); |
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57 val const_name = try (fn Const (v, _) => v); |
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58 val undef_const = Const (@{const_name undefined}, dummyT); |
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59 |
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60 fun permute_args n t = list_comb (t, map Bound (0 :: (n downto 1))) |
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61 |> fold (K (Term.abs (Name.uu, dummyT))) (0 upto n); |
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62 val abs_tuple = HOLogic.tupled_lambda o HOLogic.mk_tuple; |
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63 fun drop_All t = subst_bounds (strip_qnt_vars @{const_name all} t |> map Free |> rev, |
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64 strip_qnt_body @{const_name all} t) |
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65 fun abstract vs = |
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66 let fun a n (t $ u) = a n t $ a n u |
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67 | a n (Abs (v, T, b)) = Abs (v, T, a (n + 1) b) |
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68 | a n t = let val idx = find_index (equal t) vs in |
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69 if idx < 0 then t else Bound (n + idx) end |
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70 in a 0 end; |
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71 fun mk_prod1 Ts (t, u) = HOLogic.pair_const (fastype_of1 (Ts, t)) (fastype_of1 (Ts, u)) $ t $ u; |
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72 fun mk_tuple1 Ts = the_default HOLogic.unit o try (foldr1 (mk_prod1 Ts)); |
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73 |
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74 fun get_indices fixes t = map (fst #>> Binding.name_of #> Free) fixes |
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75 |> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE) |
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76 |> map_filter I; |
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77 |
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78 |
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79 (* Primrec *) |
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80 |
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81 type eqn_data = { |
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82 fun_name: string, |
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83 rec_type: typ, |
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84 ctr: term, |
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85 ctr_args: term list, |
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86 left_args: term list, |
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87 right_args: term list, |
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88 res_type: typ, |
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89 rhs_term: term, |
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90 user_eqn: term |
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91 }; |
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92 |
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93 fun dissect_eqn lthy fun_names eqn' = |
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94 let |
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95 val eqn = drop_All eqn' |> HOLogic.dest_Trueprop |
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96 handle TERM _ => |
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97 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn'; |
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98 val (lhs, rhs) = HOLogic.dest_eq eqn |
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99 handle TERM _ => |
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100 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn'; |
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101 val (fun_name, args) = strip_comb lhs |
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102 |>> (fn x => if is_Free x then fst (dest_Free x) |
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103 else primrec_error_eqn "malformed function equation (does not start with free)" eqn); |
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104 val (left_args, rest) = take_prefix is_Free args; |
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105 val (nonfrees, right_args) = take_suffix is_Free rest; |
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106 val num_nonfrees = length nonfrees; |
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107 val _ = num_nonfrees = 1 orelse if num_nonfrees = 0 then |
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108 primrec_error_eqn "constructor pattern missing in left-hand side" eqn else |
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109 primrec_error_eqn "more than one non-variable argument in left-hand side" eqn; |
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110 val _ = member (op =) fun_names fun_name orelse |
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111 primrec_error_eqn "malformed function equation (does not start with function name)" eqn |
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112 |
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113 val (ctr, ctr_args) = strip_comb (the_single nonfrees); |
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114 val _ = try (num_binder_types o fastype_of) ctr = SOME (length ctr_args) orelse |
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115 primrec_error_eqn "partially applied constructor in pattern" eqn; |
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116 val _ = let val d = duplicates (op =) (left_args @ ctr_args @ right_args) in null d orelse |
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117 primrec_error_eqn ("duplicate variable \"" ^ Syntax.string_of_term lthy (hd d) ^ |
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118 "\" in left-hand side") eqn end; |
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119 val _ = forall is_Free ctr_args orelse |
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120 primrec_error_eqn "non-primitive pattern in left-hand side" eqn; |
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121 val _ = |
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122 let val b = fold_aterms (fn x as Free (v, _) => |
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123 if (not (member (op =) (left_args @ ctr_args @ right_args) x) andalso |
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124 not (member (op =) fun_names v) andalso |
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125 not (Variable.is_fixed lthy v)) then cons x else I | _ => I) rhs [] |
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126 in |
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127 null b orelse |
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128 primrec_error_eqn ("extra variable(s) in right-hand side: " ^ |
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129 commas (map (Syntax.string_of_term lthy) b)) eqn |
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130 end; |
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131 in |
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132 {fun_name = fun_name, |
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133 rec_type = body_type (type_of ctr), |
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134 ctr = ctr, |
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135 ctr_args = ctr_args, |
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136 left_args = left_args, |
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137 right_args = right_args, |
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138 res_type = map fastype_of (left_args @ right_args) ---> fastype_of rhs, |
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139 rhs_term = rhs, |
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140 user_eqn = eqn'} |
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141 end; |
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142 |
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143 fun rewrite_map_arg get_ctr_pos rec_type res_type = |
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144 let |
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145 val pT = HOLogic.mk_prodT (rec_type, res_type); |
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146 |
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147 val maybe_suc = Option.map (fn x => x + 1); |
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148 fun subst d (t as Bound d') = t |> d = SOME d' ? curry (op $) (fst_const pT) |
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149 | 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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150 | subst d t = |
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151 let |
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152 val (u, vs) = strip_comb t; |
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153 val ctr_pos = try (get_ctr_pos o the) (free_name u) |> the_default ~1; |
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154 in |
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155 if ctr_pos >= 0 then |
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156 if d = SOME ~1 andalso length vs = ctr_pos then |
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157 list_comb (permute_args ctr_pos (snd_const pT), vs) |
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158 else if length vs > ctr_pos andalso is_some d |
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159 andalso d = try (fn Bound n => n) (nth vs ctr_pos) then |
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160 list_comb (snd_const pT $ nth vs ctr_pos, map (subst d) (nth_drop ctr_pos vs)) |
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161 else |
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162 primrec_error_eqn ("recursive call not directly applied to constructor argument") t |
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163 else |
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164 list_comb (u, map (subst (d |> d = SOME ~1 ? K NONE)) vs) |
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165 end |
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166 in |
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167 subst (SOME ~1) |
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168 end; |
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169 |
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170 fun subst_rec_calls lthy get_ctr_pos has_call ctr_args mutual_calls nested_calls = |
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171 let |
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172 fun try_nested_rec bound_Ts y t = |
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173 AList.lookup (op =) nested_calls y |
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174 |> Option.map (fn y' => |
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175 massage_nested_rec_call lthy has_call (rewrite_map_arg get_ctr_pos) bound_Ts y y' t); |
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176 |
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177 fun subst bound_Ts (t as g' $ y) = |
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178 let |
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179 fun subst_rec () = subst bound_Ts g' $ subst bound_Ts y; |
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180 val y_head = head_of y; |
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181 in |
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182 if not (member (op =) ctr_args y_head) then |
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183 subst_rec () |
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184 else |
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185 (case try_nested_rec bound_Ts y_head t of |
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186 SOME t' => t' |
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187 | NONE => |
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188 let val (g, g_args) = strip_comb g' in |
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189 (case try (get_ctr_pos o the) (free_name g) of |
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190 SOME ctr_pos => |
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191 (length g_args >= ctr_pos orelse |
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192 primrec_error_eqn "too few arguments in recursive call" t; |
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193 (case AList.lookup (op =) mutual_calls y of |
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194 SOME y' => list_comb (y', g_args) |
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195 | NONE => subst_rec ())) |
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196 | NONE => subst_rec ()) |
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197 end) |
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198 end |
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199 | subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b) |
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200 | subst _ t = t |
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201 |
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202 fun subst' t = |
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203 if has_call t then |
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204 (* FIXME detect this case earlier? *) |
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205 primrec_error_eqn "recursive call not directly applied to constructor argument" t |
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206 else |
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207 try_nested_rec [] (head_of t) t |> the_default t |
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208 in |
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209 subst' o subst [] |
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210 end; |
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211 |
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212 fun build_rec_arg lthy (funs_data : eqn_data list list) has_call (ctr_spec : rec_ctr_spec) |
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213 (maybe_eqn_data : eqn_data option) = |
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214 (case maybe_eqn_data of |
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215 NONE => undef_const |
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216 | SOME {ctr_args, left_args, right_args, rhs_term = t, ...} => |
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217 let |
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218 val calls = #calls ctr_spec; |
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219 val n_args = fold (Integer.add o (fn Mutual_Rec _ => 2 | _ => 1)) calls 0; |
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220 |
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221 val no_calls' = tag_list 0 calls |
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222 |> map_filter (try (apsnd (fn No_Rec p => p | Mutual_Rec (p, _) => p))); |
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223 val mutual_calls' = tag_list 0 calls |
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224 |> map_filter (try (apsnd (fn Mutual_Rec (_, p) => p))); |
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225 val nested_calls' = tag_list 0 calls |
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226 |> map_filter (try (apsnd (fn Nested_Rec p => p))); |
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227 |
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228 val args = replicate n_args ("", dummyT) |
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229 |> Term.rename_wrt_term t |
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230 |> map Free |
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231 |> fold (fn (ctr_arg_idx, (arg_idx, _)) => |
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232 nth_map arg_idx (K (nth ctr_args ctr_arg_idx))) |
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233 no_calls' |
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234 |> fold (fn (ctr_arg_idx, (arg_idx, T)) => |
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235 nth_map arg_idx (K (retype_free T (nth ctr_args ctr_arg_idx)))) |
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236 mutual_calls' |
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237 |> fold (fn (ctr_arg_idx, (arg_idx, T)) => |
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238 nth_map arg_idx (K (retype_free T (nth ctr_args ctr_arg_idx)))) |
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239 nested_calls'; |
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240 |
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241 val fun_name_ctr_pos_list = |
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242 map (fn (x :: _) => (#fun_name x, length (#left_args x))) funs_data; |
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243 val get_ctr_pos = try (the o AList.lookup (op =) fun_name_ctr_pos_list) #> the_default ~1; |
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244 val mutual_calls = map (apfst (nth ctr_args) o apsnd (nth args o fst)) mutual_calls'; |
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245 val nested_calls = map (apfst (nth ctr_args) o apsnd (nth args o fst)) nested_calls'; |
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246 in |
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247 t |
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248 |> subst_rec_calls lthy get_ctr_pos has_call ctr_args mutual_calls nested_calls |
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249 |> fold_rev lambda (args @ left_args @ right_args) |
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250 end); |
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251 |
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252 fun build_defs lthy bs mxs (funs_data : eqn_data list list) (rec_specs : rec_spec list) has_call = |
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253 let |
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254 val n_funs = length funs_data; |
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255 |
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256 val ctr_spec_eqn_data_list' = |
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257 (take n_funs rec_specs |> map #ctr_specs) ~~ funs_data |
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258 |> maps (uncurry (finds (fn (x, y) => #ctr x = #ctr y)) |
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259 ##> (fn x => null x orelse |
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260 primrec_error_eqns "excess equations in definition" (map #rhs_term x)) #> fst); |
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261 val _ = ctr_spec_eqn_data_list' |> map (fn (_, x) => length x <= 1 orelse |
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262 primrec_error_eqns ("multiple equations for constructor") (map #user_eqn x)); |
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263 |
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264 val ctr_spec_eqn_data_list = |
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265 ctr_spec_eqn_data_list' @ (drop n_funs rec_specs |> maps #ctr_specs |> map (rpair [])); |
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266 |
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267 val recs = take n_funs rec_specs |> map #recx; |
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268 val rec_args = ctr_spec_eqn_data_list |
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269 |> sort ((op <) o pairself (#offset o fst) |> make_ord) |
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270 |> map (uncurry (build_rec_arg lthy funs_data has_call) o apsnd (try the_single)); |
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271 val ctr_poss = map (fn x => |
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272 if length (distinct ((op =) o pairself (length o #left_args)) x) <> 1 then |
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273 primrec_error ("inconstant constructor pattern position for function " ^ |
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274 quote (#fun_name (hd x))) |
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275 else |
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276 hd x |> #left_args |> length) funs_data; |
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277 in |
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278 (recs, ctr_poss) |
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279 |-> map2 (fn recx => fn ctr_pos => list_comb (recx, rec_args) |> permute_args ctr_pos) |
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280 |> Syntax.check_terms lthy |
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281 |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t))) |
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282 bs mxs |
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283 end; |
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284 |
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285 fun find_rec_calls ctxt has_call ({ctr, ctr_args, rhs_term, ...} : eqn_data) = |
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286 let |
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287 fun find bound_Ts (Abs (_, T, b)) ctr_arg = find (T :: bound_Ts) b ctr_arg |
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288 | find bound_Ts (t as _ $ _) ctr_arg = |
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289 let |
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290 val typof = curry fastype_of1 bound_Ts; |
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291 val (f', args') = strip_comb t; |
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292 val n = find_index (equal ctr_arg o head_of) args'; |
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293 in |
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294 if n < 0 then |
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295 find bound_Ts f' ctr_arg @ maps (fn x => find bound_Ts x ctr_arg) args' |
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296 else |
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297 let |
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298 val (f, args as arg :: _) = chop n args' |>> curry list_comb f' |
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299 val (arg_head, arg_args) = Term.strip_comb arg; |
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300 in |
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301 if has_call f then |
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302 mk_partial_compN (length arg_args) (typof f) (typof arg_head) f :: |
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303 maps (fn x => find bound_Ts x ctr_arg) args |
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304 else |
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305 find bound_Ts f ctr_arg @ maps (fn x => find bound_Ts x ctr_arg) args |
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306 end |
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307 end |
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308 | find _ _ _ = []; |
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309 in |
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310 map (find [] rhs_term) ctr_args |
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311 |> (fn [] => NONE | callss => SOME (ctr, callss)) |
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312 end; |
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313 |
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314 fun prepare_primrec fixes specs lthy = |
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315 let |
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316 val (bs, mxs) = map_split (apfst fst) fixes; |
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317 val fun_names = map Binding.name_of bs; |
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318 val eqns_data = map (dissect_eqn lthy fun_names) specs; |
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319 val funs_data = eqns_data |
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320 |> partition_eq ((op =) o pairself #fun_name) |
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321 |> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst |
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322 |> map (fn (x, y) => the_single y handle List.Empty => |
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323 primrec_error ("missing equations for function " ^ quote x)); |
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324 |
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325 val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =)); |
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326 val arg_Ts = map (#rec_type o hd) funs_data; |
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327 val res_Ts = map (#res_type o hd) funs_data; |
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328 val callssss = funs_data |
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329 |> map (partition_eq ((op =) o pairself #ctr)) |
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330 |> map (maps (map_filter (find_rec_calls lthy has_call))); |
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331 |
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332 val ((n2m, rec_specs, _, induct_thm, induct_thms), lthy') = |
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333 rec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy; |
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334 |
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335 val actual_nn = length funs_data; |
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336 |
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337 val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in |
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338 map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse |
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339 primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^ |
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340 " is not a constructor in left-hand side") user_eqn) eqns_data end; |
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341 |
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342 val defs = build_defs lthy' bs mxs funs_data rec_specs has_call; |
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343 |
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344 fun prove lthy def_thms' ({ctr_specs, nested_map_idents, nested_map_comps, ...} : rec_spec) |
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345 (fun_data : eqn_data list) = |
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346 let |
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347 val def_thms = map (snd o snd) def_thms'; |
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348 val simp_thmss = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs |
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349 |> fst |
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350 |> map_filter (try (fn (x, [y]) => |
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351 (#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y))) |
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352 |> map (fn (user_eqn, num_extra_args, rec_thm) => |
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353 mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm |
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354 |> K |> Goal.prove lthy [] [] user_eqn |
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355 |> Thm.close_derivation); |
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356 val poss = find_indices (fn (x, y) => #ctr x = #ctr y) fun_data eqns_data; |
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357 in |
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358 (poss, simp_thmss) |
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359 end; |
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360 |
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361 val notes = |
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362 (if n2m then map2 (fn name => fn thm => |
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363 (name, inductN, [thm], [])) fun_names (take actual_nn induct_thms) else []) |
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364 |> map (fn (prefix, thmN, thms, attrs) => |
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365 ((Binding.qualify true prefix (Binding.name thmN), attrs), [(thms, [])])); |
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366 |
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367 val common_name = mk_common_name fun_names; |
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368 |
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369 val common_notes = |
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370 (if n2m then [(inductN, [induct_thm], [])] else []) |
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371 |> map (fn (thmN, thms, attrs) => |
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372 ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])])); |
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373 in |
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374 (((fun_names, defs), |
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375 fn lthy => fn defs => |
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376 split_list (map2 (prove lthy defs) (take actual_nn rec_specs) funs_data)), |
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377 lthy' |> Local_Theory.notes (notes @ common_notes) |> snd) |
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378 end; |
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379 |
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380 (* primrec definition *) |
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381 |
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382 fun add_primrec_simple fixes ts lthy = |
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383 let |
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384 val (((names, defs), prove), lthy) = prepare_primrec fixes ts lthy |
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385 handle ERROR str => primrec_error str; |
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386 in |
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387 lthy |
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388 |> fold_map Local_Theory.define defs |
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389 |-> (fn defs => `(fn lthy => (names, (map fst defs, prove lthy defs)))) |
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390 end |
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391 handle Primrec_Error (str, eqns) => |
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392 if null eqns |
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393 then error ("primrec_new error:\n " ^ str) |
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394 else error ("primrec_new error:\n " ^ str ^ "\nin\n " ^ |
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395 space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns)); |
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396 |
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397 local |
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398 |
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399 fun gen_primrec prep_spec (raw_fixes : (binding * 'a option * mixfix) list) raw_spec lthy = |
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400 let |
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401 val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes) |
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402 val _ = null d orelse primrec_error ("duplicate function name(s): " ^ commas d); |
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403 |
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404 val (fixes, specs) = fst (prep_spec raw_fixes raw_spec lthy); |
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405 |
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406 val mk_notes = |
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407 flat ooo map3 (fn poss => fn prefix => fn thms => |
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408 let |
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409 val (bs, attrss) = map_split (fst o nth specs) poss; |
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410 val notes = |
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411 map3 (fn b => fn attrs => fn thm => |
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412 ((Binding.qualify false prefix b, code_nitpicksimp_simp_attrs @ attrs), [([thm], [])])) |
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413 bs attrss thms; |
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414 in |
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415 ((Binding.qualify true prefix (Binding.name simpsN), []), [(thms, [])]) :: notes |
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416 end); |
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417 in |
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418 lthy |
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419 |> add_primrec_simple fixes (map snd specs) |
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420 |-> (fn (names, (ts, (posss, simpss))) => |
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421 Spec_Rules.add Spec_Rules.Equational (ts, flat simpss) |
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422 #> Local_Theory.notes (mk_notes posss names simpss) |
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423 #>> pair ts o map snd) |
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424 end; |
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425 |
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426 in |
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427 |
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428 val add_primrec = gen_primrec Specification.check_spec; |
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429 val add_primrec_cmd = gen_primrec Specification.read_spec; |
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430 |
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431 end; |
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432 |
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433 fun add_primrec_global fixes specs thy = |
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434 let |
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435 val lthy = Named_Target.theory_init thy; |
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436 val ((ts, simps), lthy') = add_primrec fixes specs lthy; |
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437 val simps' = burrow (Proof_Context.export lthy' lthy) simps; |
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438 in ((ts, simps'), Local_Theory.exit_global lthy') end; |
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439 |
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440 fun add_primrec_overloaded ops fixes specs thy = |
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441 let |
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442 val lthy = Overloading.overloading ops thy; |
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443 val ((ts, simps), lthy') = add_primrec fixes specs lthy; |
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444 val simps' = burrow (Proof_Context.export lthy' lthy) simps; |
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445 in ((ts, simps'), Local_Theory.exit_global lthy') end; |
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446 |
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447 |
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448 |
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449 (* Primcorec *) |
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450 |
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451 type coeqn_data_disc = { |
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452 fun_name: string, |
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453 fun_T: typ, |
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454 fun_args: term list, |
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455 ctr: term, |
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456 ctr_no: int, (*###*) |
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457 disc: term, |
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458 prems: term list, |
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459 auto_gen: bool, |
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460 maybe_ctr_rhs: term option, |
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461 maybe_code_rhs: term option, |
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462 user_eqn: term |
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463 }; |
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464 |
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465 type coeqn_data_sel = { |
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466 fun_name: string, |
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467 fun_T: typ, |
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468 fun_args: term list, |
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469 ctr: term, |
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470 sel: term, |
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471 rhs_term: term, |
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472 user_eqn: term |
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473 }; |
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474 |
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475 datatype coeqn_data = |
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476 Disc of coeqn_data_disc | |
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477 Sel of coeqn_data_sel; |
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478 |
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479 fun dissect_coeqn_disc seq fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) |
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480 maybe_ctr_rhs maybe_code_rhs prems' concl matchedsss = |
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481 let |
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482 fun find_subterm p = let (* FIXME \<exists>? *) |
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483 fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v) |
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484 | f t = if p t then SOME t else NONE |
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485 in f end; |
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486 |
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487 val applied_fun = concl |
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488 |> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of)) |
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489 |> the |
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490 handle Option.Option => primrec_error_eqn "malformed discriminator formula" concl; |
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491 val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free; |
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492 val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name; |
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493 |
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494 val discs = map #disc basic_ctr_specs; |
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495 val ctrs = map #ctr basic_ctr_specs; |
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496 val not_disc = head_of concl = @{term Not}; |
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497 val _ = not_disc andalso length ctrs <> 2 andalso |
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498 primrec_error_eqn "negated discriminator for a type with \<noteq> 2 constructors" concl; |
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499 val disc' = find_subterm (member (op =) discs o head_of) concl; |
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500 val eq_ctr0 = concl |> perhaps (try HOLogic.dest_not) |> try (HOLogic.dest_eq #> snd) |
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501 |> (fn SOME t => let val n = find_index (equal t) ctrs in |
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502 if n >= 0 then SOME n else NONE end | _ => NONE); |
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503 val _ = is_some disc' orelse is_some eq_ctr0 orelse |
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504 primrec_error_eqn "no discriminator in equation" concl; |
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505 val ctr_no' = |
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506 if is_none disc' then the eq_ctr0 else find_index (equal (head_of (the disc'))) discs; |
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507 val ctr_no = if not_disc then 1 - ctr_no' else ctr_no'; |
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508 val {ctr, disc, ...} = nth basic_ctr_specs ctr_no; |
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509 |
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510 val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_; |
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511 val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default []; |
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512 val prems = map (abstract (List.rev fun_args)) prems'; |
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513 val real_prems = |
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514 (if catch_all orelse seq then maps s_not_conj matchedss else []) @ |
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515 (if catch_all then [] else prems); |
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516 |
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517 val matchedsss' = AList.delete (op =) fun_name matchedsss |
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518 |> cons (fun_name, if seq then matchedss @ [prems] else matchedss @ [real_prems]); |
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519 |
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520 val user_eqn = |
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521 (real_prems, concl) |
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522 |>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop o abstract (List.rev fun_args) |
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523 |> curry Logic.list_all (map dest_Free fun_args) o Logic.list_implies; |
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524 in |
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525 (Disc { |
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526 fun_name = fun_name, |
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527 fun_T = fun_T, |
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528 fun_args = fun_args, |
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529 ctr = ctr, |
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530 ctr_no = ctr_no, |
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531 disc = disc, |
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532 prems = real_prems, |
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533 auto_gen = catch_all, |
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534 maybe_ctr_rhs = maybe_ctr_rhs, |
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535 maybe_code_rhs = maybe_code_rhs, |
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536 user_eqn = user_eqn |
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537 }, matchedsss') |
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538 end; |
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539 |
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540 fun dissect_coeqn_sel fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn' |
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541 maybe_of_spec eqn = |
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542 let |
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543 val (lhs, rhs) = HOLogic.dest_eq eqn |
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544 handle TERM _ => |
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545 primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn; |
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546 val sel = head_of lhs; |
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547 val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free |
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548 handle TERM _ => |
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549 primrec_error_eqn "malformed selector argument in left-hand side" eqn; |
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550 val basic_ctr_specs = the (AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name) |
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551 handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn; |
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552 val {ctr, ...} = |
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553 (case maybe_of_spec of |
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554 SOME of_spec => the (find_first (equal of_spec o #ctr) basic_ctr_specs) |
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555 | NONE => filter (exists (equal sel) o #sels) basic_ctr_specs |> the_single |
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556 handle List.Empty => primrec_error_eqn "ambiguous selector - use \"of\"" eqn); |
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557 val user_eqn = drop_All eqn'; |
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558 in |
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559 Sel { |
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560 fun_name = fun_name, |
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561 fun_T = fun_T, |
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562 fun_args = fun_args, |
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563 ctr = ctr, |
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564 sel = sel, |
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565 rhs_term = rhs, |
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566 user_eqn = user_eqn |
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567 } |
|
568 end; |
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569 |
|
570 fun dissect_coeqn_ctr seq fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn' |
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571 maybe_code_rhs prems concl matchedsss = |
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572 let |
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573 val (lhs, rhs) = HOLogic.dest_eq concl; |
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574 val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free; |
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575 val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name; |
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576 val (ctr, ctr_args) = strip_comb (unfold_let rhs); |
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577 val {disc, sels, ...} = the (find_first (equal ctr o #ctr) basic_ctr_specs) |
|
578 handle Option.Option => primrec_error_eqn "not a constructor" ctr; |
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579 |
|
580 val disc_concl = betapply (disc, lhs); |
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581 val (maybe_eqn_data_disc, matchedsss') = if length basic_ctr_specs = 1 |
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582 then (NONE, matchedsss) |
|
583 else apfst SOME (dissect_coeqn_disc seq fun_names basic_ctr_specss |
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584 (SOME (abstract (List.rev fun_args) rhs)) maybe_code_rhs prems disc_concl matchedsss); |
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585 |
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586 val sel_concls = sels ~~ ctr_args |
|
587 |> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg)); |
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588 |
|
589 (* |
|
590 val _ = tracing ("reduced\n " ^ Syntax.string_of_term @{context} concl ^ "\nto\n \<cdot> " ^ |
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591 (is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_concl ^ "\n \<cdot> ")) "" ^ |
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592 space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) sel_concls) ^ |
|
593 "\nfor premise(s)\n \<cdot> " ^ |
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594 space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) prems)); |
|
595 *) |
|
596 |
|
597 val eqns_data_sel = |
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598 map (dissect_coeqn_sel fun_names basic_ctr_specss eqn' (SOME ctr)) sel_concls; |
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599 in |
|
600 (the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss') |
|
601 end; |
|
602 |
|
603 fun dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn' concl matchedsss = |
|
604 let |
|
605 val (lhs, (rhs', rhs)) = HOLogic.dest_eq concl ||> `(expand_corec_code_rhs lthy has_call []); |
|
606 val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free; |
|
607 val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name; |
|
608 |
|
609 val cond_ctrs = fold_rev_corec_code_rhs lthy (fn cs => fn ctr => fn _ => |
|
610 if member ((op =) o apsnd #ctr) basic_ctr_specs ctr |
|
611 then cons (ctr, cs) |
|
612 else primrec_error_eqn "not a constructor" ctr) [] rhs' [] |
|
613 |> AList.group (op =); |
|
614 |
|
615 val ctr_premss = (case cond_ctrs of [_] => [[]] | _ => map (s_dnf o snd) cond_ctrs); |
|
616 val ctr_concls = cond_ctrs |> map (fn (ctr, _) => |
|
617 binder_types (fastype_of ctr) |
|
618 |> map_index (fn (n, T) => massage_corec_code_rhs lthy (fn _ => fn ctr' => fn args => |
|
619 if ctr' = ctr then nth args n else Const (@{const_name undefined}, T)) [] rhs') |
|
620 |> curry list_comb ctr |
|
621 |> curry HOLogic.mk_eq lhs); |
|
622 in |
|
623 fold_map2 (dissect_coeqn_ctr false fun_names basic_ctr_specss eqn' |
|
624 (SOME (abstract (List.rev fun_args) rhs))) |
|
625 ctr_premss ctr_concls matchedsss |
|
626 end; |
|
627 |
|
628 fun dissect_coeqn lthy seq has_call fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) |
|
629 eqn' maybe_of_spec matchedsss = |
|
630 let |
|
631 val eqn = drop_All eqn' |
|
632 handle TERM _ => primrec_error_eqn "malformed function equation" eqn'; |
|
633 val (prems, concl) = Logic.strip_horn eqn |
|
634 |> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop; |
|
635 |
|
636 val head = concl |
|
637 |> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq)) |
|
638 |> head_of; |
|
639 |
|
640 val maybe_rhs = concl |> perhaps (try HOLogic.dest_not) |> try (snd o HOLogic.dest_eq); |
|
641 |
|
642 val discs = maps (map #disc) basic_ctr_specss; |
|
643 val sels = maps (maps #sels) basic_ctr_specss; |
|
644 val ctrs = maps (map #ctr) basic_ctr_specss; |
|
645 in |
|
646 if member (op =) discs head orelse |
|
647 is_some maybe_rhs andalso |
|
648 member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then |
|
649 dissect_coeqn_disc seq fun_names basic_ctr_specss NONE NONE prems concl matchedsss |
|
650 |>> single |
|
651 else if member (op =) sels head then |
|
652 ([dissect_coeqn_sel fun_names basic_ctr_specss eqn' maybe_of_spec concl], matchedsss) |
|
653 else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso |
|
654 member (op =) ctrs (head_of (unfold_let (the maybe_rhs))) then |
|
655 dissect_coeqn_ctr seq fun_names basic_ctr_specss eqn' NONE prems concl matchedsss |
|
656 else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso |
|
657 null prems then |
|
658 dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn' concl matchedsss |
|
659 |>> flat |
|
660 else |
|
661 primrec_error_eqn "malformed function equation" eqn |
|
662 end; |
|
663 |
|
664 fun build_corec_arg_disc (ctr_specs : corec_ctr_spec list) |
|
665 ({fun_args, ctr_no, prems, ...} : coeqn_data_disc) = |
|
666 if is_none (#pred (nth ctr_specs ctr_no)) then I else |
|
667 s_conjs prems |
|
668 |> curry subst_bounds (List.rev fun_args) |
|
669 |> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args) |
|
670 |> K |> nth_map (the (#pred (nth ctr_specs ctr_no))); |
|
671 |
|
672 fun build_corec_arg_no_call (sel_eqns : coeqn_data_sel list) sel = |
|
673 find_first (equal sel o #sel) sel_eqns |
|
674 |> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term) |
|
675 |> the_default undef_const |
|
676 |> K; |
|
677 |
|
678 fun build_corec_args_mutual_call lthy has_call (sel_eqns : coeqn_data_sel list) sel = |
|
679 (case find_first (equal sel o #sel) sel_eqns of |
|
680 NONE => (I, I, I) |
|
681 | SOME {fun_args, rhs_term, ... } => |
|
682 let |
|
683 val bound_Ts = List.rev (map fastype_of fun_args); |
|
684 fun rewrite_stop _ t = if has_call t then @{term False} else @{term True}; |
|
685 fun rewrite_end _ t = if has_call t then undef_const else t; |
|
686 fun rewrite_cont bound_Ts t = |
|
687 if has_call t then mk_tuple1 bound_Ts (snd (strip_comb t)) else undef_const; |
|
688 fun massage f _ = massage_mutual_corec_call lthy has_call f bound_Ts rhs_term |
|
689 |> abs_tuple fun_args; |
|
690 in |
|
691 (massage rewrite_stop, massage rewrite_end, massage rewrite_cont) |
|
692 end); |
|
693 |
|
694 fun build_corec_arg_nested_call lthy has_call (sel_eqns : coeqn_data_sel list) sel = |
|
695 (case find_first (equal sel o #sel) sel_eqns of |
|
696 NONE => I |
|
697 | SOME {fun_args, rhs_term, ...} => |
|
698 let |
|
699 val bound_Ts = List.rev (map fastype_of fun_args); |
|
700 fun rewrite bound_Ts U T (Abs (v, V, b)) = Abs (v, V, rewrite (V :: bound_Ts) U T b) |
|
701 | rewrite bound_Ts U T (t as _ $ _) = |
|
702 let val (u, vs) = strip_comb t in |
|
703 if is_Free u andalso has_call u then |
|
704 Inr_const U T $ mk_tuple1 bound_Ts vs |
|
705 else if const_name u = SOME @{const_name prod_case} then |
|
706 map (rewrite bound_Ts U T) vs |> chop 1 |>> HOLogic.mk_split o the_single |> list_comb |
|
707 else |
|
708 list_comb (rewrite bound_Ts U T u, map (rewrite bound_Ts U T) vs) |
|
709 end |
|
710 | rewrite _ U T t = |
|
711 if is_Free t andalso has_call t then Inr_const U T $ HOLogic.unit else t; |
|
712 fun massage t = |
|
713 rhs_term |
|
714 |> massage_nested_corec_call lthy has_call rewrite bound_Ts (range_type (fastype_of t)) |
|
715 |> abs_tuple fun_args; |
|
716 in |
|
717 massage |
|
718 end); |
|
719 |
|
720 fun build_corec_args_sel lthy has_call (all_sel_eqns : coeqn_data_sel list) |
|
721 (ctr_spec : corec_ctr_spec) = |
|
722 (case filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns of |
|
723 [] => I |
|
724 | sel_eqns => |
|
725 let |
|
726 val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec; |
|
727 val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list; |
|
728 val mutual_calls' = map_filter (try (apsnd (fn Mutual_Corec n => n))) sel_call_list; |
|
729 val nested_calls' = map_filter (try (apsnd (fn Nested_Corec n => n))) sel_call_list; |
|
730 in |
|
731 I |
|
732 #> fold (fn (sel, n) => nth_map n (build_corec_arg_no_call sel_eqns sel)) no_calls' |
|
733 #> fold (fn (sel, (q, g, h)) => |
|
734 let val (fq, fg, fh) = build_corec_args_mutual_call lthy has_call sel_eqns sel in |
|
735 nth_map q fq o nth_map g fg o nth_map h fh end) mutual_calls' |
|
736 #> fold (fn (sel, n) => nth_map n |
|
737 (build_corec_arg_nested_call lthy has_call sel_eqns sel)) nested_calls' |
|
738 end); |
|
739 |
|
740 fun build_codefs lthy bs mxs has_call arg_Tss (corec_specs : corec_spec list) |
|
741 (disc_eqnss : coeqn_data_disc list list) (sel_eqnss : coeqn_data_sel list list) = |
|
742 let |
|
743 val corecs = map #corec corec_specs; |
|
744 val ctr_specss = map #ctr_specs corec_specs; |
|
745 val corec_args = hd corecs |
|
746 |> fst o split_last o binder_types o fastype_of |
|
747 |> map (Const o pair @{const_name undefined}) |
|
748 |> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss |
|
749 |> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss; |
|
750 fun currys [] t = t |
|
751 | currys Ts t = t $ mk_tuple1 (List.rev Ts) (map Bound (length Ts - 1 downto 0)) |
|
752 |> fold_rev (Term.abs o pair Name.uu) Ts; |
|
753 |
|
754 (* |
|
755 val _ = tracing ("corecursor arguments:\n \<cdot> " ^ |
|
756 space_implode "\n \<cdot> " (map (Syntax.string_of_term lthy) corec_args)); |
|
757 *) |
|
758 |
|
759 val exclss' = |
|
760 disc_eqnss |
|
761 |> map (map (fn x => (#fun_args x, #ctr_no x, #prems x, #auto_gen x)) |
|
762 #> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs []) |
|
763 #> maps (uncurry (map o pair) |
|
764 #> map (fn ((fun_args, c, x, a), (_, c', y, a')) => |
|
765 ((c, c', a orelse a'), (x, s_not (s_conjs y))) |
|
766 ||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop |
|
767 ||> Logic.list_implies |
|
768 ||> curry Logic.list_all (map dest_Free fun_args)))) |
|
769 in |
|
770 map (list_comb o rpair corec_args) corecs |
|
771 |> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss |
|
772 |> map2 currys arg_Tss |
|
773 |> Syntax.check_terms lthy |
|
774 |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t))) |
|
775 bs mxs |
|
776 |> rpair exclss' |
|
777 end; |
|
778 |
|
779 fun mk_real_disc_eqns fun_binding arg_Ts ({ctr_specs, ...} : corec_spec) |
|
780 (sel_eqns : coeqn_data_sel list) (disc_eqns : coeqn_data_disc list) = |
|
781 if length disc_eqns <> length ctr_specs - 1 then disc_eqns else |
|
782 let |
|
783 val n = 0 upto length ctr_specs |
|
784 |> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns)); |
|
785 val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns) |
|
786 |> the_default (map (curry Free Name.uu) arg_Ts) o merge_options; |
|
787 val extra_disc_eqn = { |
|
788 fun_name = Binding.name_of fun_binding, |
|
789 fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))), |
|
790 fun_args = fun_args, |
|
791 ctr = #ctr (nth ctr_specs n), |
|
792 ctr_no = n, |
|
793 disc = #disc (nth ctr_specs n), |
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794 prems = maps (s_not_conj o #prems) disc_eqns, |
|
795 auto_gen = true, |
|
796 maybe_ctr_rhs = NONE, |
|
797 maybe_code_rhs = NONE, |
|
798 user_eqn = undef_const}; |
|
799 in |
|
800 chop n disc_eqns ||> cons extra_disc_eqn |> (op @) |
|
801 end; |
|
802 |
|
803 fun find_corec_calls ctxt has_call basic_ctr_specs ({ctr, sel, rhs_term, ...} : coeqn_data_sel) = |
|
804 let |
|
805 val sel_no = find_first (equal ctr o #ctr) basic_ctr_specs |
|
806 |> find_index (equal sel) o #sels o the; |
|
807 fun find t = if has_call t then snd (fold_rev_corec_call ctxt (K cons) [] t []) else []; |
|
808 in |
|
809 find rhs_term |
|
810 |> K |> nth_map sel_no |> AList.map_entry (op =) ctr |
|
811 end; |
|
812 |
|
813 fun add_primcorec_ursive maybe_tac seq fixes specs maybe_of_specs lthy = |
|
814 let |
|
815 val (bs, mxs) = map_split (apfst fst) fixes; |
|
816 val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list; |
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817 |
|
818 val fun_names = map Binding.name_of bs; |
|
819 val basic_ctr_specss = map (basic_corec_specs_of lthy) res_Ts; |
|
820 val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =)); |
|
821 val eqns_data = |
|
822 fold_map2 (dissect_coeqn lthy seq has_call fun_names basic_ctr_specss) (map snd specs) |
|
823 maybe_of_specs [] |
|
824 |> flat o fst; |
|
825 |
|
826 val callssss = |
|
827 map_filter (try (fn Sel x => x)) eqns_data |
|
828 |> partition_eq ((op =) o pairself #fun_name) |
|
829 |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names |
|
830 |> map (flat o snd) |
|
831 |> map2 (fold o find_corec_calls lthy has_call) basic_ctr_specss |
|
832 |> map2 (curry (op |>)) (map (map (fn {ctr, sels, ...} => |
|
833 (ctr, map (K []) sels))) basic_ctr_specss); |
|
834 |
|
835 (* |
|
836 val _ = tracing ("callssss = " ^ @{make_string} callssss); |
|
837 *) |
|
838 |
|
839 val ((n2m, corec_specs', _, coinduct_thm, strong_coinduct_thm, coinduct_thms, |
|
840 strong_coinduct_thms), lthy') = |
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841 corec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy; |
|
842 val actual_nn = length bs; |
|
843 val corec_specs = take actual_nn corec_specs'; (*###*) |
|
844 val ctr_specss = map #ctr_specs corec_specs; |
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845 |
|
846 val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data |
|
847 |> partition_eq ((op =) o pairself #fun_name) |
|
848 |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names |
|
849 |> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd); |
|
850 val _ = disc_eqnss' |> map (fn x => |
|
851 let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse |
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852 primrec_error_eqns "excess discriminator formula in definition" |
|
853 (maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end); |
|
854 |
|
855 val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data |
|
856 |> partition_eq ((op =) o pairself #fun_name) |
|
857 |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names |
|
858 |> map (flat o snd); |
|
859 |
|
860 val arg_Tss = map (binder_types o snd o fst) fixes; |
|
861 val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss'; |
|
862 val (defs, exclss') = |
|
863 build_codefs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss; |
|
864 |
|
865 fun excl_tac (c, c', a) = |
|
866 if a orelse c = c' orelse seq then SOME (K (HEADGOAL (mk_primcorec_assumption_tac lthy []))) |
|
867 else maybe_tac; |
|
868 |
|
869 (* |
|
870 val _ = tracing ("exclusiveness properties:\n \<cdot> " ^ |
|
871 space_implode "\n \<cdot> " (maps (map (Syntax.string_of_term lthy o snd)) exclss')); |
|
872 *) |
|
873 |
|
874 val exclss'' = exclss' |> map (map (fn (idx, t) => |
|
875 (idx, (Option.map (Goal.prove lthy [] [] t #> Thm.close_derivation) (excl_tac idx), t)))); |
|
876 val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss''; |
|
877 val (goal_idxss, goalss) = exclss'' |
|
878 |> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd)) |
|
879 |> split_list o map split_list; |
|
880 |
|
881 fun prove thmss' def_thms' lthy = |
|
882 let |
|
883 val def_thms = map (snd o snd) def_thms'; |
|
884 |
|
885 val exclss' = map (op ~~) (goal_idxss ~~ thmss'); |
|
886 fun mk_exclsss excls n = |
|
887 (excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1)) |
|
888 |-> fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm]))); |
|
889 val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs) |
|
890 |-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs)); |
|
891 |
|
892 fun prove_disc ({ctr_specs, ...} : corec_spec) exclsss |
|
893 ({fun_name, fun_T, fun_args, ctr_no, prems, ...} : coeqn_data_disc) = |
|
894 if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then [] else |
|
895 let |
|
896 val {disc_corec, ...} = nth ctr_specs ctr_no; |
|
897 val k = 1 + ctr_no; |
|
898 val m = length prems; |
|
899 val t = |
|
900 list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0)) |
|
901 |> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*) |
|
902 |> HOLogic.mk_Trueprop |
|
903 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems) |
|
904 |> curry Logic.list_all (map dest_Free fun_args); |
|
905 in |
|
906 if prems = [@{term False}] then [] else |
|
907 mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss |
|
908 |> K |> Goal.prove lthy [] [] t |
|
909 |> Thm.close_derivation |
|
910 |> pair (#disc (nth ctr_specs ctr_no)) |
|
911 |> single |
|
912 end; |
|
913 |
|
914 fun prove_sel ({nested_maps, nested_map_idents, nested_map_comps, ctr_specs, ...} |
|
915 : corec_spec) (disc_eqns : coeqn_data_disc list) exclsss |
|
916 ({fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} : coeqn_data_sel) = |
|
917 let |
|
918 val SOME ctr_spec = find_first (equal ctr o #ctr) ctr_specs; |
|
919 val ctr_no = find_index (equal ctr o #ctr) ctr_specs; |
|
920 val prems = the_default (maps (s_not_conj o #prems) disc_eqns) |
|
921 (find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems); |
|
922 val sel_corec = find_index (equal sel) (#sels ctr_spec) |
|
923 |> nth (#sel_corecs ctr_spec); |
|
924 val k = 1 + ctr_no; |
|
925 val m = length prems; |
|
926 val t = |
|
927 list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0)) |
|
928 |> curry betapply sel |
|
929 |> rpair (abstract (List.rev fun_args) rhs_term) |
|
930 |> HOLogic.mk_Trueprop o HOLogic.mk_eq |
|
931 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems) |
|
932 |> curry Logic.list_all (map dest_Free fun_args); |
|
933 val (distincts, _, sel_splits, sel_split_asms) = case_thms_of_term lthy [] rhs_term; |
|
934 in |
|
935 mk_primcorec_sel_tac lthy def_thms distincts sel_splits sel_split_asms nested_maps |
|
936 nested_map_idents nested_map_comps sel_corec k m exclsss |
|
937 |> K |> Goal.prove lthy [] [] t |
|
938 |> Thm.close_derivation |
|
939 |> pair sel |
|
940 end; |
|
941 |
|
942 fun prove_ctr disc_alist sel_alist (disc_eqns : coeqn_data_disc list) |
|
943 (sel_eqns : coeqn_data_sel list) ({ctr, disc, sels, collapse, ...} : corec_ctr_spec) = |
|
944 (* don't try to prove theorems when some sel_eqns are missing *) |
|
945 if not (exists (equal ctr o #ctr) disc_eqns) |
|
946 andalso not (exists (equal ctr o #ctr) sel_eqns) |
|
947 orelse |
|
948 filter (equal ctr o #ctr) sel_eqns |
|
949 |> fst o finds ((op =) o apsnd #sel) sels |
|
950 |> exists (null o snd) |
|
951 then [] else |
|
952 let |
|
953 val (fun_name, fun_T, fun_args, prems, maybe_rhs) = |
|
954 (find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns) |
|
955 |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x, |
|
956 #maybe_ctr_rhs x)) |
|
957 ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, [], NONE)) |
|
958 |> the o merge_options; |
|
959 val m = length prems; |
|
960 val t = (if is_some maybe_rhs then the maybe_rhs else |
|
961 filter (equal ctr o #ctr) sel_eqns |
|
962 |> fst o finds ((op =) o apsnd #sel) sels |
|
963 |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract) |
|
964 |> curry list_comb ctr) |
|
965 |> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T), |
|
966 map Bound (length fun_args - 1 downto 0))) |
|
967 |> HOLogic.mk_Trueprop |
|
968 |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems) |
|
969 |> curry Logic.list_all (map dest_Free fun_args); |
|
970 val maybe_disc_thm = AList.lookup (op =) disc_alist disc; |
|
971 val sel_thms = map snd (filter (member (op =) sels o fst) sel_alist); |
|
972 in |
|
973 if prems = [@{term False}] then [] else |
|
974 mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms |
|
975 |> K |> Goal.prove lthy [] [] t |
|
976 |> Thm.close_derivation |
|
977 |> pair ctr |
|
978 |> single |
|
979 end; |
|
980 |
|
981 fun prove_code disc_eqns sel_eqns ctr_alist ctr_specs = |
|
982 let |
|
983 val (fun_name, fun_T, fun_args, maybe_rhs) = |
|
984 (find_first (member (op =) (map #ctr ctr_specs) o #ctr) disc_eqns, |
|
985 find_first (member (op =) (map #ctr ctr_specs) o #ctr) sel_eqns) |
|
986 |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #maybe_code_rhs x)) |
|
987 ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, NONE)) |
|
988 |> the o merge_options; |
|
989 |
|
990 val bound_Ts = List.rev (map fastype_of fun_args); |
|
991 |
|
992 val lhs = list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0)); |
|
993 val maybe_rhs_info = |
|
994 (case maybe_rhs of |
|
995 SOME rhs => |
|
996 let |
|
997 val raw_rhs = expand_corec_code_rhs lthy has_call bound_Ts rhs; |
|
998 val cond_ctrs = |
|
999 fold_rev_corec_code_rhs lthy (K oo (cons oo pair)) bound_Ts raw_rhs []; |
|
1000 val ctr_thms = map (the o AList.lookup (op =) ctr_alist o snd) cond_ctrs; |
|
1001 in SOME (rhs, raw_rhs, ctr_thms) end |
|
1002 | NONE => |
|
1003 let |
|
1004 fun prove_code_ctr {ctr, sels, ...} = |
|
1005 if not (exists (equal ctr o fst) ctr_alist) then NONE else |
|
1006 let |
|
1007 val prems = find_first (equal ctr o #ctr) disc_eqns |
|
1008 |> Option.map #prems |> the_default []; |
|
1009 val t = |
|
1010 filter (equal ctr o #ctr) sel_eqns |
|
1011 |> fst o finds ((op =) o apsnd #sel) sels |
|
1012 |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) |
|
1013 #-> abstract) |
|
1014 |> curry list_comb ctr; |
|
1015 in |
|
1016 SOME (prems, t) |
|
1017 end; |
|
1018 val maybe_ctr_conds_argss = map prove_code_ctr ctr_specs; |
|
1019 in |
|
1020 if exists is_none maybe_ctr_conds_argss then NONE else |
|
1021 let |
|
1022 val rhs = fold_rev (fn SOME (prems, u) => fn t => mk_If (s_conjs prems) u t) |
|
1023 maybe_ctr_conds_argss |
|
1024 (Const (@{const_name Code.abort}, @{typ String.literal} --> |
|
1025 (@{typ unit} --> body_type fun_T) --> body_type fun_T) $ |
|
1026 HOLogic.mk_literal fun_name $ |
|
1027 absdummy @{typ unit} (incr_boundvars 1 lhs)); |
|
1028 in SOME (rhs, rhs, map snd ctr_alist) end |
|
1029 end); |
|
1030 in |
|
1031 (case maybe_rhs_info of |
|
1032 NONE => [] |
|
1033 | SOME (rhs, raw_rhs, ctr_thms) => |
|
1034 let |
|
1035 val ms = map (Logic.count_prems o prop_of) ctr_thms; |
|
1036 val (raw_t, t) = (raw_rhs, rhs) |
|
1037 |> pairself |
|
1038 (curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T), |
|
1039 map Bound (length fun_args - 1 downto 0))) |
|
1040 #> HOLogic.mk_Trueprop |
|
1041 #> curry Logic.list_all (map dest_Free fun_args)); |
|
1042 val (distincts, discIs, sel_splits, sel_split_asms) = |
|
1043 case_thms_of_term lthy bound_Ts raw_rhs; |
|
1044 |
|
1045 val raw_code_thm = mk_primcorec_raw_code_of_ctr_tac lthy distincts discIs sel_splits |
|
1046 sel_split_asms ms ctr_thms |
|
1047 |> K |> Goal.prove lthy [] [] raw_t |
|
1048 |> Thm.close_derivation; |
|
1049 in |
|
1050 mk_primcorec_code_of_raw_code_tac lthy distincts sel_splits raw_code_thm |
|
1051 |> K |> Goal.prove lthy [] [] t |
|
1052 |> Thm.close_derivation |
|
1053 |> single |
|
1054 end) |
|
1055 end; |
|
1056 |
|
1057 val disc_alists = map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss; |
|
1058 val sel_alists = map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss; |
|
1059 val disc_thmss = map (map snd) disc_alists; |
|
1060 val sel_thmss = map (map snd) sel_alists; |
|
1061 |
|
1062 val ctr_alists = map5 (maps oooo prove_ctr) disc_alists sel_alists disc_eqnss sel_eqnss |
|
1063 ctr_specss; |
|
1064 val ctr_thmss = map (map snd) ctr_alists; |
|
1065 |
|
1066 val code_thmss = map4 prove_code disc_eqnss sel_eqnss ctr_alists ctr_specss; |
|
1067 |
|
1068 val simp_thmss = map2 append disc_thmss sel_thmss |
|
1069 |
|
1070 val common_name = mk_common_name fun_names; |
|
1071 |
|
1072 val notes = |
|
1073 [(coinductN, map (if n2m then single else K []) coinduct_thms, []), |
|
1074 (codeN, code_thmss, code_nitpicksimp_attrs), |
|
1075 (ctrN, ctr_thmss, []), |
|
1076 (discN, disc_thmss, simp_attrs), |
|
1077 (selN, sel_thmss, simp_attrs), |
|
1078 (simpsN, simp_thmss, []), |
|
1079 (strong_coinductN, map (if n2m then single else K []) strong_coinduct_thms, [])] |
|
1080 |> maps (fn (thmN, thmss, attrs) => |
|
1081 map2 (fn fun_name => fn thms => |
|
1082 ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])])) |
|
1083 fun_names (take actual_nn thmss)) |
|
1084 |> filter_out (null o fst o hd o snd); |
|
1085 |
|
1086 val common_notes = |
|
1087 [(coinductN, if n2m then [coinduct_thm] else [], []), |
|
1088 (strong_coinductN, if n2m then [strong_coinduct_thm] else [], [])] |
|
1089 |> filter_out (null o #2) |
|
1090 |> map (fn (thmN, thms, attrs) => |
|
1091 ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])])); |
|
1092 in |
|
1093 lthy |> Local_Theory.notes (notes @ common_notes) |> snd |
|
1094 end; |
|
1095 |
|
1096 fun after_qed thmss' = fold_map Local_Theory.define defs #-> prove thmss'; |
|
1097 in |
|
1098 (goalss, after_qed, lthy') |
|
1099 end; |
|
1100 |
|
1101 fun add_primcorec_ursive_cmd maybe_tac seq (raw_fixes, raw_specs') lthy = |
|
1102 let |
|
1103 val (raw_specs, maybe_of_specs) = |
|
1104 split_list raw_specs' ||> map (Option.map (Syntax.read_term lthy)); |
|
1105 val ((fixes, specs), _) = Specification.read_spec raw_fixes raw_specs lthy; |
|
1106 in |
|
1107 add_primcorec_ursive maybe_tac seq fixes specs maybe_of_specs lthy |
|
1108 handle ERROR str => primrec_error str |
|
1109 end |
|
1110 handle Primrec_Error (str, eqns) => |
|
1111 if null eqns |
|
1112 then error ("primcorec error:\n " ^ str) |
|
1113 else error ("primcorec error:\n " ^ str ^ "\nin\n " ^ |
|
1114 space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns)); |
|
1115 |
|
1116 val add_primcorecursive_cmd = (fn (goalss, after_qed, lthy) => |
|
1117 lthy |
|
1118 |> Proof.theorem NONE after_qed goalss |
|
1119 |> Proof.refine (Method.primitive_text I) |
|
1120 |> Seq.hd) ooo add_primcorec_ursive_cmd NONE; |
|
1121 |
|
1122 val add_primcorec_cmd = (fn (goalss, after_qed, lthy) => |
|
1123 lthy |
|
1124 |> after_qed (map (fn [] => [] |
|
1125 | _ => primrec_error "need exclusiveness proofs - use primcorecursive instead of primcorec") |
|
1126 goalss)) ooo add_primcorec_ursive_cmd (SOME (fn {context = ctxt, ...} => auto_tac ctxt)); |
|
1127 |
|
1128 end; |
|