1 (* Title: HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML |
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2 Author: Lawrence C. Paulson, Cambridge University Computer Laboratory |
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3 Author: Claire Quigley, Cambridge University Computer Laboratory |
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4 Author: Jasmin Blanchette, TU Muenchen |
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5 |
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6 Transfer of proofs from external provers. |
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7 *) |
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8 |
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9 signature SLEDGEHAMMER_PROOF_RECONSTRUCT = |
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10 sig |
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11 type locality = Sledgehammer_Fact_Filter.locality |
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12 type minimize_command = string list -> string |
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13 type metis_params = |
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14 bool * minimize_command * string * (string * locality) list vector * thm |
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15 * int |
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16 type isar_params = |
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17 string Symtab.table * bool * int * Proof.context * int list list |
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18 type text_result = string * (string * locality) list |
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19 |
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20 val metis_proof_text : metis_params -> text_result |
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21 val isar_proof_text : isar_params -> metis_params -> text_result |
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22 val proof_text : bool -> isar_params -> metis_params -> text_result |
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23 end; |
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24 |
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25 structure Sledgehammer_Proof_Reconstruct : SLEDGEHAMMER_PROOF_RECONSTRUCT = |
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26 struct |
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27 |
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28 open ATP_Problem |
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29 open Metis_Clauses |
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30 open Sledgehammer_Util |
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31 open Sledgehammer_Fact_Filter |
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32 open Sledgehammer_Translate |
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33 |
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34 type minimize_command = string list -> string |
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35 type metis_params = |
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36 bool * minimize_command * string * (string * locality) list vector * thm * int |
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37 type isar_params = |
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38 string Symtab.table * bool * int * Proof.context * int list list |
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39 type text_result = string * (string * locality) list |
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40 |
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41 (* Simple simplifications to ensure that sort annotations don't leave a trail of |
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42 spurious "True"s. *) |
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43 fun s_not @{const False} = @{const True} |
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44 | s_not @{const True} = @{const False} |
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45 | s_not (@{const Not} $ t) = t |
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46 | s_not t = @{const Not} $ t |
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47 fun s_conj (@{const True}, t2) = t2 |
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48 | s_conj (t1, @{const True}) = t1 |
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49 | s_conj p = HOLogic.mk_conj p |
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50 fun s_disj (@{const False}, t2) = t2 |
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51 | s_disj (t1, @{const False}) = t1 |
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52 | s_disj p = HOLogic.mk_disj p |
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53 fun s_imp (@{const True}, t2) = t2 |
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54 | s_imp (t1, @{const False}) = s_not t1 |
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55 | s_imp p = HOLogic.mk_imp p |
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56 fun s_iff (@{const True}, t2) = t2 |
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57 | s_iff (t1, @{const True}) = t1 |
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58 | s_iff (t1, t2) = HOLogic.eq_const HOLogic.boolT $ t1 $ t2 |
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59 |
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60 fun mk_anot (AConn (ANot, [phi])) = phi |
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61 | mk_anot phi = AConn (ANot, [phi]) |
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62 fun mk_aconn c (phi1, phi2) = AConn (c, [phi1, phi2]) |
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63 |
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64 fun index_in_shape x = find_index (exists (curry (op =) x)) |
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65 fun is_axiom_number axiom_names num = |
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66 num > 0 andalso num <= Vector.length axiom_names andalso |
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67 not (null (Vector.sub (axiom_names, num - 1))) |
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68 fun is_conjecture_number conjecture_shape num = |
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69 index_in_shape num conjecture_shape >= 0 |
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70 |
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71 fun negate_term (Const (@{const_name All}, T) $ Abs (s, T', t')) = |
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72 Const (@{const_name Ex}, T) $ Abs (s, T', negate_term t') |
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73 | negate_term (Const (@{const_name Ex}, T) $ Abs (s, T', t')) = |
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74 Const (@{const_name All}, T) $ Abs (s, T', negate_term t') |
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75 | negate_term (@{const HOL.implies} $ t1 $ t2) = |
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76 @{const HOL.conj} $ t1 $ negate_term t2 |
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77 | negate_term (@{const HOL.conj} $ t1 $ t2) = |
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78 @{const HOL.disj} $ negate_term t1 $ negate_term t2 |
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79 | negate_term (@{const HOL.disj} $ t1 $ t2) = |
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80 @{const HOL.conj} $ negate_term t1 $ negate_term t2 |
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81 | negate_term (@{const Not} $ t) = t |
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82 | negate_term t = @{const Not} $ t |
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83 |
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84 datatype ('a, 'b, 'c, 'd, 'e) raw_step = |
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85 Definition of 'a * 'b * 'c | |
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86 Inference of 'a * 'd * 'e list |
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87 |
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88 fun raw_step_number (Definition (num, _, _)) = num |
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89 | raw_step_number (Inference (num, _, _)) = num |
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90 |
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91 (**** PARSING OF TSTP FORMAT ****) |
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92 |
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93 (*Strings enclosed in single quotes, e.g. filenames*) |
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94 val scan_quoted = $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode; |
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95 |
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96 val scan_dollar_name = |
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97 Scan.repeat ($$ "$") -- Symbol.scan_id >> (fn (ss, s) => implode ss ^ s) |
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98 |
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99 fun repair_name _ "$true" = "c_True" |
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100 | repair_name _ "$false" = "c_False" |
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101 | repair_name _ "$$e" = "c_equal" (* seen in Vampire proofs *) |
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102 | repair_name _ "equal" = "c_equal" (* needed by SPASS? *) |
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103 | repair_name pool s = |
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104 case Symtab.lookup pool s of |
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105 SOME s' => s' |
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106 | NONE => |
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107 if String.isPrefix "sQ" s andalso String.isSuffix "_eqProxy" s then |
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108 "c_equal" (* seen in Vampire proofs *) |
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109 else |
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110 s |
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111 (* Generalized first-order terms, which include file names, numbers, etc. *) |
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112 val parse_potential_integer = |
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113 (scan_dollar_name || scan_quoted) >> K NONE |
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114 || scan_integer >> SOME |
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115 fun parse_annotation x = |
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116 ((parse_potential_integer ::: Scan.repeat ($$ " " |-- parse_potential_integer) |
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117 >> map_filter I) -- Scan.optional parse_annotation [] |
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118 >> uncurry (union (op =)) |
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119 || $$ "(" |-- parse_annotations --| $$ ")" |
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120 || $$ "[" |-- parse_annotations --| $$ "]") x |
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121 and parse_annotations x = |
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122 (Scan.optional (parse_annotation |
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123 ::: Scan.repeat ($$ "," |-- parse_annotation)) [] |
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124 >> (fn numss => fold (union (op =)) numss [])) x |
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125 |
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126 (* Vampire proof lines sometimes contain needless information such as "(0:3)", |
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127 which can be hard to disambiguate from function application in an LL(1) |
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128 parser. As a workaround, we extend the TPTP term syntax with such detritus |
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129 and ignore it. *) |
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130 fun parse_vampire_detritus x = |
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131 (scan_integer |-- $$ ":" --| scan_integer >> K []) x |
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132 |
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133 fun parse_term pool x = |
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134 ((scan_dollar_name >> repair_name pool) |
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135 -- Scan.optional ($$ "(" |-- (parse_vampire_detritus || parse_terms pool) |
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136 --| $$ ")") [] |
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137 --| Scan.optional ($$ "(" |-- parse_vampire_detritus --| $$ ")") [] |
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138 >> ATerm) x |
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139 and parse_terms pool x = |
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140 (parse_term pool ::: Scan.repeat ($$ "," |-- parse_term pool)) x |
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141 |
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142 fun parse_atom pool = |
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143 parse_term pool -- Scan.option (Scan.option ($$ "!") --| $$ "=" |
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144 -- parse_term pool) |
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145 >> (fn (u1, NONE) => AAtom u1 |
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146 | (u1, SOME (NONE, u2)) => AAtom (ATerm ("c_equal", [u1, u2])) |
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147 | (u1, SOME (SOME _, u2)) => |
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148 mk_anot (AAtom (ATerm ("c_equal", [u1, u2])))) |
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149 |
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150 fun fo_term_head (ATerm (s, _)) = s |
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151 |
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152 (* TPTP formulas are fully parenthesized, so we don't need to worry about |
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153 operator precedence. *) |
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154 fun parse_formula pool x = |
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155 (($$ "(" |-- parse_formula pool --| $$ ")" |
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156 || ($$ "!" >> K AForall || $$ "?" >> K AExists) |
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157 --| $$ "[" -- parse_terms pool --| $$ "]" --| $$ ":" |
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158 -- parse_formula pool |
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159 >> (fn ((q, ts), phi) => AQuant (q, map fo_term_head ts, phi)) |
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160 || $$ "~" |-- parse_formula pool >> mk_anot |
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161 || parse_atom pool) |
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162 -- Scan.option ((Scan.this_string "=>" >> K AImplies |
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163 || Scan.this_string "<=>" >> K AIff |
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164 || Scan.this_string "<~>" >> K ANotIff |
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165 || Scan.this_string "<=" >> K AIf |
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166 || $$ "|" >> K AOr || $$ "&" >> K AAnd) |
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167 -- parse_formula pool) |
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168 >> (fn (phi1, NONE) => phi1 |
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169 | (phi1, SOME (c, phi2)) => mk_aconn c (phi1, phi2))) x |
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170 |
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171 val parse_tstp_extra_arguments = |
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172 Scan.optional ($$ "," |-- parse_annotation |
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173 --| Scan.option ($$ "," |-- parse_annotations)) [] |
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174 |
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175 (* Syntax: (fof|cnf)\(<num>, <formula_role>, <formula> <extra_arguments>\). |
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176 The <num> could be an identifier, but we assume integers. *) |
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177 fun parse_tstp_line pool = |
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178 ((Scan.this_string "fof" || Scan.this_string "cnf") -- $$ "(") |
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179 |-- scan_integer --| $$ "," -- Symbol.scan_id --| $$ "," |
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180 -- parse_formula pool -- parse_tstp_extra_arguments --| $$ ")" --| $$ "." |
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181 >> (fn (((num, role), phi), deps) => |
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182 case role of |
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183 "definition" => |
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184 (case phi of |
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185 AConn (AIff, [phi1 as AAtom _, phi2]) => |
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186 Definition (num, phi1, phi2) |
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187 | AAtom (ATerm ("c_equal", _)) => |
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188 Inference (num, phi, deps) (* Vampire's equality proxy axiom *) |
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189 | _ => raise Fail "malformed definition") |
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190 | _ => Inference (num, phi, deps)) |
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191 |
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192 (**** PARSING OF VAMPIRE OUTPUT ****) |
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193 |
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194 (* Syntax: <num>. <formula> <annotation> *) |
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195 fun parse_vampire_line pool = |
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196 scan_integer --| $$ "." -- parse_formula pool -- parse_annotation |
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197 >> (fn ((num, phi), deps) => Inference (num, phi, deps)) |
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198 |
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199 (**** PARSING OF SPASS OUTPUT ****) |
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200 |
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201 (* SPASS returns clause references of the form "x.y". We ignore "y", whose role |
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202 is not clear anyway. *) |
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203 val parse_dot_name = scan_integer --| $$ "." --| scan_integer |
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204 |
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205 val parse_spass_annotations = |
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206 Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name |
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207 --| Scan.option ($$ ","))) [] |
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208 |
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209 (* It is not clear why some literals are followed by sequences of stars and/or |
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210 pluses. We ignore them. *) |
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211 fun parse_decorated_atom pool = |
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212 parse_atom pool --| Scan.repeat ($$ "*" || $$ "+" || $$ " ") |
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213 |
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214 fun mk_horn ([], []) = AAtom (ATerm ("c_False", [])) |
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215 | mk_horn ([], pos_lits) = foldr1 (mk_aconn AOr) pos_lits |
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216 | mk_horn (neg_lits, []) = mk_anot (foldr1 (mk_aconn AAnd) neg_lits) |
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217 | mk_horn (neg_lits, pos_lits) = |
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218 mk_aconn AImplies (foldr1 (mk_aconn AAnd) neg_lits, |
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219 foldr1 (mk_aconn AOr) pos_lits) |
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220 |
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221 fun parse_horn_clause pool = |
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222 Scan.repeat (parse_decorated_atom pool) --| $$ "|" --| $$ "|" |
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223 -- Scan.repeat (parse_decorated_atom pool) --| $$ "-" --| $$ ">" |
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224 -- Scan.repeat (parse_decorated_atom pool) |
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225 >> (mk_horn o apfst (op @)) |
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226 |
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227 (* Syntax: <num>[0:<inference><annotations>] |
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228 <atoms> || <atoms> -> <atoms>. *) |
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229 fun parse_spass_line pool = |
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230 scan_integer --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id |
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231 -- parse_spass_annotations --| $$ "]" -- parse_horn_clause pool --| $$ "." |
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232 >> (fn ((num, deps), u) => Inference (num, u, deps)) |
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233 |
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234 fun parse_line pool = |
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235 parse_tstp_line pool || parse_vampire_line pool || parse_spass_line pool |
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236 fun parse_lines pool = Scan.repeat1 (parse_line pool) |
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237 fun parse_proof pool = |
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238 fst o Scan.finite Symbol.stopper |
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239 (Scan.error (!! (fn _ => raise Fail "unrecognized ATP output") |
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240 (parse_lines pool))) |
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241 o explode o strip_spaces_except_between_ident_chars |
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242 |
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243 (**** INTERPRETATION OF TSTP SYNTAX TREES ****) |
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244 |
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245 exception FO_TERM of string fo_term list |
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246 exception FORMULA of (string, string fo_term) formula list |
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247 exception SAME of unit |
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248 |
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249 (* Type variables are given the basic sort "HOL.type". Some will later be |
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250 constrained by information from type literals, or by type inference. *) |
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251 fun type_from_fo_term tfrees (u as ATerm (a, us)) = |
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252 let val Ts = map (type_from_fo_term tfrees) us in |
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253 case strip_prefix_and_unascii type_const_prefix a of |
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254 SOME b => Type (invert_const b, Ts) |
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255 | NONE => |
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256 if not (null us) then |
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257 raise FO_TERM [u] (* only "tconst"s have type arguments *) |
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258 else case strip_prefix_and_unascii tfree_prefix a of |
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259 SOME b => |
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260 let val s = "'" ^ b in |
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261 TFree (s, AList.lookup (op =) tfrees s |> the_default HOLogic.typeS) |
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262 end |
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263 | NONE => |
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264 case strip_prefix_and_unascii tvar_prefix a of |
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265 SOME b => TVar (("'" ^ b, 0), HOLogic.typeS) |
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266 | NONE => |
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267 (* Variable from the ATP, say "X1" *) |
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268 Type_Infer.param 0 (a, HOLogic.typeS) |
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269 end |
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270 |
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271 (* Type class literal applied to a type. Returns triple of polarity, class, |
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272 type. *) |
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273 fun type_constraint_from_term pos tfrees (u as ATerm (a, us)) = |
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274 case (strip_prefix_and_unascii class_prefix a, |
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275 map (type_from_fo_term tfrees) us) of |
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276 (SOME b, [T]) => (pos, b, T) |
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277 | _ => raise FO_TERM [u] |
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278 |
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279 (** Accumulate type constraints in a formula: negative type literals **) |
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280 fun add_var (key, z) = Vartab.map_default (key, []) (cons z) |
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281 fun add_type_constraint (false, cl, TFree (a ,_)) = add_var ((a, ~1), cl) |
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282 | add_type_constraint (false, cl, TVar (ix, _)) = add_var (ix, cl) |
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283 | add_type_constraint _ = I |
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284 |
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285 fun repair_atp_variable_name f s = |
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286 let |
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287 fun subscript_name s n = s ^ nat_subscript n |
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288 val s = String.map f s |
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289 in |
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290 case space_explode "_" s of |
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291 [_] => (case take_suffix Char.isDigit (String.explode s) of |
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292 (cs1 as _ :: _, cs2 as _ :: _) => |
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293 subscript_name (String.implode cs1) |
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294 (the (Int.fromString (String.implode cs2))) |
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295 | (_, _) => s) |
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296 | [s1, s2] => (case Int.fromString s2 of |
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297 SOME n => subscript_name s1 n |
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298 | NONE => s) |
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299 | _ => s |
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300 end |
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301 |
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302 (* First-order translation. No types are known for variables. "HOLogic.typeT" |
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303 should allow them to be inferred. *) |
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304 fun raw_term_from_pred thy full_types tfrees = |
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305 let |
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306 fun aux opt_T extra_us u = |
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307 case u of |
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308 ATerm ("hBOOL", [u1]) => aux (SOME @{typ bool}) [] u1 |
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309 | ATerm ("hAPP", [u1, u2]) => aux opt_T (u2 :: extra_us) u1 |
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310 | ATerm (a, us) => |
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311 if a = type_wrapper_name then |
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312 case us of |
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313 [typ_u, term_u] => |
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314 aux (SOME (type_from_fo_term tfrees typ_u)) extra_us term_u |
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315 | _ => raise FO_TERM us |
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316 else case strip_prefix_and_unascii const_prefix a of |
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317 SOME "equal" => |
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318 list_comb (Const (@{const_name HOL.eq}, HOLogic.typeT), |
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319 map (aux NONE []) us) |
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320 | SOME b => |
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321 let |
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322 val c = invert_const b |
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323 val num_type_args = num_type_args thy c |
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324 val (type_us, term_us) = |
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325 chop (if full_types then 0 else num_type_args) us |
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326 (* Extra args from "hAPP" come after any arguments given directly to |
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327 the constant. *) |
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328 val term_ts = map (aux NONE []) term_us |
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329 val extra_ts = map (aux NONE []) extra_us |
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330 val t = |
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331 Const (c, if full_types then |
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332 case opt_T of |
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333 SOME T => map fastype_of term_ts ---> T |
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334 | NONE => |
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335 if num_type_args = 0 then |
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336 Sign.const_instance thy (c, []) |
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337 else |
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338 raise Fail ("no type information for " ^ quote c) |
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339 else |
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340 Sign.const_instance thy (c, |
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341 map (type_from_fo_term tfrees) type_us)) |
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342 in list_comb (t, term_ts @ extra_ts) end |
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343 | NONE => (* a free or schematic variable *) |
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344 let |
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345 val ts = map (aux NONE []) (us @ extra_us) |
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346 val T = map fastype_of ts ---> HOLogic.typeT |
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347 val t = |
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348 case strip_prefix_and_unascii fixed_var_prefix a of |
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349 SOME b => Free (b, T) |
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350 | NONE => |
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351 case strip_prefix_and_unascii schematic_var_prefix a of |
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352 SOME b => Var ((b, 0), T) |
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353 | NONE => |
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354 if is_tptp_variable a then |
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355 Var ((repair_atp_variable_name Char.toLower a, 0), T) |
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356 else |
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357 (* Skolem constants? *) |
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358 Var ((repair_atp_variable_name Char.toUpper a, 0), T) |
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359 in list_comb (t, ts) end |
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360 in aux (SOME HOLogic.boolT) [] end |
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361 |
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362 fun term_from_pred thy full_types tfrees pos (u as ATerm (s, _)) = |
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363 if String.isPrefix class_prefix s then |
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364 add_type_constraint (type_constraint_from_term pos tfrees u) |
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365 #> pair @{const True} |
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366 else |
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367 pair (raw_term_from_pred thy full_types tfrees u) |
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368 |
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369 val combinator_table = |
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370 [(@{const_name COMBI}, @{thm COMBI_def_raw}), |
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371 (@{const_name COMBK}, @{thm COMBK_def_raw}), |
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372 (@{const_name COMBB}, @{thm COMBB_def_raw}), |
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373 (@{const_name COMBC}, @{thm COMBC_def_raw}), |
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374 (@{const_name COMBS}, @{thm COMBS_def_raw})] |
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375 |
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376 fun uncombine_term (t1 $ t2) = betapply (pairself uncombine_term (t1, t2)) |
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377 | uncombine_term (Abs (s, T, t')) = Abs (s, T, uncombine_term t') |
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378 | uncombine_term (t as Const (x as (s, _))) = |
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379 (case AList.lookup (op =) combinator_table s of |
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380 SOME thm => thm |> prop_of |> specialize_type @{theory} x |> Logic.dest_equals |> snd |
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381 | NONE => t) |
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382 | uncombine_term t = t |
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383 |
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384 (* Update schematic type variables with detected sort constraints. It's not |
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385 totally clear when this code is necessary. *) |
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386 fun repair_tvar_sorts (t, tvar_tab) = |
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387 let |
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388 fun do_type (Type (a, Ts)) = Type (a, map do_type Ts) |
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389 | do_type (TVar (xi, s)) = |
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390 TVar (xi, the_default s (Vartab.lookup tvar_tab xi)) |
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391 | do_type (TFree z) = TFree z |
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392 fun do_term (Const (a, T)) = Const (a, do_type T) |
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393 | do_term (Free (a, T)) = Free (a, do_type T) |
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394 | do_term (Var (xi, T)) = Var (xi, do_type T) |
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395 | do_term (t as Bound _) = t |
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396 | do_term (Abs (a, T, t)) = Abs (a, do_type T, do_term t) |
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397 | do_term (t1 $ t2) = do_term t1 $ do_term t2 |
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398 in t |> not (Vartab.is_empty tvar_tab) ? do_term end |
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399 |
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400 fun quantify_over_free quant_s free_s body_t = |
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401 case Term.add_frees body_t [] |> filter (curry (op =) free_s o fst) of |
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402 [] => body_t |
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403 | frees as (_, free_T) :: _ => |
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404 Abs (free_s, free_T, fold (curry abstract_over) (map Free frees) body_t) |
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405 |
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406 (* Interpret an ATP formula as a HOL term, extracting sort constraints as they |
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407 appear in the formula. *) |
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408 fun prop_from_formula thy full_types tfrees phi = |
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409 let |
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410 fun do_formula pos phi = |
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411 case phi of |
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412 AQuant (_, [], phi) => do_formula pos phi |
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413 | AQuant (q, x :: xs, phi') => |
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414 do_formula pos (AQuant (q, xs, phi')) |
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415 #>> quantify_over_free (case q of |
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416 AForall => @{const_name All} |
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417 | AExists => @{const_name Ex}) |
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418 (repair_atp_variable_name Char.toLower x) |
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419 | AConn (ANot, [phi']) => do_formula (not pos) phi' #>> s_not |
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420 | AConn (c, [phi1, phi2]) => |
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421 do_formula (pos |> c = AImplies ? not) phi1 |
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422 ##>> do_formula pos phi2 |
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423 #>> (case c of |
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424 AAnd => s_conj |
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425 | AOr => s_disj |
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426 | AImplies => s_imp |
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427 | AIf => s_imp o swap |
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428 | AIff => s_iff |
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429 | ANotIff => s_not o s_iff) |
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430 | AAtom tm => term_from_pred thy full_types tfrees pos tm |
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431 | _ => raise FORMULA [phi] |
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432 in repair_tvar_sorts (do_formula true phi Vartab.empty) end |
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433 |
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434 fun check_formula ctxt = |
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435 Type_Infer.constrain HOLogic.boolT |
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436 #> Syntax.check_term (ProofContext.set_mode ProofContext.mode_schematic ctxt) |
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437 |
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438 |
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439 (**** Translation of TSTP files to Isar Proofs ****) |
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440 |
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441 fun unvarify_term (Var ((s, 0), T)) = Free (s, T) |
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442 | unvarify_term t = raise TERM ("unvarify_term: non-Var", [t]) |
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443 |
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444 fun decode_line full_types tfrees (Definition (num, phi1, phi2)) ctxt = |
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445 let |
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446 val thy = ProofContext.theory_of ctxt |
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447 val t1 = prop_from_formula thy full_types tfrees phi1 |
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448 val vars = snd (strip_comb t1) |
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449 val frees = map unvarify_term vars |
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450 val unvarify_args = subst_atomic (vars ~~ frees) |
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451 val t2 = prop_from_formula thy full_types tfrees phi2 |
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452 val (t1, t2) = |
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453 HOLogic.eq_const HOLogic.typeT $ t1 $ t2 |
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454 |> unvarify_args |> uncombine_term |> check_formula ctxt |
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455 |> HOLogic.dest_eq |
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456 in |
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457 (Definition (num, t1, t2), |
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458 fold Variable.declare_term (maps OldTerm.term_frees [t1, t2]) ctxt) |
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459 end |
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460 | decode_line full_types tfrees (Inference (num, u, deps)) ctxt = |
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461 let |
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462 val thy = ProofContext.theory_of ctxt |
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463 val t = u |> prop_from_formula thy full_types tfrees |
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464 |> uncombine_term |> check_formula ctxt |
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465 in |
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466 (Inference (num, t, deps), |
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467 fold Variable.declare_term (OldTerm.term_frees t) ctxt) |
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468 end |
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469 fun decode_lines ctxt full_types tfrees lines = |
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470 fst (fold_map (decode_line full_types tfrees) lines ctxt) |
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471 |
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472 fun is_same_inference _ (Definition _) = false |
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473 | is_same_inference t (Inference (_, t', _)) = t aconv t' |
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474 |
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475 (* No "real" literals means only type information (tfree_tcs, clsrel, or |
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476 clsarity). *) |
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477 val is_only_type_information = curry (op aconv) HOLogic.true_const |
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478 |
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479 fun replace_one_dep (old, new) dep = if dep = old then new else [dep] |
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480 fun replace_deps_in_line _ (line as Definition _) = line |
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481 | replace_deps_in_line p (Inference (num, t, deps)) = |
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482 Inference (num, t, fold (union (op =) o replace_one_dep p) deps []) |
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483 |
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484 (* Discard axioms; consolidate adjacent lines that prove the same formula, since |
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485 they differ only in type information.*) |
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486 fun add_line _ _ (line as Definition _) lines = line :: lines |
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487 | add_line conjecture_shape axiom_names (Inference (num, t, [])) lines = |
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488 (* No dependencies: axiom, conjecture, or (for Vampire) internal axioms or |
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489 definitions. *) |
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490 if is_axiom_number axiom_names num then |
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491 (* Axioms are not proof lines. *) |
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492 if is_only_type_information t then |
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493 map (replace_deps_in_line (num, [])) lines |
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494 (* Is there a repetition? If so, replace later line by earlier one. *) |
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495 else case take_prefix (not o is_same_inference t) lines of |
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496 (_, []) => lines (*no repetition of proof line*) |
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497 | (pre, Inference (num', _, _) :: post) => |
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498 pre @ map (replace_deps_in_line (num', [num])) post |
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499 else if is_conjecture_number conjecture_shape num then |
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500 Inference (num, negate_term t, []) :: lines |
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501 else |
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502 map (replace_deps_in_line (num, [])) lines |
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503 | add_line _ _ (Inference (num, t, deps)) lines = |
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504 (* Type information will be deleted later; skip repetition test. *) |
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505 if is_only_type_information t then |
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506 Inference (num, t, deps) :: lines |
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507 (* Is there a repetition? If so, replace later line by earlier one. *) |
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508 else case take_prefix (not o is_same_inference t) lines of |
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509 (* FIXME: Doesn't this code risk conflating proofs involving different |
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510 types? *) |
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511 (_, []) => Inference (num, t, deps) :: lines |
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512 | (pre, Inference (num', t', _) :: post) => |
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513 Inference (num, t', deps) :: |
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514 pre @ map (replace_deps_in_line (num', [num])) post |
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515 |
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516 (* Recursively delete empty lines (type information) from the proof. *) |
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517 fun add_nontrivial_line (Inference (num, t, [])) lines = |
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518 if is_only_type_information t then delete_dep num lines |
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519 else Inference (num, t, []) :: lines |
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520 | add_nontrivial_line line lines = line :: lines |
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521 and delete_dep num lines = |
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522 fold_rev add_nontrivial_line (map (replace_deps_in_line (num, [])) lines) [] |
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523 |
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524 (* ATPs sometimes reuse free variable names in the strangest ways. Removing |
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525 offending lines often does the trick. *) |
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526 fun is_bad_free frees (Free x) = not (member (op =) frees x) |
|
527 | is_bad_free _ _ = false |
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528 |
|
529 (* Vampire is keen on producing these. *) |
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530 fun is_trivial_formula (@{const Not} $ (Const (@{const_name HOL.eq}, _) |
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531 $ t1 $ t2)) = (t1 aconv t2) |
|
532 | is_trivial_formula _ = false |
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533 |
|
534 fun add_desired_line _ _ _ _ (line as Definition (num, _, _)) (j, lines) = |
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535 (j, line :: map (replace_deps_in_line (num, [])) lines) |
|
536 | add_desired_line isar_shrink_factor conjecture_shape axiom_names frees |
|
537 (Inference (num, t, deps)) (j, lines) = |
|
538 (j + 1, |
|
539 if is_axiom_number axiom_names num orelse |
|
540 is_conjecture_number conjecture_shape num orelse |
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541 (not (is_only_type_information t) andalso |
|
542 null (Term.add_tvars t []) andalso |
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543 not (exists_subterm (is_bad_free frees) t) andalso |
|
544 not (is_trivial_formula t) andalso |
|
545 (null lines orelse (* last line must be kept *) |
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546 (length deps >= 2 andalso j mod isar_shrink_factor = 0))) then |
|
547 Inference (num, t, deps) :: lines (* keep line *) |
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548 else |
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549 map (replace_deps_in_line (num, deps)) lines) (* drop line *) |
|
550 |
|
551 (** EXTRACTING LEMMAS **) |
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552 |
|
553 (* Like "split_line", but ignores "\n" that follow a comma (as in SNARK's |
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554 output). *) |
|
555 val split_proof_lines = |
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556 let |
|
557 fun aux [] [] = [] |
|
558 | aux line [] = [implode (rev line)] |
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559 | aux line ("," :: "\n" :: rest) = aux ("," :: line) rest |
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560 | aux line ("\n" :: rest) = aux line [] @ aux [] rest |
|
561 | aux line (s :: rest) = aux (s :: line) rest |
|
562 in aux [] o explode end |
|
563 |
|
564 (* A list consisting of the first number in each line is returned. For TSTP, |
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565 interesting lines have the form "fof(108, axiom, ...)", where the number |
|
566 (108) is extracted. For SPASS, lines have the form "108[0:Inp] ...", where |
|
567 the first number (108) is extracted. For Vampire, we look for |
|
568 "108. ... [input]". *) |
|
569 fun used_facts_in_atp_proof axiom_names atp_proof = |
|
570 let |
|
571 fun axiom_names_at_index num = |
|
572 let val j = Int.fromString num |> the_default ~1 in |
|
573 if is_axiom_number axiom_names j then Vector.sub (axiom_names, j - 1) |
|
574 else [] |
|
575 end |
|
576 val tokens_of = |
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577 String.tokens (fn c => not (Char.isAlphaNum c) andalso c <> #"_") |
|
578 fun do_line (tag :: num :: "axiom" :: (rest as _ :: _)) = |
|
579 if tag = "cnf" orelse tag = "fof" then |
|
580 (case strip_prefix_and_unascii axiom_prefix (List.last rest) of |
|
581 SOME name => |
|
582 if member (op =) rest "file" then |
|
583 ([(name, name |> find_first_in_list_vector axiom_names |> the)] |
|
584 handle Option.Option => |
|
585 error ("No such fact: " ^ quote name ^ ".")) |
|
586 else |
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587 axiom_names_at_index num |
|
588 | NONE => axiom_names_at_index num) |
|
589 else |
|
590 [] |
|
591 | do_line (num :: "0" :: "Inp" :: _) = axiom_names_at_index num |
|
592 | do_line (num :: rest) = |
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593 (case List.last rest of "input" => axiom_names_at_index num | _ => []) |
|
594 | do_line _ = [] |
|
595 in atp_proof |> split_proof_lines |> maps (do_line o tokens_of) end |
|
596 |
|
597 val indent_size = 2 |
|
598 val no_label = ("", ~1) |
|
599 |
|
600 val raw_prefix = "X" |
|
601 val assum_prefix = "A" |
|
602 val fact_prefix = "F" |
|
603 |
|
604 fun string_for_label (s, num) = s ^ string_of_int num |
|
605 |
|
606 fun metis_using [] = "" |
|
607 | metis_using ls = |
|
608 "using " ^ space_implode " " (map string_for_label ls) ^ " " |
|
609 fun metis_apply _ 1 = "by " |
|
610 | metis_apply 1 _ = "apply " |
|
611 | metis_apply i _ = "prefer " ^ string_of_int i ^ " apply " |
|
612 fun metis_name full_types = if full_types then "metisFT" else "metis" |
|
613 fun metis_call full_types [] = metis_name full_types |
|
614 | metis_call full_types ss = |
|
615 "(" ^ metis_name full_types ^ " " ^ space_implode " " ss ^ ")" |
|
616 fun metis_command full_types i n (ls, ss) = |
|
617 metis_using ls ^ metis_apply i n ^ metis_call full_types ss |
|
618 fun metis_line full_types i n ss = |
|
619 "Try this command: " ^ |
|
620 Markup.markup Markup.sendback (metis_command full_types i n ([], ss)) ^ "." |
|
621 fun minimize_line _ [] = "" |
|
622 | minimize_line minimize_command ss = |
|
623 case minimize_command ss of |
|
624 "" => "" |
|
625 | command => |
|
626 "\nTo minimize the number of lemmas, try this: " ^ |
|
627 Markup.markup Markup.sendback command ^ "." |
|
628 |
|
629 fun used_facts axiom_names = |
|
630 used_facts_in_atp_proof axiom_names |
|
631 #> List.partition (curry (op =) Chained o snd) |
|
632 #> pairself (sort_distinct (string_ord o pairself fst)) |
|
633 |
|
634 fun metis_proof_text (full_types, minimize_command, atp_proof, axiom_names, |
|
635 goal, i) = |
|
636 let |
|
637 val (chained_lemmas, other_lemmas) = used_facts axiom_names atp_proof |
|
638 val n = Logic.count_prems (prop_of goal) |
|
639 in |
|
640 (metis_line full_types i n (map fst other_lemmas) ^ |
|
641 minimize_line minimize_command (map fst (other_lemmas @ chained_lemmas)), |
|
642 other_lemmas @ chained_lemmas) |
|
643 end |
|
644 |
|
645 (** Isar proof construction and manipulation **) |
|
646 |
|
647 fun merge_fact_sets (ls1, ss1) (ls2, ss2) = |
|
648 (union (op =) ls1 ls2, union (op =) ss1 ss2) |
|
649 |
|
650 type label = string * int |
|
651 type facts = label list * string list |
|
652 |
|
653 datatype qualifier = Show | Then | Moreover | Ultimately |
|
654 |
|
655 datatype step = |
|
656 Fix of (string * typ) list | |
|
657 Let of term * term | |
|
658 Assume of label * term | |
|
659 Have of qualifier list * label * term * byline |
|
660 and byline = |
|
661 ByMetis of facts | |
|
662 CaseSplit of step list list * facts |
|
663 |
|
664 fun smart_case_split [] facts = ByMetis facts |
|
665 | smart_case_split proofs facts = CaseSplit (proofs, facts) |
|
666 |
|
667 fun add_fact_from_dep axiom_names num = |
|
668 if is_axiom_number axiom_names num then |
|
669 apsnd (union (op =) (map fst (Vector.sub (axiom_names, num - 1)))) |
|
670 else |
|
671 apfst (insert (op =) (raw_prefix, num)) |
|
672 |
|
673 fun forall_of v t = HOLogic.all_const (fastype_of v) $ lambda v t |
|
674 fun forall_vars t = fold_rev forall_of (map Var (Term.add_vars t [])) t |
|
675 |
|
676 fun step_for_line _ _ (Definition (_, t1, t2)) = Let (t1, t2) |
|
677 | step_for_line _ _ (Inference (num, t, [])) = Assume ((raw_prefix, num), t) |
|
678 | step_for_line axiom_names j (Inference (num, t, deps)) = |
|
679 Have (if j = 1 then [Show] else [], (raw_prefix, num), |
|
680 forall_vars t, |
|
681 ByMetis (fold (add_fact_from_dep axiom_names) deps ([], []))) |
|
682 |
|
683 fun proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor |
|
684 atp_proof conjecture_shape axiom_names params frees = |
|
685 let |
|
686 val lines = |
|
687 atp_proof ^ "$" (* the $ sign acts as a sentinel (FIXME: needed?) *) |
|
688 |> parse_proof pool |
|
689 |> sort (int_ord o pairself raw_step_number) |
|
690 |> decode_lines ctxt full_types tfrees |
|
691 |> rpair [] |-> fold_rev (add_line conjecture_shape axiom_names) |
|
692 |> rpair [] |-> fold_rev add_nontrivial_line |
|
693 |> rpair (0, []) |-> fold_rev (add_desired_line isar_shrink_factor |
|
694 conjecture_shape axiom_names frees) |
|
695 |> snd |
|
696 in |
|
697 (if null params then [] else [Fix params]) @ |
|
698 map2 (step_for_line axiom_names) (length lines downto 1) lines |
|
699 end |
|
700 |
|
701 (* When redirecting proofs, we keep information about the labels seen so far in |
|
702 the "backpatches" data structure. The first component indicates which facts |
|
703 should be associated with forthcoming proof steps. The second component is a |
|
704 pair ("assum_ls", "drop_ls"), where "assum_ls" are the labels that should |
|
705 become assumptions and "drop_ls" are the labels that should be dropped in a |
|
706 case split. *) |
|
707 type backpatches = (label * facts) list * (label list * label list) |
|
708 |
|
709 fun used_labels_of_step (Have (_, _, _, by)) = |
|
710 (case by of |
|
711 ByMetis (ls, _) => ls |
|
712 | CaseSplit (proofs, (ls, _)) => |
|
713 fold (union (op =) o used_labels_of) proofs ls) |
|
714 | used_labels_of_step _ = [] |
|
715 and used_labels_of proof = fold (union (op =) o used_labels_of_step) proof [] |
|
716 |
|
717 fun new_labels_of_step (Fix _) = [] |
|
718 | new_labels_of_step (Let _) = [] |
|
719 | new_labels_of_step (Assume (l, _)) = [l] |
|
720 | new_labels_of_step (Have (_, l, _, _)) = [l] |
|
721 val new_labels_of = maps new_labels_of_step |
|
722 |
|
723 val join_proofs = |
|
724 let |
|
725 fun aux _ [] = NONE |
|
726 | aux proof_tail (proofs as (proof1 :: _)) = |
|
727 if exists null proofs then |
|
728 NONE |
|
729 else if forall (curry (op =) (hd proof1) o hd) (tl proofs) then |
|
730 aux (hd proof1 :: proof_tail) (map tl proofs) |
|
731 else case hd proof1 of |
|
732 Have ([], l, t, _) => (* FIXME: should we really ignore the "by"? *) |
|
733 if forall (fn Have ([], l', t', _) :: _ => (l, t) = (l', t') |
|
734 | _ => false) (tl proofs) andalso |
|
735 not (exists (member (op =) (maps new_labels_of proofs)) |
|
736 (used_labels_of proof_tail)) then |
|
737 SOME (l, t, map rev proofs, proof_tail) |
|
738 else |
|
739 NONE |
|
740 | _ => NONE |
|
741 in aux [] o map rev end |
|
742 |
|
743 fun case_split_qualifiers proofs = |
|
744 case length proofs of |
|
745 0 => [] |
|
746 | 1 => [Then] |
|
747 | _ => [Ultimately] |
|
748 |
|
749 fun redirect_proof conjecture_shape hyp_ts concl_t proof = |
|
750 let |
|
751 (* The first pass outputs those steps that are independent of the negated |
|
752 conjecture. The second pass flips the proof by contradiction to obtain a |
|
753 direct proof, introducing case splits when an inference depends on |
|
754 several facts that depend on the negated conjecture. *) |
|
755 fun find_hyp num = |
|
756 nth hyp_ts (index_in_shape num conjecture_shape) |
|
757 handle Subscript => |
|
758 raise Fail ("Cannot find hypothesis " ^ Int.toString num) |
|
759 val concl_ls = map (pair raw_prefix) (List.last conjecture_shape) |
|
760 val canonicalize_labels = |
|
761 map (fn l => if member (op =) concl_ls l then hd concl_ls else l) |
|
762 #> distinct (op =) |
|
763 fun first_pass ([], contra) = ([], contra) |
|
764 | first_pass ((step as Fix _) :: proof, contra) = |
|
765 first_pass (proof, contra) |>> cons step |
|
766 | first_pass ((step as Let _) :: proof, contra) = |
|
767 first_pass (proof, contra) |>> cons step |
|
768 | first_pass ((step as Assume (l as (_, num), _)) :: proof, contra) = |
|
769 if member (op =) concl_ls l then |
|
770 first_pass (proof, contra ||> l = hd concl_ls ? cons step) |
|
771 else |
|
772 first_pass (proof, contra) |>> cons (Assume (l, find_hyp num)) |
|
773 | first_pass (Have (qs, l, t, ByMetis (ls, ss)) :: proof, contra) = |
|
774 let |
|
775 val ls = canonicalize_labels ls |
|
776 val step = Have (qs, l, t, ByMetis (ls, ss)) |
|
777 in |
|
778 if exists (member (op =) (fst contra)) ls then |
|
779 first_pass (proof, contra |>> cons l ||> cons step) |
|
780 else |
|
781 first_pass (proof, contra) |>> cons step |
|
782 end |
|
783 | first_pass _ = raise Fail "malformed proof" |
|
784 val (proof_top, (contra_ls, contra_proof)) = |
|
785 first_pass (proof, (concl_ls, [])) |
|
786 val backpatch_label = the_default ([], []) oo AList.lookup (op =) o fst |
|
787 fun backpatch_labels patches ls = |
|
788 fold merge_fact_sets (map (backpatch_label patches) ls) ([], []) |
|
789 fun second_pass end_qs ([], assums, patches) = |
|
790 ([Have (end_qs, no_label, concl_t, |
|
791 ByMetis (backpatch_labels patches (map snd assums)))], patches) |
|
792 | second_pass end_qs (Assume (l, t) :: proof, assums, patches) = |
|
793 second_pass end_qs (proof, (t, l) :: assums, patches) |
|
794 | second_pass end_qs (Have (qs, l, t, ByMetis (ls, ss)) :: proof, assums, |
|
795 patches) = |
|
796 if member (op =) (snd (snd patches)) l andalso |
|
797 not (member (op =) (fst (snd patches)) l) andalso |
|
798 not (AList.defined (op =) (fst patches) l) then |
|
799 second_pass end_qs (proof, assums, patches ||> apsnd (append ls)) |
|
800 else |
|
801 (case List.partition (member (op =) contra_ls) ls of |
|
802 ([contra_l], co_ls) => |
|
803 if member (op =) qs Show then |
|
804 second_pass end_qs (proof, assums, |
|
805 patches |>> cons (contra_l, (co_ls, ss))) |
|
806 else |
|
807 second_pass end_qs |
|
808 (proof, assums, |
|
809 patches |>> cons (contra_l, (l :: co_ls, ss))) |
|
810 |>> cons (if member (op =) (fst (snd patches)) l then |
|
811 Assume (l, negate_term t) |
|
812 else |
|
813 Have (qs, l, negate_term t, |
|
814 ByMetis (backpatch_label patches l))) |
|
815 | (contra_ls as _ :: _, co_ls) => |
|
816 let |
|
817 val proofs = |
|
818 map_filter |
|
819 (fn l => |
|
820 if member (op =) concl_ls l then |
|
821 NONE |
|
822 else |
|
823 let |
|
824 val drop_ls = filter (curry (op <>) l) contra_ls |
|
825 in |
|
826 second_pass [] |
|
827 (proof, assums, |
|
828 patches ||> apfst (insert (op =) l) |
|
829 ||> apsnd (union (op =) drop_ls)) |
|
830 |> fst |> SOME |
|
831 end) contra_ls |
|
832 val (assumes, facts) = |
|
833 if member (op =) (fst (snd patches)) l then |
|
834 ([Assume (l, negate_term t)], (l :: co_ls, ss)) |
|
835 else |
|
836 ([], (co_ls, ss)) |
|
837 in |
|
838 (case join_proofs proofs of |
|
839 SOME (l, t, proofs, proof_tail) => |
|
840 Have (case_split_qualifiers proofs @ |
|
841 (if null proof_tail then end_qs else []), l, t, |
|
842 smart_case_split proofs facts) :: proof_tail |
|
843 | NONE => |
|
844 [Have (case_split_qualifiers proofs @ end_qs, no_label, |
|
845 concl_t, smart_case_split proofs facts)], |
|
846 patches) |
|
847 |>> append assumes |
|
848 end |
|
849 | _ => raise Fail "malformed proof") |
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850 | second_pass _ _ = raise Fail "malformed proof" |
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851 val proof_bottom = |
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852 second_pass [Show] (contra_proof, [], ([], ([], []))) |> fst |
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853 in proof_top @ proof_bottom end |
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854 |
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855 (* FIXME: Still needed? Probably not. *) |
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856 val kill_duplicate_assumptions_in_proof = |
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857 let |
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858 fun relabel_facts subst = |
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859 apfst (map (fn l => AList.lookup (op =) subst l |> the_default l)) |
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860 fun do_step (step as Assume (l, t)) (proof, subst, assums) = |
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861 (case AList.lookup (op aconv) assums t of |
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862 SOME l' => (proof, (l, l') :: subst, assums) |
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863 | NONE => (step :: proof, subst, (t, l) :: assums)) |
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864 | do_step (Have (qs, l, t, by)) (proof, subst, assums) = |
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865 (Have (qs, l, t, |
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866 case by of |
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867 ByMetis facts => ByMetis (relabel_facts subst facts) |
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868 | CaseSplit (proofs, facts) => |
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869 CaseSplit (map do_proof proofs, relabel_facts subst facts)) :: |
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870 proof, subst, assums) |
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871 | do_step step (proof, subst, assums) = (step :: proof, subst, assums) |
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872 and do_proof proof = fold do_step proof ([], [], []) |> #1 |> rev |
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873 in do_proof end |
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874 |
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875 val then_chain_proof = |
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876 let |
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877 fun aux _ [] = [] |
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878 | aux _ ((step as Assume (l, _)) :: proof) = step :: aux l proof |
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879 | aux l' (Have (qs, l, t, by) :: proof) = |
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880 (case by of |
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881 ByMetis (ls, ss) => |
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882 Have (if member (op =) ls l' then |
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883 (Then :: qs, l, t, |
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884 ByMetis (filter_out (curry (op =) l') ls, ss)) |
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885 else |
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886 (qs, l, t, ByMetis (ls, ss))) |
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887 | CaseSplit (proofs, facts) => |
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888 Have (qs, l, t, CaseSplit (map (aux no_label) proofs, facts))) :: |
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889 aux l proof |
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890 | aux _ (step :: proof) = step :: aux no_label proof |
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891 in aux no_label end |
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892 |
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893 fun kill_useless_labels_in_proof proof = |
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894 let |
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895 val used_ls = used_labels_of proof |
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896 fun do_label l = if member (op =) used_ls l then l else no_label |
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897 fun do_step (Assume (l, t)) = Assume (do_label l, t) |
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898 | do_step (Have (qs, l, t, by)) = |
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899 Have (qs, do_label l, t, |
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900 case by of |
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901 CaseSplit (proofs, facts) => |
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902 CaseSplit (map (map do_step) proofs, facts) |
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903 | _ => by) |
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904 | do_step step = step |
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905 in map do_step proof end |
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906 |
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907 fun prefix_for_depth n = replicate_string (n + 1) |
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908 |
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909 val relabel_proof = |
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910 let |
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911 fun aux _ _ _ [] = [] |
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912 | aux subst depth (next_assum, next_fact) (Assume (l, t) :: proof) = |
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913 if l = no_label then |
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914 Assume (l, t) :: aux subst depth (next_assum, next_fact) proof |
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915 else |
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916 let val l' = (prefix_for_depth depth assum_prefix, next_assum) in |
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917 Assume (l', t) :: |
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918 aux ((l, l') :: subst) depth (next_assum + 1, next_fact) proof |
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919 end |
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920 | aux subst depth (next_assum, next_fact) (Have (qs, l, t, by) :: proof) = |
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921 let |
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922 val (l', subst, next_fact) = |
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923 if l = no_label then |
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924 (l, subst, next_fact) |
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925 else |
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926 let |
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927 val l' = (prefix_for_depth depth fact_prefix, next_fact) |
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928 in (l', (l, l') :: subst, next_fact + 1) end |
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929 val relabel_facts = |
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930 apfst (map (fn l => |
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931 case AList.lookup (op =) subst l of |
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932 SOME l' => l' |
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933 | NONE => raise Fail ("unknown label " ^ |
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934 quote (string_for_label l)))) |
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935 val by = |
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936 case by of |
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937 ByMetis facts => ByMetis (relabel_facts facts) |
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938 | CaseSplit (proofs, facts) => |
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939 CaseSplit (map (aux subst (depth + 1) (1, 1)) proofs, |
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940 relabel_facts facts) |
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941 in |
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942 Have (qs, l', t, by) :: |
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943 aux subst depth (next_assum, next_fact) proof |
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944 end |
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945 | aux subst depth nextp (step :: proof) = |
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946 step :: aux subst depth nextp proof |
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947 in aux [] 0 (1, 1) end |
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948 |
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949 fun string_for_proof ctxt full_types i n = |
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950 let |
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951 fun fix_print_mode f x = |
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952 setmp_CRITICAL show_no_free_types true |
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953 (setmp_CRITICAL show_types true |
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954 (Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN) |
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955 (print_mode_value ())) f)) x |
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956 fun do_indent ind = replicate_string (ind * indent_size) " " |
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957 fun do_free (s, T) = |
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958 maybe_quote s ^ " :: " ^ |
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959 maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T) |
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960 fun do_label l = if l = no_label then "" else string_for_label l ^ ": " |
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961 fun do_have qs = |
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962 (if member (op =) qs Moreover then "moreover " else "") ^ |
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963 (if member (op =) qs Ultimately then "ultimately " else "") ^ |
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964 (if member (op =) qs Then then |
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965 if member (op =) qs Show then "thus" else "hence" |
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966 else |
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967 if member (op =) qs Show then "show" else "have") |
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968 val do_term = maybe_quote o fix_print_mode (Syntax.string_of_term ctxt) |
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969 fun do_facts (ls, ss) = |
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970 metis_command full_types 1 1 |
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971 (ls |> sort_distinct (prod_ord string_ord int_ord), |
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972 ss |> sort_distinct string_ord) |
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973 and do_step ind (Fix xs) = |
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974 do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n" |
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975 | do_step ind (Let (t1, t2)) = |
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976 do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n" |
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977 | do_step ind (Assume (l, t)) = |
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978 do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n" |
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979 | do_step ind (Have (qs, l, t, ByMetis facts)) = |
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980 do_indent ind ^ do_have qs ^ " " ^ |
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981 do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n" |
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982 | do_step ind (Have (qs, l, t, CaseSplit (proofs, facts))) = |
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983 space_implode (do_indent ind ^ "moreover\n") |
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984 (map (do_block ind) proofs) ^ |
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985 do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^ |
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986 do_facts facts ^ "\n" |
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987 and do_steps prefix suffix ind steps = |
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988 let val s = implode (map (do_step ind) steps) in |
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989 replicate_string (ind * indent_size - size prefix) " " ^ prefix ^ |
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990 String.extract (s, ind * indent_size, |
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991 SOME (size s - ind * indent_size - 1)) ^ |
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992 suffix ^ "\n" |
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993 end |
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994 and do_block ind proof = do_steps "{ " " }" (ind + 1) proof |
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995 (* One-step proofs are pointless; better use the Metis one-liner |
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996 directly. *) |
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997 and do_proof [Have (_, _, _, ByMetis _)] = "" |
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998 | do_proof proof = |
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999 (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^ |
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1000 do_indent 0 ^ "proof -\n" ^ |
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1001 do_steps "" "" 1 proof ^ |
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1002 do_indent 0 ^ (if n <> 1 then "next" else "qed") |
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1003 in do_proof end |
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1004 |
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1005 fun isar_proof_text (pool, debug, isar_shrink_factor, ctxt, conjecture_shape) |
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1006 (other_params as (full_types, _, atp_proof, axiom_names, |
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1007 goal, i)) = |
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1008 let |
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1009 val (params, hyp_ts, concl_t) = strip_subgoal goal i |
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1010 val frees = fold Term.add_frees (concl_t :: hyp_ts) [] |
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1011 val tfrees = fold Term.add_tfrees (concl_t :: hyp_ts) [] |
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1012 val n = Logic.count_prems (prop_of goal) |
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1013 val (one_line_proof, lemma_names) = metis_proof_text other_params |
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1014 fun isar_proof_for () = |
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1015 case proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor |
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1016 atp_proof conjecture_shape axiom_names params |
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1017 frees |
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1018 |> redirect_proof conjecture_shape hyp_ts concl_t |
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1019 |> kill_duplicate_assumptions_in_proof |
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1020 |> then_chain_proof |
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1021 |> kill_useless_labels_in_proof |
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1022 |> relabel_proof |
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1023 |> string_for_proof ctxt full_types i n of |
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1024 "" => "\nNo structured proof available." |
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1025 | proof => "\n\nStructured proof:\n" ^ Markup.markup Markup.sendback proof |
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1026 val isar_proof = |
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1027 if debug then |
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1028 isar_proof_for () |
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1029 else |
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1030 try isar_proof_for () |
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1031 |> the_default "\nWarning: The Isar proof construction failed." |
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1032 in (one_line_proof ^ isar_proof, lemma_names) end |
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1033 |
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1034 fun proof_text isar_proof isar_params other_params = |
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1035 (if isar_proof then isar_proof_text isar_params else metis_proof_text) |
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1036 other_params |
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1037 |
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1038 end; |
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