1 (* Title: HOL/Tools/ATP/atp_translate.ML |
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2 Author: Fabian Immler, TU Muenchen |
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3 Author: Makarius |
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4 Author: Jasmin Blanchette, TU Muenchen |
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5 |
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6 Translation of HOL to FOL for Metis and Sledgehammer. |
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7 *) |
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8 |
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9 signature ATP_TRANSLATE = |
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10 sig |
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11 type ('a, 'b) ho_term = ('a, 'b) ATP_Problem.ho_term |
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12 type connective = ATP_Problem.connective |
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13 type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula |
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14 type atp_format = ATP_Problem.atp_format |
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15 type formula_kind = ATP_Problem.formula_kind |
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16 type 'a problem = 'a ATP_Problem.problem |
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17 |
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18 datatype locality = |
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19 General | Helper | Induction | Intro | Elim | Simp | Local | Assum | Chained |
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20 |
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21 datatype polymorphism = Polymorphic | Raw_Monomorphic | Mangled_Monomorphic |
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22 datatype soundness = Sound_Modulo_Infinity | Sound |
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23 datatype granularity = All_Vars | Positively_Naked_Vars | Ghost_Type_Arg_Vars |
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24 datatype type_level = |
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25 All_Types | |
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26 Noninf_Nonmono_Types of soundness * granularity | |
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27 Fin_Nonmono_Types of granularity | |
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28 Const_Arg_Types | |
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29 No_Types |
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30 type type_enc |
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31 |
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32 val type_tag_idempotence : bool Config.T |
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33 val type_tag_arguments : bool Config.T |
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34 val no_lamsN : string |
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35 val hide_lamsN : string |
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36 val lam_liftingN : string |
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37 val combinatorsN : string |
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38 val hybrid_lamsN : string |
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39 val keep_lamsN : string |
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40 val schematic_var_prefix : string |
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41 val fixed_var_prefix : string |
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42 val tvar_prefix : string |
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43 val tfree_prefix : string |
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44 val const_prefix : string |
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45 val type_const_prefix : string |
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46 val class_prefix : string |
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47 val lam_lifted_prefix : string |
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48 val lam_lifted_mono_prefix : string |
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49 val lam_lifted_poly_prefix : string |
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50 val skolem_const_prefix : string |
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51 val old_skolem_const_prefix : string |
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52 val new_skolem_const_prefix : string |
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53 val combinator_prefix : string |
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54 val type_decl_prefix : string |
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55 val sym_decl_prefix : string |
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56 val guards_sym_formula_prefix : string |
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57 val tags_sym_formula_prefix : string |
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58 val fact_prefix : string |
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59 val conjecture_prefix : string |
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60 val helper_prefix : string |
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61 val class_rel_clause_prefix : string |
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62 val arity_clause_prefix : string |
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63 val tfree_clause_prefix : string |
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64 val lam_fact_prefix : string |
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65 val typed_helper_suffix : string |
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66 val untyped_helper_suffix : string |
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67 val type_tag_idempotence_helper_name : string |
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68 val predicator_name : string |
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69 val app_op_name : string |
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70 val type_guard_name : string |
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71 val type_tag_name : string |
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72 val simple_type_prefix : string |
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73 val prefixed_predicator_name : string |
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74 val prefixed_app_op_name : string |
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75 val prefixed_type_tag_name : string |
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76 val ascii_of : string -> string |
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77 val unascii_of : string -> string |
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78 val unprefix_and_unascii : string -> string -> string option |
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79 val proxy_table : (string * (string * (thm * (string * string)))) list |
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80 val proxify_const : string -> (string * string) option |
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81 val invert_const : string -> string |
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82 val unproxify_const : string -> string |
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83 val new_skolem_var_name_from_const : string -> string |
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84 val atp_irrelevant_consts : string list |
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85 val atp_schematic_consts_of : term -> typ list Symtab.table |
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86 val is_type_enc_higher_order : type_enc -> bool |
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87 val polymorphism_of_type_enc : type_enc -> polymorphism |
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88 val level_of_type_enc : type_enc -> type_level |
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89 val is_type_enc_quasi_sound : type_enc -> bool |
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90 val is_type_enc_fairly_sound : type_enc -> bool |
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91 val type_enc_from_string : soundness -> string -> type_enc |
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92 val adjust_type_enc : atp_format -> type_enc -> type_enc |
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93 val mk_aconns : |
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94 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula |
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95 val unmangled_const : string -> string * (string, 'b) ho_term list |
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96 val unmangled_const_name : string -> string |
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97 val helper_table : ((string * bool) * thm list) list |
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98 val trans_lams_from_string : |
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99 Proof.context -> type_enc -> string -> term list -> term list * term list |
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100 val factsN : string |
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101 val prepare_atp_problem : |
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102 Proof.context -> atp_format -> formula_kind -> formula_kind -> type_enc |
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103 -> bool -> string -> bool -> bool -> term list -> term |
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104 -> ((string * locality) * term) list |
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105 -> string problem * string Symtab.table * (string * locality) list vector |
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106 * (string * term) list * int Symtab.table |
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107 val atp_problem_weights : string problem -> (string * real) list |
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108 end; |
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109 |
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110 structure ATP_Translate : ATP_TRANSLATE = |
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111 struct |
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112 |
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113 open ATP_Util |
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114 open ATP_Problem |
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115 |
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116 type name = string * string |
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117 |
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118 val type_tag_idempotence = |
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119 Attrib.setup_config_bool @{binding atp_type_tag_idempotence} (K false) |
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120 val type_tag_arguments = |
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121 Attrib.setup_config_bool @{binding atp_type_tag_arguments} (K false) |
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122 |
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123 val no_lamsN = "no_lams" (* used internally; undocumented *) |
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124 val hide_lamsN = "hide_lams" |
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125 val lam_liftingN = "lam_lifting" |
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126 val combinatorsN = "combinators" |
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127 val hybrid_lamsN = "hybrid_lams" |
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128 val keep_lamsN = "keep_lams" |
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129 |
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130 (* It's still unclear whether all TFF1 implementations will support type |
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131 signatures such as "!>[A : $tType] : $o", with ghost type variables. *) |
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132 val avoid_first_order_ghost_type_vars = false |
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133 |
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134 val bound_var_prefix = "B_" |
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135 val all_bound_var_prefix = "BA_" |
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136 val exist_bound_var_prefix = "BE_" |
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137 val schematic_var_prefix = "V_" |
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138 val fixed_var_prefix = "v_" |
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139 val tvar_prefix = "T_" |
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140 val tfree_prefix = "t_" |
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141 val const_prefix = "c_" |
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142 val type_const_prefix = "tc_" |
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143 val simple_type_prefix = "s_" |
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144 val class_prefix = "cl_" |
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145 |
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146 (* Freshness almost guaranteed! *) |
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147 val atp_weak_prefix = "ATP:" |
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148 |
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149 val lam_lifted_prefix = atp_weak_prefix ^ "Lam" |
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150 val lam_lifted_mono_prefix = lam_lifted_prefix ^ "m" |
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151 val lam_lifted_poly_prefix = lam_lifted_prefix ^ "p" |
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152 |
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153 val skolem_const_prefix = "ATP" ^ Long_Name.separator ^ "Sko" |
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154 val old_skolem_const_prefix = skolem_const_prefix ^ "o" |
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155 val new_skolem_const_prefix = skolem_const_prefix ^ "n" |
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156 |
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157 val combinator_prefix = "COMB" |
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158 |
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159 val type_decl_prefix = "ty_" |
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160 val sym_decl_prefix = "sy_" |
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161 val guards_sym_formula_prefix = "gsy_" |
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162 val tags_sym_formula_prefix = "tsy_" |
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163 val fact_prefix = "fact_" |
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164 val conjecture_prefix = "conj_" |
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165 val helper_prefix = "help_" |
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166 val class_rel_clause_prefix = "clar_" |
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167 val arity_clause_prefix = "arity_" |
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168 val tfree_clause_prefix = "tfree_" |
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169 |
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170 val lam_fact_prefix = "ATP.lambda_" |
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171 val typed_helper_suffix = "_T" |
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172 val untyped_helper_suffix = "_U" |
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173 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem" |
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174 |
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175 val predicator_name = "pp" |
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176 val app_op_name = "aa" |
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177 val type_guard_name = "gg" |
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178 val type_tag_name = "tt" |
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179 |
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180 val prefixed_predicator_name = const_prefix ^ predicator_name |
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181 val prefixed_app_op_name = const_prefix ^ app_op_name |
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182 val prefixed_type_tag_name = const_prefix ^ type_tag_name |
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183 |
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184 (*Escaping of special characters. |
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185 Alphanumeric characters are left unchanged. |
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186 The character _ goes to __ |
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187 Characters in the range ASCII space to / go to _A to _P, respectively. |
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188 Other characters go to _nnn where nnn is the decimal ASCII code.*) |
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189 val upper_a_minus_space = Char.ord #"A" - Char.ord #" " |
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190 |
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191 fun stringN_of_int 0 _ = "" |
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192 | stringN_of_int k n = |
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193 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10) |
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194 |
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195 fun ascii_of_char c = |
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196 if Char.isAlphaNum c then |
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197 String.str c |
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198 else if c = #"_" then |
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199 "__" |
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200 else if #" " <= c andalso c <= #"/" then |
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201 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space)) |
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202 else |
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203 (* fixed width, in case more digits follow *) |
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204 "_" ^ stringN_of_int 3 (Char.ord c) |
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205 |
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206 val ascii_of = String.translate ascii_of_char |
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207 |
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208 (** Remove ASCII armoring from names in proof files **) |
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209 |
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210 (* We don't raise error exceptions because this code can run inside a worker |
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211 thread. Also, the errors are impossible. *) |
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212 val unascii_of = |
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213 let |
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214 fun un rcs [] = String.implode(rev rcs) |
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215 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *) |
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216 (* Three types of _ escapes: __, _A to _P, _nnn *) |
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217 | un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs |
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218 | un rcs (#"_" :: c :: cs) = |
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219 if #"A" <= c andalso c<= #"P" then |
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220 (* translation of #" " to #"/" *) |
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221 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs |
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222 else |
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223 let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in |
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224 case Int.fromString (String.implode digits) of |
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225 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2)) |
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226 | NONE => un (c :: #"_" :: rcs) cs (* ERROR *) |
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227 end |
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228 | un rcs (c :: cs) = un (c :: rcs) cs |
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229 in un [] o String.explode end |
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230 |
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231 (* If string s has the prefix s1, return the result of deleting it, |
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232 un-ASCII'd. *) |
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233 fun unprefix_and_unascii s1 s = |
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234 if String.isPrefix s1 s then |
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235 SOME (unascii_of (String.extract (s, size s1, NONE))) |
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236 else |
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237 NONE |
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238 |
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239 val proxy_table = |
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240 [("c_False", (@{const_name False}, (@{thm fFalse_def}, |
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241 ("fFalse", @{const_name ATP.fFalse})))), |
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242 ("c_True", (@{const_name True}, (@{thm fTrue_def}, |
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243 ("fTrue", @{const_name ATP.fTrue})))), |
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244 ("c_Not", (@{const_name Not}, (@{thm fNot_def}, |
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245 ("fNot", @{const_name ATP.fNot})))), |
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246 ("c_conj", (@{const_name conj}, (@{thm fconj_def}, |
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247 ("fconj", @{const_name ATP.fconj})))), |
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248 ("c_disj", (@{const_name disj}, (@{thm fdisj_def}, |
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249 ("fdisj", @{const_name ATP.fdisj})))), |
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250 ("c_implies", (@{const_name implies}, (@{thm fimplies_def}, |
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251 ("fimplies", @{const_name ATP.fimplies})))), |
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252 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def}, |
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253 ("fequal", @{const_name ATP.fequal})))), |
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254 ("c_All", (@{const_name All}, (@{thm fAll_def}, |
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255 ("fAll", @{const_name ATP.fAll})))), |
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256 ("c_Ex", (@{const_name Ex}, (@{thm fEx_def}, |
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257 ("fEx", @{const_name ATP.fEx}))))] |
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258 |
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259 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd) |
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260 |
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261 (* Readable names for the more common symbolic functions. Do not mess with the |
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262 table unless you know what you are doing. *) |
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263 val const_trans_table = |
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264 [(@{type_name Product_Type.prod}, "prod"), |
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265 (@{type_name Sum_Type.sum}, "sum"), |
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266 (@{const_name False}, "False"), |
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267 (@{const_name True}, "True"), |
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268 (@{const_name Not}, "Not"), |
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269 (@{const_name conj}, "conj"), |
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270 (@{const_name disj}, "disj"), |
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271 (@{const_name implies}, "implies"), |
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272 (@{const_name HOL.eq}, "equal"), |
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273 (@{const_name All}, "All"), |
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274 (@{const_name Ex}, "Ex"), |
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275 (@{const_name If}, "If"), |
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276 (@{const_name Set.member}, "member"), |
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277 (@{const_name Meson.COMBI}, combinator_prefix ^ "I"), |
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278 (@{const_name Meson.COMBK}, combinator_prefix ^ "K"), |
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279 (@{const_name Meson.COMBB}, combinator_prefix ^ "B"), |
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280 (@{const_name Meson.COMBC}, combinator_prefix ^ "C"), |
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281 (@{const_name Meson.COMBS}, combinator_prefix ^ "S")] |
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282 |> Symtab.make |
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283 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table |
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284 |
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285 (* Invert the table of translations between Isabelle and ATPs. *) |
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286 val const_trans_table_inv = |
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287 const_trans_table |> Symtab.dest |> map swap |> Symtab.make |
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288 val const_trans_table_unprox = |
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289 Symtab.empty |
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290 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table |
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291 |
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292 val invert_const = perhaps (Symtab.lookup const_trans_table_inv) |
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293 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox) |
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294 |
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295 fun lookup_const c = |
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296 case Symtab.lookup const_trans_table c of |
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297 SOME c' => c' |
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298 | NONE => ascii_of c |
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299 |
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300 fun ascii_of_indexname (v, 0) = ascii_of v |
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301 | ascii_of_indexname (v, i) = ascii_of v ^ "_" ^ string_of_int i |
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302 |
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303 fun make_bound_var x = bound_var_prefix ^ ascii_of x |
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304 fun make_all_bound_var x = all_bound_var_prefix ^ ascii_of x |
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305 fun make_exist_bound_var x = exist_bound_var_prefix ^ ascii_of x |
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306 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v |
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307 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x |
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308 |
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309 fun make_schematic_type_var (x, i) = |
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310 tvar_prefix ^ (ascii_of_indexname (unprefix "'" x, i)) |
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311 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x)) |
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312 |
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313 (* "HOL.eq" and choice are mapped to the ATP's equivalents *) |
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314 local |
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315 val choice_const = (fst o dest_Const o HOLogic.choice_const) Term.dummyT |
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316 fun default c = const_prefix ^ lookup_const c |
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317 in |
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318 fun make_fixed_const _ @{const_name HOL.eq} = tptp_old_equal |
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319 | make_fixed_const (SOME (THF (_, _, THF_With_Choice))) c = |
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320 if c = choice_const then tptp_choice else default c |
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321 | make_fixed_const _ c = default c |
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322 end |
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323 |
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324 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c |
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325 |
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326 fun make_type_class clas = class_prefix ^ ascii_of clas |
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327 |
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328 fun new_skolem_var_name_from_const s = |
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329 let val ss = s |> space_explode Long_Name.separator in |
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330 nth ss (length ss - 2) |
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331 end |
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332 |
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333 (* These are either simplified away by "Meson.presimplify" (most of the time) or |
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334 handled specially via "fFalse", "fTrue", ..., "fequal". *) |
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335 val atp_irrelevant_consts = |
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336 [@{const_name False}, @{const_name True}, @{const_name Not}, |
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337 @{const_name conj}, @{const_name disj}, @{const_name implies}, |
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338 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}] |
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339 |
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340 val atp_monomorph_bad_consts = |
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341 atp_irrelevant_consts @ |
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342 (* These are ignored anyway by the relevance filter (unless they appear in |
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343 higher-order places) but not by the monomorphizer. *) |
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344 [@{const_name all}, @{const_name "==>"}, @{const_name "=="}, |
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345 @{const_name Trueprop}, @{const_name All}, @{const_name Ex}, |
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346 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}] |
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347 |
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348 fun add_schematic_const (x as (_, T)) = |
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349 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x |
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350 val add_schematic_consts_of = |
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351 Term.fold_aterms (fn Const (x as (s, _)) => |
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352 not (member (op =) atp_monomorph_bad_consts s) |
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353 ? add_schematic_const x |
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354 | _ => I) |
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355 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty |
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356 |
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357 (** Definitions and functions for FOL clauses and formulas for TPTP **) |
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358 |
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359 (** Isabelle arities **) |
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360 |
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361 type arity_atom = name * name * name list |
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362 |
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363 val type_class = the_single @{sort type} |
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364 |
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365 type arity_clause = |
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366 {name : string, |
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367 prem_atoms : arity_atom list, |
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368 concl_atom : arity_atom} |
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369 |
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370 fun add_prem_atom tvar = |
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371 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar, [])) |
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372 |
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373 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *) |
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374 fun make_axiom_arity_clause (tcons, name, (cls, args)) = |
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375 let |
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376 val tvars = map (prefix tvar_prefix o string_of_int) (1 upto length args) |
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377 val tvars_srts = ListPair.zip (tvars, args) |
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378 in |
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379 {name = name, |
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380 prem_atoms = [] |> fold (uncurry add_prem_atom) tvars_srts, |
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381 concl_atom = (`make_type_class cls, `make_fixed_type_const tcons, |
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382 tvars ~~ tvars)} |
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383 end |
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384 |
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385 fun arity_clause _ _ (_, []) = [] |
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386 | arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *) |
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387 arity_clause seen n (tcons, ars) |
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388 | arity_clause seen n (tcons, (ar as (class, _)) :: ars) = |
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389 if member (op =) seen class then |
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390 (* multiple arities for the same (tycon, class) pair *) |
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391 make_axiom_arity_clause (tcons, |
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392 lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n, |
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393 ar) :: |
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394 arity_clause seen (n + 1) (tcons, ars) |
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395 else |
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396 make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^ |
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397 ascii_of class, ar) :: |
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398 arity_clause (class :: seen) n (tcons, ars) |
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399 |
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400 fun multi_arity_clause [] = [] |
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401 | multi_arity_clause ((tcons, ars) :: tc_arlists) = |
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402 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists |
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403 |
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404 (* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in |
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405 theory thy provided its arguments have the corresponding sorts. *) |
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406 fun type_class_pairs thy tycons classes = |
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407 let |
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408 val alg = Sign.classes_of thy |
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409 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single |
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410 fun add_class tycon class = |
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411 cons (class, domain_sorts tycon class) |
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412 handle Sorts.CLASS_ERROR _ => I |
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413 fun try_classes tycon = (tycon, fold (add_class tycon) classes []) |
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414 in map try_classes tycons end |
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415 |
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416 (*Proving one (tycon, class) membership may require proving others, so iterate.*) |
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417 fun iter_type_class_pairs _ _ [] = ([], []) |
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418 | iter_type_class_pairs thy tycons classes = |
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419 let |
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420 fun maybe_insert_class s = |
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421 (s <> type_class andalso not (member (op =) classes s)) |
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422 ? insert (op =) s |
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423 val cpairs = type_class_pairs thy tycons classes |
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424 val newclasses = |
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425 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs |
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426 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses |
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427 in (classes' @ classes, union (op =) cpairs' cpairs) end |
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428 |
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429 fun make_arity_clauses thy tycons = |
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430 iter_type_class_pairs thy tycons ##> multi_arity_clause |
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431 |
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432 |
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433 (** Isabelle class relations **) |
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434 |
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435 type class_rel_clause = |
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436 {name : string, |
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437 subclass : name, |
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438 superclass : name} |
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439 |
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440 (* Generate all pairs (sub, super) such that sub is a proper subclass of super |
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441 in theory "thy". *) |
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442 fun class_pairs _ [] _ = [] |
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443 | class_pairs thy subs supers = |
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444 let |
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445 val class_less = Sorts.class_less (Sign.classes_of thy) |
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446 fun add_super sub super = class_less (sub, super) ? cons (sub, super) |
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447 fun add_supers sub = fold (add_super sub) supers |
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448 in fold add_supers subs [] end |
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449 |
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450 fun make_class_rel_clause (sub, super) = |
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451 {name = sub ^ "_" ^ super, subclass = `make_type_class sub, |
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452 superclass = `make_type_class super} |
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453 |
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454 fun make_class_rel_clauses thy subs supers = |
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455 map make_class_rel_clause (class_pairs thy subs supers) |
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456 |
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457 (* intermediate terms *) |
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458 datatype iterm = |
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459 IConst of name * typ * typ list | |
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460 IVar of name * typ | |
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461 IApp of iterm * iterm | |
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462 IAbs of (name * typ) * iterm |
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463 |
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464 fun ityp_of (IConst (_, T, _)) = T |
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465 | ityp_of (IVar (_, T)) = T |
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466 | ityp_of (IApp (t1, _)) = snd (dest_funT (ityp_of t1)) |
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467 | ityp_of (IAbs ((_, T), tm)) = T --> ityp_of tm |
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468 |
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469 (*gets the head of a combinator application, along with the list of arguments*) |
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470 fun strip_iterm_comb u = |
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471 let |
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472 fun stripc (IApp (t, u), ts) = stripc (t, u :: ts) |
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473 | stripc x = x |
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474 in stripc (u, []) end |
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475 |
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476 fun atomic_types_of T = fold_atyps (insert (op =)) T [] |
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477 |
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478 val tvar_a_str = "'a" |
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479 val tvar_a = TVar ((tvar_a_str, 0), HOLogic.typeS) |
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480 val tvar_a_name = (make_schematic_type_var (tvar_a_str, 0), tvar_a_str) |
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481 val itself_name = `make_fixed_type_const @{type_name itself} |
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482 val TYPE_name = `(make_fixed_const NONE) @{const_name TYPE} |
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483 val tvar_a_atype = AType (tvar_a_name, []) |
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484 val a_itself_atype = AType (itself_name, [tvar_a_atype]) |
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485 |
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486 fun new_skolem_const_name s num_T_args = |
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487 [new_skolem_const_prefix, s, string_of_int num_T_args] |
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488 |> space_implode Long_Name.separator |
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489 |
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490 fun robust_const_type thy s = |
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491 if s = app_op_name then |
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492 Logic.varifyT_global @{typ "('a => 'b) => 'a => 'b"} |
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493 else if String.isPrefix lam_lifted_prefix s then |
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494 Logic.varifyT_global @{typ "'a => 'b"} |
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495 else |
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496 (* Old Skolems throw a "TYPE" exception here, which will be caught. *) |
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497 s |> Sign.the_const_type thy |
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498 |
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499 (* This function only makes sense if "T" is as general as possible. *) |
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500 fun robust_const_typargs thy (s, T) = |
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501 if s = app_op_name then |
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502 let val (T1, T2) = T |> domain_type |> dest_funT in [T1, T2] end |
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503 else if String.isPrefix old_skolem_const_prefix s then |
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504 [] |> Term.add_tvarsT T |> rev |> map TVar |
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505 else if String.isPrefix lam_lifted_prefix s then |
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506 if String.isPrefix lam_lifted_poly_prefix s then |
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507 let val (T1, T2) = T |> dest_funT in [T1, T2] end |
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508 else |
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509 [] |
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510 else |
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511 (s, T) |> Sign.const_typargs thy |
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512 |
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513 (* Converts an Isabelle/HOL term (with combinators) into an intermediate term. |
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514 Also accumulates sort infomation. *) |
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515 fun iterm_from_term thy format bs (P $ Q) = |
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516 let |
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517 val (P', P_atomics_Ts) = iterm_from_term thy format bs P |
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518 val (Q', Q_atomics_Ts) = iterm_from_term thy format bs Q |
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519 in (IApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end |
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520 | iterm_from_term thy format _ (Const (c, T)) = |
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521 (IConst (`(make_fixed_const (SOME format)) c, T, |
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522 robust_const_typargs thy (c, T)), |
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523 atomic_types_of T) |
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524 | iterm_from_term _ _ _ (Free (s, T)) = |
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525 (IConst (`make_fixed_var s, T, []), atomic_types_of T) |
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526 | iterm_from_term _ format _ (Var (v as (s, _), T)) = |
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527 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then |
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528 let |
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529 val Ts = T |> strip_type |> swap |> op :: |
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530 val s' = new_skolem_const_name s (length Ts) |
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531 in IConst (`(make_fixed_const (SOME format)) s', T, Ts) end |
|
532 else |
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533 IVar ((make_schematic_var v, s), T), atomic_types_of T) |
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534 | iterm_from_term _ _ bs (Bound j) = |
|
535 nth bs j |> (fn (_, (name, T)) => (IConst (name, T, []), atomic_types_of T)) |
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536 | iterm_from_term thy format bs (Abs (s, T, t)) = |
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537 let |
|
538 fun vary s = s |> AList.defined (op =) bs s ? vary o Symbol.bump_string |
|
539 val s = vary s |
|
540 val name = `make_bound_var s |
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541 val (tm, atomic_Ts) = iterm_from_term thy format ((s, (name, T)) :: bs) t |
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542 in (IAbs ((name, T), tm), union (op =) atomic_Ts (atomic_types_of T)) end |
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543 |
|
544 datatype locality = |
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545 General | Helper | Induction | Intro | Elim | Simp | Local | Assum | Chained |
|
546 |
|
547 datatype order = First_Order | Higher_Order |
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548 datatype polymorphism = Polymorphic | Raw_Monomorphic | Mangled_Monomorphic |
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549 datatype soundness = Sound_Modulo_Infinity | Sound |
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550 datatype granularity = All_Vars | Positively_Naked_Vars | Ghost_Type_Arg_Vars |
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551 datatype type_level = |
|
552 All_Types | |
|
553 Noninf_Nonmono_Types of soundness * granularity | |
|
554 Fin_Nonmono_Types of granularity | |
|
555 Const_Arg_Types | |
|
556 No_Types |
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557 |
|
558 datatype type_enc = |
|
559 Simple_Types of order * polymorphism * type_level | |
|
560 Guards of polymorphism * type_level | |
|
561 Tags of polymorphism * type_level |
|
562 |
|
563 fun is_type_enc_higher_order (Simple_Types (Higher_Order, _, _)) = true |
|
564 | is_type_enc_higher_order _ = false |
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565 |
|
566 fun polymorphism_of_type_enc (Simple_Types (_, poly, _)) = poly |
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567 | polymorphism_of_type_enc (Guards (poly, _)) = poly |
|
568 | polymorphism_of_type_enc (Tags (poly, _)) = poly |
|
569 |
|
570 fun level_of_type_enc (Simple_Types (_, _, level)) = level |
|
571 | level_of_type_enc (Guards (_, level)) = level |
|
572 | level_of_type_enc (Tags (_, level)) = level |
|
573 |
|
574 fun granularity_of_type_level (Noninf_Nonmono_Types (_, grain)) = grain |
|
575 | granularity_of_type_level (Fin_Nonmono_Types grain) = grain |
|
576 | granularity_of_type_level _ = All_Vars |
|
577 |
|
578 fun is_type_level_quasi_sound All_Types = true |
|
579 | is_type_level_quasi_sound (Noninf_Nonmono_Types _) = true |
|
580 | is_type_level_quasi_sound _ = false |
|
581 val is_type_enc_quasi_sound = is_type_level_quasi_sound o level_of_type_enc |
|
582 |
|
583 fun is_type_level_fairly_sound (Fin_Nonmono_Types _) = true |
|
584 | is_type_level_fairly_sound level = is_type_level_quasi_sound level |
|
585 val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc |
|
586 |
|
587 fun is_type_level_monotonicity_based (Noninf_Nonmono_Types _) = true |
|
588 | is_type_level_monotonicity_based (Fin_Nonmono_Types _) = true |
|
589 | is_type_level_monotonicity_based _ = false |
|
590 |
|
591 (* "_query", "_bang", and "_at" are for the ASCII-challenged Metis and |
|
592 Mirabelle. *) |
|
593 val queries = ["?", "_query"] |
|
594 val bangs = ["!", "_bang"] |
|
595 val ats = ["@", "_at"] |
|
596 |
|
597 fun try_unsuffixes ss s = |
|
598 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE |
|
599 |
|
600 fun try_nonmono constr suffixes fallback s = |
|
601 case try_unsuffixes suffixes s of |
|
602 SOME s => |
|
603 (case try_unsuffixes suffixes s of |
|
604 SOME s => (constr Positively_Naked_Vars, s) |
|
605 | NONE => |
|
606 case try_unsuffixes ats s of |
|
607 SOME s => (constr Ghost_Type_Arg_Vars, s) |
|
608 | NONE => (constr All_Vars, s)) |
|
609 | NONE => fallback s |
|
610 |
|
611 fun type_enc_from_string soundness s = |
|
612 (case try (unprefix "poly_") s of |
|
613 SOME s => (SOME Polymorphic, s) |
|
614 | NONE => |
|
615 case try (unprefix "raw_mono_") s of |
|
616 SOME s => (SOME Raw_Monomorphic, s) |
|
617 | NONE => |
|
618 case try (unprefix "mono_") s of |
|
619 SOME s => (SOME Mangled_Monomorphic, s) |
|
620 | NONE => (NONE, s)) |
|
621 ||> (pair All_Types |
|
622 |> try_nonmono Fin_Nonmono_Types bangs |
|
623 |> try_nonmono (curry Noninf_Nonmono_Types soundness) queries) |
|
624 |> (fn (poly, (level, core)) => |
|
625 case (core, (poly, level)) of |
|
626 ("simple", (SOME poly, _)) => |
|
627 (case (poly, level) of |
|
628 (Polymorphic, All_Types) => |
|
629 Simple_Types (First_Order, Polymorphic, All_Types) |
|
630 | (Mangled_Monomorphic, _) => |
|
631 if granularity_of_type_level level = All_Vars then |
|
632 Simple_Types (First_Order, Mangled_Monomorphic, level) |
|
633 else |
|
634 raise Same.SAME |
|
635 | _ => raise Same.SAME) |
|
636 | ("simple_higher", (SOME poly, _)) => |
|
637 (case (poly, level) of |
|
638 (Polymorphic, All_Types) => |
|
639 Simple_Types (Higher_Order, Polymorphic, All_Types) |
|
640 | (_, Noninf_Nonmono_Types _) => raise Same.SAME |
|
641 | (Mangled_Monomorphic, _) => |
|
642 if granularity_of_type_level level = All_Vars then |
|
643 Simple_Types (Higher_Order, Mangled_Monomorphic, level) |
|
644 else |
|
645 raise Same.SAME |
|
646 | _ => raise Same.SAME) |
|
647 | ("guards", (SOME poly, _)) => |
|
648 if poly = Mangled_Monomorphic andalso |
|
649 granularity_of_type_level level = Ghost_Type_Arg_Vars then |
|
650 raise Same.SAME |
|
651 else |
|
652 Guards (poly, level) |
|
653 | ("tags", (SOME poly, _)) => |
|
654 if granularity_of_type_level level = Ghost_Type_Arg_Vars then |
|
655 raise Same.SAME |
|
656 else |
|
657 Tags (poly, level) |
|
658 | ("args", (SOME poly, All_Types (* naja *))) => |
|
659 Guards (poly, Const_Arg_Types) |
|
660 | ("erased", (NONE, All_Types (* naja *))) => |
|
661 Guards (Polymorphic, No_Types) |
|
662 | _ => raise Same.SAME) |
|
663 handle Same.SAME => error ("Unknown type encoding: " ^ quote s ^ ".") |
|
664 |
|
665 fun adjust_type_enc (THF (TPTP_Monomorphic, _, _)) |
|
666 (Simple_Types (order, _, level)) = |
|
667 Simple_Types (order, Mangled_Monomorphic, level) |
|
668 | adjust_type_enc (THF _) type_enc = type_enc |
|
669 | adjust_type_enc (TFF (TPTP_Monomorphic, _)) (Simple_Types (_, _, level)) = |
|
670 Simple_Types (First_Order, Mangled_Monomorphic, level) |
|
671 | adjust_type_enc (DFG DFG_Sorted) (Simple_Types (_, _, level)) = |
|
672 Simple_Types (First_Order, Mangled_Monomorphic, level) |
|
673 | adjust_type_enc (TFF _) (Simple_Types (_, poly, level)) = |
|
674 Simple_Types (First_Order, poly, level) |
|
675 | adjust_type_enc format (Simple_Types (_, poly, level)) = |
|
676 adjust_type_enc format (Guards (poly, level)) |
|
677 | adjust_type_enc CNF_UEQ (type_enc as Guards stuff) = |
|
678 (if is_type_enc_fairly_sound type_enc then Tags else Guards) stuff |
|
679 | adjust_type_enc _ type_enc = type_enc |
|
680 |
|
681 fun constify_lifted (t $ u) = constify_lifted t $ constify_lifted u |
|
682 | constify_lifted (Abs (s, T, t)) = Abs (s, T, constify_lifted t) |
|
683 | constify_lifted (Free (x as (s, _))) = |
|
684 (if String.isPrefix lam_lifted_prefix s then Const else Free) x |
|
685 | constify_lifted t = t |
|
686 |
|
687 (* Requires bound variables not to clash with any schematic variables (as should |
|
688 be the case right after lambda-lifting). *) |
|
689 fun open_form (Const (@{const_name All}, _) $ Abs (s, T, t)) = |
|
690 let |
|
691 val names = Name.make_context (map fst (Term.add_var_names t [])) |
|
692 val (s, _) = Name.variant s names |
|
693 in open_form (subst_bound (Var ((s, 0), T), t)) end |
|
694 | open_form t = t |
|
695 |
|
696 fun lift_lams_part_1 ctxt type_enc = |
|
697 map close_form #> rpair ctxt |
|
698 #-> Lambda_Lifting.lift_lambdas |
|
699 (SOME ((if polymorphism_of_type_enc type_enc = Polymorphic then |
|
700 lam_lifted_poly_prefix |
|
701 else |
|
702 lam_lifted_mono_prefix) ^ "_a")) |
|
703 Lambda_Lifting.is_quantifier |
|
704 #> fst |
|
705 val lift_lams_part_2 = pairself (map (open_form o constify_lifted)) |
|
706 val lift_lams = lift_lams_part_2 ooo lift_lams_part_1 |
|
707 |
|
708 fun intentionalize_def (Const (@{const_name All}, _) $ Abs (_, _, t)) = |
|
709 intentionalize_def t |
|
710 | intentionalize_def (Const (@{const_name HOL.eq}, _) $ t $ u) = |
|
711 let |
|
712 fun lam T t = Abs (Name.uu, T, t) |
|
713 val (head, args) = strip_comb t ||> rev |
|
714 val head_T = fastype_of head |
|
715 val n = length args |
|
716 val arg_Ts = head_T |> binder_types |> take n |> rev |
|
717 val u = u |> subst_atomic (args ~~ map Bound (0 upto n - 1)) |
|
718 in HOLogic.eq_const head_T $ head $ fold lam arg_Ts u end |
|
719 | intentionalize_def t = t |
|
720 |
|
721 type translated_formula = |
|
722 {name : string, |
|
723 locality : locality, |
|
724 kind : formula_kind, |
|
725 iformula : (name, typ, iterm) formula, |
|
726 atomic_types : typ list} |
|
727 |
|
728 fun update_iformula f ({name, locality, kind, iformula, atomic_types} |
|
729 : translated_formula) = |
|
730 {name = name, locality = locality, kind = kind, iformula = f iformula, |
|
731 atomic_types = atomic_types} : translated_formula |
|
732 |
|
733 fun fact_lift f ({iformula, ...} : translated_formula) = f iformula |
|
734 |
|
735 fun insert_type ctxt get_T x xs = |
|
736 let val T = get_T x in |
|
737 if exists (type_instance ctxt T o get_T) xs then xs |
|
738 else x :: filter_out (type_generalization ctxt T o get_T) xs |
|
739 end |
|
740 |
|
741 (* The Booleans indicate whether all type arguments should be kept. *) |
|
742 datatype type_arg_policy = |
|
743 Explicit_Type_Args of bool (* infer_from_term_args *) | |
|
744 Mangled_Type_Args | |
|
745 No_Type_Args |
|
746 |
|
747 fun type_arg_policy monom_constrs type_enc s = |
|
748 let val poly = polymorphism_of_type_enc type_enc in |
|
749 if s = type_tag_name then |
|
750 if poly = Mangled_Monomorphic then Mangled_Type_Args |
|
751 else Explicit_Type_Args false |
|
752 else case type_enc of |
|
753 Simple_Types (_, Polymorphic, _) => Explicit_Type_Args false |
|
754 | Tags (_, All_Types) => No_Type_Args |
|
755 | _ => |
|
756 let val level = level_of_type_enc type_enc in |
|
757 if level = No_Types orelse s = @{const_name HOL.eq} orelse |
|
758 (s = app_op_name andalso level = Const_Arg_Types) then |
|
759 No_Type_Args |
|
760 else if poly = Mangled_Monomorphic then |
|
761 Mangled_Type_Args |
|
762 else if member (op =) monom_constrs s andalso |
|
763 granularity_of_type_level level = Positively_Naked_Vars then |
|
764 No_Type_Args |
|
765 else |
|
766 Explicit_Type_Args |
|
767 (level = All_Types orelse |
|
768 granularity_of_type_level level = Ghost_Type_Arg_Vars) |
|
769 end |
|
770 end |
|
771 |
|
772 (* Make atoms for sorted type variables. *) |
|
773 fun generic_add_sorts_on_type (_, []) = I |
|
774 | generic_add_sorts_on_type ((x, i), s :: ss) = |
|
775 generic_add_sorts_on_type ((x, i), ss) |
|
776 #> (if s = the_single @{sort HOL.type} then |
|
777 I |
|
778 else if i = ~1 then |
|
779 insert (op =) (`make_type_class s, `make_fixed_type_var x) |
|
780 else |
|
781 insert (op =) (`make_type_class s, |
|
782 (make_schematic_type_var (x, i), x))) |
|
783 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S) |
|
784 | add_sorts_on_tfree _ = I |
|
785 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z |
|
786 | add_sorts_on_tvar _ = I |
|
787 |
|
788 fun type_class_formula type_enc class arg = |
|
789 AAtom (ATerm (class, arg :: |
|
790 (case type_enc of |
|
791 Simple_Types (First_Order, Polymorphic, _) => |
|
792 if avoid_first_order_ghost_type_vars then [ATerm (TYPE_name, [arg])] |
|
793 else [] |
|
794 | _ => []))) |
|
795 fun formulas_for_types type_enc add_sorts_on_typ Ts = |
|
796 [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts |
|
797 |> map (fn (class, name) => |
|
798 type_class_formula type_enc class (ATerm (name, []))) |
|
799 |
|
800 fun mk_aconns c phis = |
|
801 let val (phis', phi') = split_last phis in |
|
802 fold_rev (mk_aconn c) phis' phi' |
|
803 end |
|
804 fun mk_ahorn [] phi = phi |
|
805 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi]) |
|
806 fun mk_aquant _ [] phi = phi |
|
807 | mk_aquant q xs (phi as AQuant (q', xs', phi')) = |
|
808 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi) |
|
809 | mk_aquant q xs phi = AQuant (q, xs, phi) |
|
810 |
|
811 fun close_universally add_term_vars phi = |
|
812 let |
|
813 fun add_formula_vars bounds (AQuant (_, xs, phi)) = |
|
814 add_formula_vars (map fst xs @ bounds) phi |
|
815 | add_formula_vars bounds (AConn (_, phis)) = |
|
816 fold (add_formula_vars bounds) phis |
|
817 | add_formula_vars bounds (AAtom tm) = add_term_vars bounds tm |
|
818 in mk_aquant AForall (add_formula_vars [] phi []) phi end |
|
819 |
|
820 fun add_term_vars bounds (ATerm (name as (s, _), tms)) = |
|
821 (if is_tptp_variable s andalso |
|
822 not (String.isPrefix tvar_prefix s) andalso |
|
823 not (member (op =) bounds name) then |
|
824 insert (op =) (name, NONE) |
|
825 else |
|
826 I) |
|
827 #> fold (add_term_vars bounds) tms |
|
828 | add_term_vars bounds (AAbs ((name, _), tm)) = |
|
829 add_term_vars (name :: bounds) tm |
|
830 fun close_formula_universally phi = close_universally add_term_vars phi |
|
831 |
|
832 fun add_iterm_vars bounds (IApp (tm1, tm2)) = |
|
833 fold (add_iterm_vars bounds) [tm1, tm2] |
|
834 | add_iterm_vars _ (IConst _) = I |
|
835 | add_iterm_vars bounds (IVar (name, T)) = |
|
836 not (member (op =) bounds name) ? insert (op =) (name, SOME T) |
|
837 | add_iterm_vars bounds (IAbs (_, tm)) = add_iterm_vars bounds tm |
|
838 fun close_iformula_universally phi = close_universally add_iterm_vars phi |
|
839 |
|
840 val fused_infinite_type_name = @{type_name ind} (* any infinite type *) |
|
841 val fused_infinite_type = Type (fused_infinite_type_name, []) |
|
842 |
|
843 fun tvar_name (x as (s, _)) = (make_schematic_type_var x, s) |
|
844 |
|
845 fun ho_term_from_typ format type_enc = |
|
846 let |
|
847 fun term (Type (s, Ts)) = |
|
848 ATerm (case (is_type_enc_higher_order type_enc, s) of |
|
849 (true, @{type_name bool}) => `I tptp_bool_type |
|
850 | (true, @{type_name fun}) => `I tptp_fun_type |
|
851 | _ => if s = fused_infinite_type_name andalso |
|
852 is_format_typed format then |
|
853 `I tptp_individual_type |
|
854 else |
|
855 `make_fixed_type_const s, |
|
856 map term Ts) |
|
857 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, []) |
|
858 | term (TVar (x, _)) = ATerm (tvar_name x, []) |
|
859 in term end |
|
860 |
|
861 fun ho_term_for_type_arg format type_enc T = |
|
862 if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T) |
|
863 |
|
864 (* This shouldn't clash with anything else. *) |
|
865 val mangled_type_sep = "\000" |
|
866 |
|
867 fun generic_mangled_type_name f (ATerm (name, [])) = f name |
|
868 | generic_mangled_type_name f (ATerm (name, tys)) = |
|
869 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys) |
|
870 ^ ")" |
|
871 | generic_mangled_type_name _ _ = raise Fail "unexpected type abstraction" |
|
872 |
|
873 fun mangled_type format type_enc = |
|
874 generic_mangled_type_name fst o ho_term_from_typ format type_enc |
|
875 |
|
876 fun make_simple_type s = |
|
877 if s = tptp_bool_type orelse s = tptp_fun_type orelse |
|
878 s = tptp_individual_type then |
|
879 s |
|
880 else |
|
881 simple_type_prefix ^ ascii_of s |
|
882 |
|
883 fun ho_type_from_ho_term type_enc pred_sym ary = |
|
884 let |
|
885 fun to_mangled_atype ty = |
|
886 AType ((make_simple_type (generic_mangled_type_name fst ty), |
|
887 generic_mangled_type_name snd ty), []) |
|
888 fun to_poly_atype (ATerm (name, tys)) = AType (name, map to_poly_atype tys) |
|
889 | to_poly_atype _ = raise Fail "unexpected type abstraction" |
|
890 val to_atype = |
|
891 if polymorphism_of_type_enc type_enc = Polymorphic then to_poly_atype |
|
892 else to_mangled_atype |
|
893 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1)) |
|
894 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty |
|
895 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys |
|
896 | to_fo _ _ = raise Fail "unexpected type abstraction" |
|
897 fun to_ho (ty as ATerm ((s, _), tys)) = |
|
898 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty |
|
899 | to_ho _ = raise Fail "unexpected type abstraction" |
|
900 in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end |
|
901 |
|
902 fun ho_type_from_typ format type_enc pred_sym ary = |
|
903 ho_type_from_ho_term type_enc pred_sym ary |
|
904 o ho_term_from_typ format type_enc |
|
905 |
|
906 fun mangled_const_name format type_enc T_args (s, s') = |
|
907 let |
|
908 val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc) |
|
909 fun type_suffix f g = |
|
910 fold_rev (curry (op ^) o g o prefix mangled_type_sep |
|
911 o generic_mangled_type_name f) ty_args "" |
|
912 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end |
|
913 |
|
914 val parse_mangled_ident = |
|
915 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode |
|
916 |
|
917 fun parse_mangled_type x = |
|
918 (parse_mangled_ident |
|
919 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")") |
|
920 [] >> ATerm) x |
|
921 and parse_mangled_types x = |
|
922 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x |
|
923 |
|
924 fun unmangled_type s = |
|
925 s |> suffix ")" |> raw_explode |
|
926 |> Scan.finite Symbol.stopper |
|
927 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^ |
|
928 quote s)) parse_mangled_type)) |
|
929 |> fst |
|
930 |
|
931 val unmangled_const_name = space_explode mangled_type_sep #> hd |
|
932 fun unmangled_const s = |
|
933 let val ss = space_explode mangled_type_sep s in |
|
934 (hd ss, map unmangled_type (tl ss)) |
|
935 end |
|
936 |
|
937 fun introduce_proxies_in_iterm type_enc = |
|
938 let |
|
939 fun tweak_ho_quant ho_quant T [IAbs _] = IConst (`I ho_quant, T, []) |
|
940 | tweak_ho_quant ho_quant (T as Type (_, [p_T as Type (_, [x_T, _]), _])) |
|
941 _ = |
|
942 (* Eta-expand "!!" and "??", to work around LEO-II 1.2.8 parser |
|
943 limitation. This works in conjuction with special code in |
|
944 "ATP_Problem" that uses the syntactic sugar "!" and "?" whenever |
|
945 possible. *) |
|
946 IAbs ((`I "P", p_T), |
|
947 IApp (IConst (`I ho_quant, T, []), |
|
948 IAbs ((`I "X", x_T), |
|
949 IApp (IConst (`I "P", p_T, []), |
|
950 IConst (`I "X", x_T, []))))) |
|
951 | tweak_ho_quant _ _ _ = raise Fail "unexpected type for quantifier" |
|
952 fun intro top_level args (IApp (tm1, tm2)) = |
|
953 IApp (intro top_level (tm2 :: args) tm1, intro false [] tm2) |
|
954 | intro top_level args (IConst (name as (s, _), T, T_args)) = |
|
955 (case proxify_const s of |
|
956 SOME proxy_base => |
|
957 if top_level orelse is_type_enc_higher_order type_enc then |
|
958 case (top_level, s) of |
|
959 (_, "c_False") => IConst (`I tptp_false, T, []) |
|
960 | (_, "c_True") => IConst (`I tptp_true, T, []) |
|
961 | (false, "c_Not") => IConst (`I tptp_not, T, []) |
|
962 | (false, "c_conj") => IConst (`I tptp_and, T, []) |
|
963 | (false, "c_disj") => IConst (`I tptp_or, T, []) |
|
964 | (false, "c_implies") => IConst (`I tptp_implies, T, []) |
|
965 | (false, "c_All") => tweak_ho_quant tptp_ho_forall T args |
|
966 | (false, "c_Ex") => tweak_ho_quant tptp_ho_exists T args |
|
967 | (false, s) => |
|
968 if is_tptp_equal s andalso length args = 2 then |
|
969 IConst (`I tptp_equal, T, []) |
|
970 else |
|
971 (* Use a proxy even for partially applied THF0 equality, |
|
972 because the LEO-II and Satallax parsers complain about not |
|
973 being able to infer the type of "=". *) |
|
974 IConst (proxy_base |>> prefix const_prefix, T, T_args) |
|
975 | _ => IConst (name, T, []) |
|
976 else |
|
977 IConst (proxy_base |>> prefix const_prefix, T, T_args) |
|
978 | NONE => if s = tptp_choice then tweak_ho_quant tptp_choice T args |
|
979 else IConst (name, T, T_args)) |
|
980 | intro _ _ (IAbs (bound, tm)) = IAbs (bound, intro false [] tm) |
|
981 | intro _ _ tm = tm |
|
982 in intro true [] end |
|
983 |
|
984 fun mangle_type_args_in_iterm format type_enc = |
|
985 if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then |
|
986 let |
|
987 fun mangle (IApp (tm1, tm2)) = IApp (mangle tm1, mangle tm2) |
|
988 | mangle (tm as IConst (_, _, [])) = tm |
|
989 | mangle (tm as IConst (name as (s, _), T, T_args)) = |
|
990 (case unprefix_and_unascii const_prefix s of |
|
991 NONE => tm |
|
992 | SOME s'' => |
|
993 case type_arg_policy [] type_enc (invert_const s'') of |
|
994 Mangled_Type_Args => |
|
995 IConst (mangled_const_name format type_enc T_args name, T, []) |
|
996 | _ => tm) |
|
997 | mangle (IAbs (bound, tm)) = IAbs (bound, mangle tm) |
|
998 | mangle tm = tm |
|
999 in mangle end |
|
1000 else |
|
1001 I |
|
1002 |
|
1003 fun chop_fun 0 T = ([], T) |
|
1004 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) = |
|
1005 chop_fun (n - 1) ran_T |>> cons dom_T |
|
1006 | chop_fun _ T = ([], T) |
|
1007 |
|
1008 fun filter_const_type_args _ _ _ [] = [] |
|
1009 | filter_const_type_args thy s ary T_args = |
|
1010 let |
|
1011 val U = robust_const_type thy s |
|
1012 val arg_U_vars = fold Term.add_tvarsT (U |> chop_fun ary |> fst) [] |
|
1013 val U_args = (s, U) |> robust_const_typargs thy |
|
1014 in |
|
1015 U_args ~~ T_args |
|
1016 |> map (fn (U, T) => |
|
1017 if member (op =) arg_U_vars (dest_TVar U) then dummyT else T) |
|
1018 end |
|
1019 handle TYPE _ => T_args |
|
1020 |
|
1021 fun filter_type_args_in_iterm thy monom_constrs type_enc = |
|
1022 let |
|
1023 fun filt ary (IApp (tm1, tm2)) = IApp (filt (ary + 1) tm1, filt 0 tm2) |
|
1024 | filt _ (tm as IConst (_, _, [])) = tm |
|
1025 | filt ary (IConst (name as (s, _), T, T_args)) = |
|
1026 (case unprefix_and_unascii const_prefix s of |
|
1027 NONE => |
|
1028 (name, |
|
1029 if level_of_type_enc type_enc = No_Types orelse s = tptp_choice then |
|
1030 [] |
|
1031 else |
|
1032 T_args) |
|
1033 | SOME s'' => |
|
1034 let |
|
1035 val s'' = invert_const s'' |
|
1036 fun filter_T_args false = T_args |
|
1037 | filter_T_args true = filter_const_type_args thy s'' ary T_args |
|
1038 in |
|
1039 case type_arg_policy monom_constrs type_enc s'' of |
|
1040 Explicit_Type_Args infer_from_term_args => |
|
1041 (name, filter_T_args infer_from_term_args) |
|
1042 | No_Type_Args => (name, []) |
|
1043 | Mangled_Type_Args => raise Fail "unexpected (un)mangled symbol" |
|
1044 end) |
|
1045 |> (fn (name, T_args) => IConst (name, T, T_args)) |
|
1046 | filt _ (IAbs (bound, tm)) = IAbs (bound, filt 0 tm) |
|
1047 | filt _ tm = tm |
|
1048 in filt 0 end |
|
1049 |
|
1050 fun iformula_from_prop ctxt format type_enc eq_as_iff = |
|
1051 let |
|
1052 val thy = Proof_Context.theory_of ctxt |
|
1053 fun do_term bs t atomic_Ts = |
|
1054 iterm_from_term thy format bs (Envir.eta_contract t) |
|
1055 |>> (introduce_proxies_in_iterm type_enc |
|
1056 #> mangle_type_args_in_iterm format type_enc |
|
1057 #> AAtom) |
|
1058 ||> union (op =) atomic_Ts |
|
1059 fun do_quant bs q pos s T t' = |
|
1060 let |
|
1061 val s = singleton (Name.variant_list (map fst bs)) s |
|
1062 val universal = Option.map (q = AExists ? not) pos |
|
1063 val name = |
|
1064 s |> `(case universal of |
|
1065 SOME true => make_all_bound_var |
|
1066 | SOME false => make_exist_bound_var |
|
1067 | NONE => make_bound_var) |
|
1068 in |
|
1069 do_formula ((s, (name, T)) :: bs) pos t' |
|
1070 #>> mk_aquant q [(name, SOME T)] |
|
1071 ##> union (op =) (atomic_types_of T) |
|
1072 end |
|
1073 and do_conn bs c pos1 t1 pos2 t2 = |
|
1074 do_formula bs pos1 t1 ##>> do_formula bs pos2 t2 #>> uncurry (mk_aconn c) |
|
1075 and do_formula bs pos t = |
|
1076 case t of |
|
1077 @{const Trueprop} $ t1 => do_formula bs pos t1 |
|
1078 | @{const Not} $ t1 => do_formula bs (Option.map not pos) t1 #>> mk_anot |
|
1079 | Const (@{const_name All}, _) $ Abs (s, T, t') => |
|
1080 do_quant bs AForall pos s T t' |
|
1081 | (t0 as Const (@{const_name All}, _)) $ t1 => |
|
1082 do_formula bs pos (t0 $ eta_expand (map (snd o snd) bs) t1 1) |
|
1083 | Const (@{const_name Ex}, _) $ Abs (s, T, t') => |
|
1084 do_quant bs AExists pos s T t' |
|
1085 | (t0 as Const (@{const_name Ex}, _)) $ t1 => |
|
1086 do_formula bs pos (t0 $ eta_expand (map (snd o snd) bs) t1 1) |
|
1087 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd pos t1 pos t2 |
|
1088 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr pos t1 pos t2 |
|
1089 | @{const HOL.implies} $ t1 $ t2 => |
|
1090 do_conn bs AImplies (Option.map not pos) t1 pos t2 |
|
1091 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 => |
|
1092 if eq_as_iff then do_conn bs AIff NONE t1 NONE t2 else do_term bs t |
|
1093 | _ => do_term bs t |
|
1094 in do_formula [] end |
|
1095 |
|
1096 fun presimplify_term ctxt t = |
|
1097 t |> exists_Const (member (op =) Meson.presimplified_consts o fst) t |
|
1098 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt) |
|
1099 #> Meson.presimplify |
|
1100 #> prop_of) |
|
1101 |
|
1102 fun concealed_bound_name j = atp_weak_prefix ^ string_of_int j |
|
1103 fun conceal_bounds Ts t = |
|
1104 subst_bounds (map (Free o apfst concealed_bound_name) |
|
1105 (0 upto length Ts - 1 ~~ Ts), t) |
|
1106 fun reveal_bounds Ts = |
|
1107 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j)) |
|
1108 (0 upto length Ts - 1 ~~ Ts)) |
|
1109 |
|
1110 fun is_fun_equality (@{const_name HOL.eq}, |
|
1111 Type (_, [Type (@{type_name fun}, _), _])) = true |
|
1112 | is_fun_equality _ = false |
|
1113 |
|
1114 fun extensionalize_term ctxt t = |
|
1115 if exists_Const is_fun_equality t then |
|
1116 let val thy = Proof_Context.theory_of ctxt in |
|
1117 t |> cterm_of thy |> Meson.extensionalize_conv ctxt |
|
1118 |> prop_of |> Logic.dest_equals |> snd |
|
1119 end |
|
1120 else |
|
1121 t |
|
1122 |
|
1123 fun simple_translate_lambdas do_lambdas ctxt t = |
|
1124 let val thy = Proof_Context.theory_of ctxt in |
|
1125 if Meson.is_fol_term thy t then |
|
1126 t |
|
1127 else |
|
1128 let |
|
1129 fun trans Ts t = |
|
1130 case t of |
|
1131 @{const Not} $ t1 => @{const Not} $ trans Ts t1 |
|
1132 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') => |
|
1133 t0 $ Abs (s, T, trans (T :: Ts) t') |
|
1134 | (t0 as Const (@{const_name All}, _)) $ t1 => |
|
1135 trans Ts (t0 $ eta_expand Ts t1 1) |
|
1136 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') => |
|
1137 t0 $ Abs (s, T, trans (T :: Ts) t') |
|
1138 | (t0 as Const (@{const_name Ex}, _)) $ t1 => |
|
1139 trans Ts (t0 $ eta_expand Ts t1 1) |
|
1140 | (t0 as @{const HOL.conj}) $ t1 $ t2 => |
|
1141 t0 $ trans Ts t1 $ trans Ts t2 |
|
1142 | (t0 as @{const HOL.disj}) $ t1 $ t2 => |
|
1143 t0 $ trans Ts t1 $ trans Ts t2 |
|
1144 | (t0 as @{const HOL.implies}) $ t1 $ t2 => |
|
1145 t0 $ trans Ts t1 $ trans Ts t2 |
|
1146 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _]))) |
|
1147 $ t1 $ t2 => |
|
1148 t0 $ trans Ts t1 $ trans Ts t2 |
|
1149 | _ => |
|
1150 if not (exists_subterm (fn Abs _ => true | _ => false) t) then t |
|
1151 else t |> Envir.eta_contract |> do_lambdas ctxt Ts |
|
1152 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single |
|
1153 in t |> trans [] |> singleton (Variable.export_terms ctxt' ctxt) end |
|
1154 end |
|
1155 |
|
1156 fun do_cheaply_conceal_lambdas Ts (t1 $ t2) = |
|
1157 do_cheaply_conceal_lambdas Ts t1 |
|
1158 $ do_cheaply_conceal_lambdas Ts t2 |
|
1159 | do_cheaply_conceal_lambdas Ts (Abs (_, T, t)) = |
|
1160 Const (lam_lifted_poly_prefix ^ serial_string (), |
|
1161 T --> fastype_of1 (T :: Ts, t)) |
|
1162 | do_cheaply_conceal_lambdas _ t = t |
|
1163 |
|
1164 fun do_introduce_combinators ctxt Ts t = |
|
1165 let val thy = Proof_Context.theory_of ctxt in |
|
1166 t |> conceal_bounds Ts |
|
1167 |> cterm_of thy |
|
1168 |> Meson_Clausify.introduce_combinators_in_cterm |
|
1169 |> prop_of |> Logic.dest_equals |> snd |
|
1170 |> reveal_bounds Ts |
|
1171 end |
|
1172 (* A type variable of sort "{}" will make abstraction fail. *) |
|
1173 handle THM _ => t |> do_cheaply_conceal_lambdas Ts |
|
1174 val introduce_combinators = simple_translate_lambdas do_introduce_combinators |
|
1175 |
|
1176 fun preprocess_abstractions_in_terms trans_lams facts = |
|
1177 let |
|
1178 val (facts, lambda_ts) = |
|
1179 facts |> map (snd o snd) |> trans_lams |
|
1180 |>> map2 (fn (name, (kind, _)) => fn t => (name, (kind, t))) facts |
|
1181 val lam_facts = |
|
1182 map2 (fn t => fn j => |
|
1183 ((lam_fact_prefix ^ Int.toString j, Helper), (Axiom, t))) |
|
1184 lambda_ts (1 upto length lambda_ts) |
|
1185 in (facts, lam_facts) end |
|
1186 |
|
1187 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the |
|
1188 same in Sledgehammer to prevent the discovery of unreplayable proofs. *) |
|
1189 fun freeze_term t = |
|
1190 let |
|
1191 fun freeze (t $ u) = freeze t $ freeze u |
|
1192 | freeze (Abs (s, T, t)) = Abs (s, T, freeze t) |
|
1193 | freeze (Var ((s, i), T)) = |
|
1194 Free (atp_weak_prefix ^ s ^ "_" ^ string_of_int i, T) |
|
1195 | freeze t = t |
|
1196 in t |> exists_subterm is_Var t ? freeze end |
|
1197 |
|
1198 fun presimp_prop ctxt role t = |
|
1199 (let |
|
1200 val thy = Proof_Context.theory_of ctxt |
|
1201 val t = t |> Envir.beta_eta_contract |
|
1202 |> transform_elim_prop |
|
1203 |> Object_Logic.atomize_term thy |
|
1204 val need_trueprop = (fastype_of t = @{typ bool}) |
|
1205 in |
|
1206 t |> need_trueprop ? HOLogic.mk_Trueprop |
|
1207 |> extensionalize_term ctxt |
|
1208 |> presimplify_term ctxt |
|
1209 |> HOLogic.dest_Trueprop |
|
1210 end |
|
1211 handle TERM _ => if role = Conjecture then @{term False} else @{term True}) |
|
1212 |> pair role |
|
1213 |
|
1214 fun make_formula ctxt format type_enc eq_as_iff name loc kind t = |
|
1215 let |
|
1216 val (iformula, atomic_Ts) = |
|
1217 iformula_from_prop ctxt format type_enc eq_as_iff |
|
1218 (SOME (kind <> Conjecture)) t [] |
|
1219 |>> close_iformula_universally |
|
1220 in |
|
1221 {name = name, locality = loc, kind = kind, iformula = iformula, |
|
1222 atomic_types = atomic_Ts} |
|
1223 end |
|
1224 |
|
1225 fun make_fact ctxt format type_enc eq_as_iff ((name, loc), t) = |
|
1226 case t |> make_formula ctxt format type_enc (eq_as_iff andalso format <> CNF) |
|
1227 name loc Axiom of |
|
1228 formula as {iformula = AAtom (IConst ((s, _), _, _)), ...} => |
|
1229 if s = tptp_true then NONE else SOME formula |
|
1230 | formula => SOME formula |
|
1231 |
|
1232 fun s_not_trueprop (@{const Trueprop} $ t) = @{const Trueprop} $ s_not t |
|
1233 | s_not_trueprop t = |
|
1234 if fastype_of t = @{typ bool} then s_not t else @{prop False} (* too meta *) |
|
1235 |
|
1236 fun make_conjecture ctxt format type_enc = |
|
1237 map (fn ((name, loc), (kind, t)) => |
|
1238 t |> kind = Conjecture ? s_not_trueprop |
|
1239 |> make_formula ctxt format type_enc (format <> CNF) name loc kind) |
|
1240 |
|
1241 (** Finite and infinite type inference **) |
|
1242 |
|
1243 fun tvar_footprint thy s ary = |
|
1244 (case unprefix_and_unascii const_prefix s of |
|
1245 SOME s => |
|
1246 s |> invert_const |> robust_const_type thy |> chop_fun ary |> fst |
|
1247 |> map (fn T => Term.add_tvarsT T [] |> map fst) |
|
1248 | NONE => []) |
|
1249 handle TYPE _ => [] |
|
1250 |
|
1251 fun ghost_type_args thy s ary = |
|
1252 if is_tptp_equal s then |
|
1253 0 upto ary - 1 |
|
1254 else |
|
1255 let |
|
1256 val footprint = tvar_footprint thy s ary |
|
1257 val eq = (s = @{const_name HOL.eq}) |
|
1258 fun ghosts _ [] = [] |
|
1259 | ghosts seen ((i, tvars) :: args) = |
|
1260 ghosts (union (op =) seen tvars) args |
|
1261 |> (eq orelse exists (fn tvar => not (member (op =) seen tvar)) tvars) |
|
1262 ? cons i |
|
1263 in |
|
1264 if forall null footprint then |
|
1265 [] |
|
1266 else |
|
1267 0 upto length footprint - 1 ~~ footprint |
|
1268 |> sort (rev_order o list_ord Term_Ord.indexname_ord o pairself snd) |
|
1269 |> ghosts [] |
|
1270 end |
|
1271 |
|
1272 type monotonicity_info = |
|
1273 {maybe_finite_Ts : typ list, |
|
1274 surely_finite_Ts : typ list, |
|
1275 maybe_infinite_Ts : typ list, |
|
1276 surely_infinite_Ts : typ list, |
|
1277 maybe_nonmono_Ts : typ list} |
|
1278 |
|
1279 (* These types witness that the type classes they belong to allow infinite |
|
1280 models and hence that any types with these type classes is monotonic. *) |
|
1281 val known_infinite_types = |
|
1282 [@{typ nat}, HOLogic.intT, HOLogic.realT, @{typ "nat => bool"}] |
|
1283 |
|
1284 fun is_type_kind_of_surely_infinite ctxt soundness cached_Ts T = |
|
1285 soundness <> Sound andalso is_type_surely_infinite ctxt true cached_Ts T |
|
1286 |
|
1287 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are |
|
1288 dangerous because their "exhaust" properties can easily lead to unsound ATP |
|
1289 proofs. On the other hand, all HOL infinite types can be given the same |
|
1290 models in first-order logic (via Löwenheim-Skolem). *) |
|
1291 |
|
1292 fun should_encode_type _ (_ : monotonicity_info) All_Types _ = true |
|
1293 | should_encode_type ctxt {maybe_finite_Ts, surely_infinite_Ts, |
|
1294 maybe_nonmono_Ts, ...} |
|
1295 (Noninf_Nonmono_Types (soundness, grain)) T = |
|
1296 grain = Ghost_Type_Arg_Vars orelse |
|
1297 (exists (type_intersect ctxt T) maybe_nonmono_Ts andalso |
|
1298 not (exists (type_instance ctxt T) surely_infinite_Ts orelse |
|
1299 (not (member (type_equiv ctxt) maybe_finite_Ts T) andalso |
|
1300 is_type_kind_of_surely_infinite ctxt soundness surely_infinite_Ts |
|
1301 T))) |
|
1302 | should_encode_type ctxt {surely_finite_Ts, maybe_infinite_Ts, |
|
1303 maybe_nonmono_Ts, ...} |
|
1304 (Fin_Nonmono_Types grain) T = |
|
1305 grain = Ghost_Type_Arg_Vars orelse |
|
1306 (exists (type_intersect ctxt T) maybe_nonmono_Ts andalso |
|
1307 (exists (type_generalization ctxt T) surely_finite_Ts orelse |
|
1308 (not (member (type_equiv ctxt) maybe_infinite_Ts T) andalso |
|
1309 is_type_surely_finite ctxt T))) |
|
1310 | should_encode_type _ _ _ _ = false |
|
1311 |
|
1312 fun should_guard_type ctxt mono (Guards (_, level)) should_guard_var T = |
|
1313 should_guard_var () andalso should_encode_type ctxt mono level T |
|
1314 | should_guard_type _ _ _ _ _ = false |
|
1315 |
|
1316 fun is_maybe_universal_var (IConst ((s, _), _, _)) = |
|
1317 String.isPrefix bound_var_prefix s orelse |
|
1318 String.isPrefix all_bound_var_prefix s |
|
1319 | is_maybe_universal_var (IVar _) = true |
|
1320 | is_maybe_universal_var _ = false |
|
1321 |
|
1322 datatype site = |
|
1323 Top_Level of bool option | |
|
1324 Eq_Arg of bool option | |
|
1325 Elsewhere |
|
1326 |
|
1327 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false |
|
1328 | should_tag_with_type ctxt mono (Tags (_, level)) site u T = |
|
1329 if granularity_of_type_level level = All_Vars then |
|
1330 should_encode_type ctxt mono level T |
|
1331 else |
|
1332 (case (site, is_maybe_universal_var u) of |
|
1333 (Eq_Arg _, true) => should_encode_type ctxt mono level T |
|
1334 | _ => false) |
|
1335 | should_tag_with_type _ _ _ _ _ _ = false |
|
1336 |
|
1337 fun fused_type ctxt mono level = |
|
1338 let |
|
1339 val should_encode = should_encode_type ctxt mono level |
|
1340 fun fuse 0 T = if should_encode T then T else fused_infinite_type |
|
1341 | fuse ary (Type (@{type_name fun}, [T1, T2])) = |
|
1342 fuse 0 T1 --> fuse (ary - 1) T2 |
|
1343 | fuse _ _ = raise Fail "expected function type" |
|
1344 in fuse end |
|
1345 |
|
1346 (** predicators and application operators **) |
|
1347 |
|
1348 type sym_info = |
|
1349 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list, |
|
1350 in_conj : bool} |
|
1351 |
|
1352 fun default_sym_tab_entries type_enc = |
|
1353 (make_fixed_const NONE @{const_name undefined}, |
|
1354 {pred_sym = false, min_ary = 0, max_ary = 0, types = [], |
|
1355 in_conj = false}) :: |
|
1356 ([tptp_false, tptp_true] |
|
1357 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = [], |
|
1358 in_conj = false})) @ |
|
1359 ([tptp_equal, tptp_old_equal] |
|
1360 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = [], |
|
1361 in_conj = false})) |
|
1362 |> not (is_type_enc_higher_order type_enc) |
|
1363 ? cons (prefixed_predicator_name, |
|
1364 {pred_sym = true, min_ary = 1, max_ary = 1, types = [], |
|
1365 in_conj = false}) |
|
1366 |
|
1367 fun sym_table_for_facts ctxt type_enc explicit_apply conjs facts = |
|
1368 let |
|
1369 fun consider_var_ary const_T var_T max_ary = |
|
1370 let |
|
1371 fun iter ary T = |
|
1372 if ary = max_ary orelse type_instance ctxt var_T T orelse |
|
1373 type_instance ctxt T var_T then |
|
1374 ary |
|
1375 else |
|
1376 iter (ary + 1) (range_type T) |
|
1377 in iter 0 const_T end |
|
1378 fun add_universal_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) = |
|
1379 if explicit_apply = NONE andalso |
|
1380 (can dest_funT T orelse T = @{typ bool}) then |
|
1381 let |
|
1382 val bool_vars' = bool_vars orelse body_type T = @{typ bool} |
|
1383 fun repair_min_ary {pred_sym, min_ary, max_ary, types, in_conj} = |
|
1384 {pred_sym = pred_sym andalso not bool_vars', |
|
1385 min_ary = fold (fn T' => consider_var_ary T' T) types min_ary, |
|
1386 max_ary = max_ary, types = types, in_conj = in_conj} |
|
1387 val fun_var_Ts' = |
|
1388 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T |
|
1389 in |
|
1390 if bool_vars' = bool_vars andalso |
|
1391 pointer_eq (fun_var_Ts', fun_var_Ts) then |
|
1392 accum |
|
1393 else |
|
1394 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_ary) sym_tab) |
|
1395 end |
|
1396 else |
|
1397 accum |
|
1398 fun add_fact_syms conj_fact = |
|
1399 let |
|
1400 fun add_iterm_syms top_level tm |
|
1401 (accum as ((bool_vars, fun_var_Ts), sym_tab)) = |
|
1402 let val (head, args) = strip_iterm_comb tm in |
|
1403 (case head of |
|
1404 IConst ((s, _), T, _) => |
|
1405 if String.isPrefix bound_var_prefix s orelse |
|
1406 String.isPrefix all_bound_var_prefix s then |
|
1407 add_universal_var T accum |
|
1408 else if String.isPrefix exist_bound_var_prefix s then |
|
1409 accum |
|
1410 else |
|
1411 let val ary = length args in |
|
1412 ((bool_vars, fun_var_Ts), |
|
1413 case Symtab.lookup sym_tab s of |
|
1414 SOME {pred_sym, min_ary, max_ary, types, in_conj} => |
|
1415 let |
|
1416 val pred_sym = |
|
1417 pred_sym andalso top_level andalso not bool_vars |
|
1418 val types' = types |> insert_type ctxt I T |
|
1419 val in_conj = in_conj orelse conj_fact |
|
1420 val min_ary = |
|
1421 if is_some explicit_apply orelse |
|
1422 pointer_eq (types', types) then |
|
1423 min_ary |
|
1424 else |
|
1425 fold (consider_var_ary T) fun_var_Ts min_ary |
|
1426 in |
|
1427 Symtab.update (s, {pred_sym = pred_sym, |
|
1428 min_ary = Int.min (ary, min_ary), |
|
1429 max_ary = Int.max (ary, max_ary), |
|
1430 types = types', in_conj = in_conj}) |
|
1431 sym_tab |
|
1432 end |
|
1433 | NONE => |
|
1434 let |
|
1435 val pred_sym = top_level andalso not bool_vars |
|
1436 val min_ary = |
|
1437 case explicit_apply of |
|
1438 SOME true => 0 |
|
1439 | SOME false => ary |
|
1440 | NONE => fold (consider_var_ary T) fun_var_Ts ary |
|
1441 in |
|
1442 Symtab.update_new (s, |
|
1443 {pred_sym = pred_sym, min_ary = min_ary, |
|
1444 max_ary = ary, types = [T], in_conj = conj_fact}) |
|
1445 sym_tab |
|
1446 end) |
|
1447 end |
|
1448 | IVar (_, T) => add_universal_var T accum |
|
1449 | IAbs ((_, T), tm) => |
|
1450 accum |> add_universal_var T |> add_iterm_syms false tm |
|
1451 | _ => accum) |
|
1452 |> fold (add_iterm_syms false) args |
|
1453 end |
|
1454 in K (add_iterm_syms true) |> formula_fold NONE |> fact_lift end |
|
1455 in |
|
1456 ((false, []), Symtab.empty) |
|
1457 |> fold (add_fact_syms true) conjs |
|
1458 |> fold (add_fact_syms false) facts |
|
1459 |> snd |
|
1460 |> fold Symtab.update (default_sym_tab_entries type_enc) |
|
1461 end |
|
1462 |
|
1463 fun min_ary_of sym_tab s = |
|
1464 case Symtab.lookup sym_tab s of |
|
1465 SOME ({min_ary, ...} : sym_info) => min_ary |
|
1466 | NONE => |
|
1467 case unprefix_and_unascii const_prefix s of |
|
1468 SOME s => |
|
1469 let val s = s |> unmangled_const_name |> invert_const in |
|
1470 if s = predicator_name then 1 |
|
1471 else if s = app_op_name then 2 |
|
1472 else if s = type_guard_name then 1 |
|
1473 else 0 |
|
1474 end |
|
1475 | NONE => 0 |
|
1476 |
|
1477 (* True if the constant ever appears outside of the top-level position in |
|
1478 literals, or if it appears with different arities (e.g., because of different |
|
1479 type instantiations). If false, the constant always receives all of its |
|
1480 arguments and is used as a predicate. *) |
|
1481 fun is_pred_sym sym_tab s = |
|
1482 case Symtab.lookup sym_tab s of |
|
1483 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) => |
|
1484 pred_sym andalso min_ary = max_ary |
|
1485 | NONE => false |
|
1486 |
|
1487 val app_op = `(make_fixed_const NONE) app_op_name |
|
1488 val predicator_combconst = |
|
1489 IConst (`(make_fixed_const NONE) predicator_name, @{typ "bool => bool"}, []) |
|
1490 |
|
1491 fun list_app head args = fold (curry (IApp o swap)) args head |
|
1492 fun predicator tm = IApp (predicator_combconst, tm) |
|
1493 |
|
1494 fun firstorderize_fact thy monom_constrs format type_enc sym_tab = |
|
1495 let |
|
1496 fun do_app arg head = |
|
1497 let |
|
1498 val head_T = ityp_of head |
|
1499 val (arg_T, res_T) = dest_funT head_T |
|
1500 val app = |
|
1501 IConst (app_op, head_T --> head_T, [arg_T, res_T]) |
|
1502 |> mangle_type_args_in_iterm format type_enc |
|
1503 in list_app app [head, arg] end |
|
1504 fun list_app_ops head args = fold do_app args head |
|
1505 fun introduce_app_ops tm = |
|
1506 case strip_iterm_comb tm of |
|
1507 (head as IConst ((s, _), _, _), args) => |
|
1508 args |> map introduce_app_ops |
|
1509 |> chop (min_ary_of sym_tab s) |
|
1510 |>> list_app head |
|
1511 |-> list_app_ops |
|
1512 | (head, args) => list_app_ops head (map introduce_app_ops args) |
|
1513 fun introduce_predicators tm = |
|
1514 case strip_iterm_comb tm of |
|
1515 (IConst ((s, _), _, _), _) => |
|
1516 if is_pred_sym sym_tab s then tm else predicator tm |
|
1517 | _ => predicator tm |
|
1518 val do_iterm = |
|
1519 not (is_type_enc_higher_order type_enc) |
|
1520 ? (introduce_app_ops #> introduce_predicators) |
|
1521 #> filter_type_args_in_iterm thy monom_constrs type_enc |
|
1522 in update_iformula (formula_map do_iterm) end |
|
1523 |
|
1524 (** Helper facts **) |
|
1525 |
|
1526 val not_ffalse = @{lemma "~ fFalse" by (unfold fFalse_def) fast} |
|
1527 val ftrue = @{lemma "fTrue" by (unfold fTrue_def) fast} |
|
1528 |
|
1529 (* The Boolean indicates that a fairly sound type encoding is needed. *) |
|
1530 val helper_table = |
|
1531 [(("COMBI", false), @{thms Meson.COMBI_def}), |
|
1532 (("COMBK", false), @{thms Meson.COMBK_def}), |
|
1533 (("COMBB", false), @{thms Meson.COMBB_def}), |
|
1534 (("COMBC", false), @{thms Meson.COMBC_def}), |
|
1535 (("COMBS", false), @{thms Meson.COMBS_def}), |
|
1536 ((predicator_name, false), [not_ffalse, ftrue]), |
|
1537 (("fFalse", false), [not_ffalse]), |
|
1538 (("fFalse", true), @{thms True_or_False}), |
|
1539 (("fTrue", false), [ftrue]), |
|
1540 (("fTrue", true), @{thms True_or_False}), |
|
1541 (("fNot", false), |
|
1542 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1] |
|
1543 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}), |
|
1544 (("fconj", false), |
|
1545 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q" |
|
1546 by (unfold fconj_def) fast+}), |
|
1547 (("fdisj", false), |
|
1548 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q" |
|
1549 by (unfold fdisj_def) fast+}), |
|
1550 (("fimplies", false), |
|
1551 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q" |
|
1552 by (unfold fimplies_def) fast+}), |
|
1553 (("fequal", true), |
|
1554 (* This is a lie: Higher-order equality doesn't need a sound type encoding. |
|
1555 However, this is done so for backward compatibility: Including the |
|
1556 equality helpers by default in Metis breaks a few existing proofs. *) |
|
1557 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1] |
|
1558 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}), |
|
1559 (* Partial characterization of "fAll" and "fEx". A complete characterization |
|
1560 would require the axiom of choice for replay with Metis. *) |
|
1561 (("fAll", false), [@{lemma "~ fAll P | P x" by (auto simp: fAll_def)}]), |
|
1562 (("fEx", false), [@{lemma "~ P x | fEx P" by (auto simp: fEx_def)}]), |
|
1563 (("If", true), @{thms if_True if_False True_or_False})] |
|
1564 |> map (apsnd (map zero_var_indexes)) |
|
1565 |
|
1566 fun atype_of_type_vars (Simple_Types (_, Polymorphic, _)) = SOME atype_of_types |
|
1567 | atype_of_type_vars _ = NONE |
|
1568 |
|
1569 fun bound_tvars type_enc sorts Ts = |
|
1570 (sorts ? mk_ahorn (formulas_for_types type_enc add_sorts_on_tvar Ts)) |
|
1571 #> mk_aquant AForall |
|
1572 (map_filter (fn TVar (x as (s, _), _) => |
|
1573 SOME ((make_schematic_type_var x, s), |
|
1574 atype_of_type_vars type_enc) |
|
1575 | _ => NONE) Ts) |
|
1576 |
|
1577 fun eq_formula type_enc atomic_Ts pred_sym tm1 tm2 = |
|
1578 (if pred_sym then AConn (AIff, [AAtom tm1, AAtom tm2]) |
|
1579 else AAtom (ATerm (`I tptp_equal, [tm1, tm2]))) |
|
1580 |> close_formula_universally |
|
1581 |> bound_tvars type_enc true atomic_Ts |
|
1582 |
|
1583 val type_tag = `(make_fixed_const NONE) type_tag_name |
|
1584 |
|
1585 fun type_tag_idempotence_fact format type_enc = |
|
1586 let |
|
1587 fun var s = ATerm (`I s, []) |
|
1588 fun tag tm = ATerm (type_tag, [var "A", tm]) |
|
1589 val tagged_var = tag (var "X") |
|
1590 in |
|
1591 Formula (type_tag_idempotence_helper_name, Axiom, |
|
1592 eq_formula type_enc [] false (tag tagged_var) tagged_var, |
|
1593 isabelle_info format simpN, NONE) |
|
1594 end |
|
1595 |
|
1596 fun should_specialize_helper type_enc t = |
|
1597 polymorphism_of_type_enc type_enc <> Polymorphic andalso |
|
1598 level_of_type_enc type_enc <> No_Types andalso |
|
1599 not (null (Term.hidden_polymorphism t)) |
|
1600 |
|
1601 fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) = |
|
1602 case unprefix_and_unascii const_prefix s of |
|
1603 SOME mangled_s => |
|
1604 let |
|
1605 val thy = Proof_Context.theory_of ctxt |
|
1606 val unmangled_s = mangled_s |> unmangled_const_name |
|
1607 fun dub needs_fairly_sound j k = |
|
1608 (unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^ |
|
1609 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^ |
|
1610 (if needs_fairly_sound then typed_helper_suffix |
|
1611 else untyped_helper_suffix), |
|
1612 Helper) |
|
1613 fun dub_and_inst needs_fairly_sound (th, j) = |
|
1614 let val t = prop_of th in |
|
1615 if should_specialize_helper type_enc t then |
|
1616 map (fn T => specialize_type thy (invert_const unmangled_s, T) t) |
|
1617 types |
|
1618 else |
|
1619 [t] |
|
1620 end |
|
1621 |> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1 |
|
1622 val make_facts = map_filter (make_fact ctxt format type_enc false) |
|
1623 val fairly_sound = is_type_enc_fairly_sound type_enc |
|
1624 in |
|
1625 helper_table |
|
1626 |> maps (fn ((helper_s, needs_fairly_sound), ths) => |
|
1627 if helper_s <> unmangled_s orelse |
|
1628 (needs_fairly_sound andalso not fairly_sound) then |
|
1629 [] |
|
1630 else |
|
1631 ths ~~ (1 upto length ths) |
|
1632 |> maps (dub_and_inst needs_fairly_sound) |
|
1633 |> make_facts) |
|
1634 end |
|
1635 | NONE => [] |
|
1636 fun helper_facts_for_sym_table ctxt format type_enc sym_tab = |
|
1637 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab |
|
1638 [] |
|
1639 |
|
1640 (***************************************************************) |
|
1641 (* Type Classes Present in the Axiom or Conjecture Clauses *) |
|
1642 (***************************************************************) |
|
1643 |
|
1644 fun set_insert (x, s) = Symtab.update (x, ()) s |
|
1645 |
|
1646 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts) |
|
1647 |
|
1648 (* Remove this trivial type class (FIXME: similar code elsewhere) *) |
|
1649 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset |
|
1650 |
|
1651 fun classes_of_terms get_Ts = |
|
1652 map (map snd o get_Ts) |
|
1653 #> List.foldl add_classes Symtab.empty |
|
1654 #> delete_type #> Symtab.keys |
|
1655 |
|
1656 val tfree_classes_of_terms = classes_of_terms Misc_Legacy.term_tfrees |
|
1657 val tvar_classes_of_terms = classes_of_terms Misc_Legacy.term_tvars |
|
1658 |
|
1659 fun fold_type_constrs f (Type (s, Ts)) x = |
|
1660 fold (fold_type_constrs f) Ts (f (s, x)) |
|
1661 | fold_type_constrs _ _ x = x |
|
1662 |
|
1663 (* Type constructors used to instantiate overloaded constants are the only ones |
|
1664 needed. *) |
|
1665 fun add_type_constrs_in_term thy = |
|
1666 let |
|
1667 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I |
|
1668 | add (t $ u) = add t #> add u |
|
1669 | add (Const x) = |
|
1670 x |> robust_const_typargs thy |> fold (fold_type_constrs set_insert) |
|
1671 | add (Abs (_, _, u)) = add u |
|
1672 | add _ = I |
|
1673 in add end |
|
1674 |
|
1675 fun type_constrs_of_terms thy ts = |
|
1676 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty) |
|
1677 |
|
1678 fun extract_lambda_def (Const (@{const_name HOL.eq}, _) $ t $ u) = |
|
1679 let val (head, args) = strip_comb t in |
|
1680 (head |> dest_Const |> fst, |
|
1681 fold_rev (fn t as Var ((s, _), T) => |
|
1682 (fn u => Abs (s, T, abstract_over (t, u))) |
|
1683 | _ => raise Fail "expected Var") args u) |
|
1684 end |
|
1685 | extract_lambda_def _ = raise Fail "malformed lifted lambda" |
|
1686 |
|
1687 fun trans_lams_from_string ctxt type_enc lam_trans = |
|
1688 if lam_trans = no_lamsN then |
|
1689 rpair [] |
|
1690 else if lam_trans = hide_lamsN then |
|
1691 lift_lams ctxt type_enc ##> K [] |
|
1692 else if lam_trans = lam_liftingN then |
|
1693 lift_lams ctxt type_enc |
|
1694 else if lam_trans = combinatorsN then |
|
1695 map (introduce_combinators ctxt) #> rpair [] |
|
1696 else if lam_trans = hybrid_lamsN then |
|
1697 lift_lams_part_1 ctxt type_enc |
|
1698 ##> maps (fn t => [t, introduce_combinators ctxt (intentionalize_def t)]) |
|
1699 #> lift_lams_part_2 |
|
1700 else if lam_trans = keep_lamsN then |
|
1701 map (Envir.eta_contract) #> rpair [] |
|
1702 else |
|
1703 error ("Unknown lambda translation scheme: " ^ quote lam_trans ^ ".") |
|
1704 |
|
1705 fun translate_formulas ctxt format prem_kind type_enc lam_trans presimp hyp_ts |
|
1706 concl_t facts = |
|
1707 let |
|
1708 val thy = Proof_Context.theory_of ctxt |
|
1709 val trans_lams = trans_lams_from_string ctxt type_enc lam_trans |
|
1710 val fact_ts = facts |> map snd |
|
1711 (* Remove existing facts from the conjecture, as this can dramatically |
|
1712 boost an ATP's performance (for some reason). *) |
|
1713 val hyp_ts = |
|
1714 hyp_ts |
|
1715 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t) |
|
1716 val facts = facts |> map (apsnd (pair Axiom)) |
|
1717 val conjs = |
|
1718 map (pair prem_kind) hyp_ts @ [(Conjecture, s_not_trueprop concl_t)] |
|
1719 |> map (apsnd freeze_term) |
|
1720 |> map2 (pair o rpair Local o string_of_int) (0 upto length hyp_ts) |
|
1721 val ((conjs, facts), lam_facts) = |
|
1722 (conjs, facts) |
|
1723 |> presimp ? pairself (map (apsnd (uncurry (presimp_prop ctxt)))) |
|
1724 |> (if lam_trans = no_lamsN then |
|
1725 rpair [] |
|
1726 else |
|
1727 op @ |
|
1728 #> preprocess_abstractions_in_terms trans_lams |
|
1729 #>> chop (length conjs)) |
|
1730 val conjs = conjs |> make_conjecture ctxt format type_enc |
|
1731 val (fact_names, facts) = |
|
1732 facts |
|
1733 |> map_filter (fn (name, (_, t)) => |
|
1734 make_fact ctxt format type_enc true (name, t) |
|
1735 |> Option.map (pair name)) |
|
1736 |> ListPair.unzip |
|
1737 val lifted = lam_facts |> map (extract_lambda_def o snd o snd) |
|
1738 val lam_facts = |
|
1739 lam_facts |> map_filter (make_fact ctxt format type_enc true o apsnd snd) |
|
1740 val all_ts = concl_t :: hyp_ts @ fact_ts |
|
1741 val subs = tfree_classes_of_terms all_ts |
|
1742 val supers = tvar_classes_of_terms all_ts |
|
1743 val tycons = type_constrs_of_terms thy all_ts |
|
1744 val (supers, arity_clauses) = |
|
1745 if level_of_type_enc type_enc = No_Types then ([], []) |
|
1746 else make_arity_clauses thy tycons supers |
|
1747 val class_rel_clauses = make_class_rel_clauses thy subs supers |
|
1748 in |
|
1749 (fact_names |> map single, union (op =) subs supers, conjs, |
|
1750 facts @ lam_facts, class_rel_clauses, arity_clauses, lifted) |
|
1751 end |
|
1752 |
|
1753 val type_guard = `(make_fixed_const NONE) type_guard_name |
|
1754 |
|
1755 fun type_guard_iterm format type_enc T tm = |
|
1756 IApp (IConst (type_guard, T --> @{typ bool}, [T]) |
|
1757 |> mangle_type_args_in_iterm format type_enc, tm) |
|
1758 |
|
1759 fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum |
|
1760 | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum = |
|
1761 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, []))) |
|
1762 | is_var_positively_naked_in_term _ _ _ _ = true |
|
1763 |
|
1764 fun is_var_ghost_type_arg_in_term thy polym_constrs name pos tm accum = |
|
1765 is_var_positively_naked_in_term name pos tm accum orelse |
|
1766 let |
|
1767 val var = ATerm (name, []) |
|
1768 fun is_nasty_in_term (ATerm (_, [])) = false |
|
1769 | is_nasty_in_term (ATerm ((s, _), tms)) = |
|
1770 let |
|
1771 val ary = length tms |
|
1772 val polym_constr = member (op =) polym_constrs s |
|
1773 val ghosts = ghost_type_args thy s ary |
|
1774 in |
|
1775 exists (fn (j, tm) => |
|
1776 if polym_constr then |
|
1777 member (op =) ghosts j andalso |
|
1778 (tm = var orelse is_nasty_in_term tm) |
|
1779 else |
|
1780 tm = var andalso member (op =) ghosts j) |
|
1781 (0 upto ary - 1 ~~ tms) |
|
1782 orelse (not polym_constr andalso exists is_nasty_in_term tms) |
|
1783 end |
|
1784 | is_nasty_in_term _ = true |
|
1785 in is_nasty_in_term tm end |
|
1786 |
|
1787 fun should_guard_var_in_formula thy polym_constrs level pos phi (SOME true) |
|
1788 name = |
|
1789 (case granularity_of_type_level level of |
|
1790 All_Vars => true |
|
1791 | Positively_Naked_Vars => |
|
1792 formula_fold pos (is_var_positively_naked_in_term name) phi false |
|
1793 | Ghost_Type_Arg_Vars => |
|
1794 formula_fold pos (is_var_ghost_type_arg_in_term thy polym_constrs name) |
|
1795 phi false) |
|
1796 | should_guard_var_in_formula _ _ _ _ _ _ _ = true |
|
1797 |
|
1798 fun always_guard_var_in_formula _ _ _ _ _ _ _ = true |
|
1799 |
|
1800 fun should_generate_tag_bound_decl _ _ _ (SOME true) _ = false |
|
1801 | should_generate_tag_bound_decl ctxt mono (Tags (_, level)) _ T = |
|
1802 granularity_of_type_level level <> All_Vars andalso |
|
1803 should_encode_type ctxt mono level T |
|
1804 | should_generate_tag_bound_decl _ _ _ _ _ = false |
|
1805 |
|
1806 fun mk_aterm format type_enc name T_args args = |
|
1807 ATerm (name, map_filter (ho_term_for_type_arg format type_enc) T_args @ args) |
|
1808 |
|
1809 fun tag_with_type ctxt format mono type_enc pos T tm = |
|
1810 IConst (type_tag, T --> T, [T]) |
|
1811 |> mangle_type_args_in_iterm format type_enc |
|
1812 |> ho_term_from_iterm ctxt format mono type_enc pos |
|
1813 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]) |
|
1814 | _ => raise Fail "unexpected lambda-abstraction") |
|
1815 and ho_term_from_iterm ctxt format mono type_enc = |
|
1816 let |
|
1817 fun term site u = |
|
1818 let |
|
1819 val (head, args) = strip_iterm_comb u |
|
1820 val pos = |
|
1821 case site of |
|
1822 Top_Level pos => pos |
|
1823 | Eq_Arg pos => pos |
|
1824 | _ => NONE |
|
1825 val t = |
|
1826 case head of |
|
1827 IConst (name as (s, _), _, T_args) => |
|
1828 let |
|
1829 val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere |
|
1830 in |
|
1831 map (term arg_site) args |> mk_aterm format type_enc name T_args |
|
1832 end |
|
1833 | IVar (name, _) => |
|
1834 map (term Elsewhere) args |> mk_aterm format type_enc name [] |
|
1835 | IAbs ((name, T), tm) => |
|
1836 AAbs ((name, ho_type_from_typ format type_enc true 0 T), |
|
1837 term Elsewhere tm) |
|
1838 | IApp _ => raise Fail "impossible \"IApp\"" |
|
1839 val T = ityp_of u |
|
1840 in |
|
1841 if should_tag_with_type ctxt mono type_enc site u T then |
|
1842 tag_with_type ctxt format mono type_enc pos T t |
|
1843 else |
|
1844 t |
|
1845 end |
|
1846 in term o Top_Level end |
|
1847 and formula_from_iformula ctxt polym_constrs format mono type_enc |
|
1848 should_guard_var = |
|
1849 let |
|
1850 val thy = Proof_Context.theory_of ctxt |
|
1851 val level = level_of_type_enc type_enc |
|
1852 val do_term = ho_term_from_iterm ctxt format mono type_enc |
|
1853 val do_bound_type = |
|
1854 case type_enc of |
|
1855 Simple_Types _ => fused_type ctxt mono level 0 |
|
1856 #> ho_type_from_typ format type_enc false 0 #> SOME |
|
1857 | _ => K NONE |
|
1858 fun do_out_of_bound_type pos phi universal (name, T) = |
|
1859 if should_guard_type ctxt mono type_enc |
|
1860 (fn () => should_guard_var thy polym_constrs level pos phi |
|
1861 universal name) T then |
|
1862 IVar (name, T) |
|
1863 |> type_guard_iterm format type_enc T |
|
1864 |> do_term pos |> AAtom |> SOME |
|
1865 else if should_generate_tag_bound_decl ctxt mono type_enc universal T then |
|
1866 let |
|
1867 val var = ATerm (name, []) |
|
1868 val tagged_var = tag_with_type ctxt format mono type_enc pos T var |
|
1869 in SOME (AAtom (ATerm (`I tptp_equal, [tagged_var, var]))) end |
|
1870 else |
|
1871 NONE |
|
1872 fun do_formula pos (AQuant (q, xs, phi)) = |
|
1873 let |
|
1874 val phi = phi |> do_formula pos |
|
1875 val universal = Option.map (q = AExists ? not) pos |
|
1876 in |
|
1877 AQuant (q, xs |> map (apsnd (fn NONE => NONE |
|
1878 | SOME T => do_bound_type T)), |
|
1879 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd)) |
|
1880 (map_filter |
|
1881 (fn (_, NONE) => NONE |
|
1882 | (s, SOME T) => |
|
1883 do_out_of_bound_type pos phi universal (s, T)) |
|
1884 xs) |
|
1885 phi) |
|
1886 end |
|
1887 | do_formula pos (AConn conn) = aconn_map pos do_formula conn |
|
1888 | do_formula pos (AAtom tm) = AAtom (do_term pos tm) |
|
1889 in do_formula end |
|
1890 |
|
1891 (* Each fact is given a unique fact number to avoid name clashes (e.g., because |
|
1892 of monomorphization). The TPTP explicitly forbids name clashes, and some of |
|
1893 the remote provers might care. *) |
|
1894 fun formula_line_for_fact ctxt polym_constrs format prefix encode freshen pos |
|
1895 mono type_enc (j, {name, locality, kind, iformula, atomic_types}) = |
|
1896 (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name, kind, |
|
1897 iformula |
|
1898 |> formula_from_iformula ctxt polym_constrs format mono type_enc |
|
1899 should_guard_var_in_formula (if pos then SOME true else NONE) |
|
1900 |> close_formula_universally |
|
1901 |> bound_tvars type_enc true atomic_types, |
|
1902 NONE, |
|
1903 case locality of |
|
1904 Intro => isabelle_info format introN |
|
1905 | Elim => isabelle_info format elimN |
|
1906 | Simp => isabelle_info format simpN |
|
1907 | _ => NONE) |
|
1908 |> Formula |
|
1909 |
|
1910 fun formula_line_for_class_rel_clause format type_enc |
|
1911 ({name, subclass, superclass, ...} : class_rel_clause) = |
|
1912 let val ty_arg = ATerm (tvar_a_name, []) in |
|
1913 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom, |
|
1914 AConn (AImplies, |
|
1915 [type_class_formula type_enc subclass ty_arg, |
|
1916 type_class_formula type_enc superclass ty_arg]) |
|
1917 |> mk_aquant AForall |
|
1918 [(tvar_a_name, atype_of_type_vars type_enc)], |
|
1919 isabelle_info format introN, NONE) |
|
1920 end |
|
1921 |
|
1922 fun formula_from_arity_atom type_enc (class, t, args) = |
|
1923 ATerm (t, map (fn arg => ATerm (arg, [])) args) |
|
1924 |> type_class_formula type_enc class |
|
1925 |
|
1926 fun formula_line_for_arity_clause format type_enc |
|
1927 ({name, prem_atoms, concl_atom} : arity_clause) = |
|
1928 Formula (arity_clause_prefix ^ name, Axiom, |
|
1929 mk_ahorn (map (formula_from_arity_atom type_enc) prem_atoms) |
|
1930 (formula_from_arity_atom type_enc concl_atom) |
|
1931 |> mk_aquant AForall |
|
1932 (map (rpair (atype_of_type_vars type_enc)) (#3 concl_atom)), |
|
1933 isabelle_info format introN, NONE) |
|
1934 |
|
1935 fun formula_line_for_conjecture ctxt polym_constrs format mono type_enc |
|
1936 ({name, kind, iformula, atomic_types, ...} : translated_formula) = |
|
1937 Formula (conjecture_prefix ^ name, kind, |
|
1938 iformula |
|
1939 |> formula_from_iformula ctxt polym_constrs format mono type_enc |
|
1940 should_guard_var_in_formula (SOME false) |
|
1941 |> close_formula_universally |
|
1942 |> bound_tvars type_enc true atomic_types, NONE, NONE) |
|
1943 |
|
1944 fun formula_line_for_free_type j phi = |
|
1945 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis, phi, NONE, NONE) |
|
1946 fun formula_lines_for_free_types type_enc (facts : translated_formula list) = |
|
1947 let |
|
1948 val phis = |
|
1949 fold (union (op =)) (map #atomic_types facts) [] |
|
1950 |> formulas_for_types type_enc add_sorts_on_tfree |
|
1951 in map2 formula_line_for_free_type (0 upto length phis - 1) phis end |
|
1952 |
|
1953 (** Symbol declarations **) |
|
1954 |
|
1955 fun decl_line_for_class order s = |
|
1956 let val name as (s, _) = `make_type_class s in |
|
1957 Decl (sym_decl_prefix ^ s, name, |
|
1958 if order = First_Order then |
|
1959 ATyAbs ([tvar_a_name], |
|
1960 if avoid_first_order_ghost_type_vars then |
|
1961 AFun (a_itself_atype, bool_atype) |
|
1962 else |
|
1963 bool_atype) |
|
1964 else |
|
1965 AFun (atype_of_types, bool_atype)) |
|
1966 end |
|
1967 |
|
1968 fun decl_lines_for_classes type_enc classes = |
|
1969 case type_enc of |
|
1970 Simple_Types (order, Polymorphic, _) => |
|
1971 map (decl_line_for_class order) classes |
|
1972 | _ => [] |
|
1973 |
|
1974 fun sym_decl_table_for_facts ctxt format type_enc sym_tab (conjs, facts) = |
|
1975 let |
|
1976 fun add_iterm_syms tm = |
|
1977 let val (head, args) = strip_iterm_comb tm in |
|
1978 (case head of |
|
1979 IConst ((s, s'), T, T_args) => |
|
1980 let |
|
1981 val (pred_sym, in_conj) = |
|
1982 case Symtab.lookup sym_tab s of |
|
1983 SOME ({pred_sym, in_conj, ...} : sym_info) => |
|
1984 (pred_sym, in_conj) |
|
1985 | NONE => (false, false) |
|
1986 val decl_sym = |
|
1987 (case type_enc of |
|
1988 Guards _ => not pred_sym |
|
1989 | _ => true) andalso |
|
1990 is_tptp_user_symbol s |
|
1991 in |
|
1992 if decl_sym then |
|
1993 Symtab.map_default (s, []) |
|
1994 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args, |
|
1995 in_conj)) |
|
1996 else |
|
1997 I |
|
1998 end |
|
1999 | IAbs (_, tm) => add_iterm_syms tm |
|
2000 | _ => I) |
|
2001 #> fold add_iterm_syms args |
|
2002 end |
|
2003 val add_fact_syms = K add_iterm_syms |> formula_fold NONE |> fact_lift |
|
2004 fun add_formula_var_types (AQuant (_, xs, phi)) = |
|
2005 fold (fn (_, SOME T) => insert_type ctxt I T | _ => I) xs |
|
2006 #> add_formula_var_types phi |
|
2007 | add_formula_var_types (AConn (_, phis)) = |
|
2008 fold add_formula_var_types phis |
|
2009 | add_formula_var_types _ = I |
|
2010 fun var_types () = |
|
2011 if polymorphism_of_type_enc type_enc = Polymorphic then [tvar_a] |
|
2012 else fold (fact_lift add_formula_var_types) (conjs @ facts) [] |
|
2013 fun add_undefined_const T = |
|
2014 let |
|
2015 val (s, s') = |
|
2016 `(make_fixed_const NONE) @{const_name undefined} |
|
2017 |> (case type_arg_policy [] type_enc @{const_name undefined} of |
|
2018 Mangled_Type_Args => mangled_const_name format type_enc [T] |
|
2019 | _ => I) |
|
2020 in |
|
2021 Symtab.map_default (s, []) |
|
2022 (insert_type ctxt #3 (s', [T], T, false, 0, false)) |
|
2023 end |
|
2024 fun add_TYPE_const () = |
|
2025 let val (s, s') = TYPE_name in |
|
2026 Symtab.map_default (s, []) |
|
2027 (insert_type ctxt #3 |
|
2028 (s', [tvar_a], @{typ "'a itself"}, false, 0, false)) |
|
2029 end |
|
2030 in |
|
2031 Symtab.empty |
|
2032 |> is_type_enc_fairly_sound type_enc |
|
2033 ? (fold (fold add_fact_syms) [conjs, facts] |
|
2034 #> (case type_enc of |
|
2035 Simple_Types (First_Order, Polymorphic, _) => |
|
2036 if avoid_first_order_ghost_type_vars then add_TYPE_const () |
|
2037 else I |
|
2038 | Simple_Types _ => I |
|
2039 | _ => fold add_undefined_const (var_types ()))) |
|
2040 end |
|
2041 |
|
2042 (* We add "bool" in case the helper "True_or_False" is included later. *) |
|
2043 fun default_mono level = |
|
2044 {maybe_finite_Ts = [@{typ bool}], |
|
2045 surely_finite_Ts = [@{typ bool}], |
|
2046 maybe_infinite_Ts = known_infinite_types, |
|
2047 surely_infinite_Ts = |
|
2048 case level of |
|
2049 Noninf_Nonmono_Types (Sound, _) => [] |
|
2050 | _ => known_infinite_types, |
|
2051 maybe_nonmono_Ts = [@{typ bool}]} |
|
2052 |
|
2053 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it |
|
2054 out with monotonicity" paper presented at CADE 2011. *) |
|
2055 fun add_iterm_mononotonicity_info _ _ (SOME false) _ mono = mono |
|
2056 | add_iterm_mononotonicity_info ctxt level _ |
|
2057 (IApp (IApp (IConst ((s, _), Type (_, [T, _]), _), tm1), tm2)) |
|
2058 (mono as {maybe_finite_Ts, surely_finite_Ts, maybe_infinite_Ts, |
|
2059 surely_infinite_Ts, maybe_nonmono_Ts}) = |
|
2060 if is_tptp_equal s andalso exists is_maybe_universal_var [tm1, tm2] then |
|
2061 case level of |
|
2062 Noninf_Nonmono_Types (soundness, _) => |
|
2063 if exists (type_instance ctxt T) surely_infinite_Ts orelse |
|
2064 member (type_equiv ctxt) maybe_finite_Ts T then |
|
2065 mono |
|
2066 else if is_type_kind_of_surely_infinite ctxt soundness |
|
2067 surely_infinite_Ts T then |
|
2068 {maybe_finite_Ts = maybe_finite_Ts, |
|
2069 surely_finite_Ts = surely_finite_Ts, |
|
2070 maybe_infinite_Ts = maybe_infinite_Ts, |
|
2071 surely_infinite_Ts = surely_infinite_Ts |> insert_type ctxt I T, |
|
2072 maybe_nonmono_Ts = maybe_nonmono_Ts} |
|
2073 else |
|
2074 {maybe_finite_Ts = maybe_finite_Ts |> insert (type_equiv ctxt) T, |
|
2075 surely_finite_Ts = surely_finite_Ts, |
|
2076 maybe_infinite_Ts = maybe_infinite_Ts, |
|
2077 surely_infinite_Ts = surely_infinite_Ts, |
|
2078 maybe_nonmono_Ts = maybe_nonmono_Ts |> insert_type ctxt I T} |
|
2079 | Fin_Nonmono_Types _ => |
|
2080 if exists (type_instance ctxt T) surely_finite_Ts orelse |
|
2081 member (type_equiv ctxt) maybe_infinite_Ts T then |
|
2082 mono |
|
2083 else if is_type_surely_finite ctxt T then |
|
2084 {maybe_finite_Ts = maybe_finite_Ts, |
|
2085 surely_finite_Ts = surely_finite_Ts |> insert_type ctxt I T, |
|
2086 maybe_infinite_Ts = maybe_infinite_Ts, |
|
2087 surely_infinite_Ts = surely_infinite_Ts, |
|
2088 maybe_nonmono_Ts = maybe_nonmono_Ts |> insert_type ctxt I T} |
|
2089 else |
|
2090 {maybe_finite_Ts = maybe_finite_Ts, |
|
2091 surely_finite_Ts = surely_finite_Ts, |
|
2092 maybe_infinite_Ts = maybe_infinite_Ts |> insert (type_equiv ctxt) T, |
|
2093 surely_infinite_Ts = surely_infinite_Ts, |
|
2094 maybe_nonmono_Ts = maybe_nonmono_Ts} |
|
2095 | _ => mono |
|
2096 else |
|
2097 mono |
|
2098 | add_iterm_mononotonicity_info _ _ _ _ mono = mono |
|
2099 fun add_fact_mononotonicity_info ctxt level |
|
2100 ({kind, iformula, ...} : translated_formula) = |
|
2101 formula_fold (SOME (kind <> Conjecture)) |
|
2102 (add_iterm_mononotonicity_info ctxt level) iformula |
|
2103 fun mononotonicity_info_for_facts ctxt type_enc facts = |
|
2104 let val level = level_of_type_enc type_enc in |
|
2105 default_mono level |
|
2106 |> is_type_level_monotonicity_based level |
|
2107 ? fold (add_fact_mononotonicity_info ctxt level) facts |
|
2108 end |
|
2109 |
|
2110 fun add_iformula_monotonic_types ctxt mono type_enc = |
|
2111 let |
|
2112 val level = level_of_type_enc type_enc |
|
2113 val should_encode = should_encode_type ctxt mono level |
|
2114 fun add_type T = not (should_encode T) ? insert_type ctxt I T |
|
2115 fun add_args (IApp (tm1, tm2)) = add_args tm1 #> add_term tm2 |
|
2116 | add_args _ = I |
|
2117 and add_term tm = add_type (ityp_of tm) #> add_args tm |
|
2118 in formula_fold NONE (K add_term) end |
|
2119 fun add_fact_monotonic_types ctxt mono type_enc = |
|
2120 add_iformula_monotonic_types ctxt mono type_enc |> fact_lift |
|
2121 fun monotonic_types_for_facts ctxt mono type_enc facts = |
|
2122 let val level = level_of_type_enc type_enc in |
|
2123 [] |> (polymorphism_of_type_enc type_enc = Polymorphic andalso |
|
2124 is_type_level_monotonicity_based level andalso |
|
2125 granularity_of_type_level level <> Ghost_Type_Arg_Vars) |
|
2126 ? fold (add_fact_monotonic_types ctxt mono type_enc) facts |
|
2127 end |
|
2128 |
|
2129 fun formula_line_for_guards_mono_type ctxt format mono type_enc T = |
|
2130 Formula (guards_sym_formula_prefix ^ |
|
2131 ascii_of (mangled_type format type_enc T), |
|
2132 Axiom, |
|
2133 IConst (`make_bound_var "X", T, []) |
|
2134 |> type_guard_iterm format type_enc T |
|
2135 |> AAtom |
|
2136 |> formula_from_iformula ctxt [] format mono type_enc |
|
2137 always_guard_var_in_formula (SOME true) |
|
2138 |> close_formula_universally |
|
2139 |> bound_tvars type_enc true (atomic_types_of T), |
|
2140 isabelle_info format introN, NONE) |
|
2141 |
|
2142 fun formula_line_for_tags_mono_type ctxt format mono type_enc T = |
|
2143 let val x_var = ATerm (`make_bound_var "X", []) in |
|
2144 Formula (tags_sym_formula_prefix ^ |
|
2145 ascii_of (mangled_type format type_enc T), |
|
2146 Axiom, |
|
2147 eq_formula type_enc (atomic_types_of T) false |
|
2148 (tag_with_type ctxt format mono type_enc NONE T x_var) x_var, |
|
2149 isabelle_info format simpN, NONE) |
|
2150 end |
|
2151 |
|
2152 fun problem_lines_for_mono_types ctxt format mono type_enc Ts = |
|
2153 case type_enc of |
|
2154 Simple_Types _ => [] |
|
2155 | Guards _ => |
|
2156 map (formula_line_for_guards_mono_type ctxt format mono type_enc) Ts |
|
2157 | Tags _ => map (formula_line_for_tags_mono_type ctxt format mono type_enc) Ts |
|
2158 |
|
2159 fun decl_line_for_sym ctxt format mono type_enc s |
|
2160 (s', T_args, T, pred_sym, ary, _) = |
|
2161 let |
|
2162 val thy = Proof_Context.theory_of ctxt |
|
2163 val (T, T_args) = |
|
2164 if null T_args then |
|
2165 (T, []) |
|
2166 else case unprefix_and_unascii const_prefix s of |
|
2167 SOME s' => |
|
2168 let |
|
2169 val s' = s' |> invert_const |
|
2170 val T = s' |> robust_const_type thy |
|
2171 in (T, robust_const_typargs thy (s', T)) end |
|
2172 | NONE => raise Fail "unexpected type arguments" |
|
2173 in |
|
2174 Decl (sym_decl_prefix ^ s, (s, s'), |
|
2175 T |> fused_type ctxt mono (level_of_type_enc type_enc) ary |
|
2176 |> ho_type_from_typ format type_enc pred_sym ary |
|
2177 |> not (null T_args) |
|
2178 ? curry ATyAbs (map (tvar_name o fst o dest_TVar) T_args)) |
|
2179 end |
|
2180 |
|
2181 fun formula_line_for_guards_sym_decl ctxt format conj_sym_kind mono type_enc n s |
|
2182 j (s', T_args, T, _, ary, in_conj) = |
|
2183 let |
|
2184 val thy = Proof_Context.theory_of ctxt |
|
2185 val (kind, maybe_negate) = |
|
2186 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot) |
|
2187 else (Axiom, I) |
|
2188 val (arg_Ts, res_T) = chop_fun ary T |
|
2189 val bound_names = 1 upto ary |> map (`I o make_bound_var o string_of_int) |
|
2190 val bounds = |
|
2191 bound_names ~~ arg_Ts |> map (fn (name, T) => IConst (name, T, [])) |
|
2192 val bound_Ts = |
|
2193 if exists (curry (op =) dummyT) T_args then |
|
2194 case level_of_type_enc type_enc of |
|
2195 All_Types => map SOME arg_Ts |
|
2196 | level => |
|
2197 if granularity_of_type_level level = Ghost_Type_Arg_Vars then |
|
2198 let val ghosts = ghost_type_args thy s ary in |
|
2199 map2 (fn j => if member (op =) ghosts j then SOME else K NONE) |
|
2200 (0 upto ary - 1) arg_Ts |
|
2201 end |
|
2202 else |
|
2203 replicate ary NONE |
|
2204 else |
|
2205 replicate ary NONE |
|
2206 in |
|
2207 Formula (guards_sym_formula_prefix ^ s ^ |
|
2208 (if n > 1 then "_" ^ string_of_int j else ""), kind, |
|
2209 IConst ((s, s'), T, T_args) |
|
2210 |> fold (curry (IApp o swap)) bounds |
|
2211 |> type_guard_iterm format type_enc res_T |
|
2212 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts) |
|
2213 |> formula_from_iformula ctxt [] format mono type_enc |
|
2214 always_guard_var_in_formula (SOME true) |
|
2215 |> close_formula_universally |
|
2216 |> bound_tvars type_enc (n > 1) (atomic_types_of T) |
|
2217 |> maybe_negate, |
|
2218 isabelle_info format introN, NONE) |
|
2219 end |
|
2220 |
|
2221 fun formula_lines_for_tags_sym_decl ctxt format conj_sym_kind mono type_enc n s |
|
2222 (j, (s', T_args, T, pred_sym, ary, in_conj)) = |
|
2223 let |
|
2224 val thy = Proof_Context.theory_of ctxt |
|
2225 val level = level_of_type_enc type_enc |
|
2226 val grain = granularity_of_type_level level |
|
2227 val ident_base = |
|
2228 tags_sym_formula_prefix ^ s ^ |
|
2229 (if n > 1 then "_" ^ string_of_int j else "") |
|
2230 val (kind, maybe_negate) = |
|
2231 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot) |
|
2232 else (Axiom, I) |
|
2233 val (arg_Ts, res_T) = chop_fun ary T |
|
2234 val bound_names = 1 upto ary |> map (`I o make_bound_var o string_of_int) |
|
2235 val bounds = bound_names |> map (fn name => ATerm (name, [])) |
|
2236 val cst = mk_aterm format type_enc (s, s') T_args |
|
2237 val eq = maybe_negate oo eq_formula type_enc (atomic_types_of T) pred_sym |
|
2238 val should_encode = should_encode_type ctxt mono level |
|
2239 val tag_with = tag_with_type ctxt format mono type_enc NONE |
|
2240 val add_formula_for_res = |
|
2241 if should_encode res_T then |
|
2242 let |
|
2243 val tagged_bounds = |
|
2244 if grain = Ghost_Type_Arg_Vars then |
|
2245 let val ghosts = ghost_type_args thy s ary in |
|
2246 map2 (fn (j, arg_T) => member (op =) ghosts j ? tag_with arg_T) |
|
2247 (0 upto ary - 1 ~~ arg_Ts) bounds |
|
2248 end |
|
2249 else |
|
2250 bounds |
|
2251 in |
|
2252 cons (Formula (ident_base ^ "_res", kind, |
|
2253 eq (tag_with res_T (cst bounds)) (cst tagged_bounds), |
|
2254 isabelle_info format simpN, NONE)) |
|
2255 end |
|
2256 else |
|
2257 I |
|
2258 fun add_formula_for_arg k = |
|
2259 let val arg_T = nth arg_Ts k in |
|
2260 if should_encode arg_T then |
|
2261 case chop k bounds of |
|
2262 (bounds1, bound :: bounds2) => |
|
2263 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind, |
|
2264 eq (cst (bounds1 @ tag_with arg_T bound :: bounds2)) |
|
2265 (cst bounds), |
|
2266 isabelle_info format simpN, NONE)) |
|
2267 | _ => raise Fail "expected nonempty tail" |
|
2268 else |
|
2269 I |
|
2270 end |
|
2271 in |
|
2272 [] |> not pred_sym ? add_formula_for_res |
|
2273 |> (Config.get ctxt type_tag_arguments andalso |
|
2274 grain = Positively_Naked_Vars) |
|
2275 ? fold add_formula_for_arg (ary - 1 downto 0) |
|
2276 end |
|
2277 |
|
2278 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd |
|
2279 |
|
2280 fun rationalize_decls ctxt (decls as decl :: (decls' as _ :: _)) = |
|
2281 let |
|
2282 val T = result_type_of_decl decl |
|
2283 |> map_type_tvar (fn (z, _) => TVar (z, HOLogic.typeS)) |
|
2284 in |
|
2285 if forall (type_generalization ctxt T o result_type_of_decl) decls' then |
|
2286 [decl] |
|
2287 else |
|
2288 decls |
|
2289 end |
|
2290 | rationalize_decls _ decls = decls |
|
2291 |
|
2292 fun problem_lines_for_sym_decls ctxt format conj_sym_kind mono type_enc |
|
2293 (s, decls) = |
|
2294 case type_enc of |
|
2295 Simple_Types _ => [decl_line_for_sym ctxt format mono type_enc s (hd decls)] |
|
2296 | Guards (_, level) => |
|
2297 let |
|
2298 val decls = decls |> rationalize_decls ctxt |
|
2299 val n = length decls |
|
2300 val decls = |
|
2301 decls |> filter (should_encode_type ctxt mono level |
|
2302 o result_type_of_decl) |
|
2303 in |
|
2304 (0 upto length decls - 1, decls) |
|
2305 |-> map2 (formula_line_for_guards_sym_decl ctxt format conj_sym_kind mono |
|
2306 type_enc n s) |
|
2307 end |
|
2308 | Tags (_, level) => |
|
2309 if granularity_of_type_level level = All_Vars then |
|
2310 [] |
|
2311 else |
|
2312 let val n = length decls in |
|
2313 (0 upto n - 1 ~~ decls) |
|
2314 |> maps (formula_lines_for_tags_sym_decl ctxt format conj_sym_kind mono |
|
2315 type_enc n s) |
|
2316 end |
|
2317 |
|
2318 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind mono type_enc |
|
2319 mono_Ts sym_decl_tab = |
|
2320 let |
|
2321 val syms = sym_decl_tab |> Symtab.dest |> sort_wrt fst |
|
2322 val mono_lines = |
|
2323 problem_lines_for_mono_types ctxt format mono type_enc mono_Ts |
|
2324 val decl_lines = |
|
2325 fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind |
|
2326 mono type_enc) |
|
2327 syms [] |
|
2328 in mono_lines @ decl_lines end |
|
2329 |
|
2330 fun needs_type_tag_idempotence ctxt (Tags (poly, level)) = |
|
2331 Config.get ctxt type_tag_idempotence andalso |
|
2332 is_type_level_monotonicity_based level andalso |
|
2333 poly <> Mangled_Monomorphic |
|
2334 | needs_type_tag_idempotence _ _ = false |
|
2335 |
|
2336 val implicit_declsN = "Should-be-implicit typings" |
|
2337 val explicit_declsN = "Explicit typings" |
|
2338 val factsN = "Relevant facts" |
|
2339 val class_relsN = "Class relationships" |
|
2340 val aritiesN = "Arities" |
|
2341 val helpersN = "Helper facts" |
|
2342 val conjsN = "Conjectures" |
|
2343 val free_typesN = "Type variables" |
|
2344 |
|
2345 (* TFF allows implicit declarations of types, function symbols, and predicate |
|
2346 symbols (with "$i" as the type of individuals), but some provers (e.g., |
|
2347 SNARK) require explicit declarations. The situation is similar for THF. *) |
|
2348 |
|
2349 fun default_type type_enc pred_sym s = |
|
2350 let |
|
2351 val ind = |
|
2352 case type_enc of |
|
2353 Simple_Types _ => |
|
2354 if String.isPrefix type_const_prefix s then atype_of_types |
|
2355 else individual_atype |
|
2356 | _ => individual_atype |
|
2357 fun typ 0 = if pred_sym then bool_atype else ind |
|
2358 | typ ary = AFun (ind, typ (ary - 1)) |
|
2359 in typ end |
|
2360 |
|
2361 fun nary_type_constr_type n = |
|
2362 funpow n (curry AFun atype_of_types) atype_of_types |
|
2363 |
|
2364 fun undeclared_syms_in_problem type_enc problem = |
|
2365 let |
|
2366 val declared = declared_syms_in_problem problem |
|
2367 fun do_sym name ty = |
|
2368 if member (op =) declared name then I else AList.default (op =) (name, ty) |
|
2369 fun do_type (AType (name as (s, _), tys)) = |
|
2370 is_tptp_user_symbol s |
|
2371 ? do_sym name (fn () => nary_type_constr_type (length tys)) |
|
2372 #> fold do_type tys |
|
2373 | do_type (AFun (ty1, ty2)) = do_type ty1 #> do_type ty2 |
|
2374 | do_type (ATyAbs (_, ty)) = do_type ty |
|
2375 fun do_term pred_sym (ATerm (name as (s, _), tms)) = |
|
2376 is_tptp_user_symbol s |
|
2377 ? do_sym name (fn _ => default_type type_enc pred_sym s (length tms)) |
|
2378 #> fold (do_term false) tms |
|
2379 | do_term _ (AAbs ((_, ty), tm)) = do_type ty #> do_term false tm |
|
2380 fun do_formula (AQuant (_, xs, phi)) = |
|
2381 fold do_type (map_filter snd xs) #> do_formula phi |
|
2382 | do_formula (AConn (_, phis)) = fold do_formula phis |
|
2383 | do_formula (AAtom tm) = do_term true tm |
|
2384 fun do_problem_line (Decl (_, _, ty)) = do_type ty |
|
2385 | do_problem_line (Formula (_, _, phi, _, _)) = do_formula phi |
|
2386 in |
|
2387 fold (fold do_problem_line o snd) problem [] |
|
2388 |> filter_out (is_built_in_tptp_symbol o fst o fst) |
|
2389 end |
|
2390 |
|
2391 fun declare_undeclared_syms_in_atp_problem type_enc problem = |
|
2392 let |
|
2393 val decls = |
|
2394 problem |
|
2395 |> undeclared_syms_in_problem type_enc |
|
2396 |> sort_wrt (fst o fst) |
|
2397 |> map (fn (x as (s, _), ty) => Decl (type_decl_prefix ^ s, x, ty ())) |
|
2398 in (implicit_declsN, decls) :: problem end |
|
2399 |
|
2400 fun exists_subdtype P = |
|
2401 let |
|
2402 fun ex U = P U orelse |
|
2403 (case U of Datatype.DtType (_, Us) => exists ex Us | _ => false) |
|
2404 in ex end |
|
2405 |
|
2406 fun is_poly_constr (_, Us) = |
|
2407 exists (exists_subdtype (fn Datatype.DtTFree _ => true | _ => false)) Us |
|
2408 |
|
2409 fun all_constrs_of_polymorphic_datatypes thy = |
|
2410 Symtab.fold (snd |
|
2411 #> #descr |
|
2412 #> maps (snd #> #3) |
|
2413 #> (fn cs => exists is_poly_constr cs ? append cs)) |
|
2414 (Datatype.get_all thy) [] |
|
2415 |> List.partition is_poly_constr |
|
2416 |> pairself (map fst) |
|
2417 |
|
2418 (* Forcing explicit applications is expensive for polymorphic encodings, because |
|
2419 it takes only one existential variable ranging over "'a => 'b" to ruin |
|
2420 everything. Hence we do it only if there are few facts (is normally the case |
|
2421 for "metis" and the minimizer. *) |
|
2422 val explicit_apply_threshold = 50 |
|
2423 |
|
2424 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc exporter |
|
2425 lam_trans readable_names preproc hyp_ts concl_t facts = |
|
2426 let |
|
2427 val thy = Proof_Context.theory_of ctxt |
|
2428 val type_enc = type_enc |> adjust_type_enc format |
|
2429 val explicit_apply = |
|
2430 if polymorphism_of_type_enc type_enc <> Polymorphic orelse |
|
2431 length facts <= explicit_apply_threshold then |
|
2432 NONE |
|
2433 else |
|
2434 SOME false |
|
2435 val lam_trans = |
|
2436 if lam_trans = keep_lamsN andalso |
|
2437 not (is_type_enc_higher_order type_enc) then |
|
2438 error ("Lambda translation scheme incompatible with first-order \ |
|
2439 \encoding.") |
|
2440 else |
|
2441 lam_trans |
|
2442 val (fact_names, classes, conjs, facts, class_rel_clauses, arity_clauses, |
|
2443 lifted) = |
|
2444 translate_formulas ctxt format prem_kind type_enc lam_trans preproc hyp_ts |
|
2445 concl_t facts |
|
2446 val sym_tab = sym_table_for_facts ctxt type_enc explicit_apply conjs facts |
|
2447 val mono = conjs @ facts |> mononotonicity_info_for_facts ctxt type_enc |
|
2448 val (polym_constrs, monom_constrs) = |
|
2449 all_constrs_of_polymorphic_datatypes thy |
|
2450 |>> map (make_fixed_const (SOME format)) |
|
2451 val firstorderize = |
|
2452 firstorderize_fact thy monom_constrs format type_enc sym_tab |
|
2453 val (conjs, facts) = (conjs, facts) |> pairself (map firstorderize) |
|
2454 val sym_tab = sym_table_for_facts ctxt type_enc (SOME false) conjs facts |
|
2455 val helpers = |
|
2456 sym_tab |> helper_facts_for_sym_table ctxt format type_enc |
|
2457 |> map firstorderize |
|
2458 val mono_Ts = |
|
2459 helpers @ conjs @ facts |> monotonic_types_for_facts ctxt mono type_enc |
|
2460 val class_decl_lines = decl_lines_for_classes type_enc classes |
|
2461 val sym_decl_lines = |
|
2462 (conjs, helpers @ facts) |
|
2463 |> sym_decl_table_for_facts ctxt format type_enc sym_tab |
|
2464 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind mono |
|
2465 type_enc mono_Ts |
|
2466 val helper_lines = |
|
2467 0 upto length helpers - 1 ~~ helpers |
|
2468 |> map (formula_line_for_fact ctxt polym_constrs format helper_prefix I |
|
2469 false true mono type_enc) |
|
2470 |> (if needs_type_tag_idempotence ctxt type_enc then |
|
2471 cons (type_tag_idempotence_fact format type_enc) |
|
2472 else |
|
2473 I) |
|
2474 (* Reordering these might confuse the proof reconstruction code or the SPASS |
|
2475 FLOTTER hack. *) |
|
2476 val problem = |
|
2477 [(explicit_declsN, class_decl_lines @ sym_decl_lines), |
|
2478 (factsN, |
|
2479 map (formula_line_for_fact ctxt polym_constrs format fact_prefix |
|
2480 ascii_of (not exporter) (not exporter) mono type_enc) |
|
2481 (0 upto length facts - 1 ~~ facts)), |
|
2482 (class_relsN, |
|
2483 map (formula_line_for_class_rel_clause format type_enc) |
|
2484 class_rel_clauses), |
|
2485 (aritiesN, |
|
2486 map (formula_line_for_arity_clause format type_enc) arity_clauses), |
|
2487 (helpersN, helper_lines), |
|
2488 (conjsN, |
|
2489 map (formula_line_for_conjecture ctxt polym_constrs format mono |
|
2490 type_enc) conjs), |
|
2491 (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))] |
|
2492 val problem = |
|
2493 problem |
|
2494 |> (case format of |
|
2495 CNF => ensure_cnf_problem |
|
2496 | CNF_UEQ => filter_cnf_ueq_problem |
|
2497 | FOF => I |
|
2498 | TFF (_, TPTP_Implicit) => I |
|
2499 | THF (_, TPTP_Implicit, _) => I |
|
2500 | _ => declare_undeclared_syms_in_atp_problem type_enc) |
|
2501 val (problem, pool) = problem |> nice_atp_problem readable_names format |
|
2502 fun add_sym_ary (s, {min_ary, ...} : sym_info) = |
|
2503 min_ary > 0 ? Symtab.insert (op =) (s, min_ary) |
|
2504 in |
|
2505 (problem, |
|
2506 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty, |
|
2507 fact_names |> Vector.fromList, |
|
2508 lifted, |
|
2509 Symtab.empty |> Symtab.fold add_sym_ary sym_tab) |
|
2510 end |
|
2511 |
|
2512 (* FUDGE *) |
|
2513 val conj_weight = 0.0 |
|
2514 val hyp_weight = 0.1 |
|
2515 val fact_min_weight = 0.2 |
|
2516 val fact_max_weight = 1.0 |
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2517 val type_info_default_weight = 0.8 |
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2518 |
|
2519 fun add_term_weights weight (ATerm (s, tms)) = |
|
2520 is_tptp_user_symbol s ? Symtab.default (s, weight) |
|
2521 #> fold (add_term_weights weight) tms |
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2522 | add_term_weights weight (AAbs (_, tm)) = add_term_weights weight tm |
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2523 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) = |
|
2524 formula_fold NONE (K (add_term_weights weight)) phi |
|
2525 | add_problem_line_weights _ _ = I |
|
2526 |
|
2527 fun add_conjectures_weights [] = I |
|
2528 | add_conjectures_weights conjs = |
|
2529 let val (hyps, conj) = split_last conjs in |
|
2530 add_problem_line_weights conj_weight conj |
|
2531 #> fold (add_problem_line_weights hyp_weight) hyps |
|
2532 end |
|
2533 |
|
2534 fun add_facts_weights facts = |
|
2535 let |
|
2536 val num_facts = length facts |
|
2537 fun weight_of j = |
|
2538 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j |
|
2539 / Real.fromInt num_facts |
|
2540 in |
|
2541 map weight_of (0 upto num_facts - 1) ~~ facts |
|
2542 |> fold (uncurry add_problem_line_weights) |
|
2543 end |
|
2544 |
|
2545 (* Weights are from 0.0 (most important) to 1.0 (least important). *) |
|
2546 fun atp_problem_weights problem = |
|
2547 let val get = these o AList.lookup (op =) problem in |
|
2548 Symtab.empty |
|
2549 |> add_conjectures_weights (get free_typesN @ get conjsN) |
|
2550 |> add_facts_weights (get factsN) |
|
2551 |> fold (fold (add_problem_line_weights type_info_default_weight) o get) |
|
2552 [explicit_declsN, class_relsN, aritiesN] |
|
2553 |> Symtab.dest |
|
2554 |> sort (prod_ord Real.compare string_ord o pairself swap) |
|
2555 end |
|
2556 |
|
2557 end; |
|