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1 (* Title: HOL/Tools/Sledgehammer/sledgehammer_fact.ML |
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2 Author: Jia Meng, Cambridge University Computer Laboratory and NICTA |
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3 Author: Jasmin Blanchette, TU Muenchen |
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4 |
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5 Sledgehammer fact handling. |
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6 *) |
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7 |
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8 signature SLEDGEHAMMER_FACT = |
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9 sig |
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10 type status = ATP_Problem_Generate.status |
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11 type stature = ATP_Problem_Generate.stature |
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12 |
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13 type relevance_override = |
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14 {add : (Facts.ref * Attrib.src list) list, |
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15 del : (Facts.ref * Attrib.src list) list, |
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16 only : bool} |
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17 |
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18 val ignore_no_atp : bool Config.T |
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19 val instantiate_inducts : bool Config.T |
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20 val no_relevance_override : relevance_override |
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21 val fact_from_ref : |
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22 Proof.context -> unit Symtab.table -> thm list -> status Termtab.table |
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23 -> Facts.ref * Attrib.src list -> ((string * stature) * thm) list |
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24 val all_facts : |
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25 Proof.context -> bool -> 'a Symtab.table -> bool -> thm list |
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26 -> thm list -> status Termtab.table |
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27 -> (((unit -> string) * stature) * thm) list |
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28 val clasimpset_rule_table_of : Proof.context -> status Termtab.table |
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29 val maybe_instantiate_inducts : |
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30 Proof.context -> term list -> term -> (((unit -> string) * 'a) * thm) list |
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31 -> (((unit -> string) * 'a) * thm) list |
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32 val maybe_filter_no_atps : Proof.context -> ('a * thm) list -> ('a * thm) list |
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33 val nearly_all_facts : |
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34 Proof.context -> bool -> relevance_override -> thm list -> term list -> term |
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35 -> (((unit -> string) * stature) * thm) list |
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36 end; |
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37 |
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38 structure Sledgehammer_Fact : SLEDGEHAMMER_FACT = |
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39 struct |
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40 |
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41 open ATP_Problem_Generate |
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42 open Metis_Tactic |
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43 open Sledgehammer_Util |
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44 |
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45 type relevance_override = |
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46 {add : (Facts.ref * Attrib.src list) list, |
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47 del : (Facts.ref * Attrib.src list) list, |
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48 only : bool} |
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49 |
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50 val sledgehammer_prefix = "Sledgehammer" ^ Long_Name.separator |
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51 |
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52 (* experimental features *) |
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53 val ignore_no_atp = |
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54 Attrib.setup_config_bool @{binding sledgehammer_ignore_no_atp} (K false) |
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55 val instantiate_inducts = |
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56 Attrib.setup_config_bool @{binding sledgehammer_instantiate_inducts} (K false) |
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57 |
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58 val no_relevance_override = {add = [], del = [], only = false} |
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59 |
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60 fun needs_quoting reserved s = |
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61 Symtab.defined reserved s orelse |
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62 exists (not o Lexicon.is_identifier) (Long_Name.explode s) |
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63 |
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64 fun make_name reserved multi j name = |
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65 (name |> needs_quoting reserved name ? quote) ^ |
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66 (if multi then "(" ^ string_of_int j ^ ")" else "") |
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67 |
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68 fun explode_interval _ (Facts.FromTo (i, j)) = i upto j |
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69 | explode_interval max (Facts.From i) = i upto i + max - 1 |
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70 | explode_interval _ (Facts.Single i) = [i] |
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71 |
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72 val backquote = |
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73 raw_explode #> map (fn "`" => "\\`" | s => s) #> implode #> enclose "`" "`" |
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74 |
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75 (* unfolding these can yield really huge terms *) |
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76 val risky_defs = @{thms Bit0_def Bit1_def} |
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77 |
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78 fun is_rec_eq lhs = Term.exists_subterm (curry (op =) (head_of lhs)) |
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79 fun is_rec_def (@{const Trueprop} $ t) = is_rec_def t |
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80 | is_rec_def (@{const ==>} $ _ $ t2) = is_rec_def t2 |
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81 | is_rec_def (Const (@{const_name "=="}, _) $ t1 $ t2) = is_rec_eq t1 t2 |
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82 | is_rec_def (Const (@{const_name HOL.eq}, _) $ t1 $ t2) = is_rec_eq t1 t2 |
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83 | is_rec_def _ = false |
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84 |
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85 fun is_assum assms th = exists (fn ct => prop_of th aconv term_of ct) assms |
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86 fun is_chained chained_ths = member Thm.eq_thm_prop chained_ths |
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87 |
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88 fun scope_of_thm global assms chained_ths th = |
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89 if is_chained chained_ths th then Chained |
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90 else if global then Global |
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91 else if is_assum assms th then Assum |
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92 else Local |
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93 |
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94 val may_be_induction = |
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95 exists_subterm (fn Var (_, Type (@{type_name fun}, [_, T])) => |
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96 body_type T = @{typ bool} |
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97 | _ => false) |
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98 |
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99 fun status_of_thm css_table name th = |
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100 (* FIXME: use structured name *) |
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101 if (String.isSubstring ".induct" name orelse |
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102 String.isSubstring ".inducts" name) andalso |
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103 may_be_induction (prop_of th) then |
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104 Induction |
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105 else case Termtab.lookup css_table (prop_of th) of |
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106 SOME status => status |
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107 | NONE => General |
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108 |
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109 fun stature_of_thm global assms chained_ths css_table name th = |
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110 (scope_of_thm global assms chained_ths th, status_of_thm css_table name th) |
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111 |
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112 fun fact_from_ref ctxt reserved chained_ths css_table (xthm as (xref, args)) = |
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113 let |
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114 val ths = Attrib.eval_thms ctxt [xthm] |
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115 val bracket = |
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116 map (enclose "[" "]" o Pretty.str_of o Args.pretty_src ctxt) args |
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117 |> implode |
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118 fun nth_name j = |
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119 case xref of |
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120 Facts.Fact s => backquote s ^ bracket |
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121 | Facts.Named (("", _), _) => "[" ^ bracket ^ "]" |
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122 | Facts.Named ((name, _), NONE) => |
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123 make_name reserved (length ths > 1) (j + 1) name ^ bracket |
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124 | Facts.Named ((name, _), SOME intervals) => |
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125 make_name reserved true |
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126 (nth (maps (explode_interval (length ths)) intervals) j) name ^ |
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127 bracket |
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128 in |
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129 (ths, (0, [])) |
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130 |-> fold (fn th => fn (j, rest) => |
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131 let val name = nth_name j in |
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132 (j + 1, ((name, stature_of_thm false [] chained_ths |
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133 css_table name th), th) :: rest) |
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134 end) |
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135 |> snd |
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136 end |
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137 |
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138 (* Reject theorems with names like "List.filter.filter_list_def" or |
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139 "Accessible_Part.acc.defs", as these are definitions arising from packages. *) |
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140 fun is_package_def a = |
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141 let val names = Long_Name.explode a in |
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142 (length names > 2 andalso not (hd names = "local") andalso |
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143 String.isSuffix "_def" a) orelse String.isSuffix "_defs" a |
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144 end |
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145 |
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146 (* FIXME: put other record thms here, or declare as "no_atp" *) |
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147 fun multi_base_blacklist ctxt ho_atp = |
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148 ["defs", "select_defs", "update_defs", "split", "splits", "split_asm", |
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149 "cases", "ext_cases", "eq.simps", "eq.refl", "nchotomy", "case_cong", |
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150 "weak_case_cong"] |
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151 |> not (ho_atp orelse (Config.get ctxt instantiate_inducts)) ? |
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152 append ["induct", "inducts"] |
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153 |> map (prefix ".") |
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154 |
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155 val max_lambda_nesting = 3 (*only applies if not ho_atp*) |
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156 |
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157 fun term_has_too_many_lambdas max (t1 $ t2) = |
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158 exists (term_has_too_many_lambdas max) [t1, t2] |
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159 | term_has_too_many_lambdas max (Abs (_, _, t)) = |
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160 max = 0 orelse term_has_too_many_lambdas (max - 1) t |
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161 | term_has_too_many_lambdas _ _ = false |
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162 |
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163 (* Don't count nested lambdas at the level of formulas, since they are |
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164 quantifiers. *) |
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165 fun formula_has_too_many_lambdas true _ _ = false (*i.e. ho_atp*) |
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166 | formula_has_too_many_lambdas _ Ts (Abs (_, T, t)) = |
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167 formula_has_too_many_lambdas false (T :: Ts) t |
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168 | formula_has_too_many_lambdas _ Ts t = |
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169 if member (op =) [HOLogic.boolT, propT] (fastype_of1 (Ts, t)) then |
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170 exists (formula_has_too_many_lambdas false Ts) (#2 (strip_comb t)) |
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171 else |
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172 term_has_too_many_lambdas max_lambda_nesting t |
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173 |
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174 (* The max apply depth of any "metis" call in "Metis_Examples" (on 2007-10-31) |
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175 was 11. *) |
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176 val max_apply_depth = 15 |
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177 |
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178 fun apply_depth (f $ t) = Int.max (apply_depth f, apply_depth t + 1) |
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179 | apply_depth (Abs (_, _, t)) = apply_depth t |
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180 | apply_depth _ = 0 |
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181 |
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182 fun is_formula_too_complex ho_atp t = |
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183 apply_depth t > max_apply_depth orelse formula_has_too_many_lambdas ho_atp [] t |
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184 |
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185 (* FIXME: Extend to "Meson" and "Metis" *) |
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186 val exists_sledgehammer_const = |
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187 exists_Const (fn (s, _) => String.isPrefix sledgehammer_prefix s) |
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188 |
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189 (* FIXME: make more reliable *) |
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190 val exists_low_level_class_const = |
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191 exists_Const (fn (s, _) => |
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192 s = @{const_name equal_class.equal} orelse |
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193 String.isSubstring (Long_Name.separator ^ "class" ^ Long_Name.separator) s) |
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194 |
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195 fun is_metastrange_theorem th = |
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196 case head_of (concl_of th) of |
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197 Const (s, _) => (s <> @{const_name Trueprop} andalso |
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198 s <> @{const_name "=="}) |
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199 | _ => false |
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200 |
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201 fun is_that_fact th = |
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202 String.isSuffix (Long_Name.separator ^ Obtain.thatN) (Thm.get_name_hint th) |
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203 andalso exists_subterm (fn Free (s, _) => s = Name.skolem Auto_Bind.thesisN |
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204 | _ => false) (prop_of th) |
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205 |
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206 fun is_theorem_bad_for_atps ho_atp exporter thm = |
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207 is_metastrange_theorem thm orelse |
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208 (not exporter andalso |
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209 let val t = prop_of thm in |
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210 is_formula_too_complex ho_atp t orelse exists_type type_has_top_sort t orelse |
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211 exists_sledgehammer_const t orelse exists_low_level_class_const t orelse |
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212 is_that_fact thm |
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213 end) |
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214 |
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215 fun hackish_string_for_term ctxt t = |
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216 Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN) |
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217 (print_mode_value ())) (Syntax.string_of_term ctxt) t |
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218 |> String.translate (fn c => if Char.isPrint c then str c else "") |
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219 |> simplify_spaces |
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220 |
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221 (* This is a terrible hack. Free variables are sometimes coded as "M__" when |
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222 they are displayed as "M" and we want to avoid clashes with these. But |
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223 sometimes it's even worse: "Ma__" encodes "M". So we simply reserve all |
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224 prefixes of all free variables. In the worse case scenario, where the fact |
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225 won't be resolved correctly, the user can fix it manually, e.g., by naming |
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226 the fact in question. Ideally we would need nothing of it, but backticks |
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227 simply don't work with schematic variables. *) |
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228 fun all_prefixes_of s = |
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229 map (fn i => String.extract (s, 0, SOME i)) (1 upto size s - 1) |
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230 |
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231 fun close_form t = |
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232 (t, [] |> Term.add_free_names t |> maps all_prefixes_of) |
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233 |> fold (fn ((s, i), T) => fn (t', taken) => |
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234 let val s' = singleton (Name.variant_list taken) s in |
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235 ((if fastype_of t' = HOLogic.boolT then HOLogic.all_const |
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236 else Logic.all_const) T |
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237 $ Abs (s', T, abstract_over (Var ((s, i), T), t')), |
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238 s' :: taken) |
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239 end) |
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240 (Term.add_vars t [] |> sort_wrt (fst o fst)) |
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241 |> fst |
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242 |
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243 fun all_facts ctxt ho_atp reserved exporter add_ths chained_ths css_table = |
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244 let |
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245 val thy = Proof_Context.theory_of ctxt |
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246 val global_facts = Global_Theory.facts_of thy |
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247 val local_facts = Proof_Context.facts_of ctxt |
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248 val named_locals = local_facts |> Facts.dest_static [] |
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249 val assms = Assumption.all_assms_of ctxt |
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250 fun is_good_unnamed_local th = |
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251 not (Thm.has_name_hint th) andalso |
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252 forall (fn (_, ths) => not (member Thm.eq_thm_prop ths th)) named_locals |
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253 val unnamed_locals = |
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254 union Thm.eq_thm_prop (Facts.props local_facts) chained_ths |
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255 |> filter is_good_unnamed_local |> map (pair "" o single) |
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256 val full_space = |
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257 Name_Space.merge (Facts.space_of global_facts, Facts.space_of local_facts) |
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258 fun add_facts global foldx facts = |
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259 foldx (fn (name0, ths) => |
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260 if not exporter andalso name0 <> "" andalso |
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261 forall (not o member Thm.eq_thm_prop add_ths) ths andalso |
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262 (Facts.is_concealed facts name0 orelse |
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263 (not (Config.get ctxt ignore_no_atp) andalso |
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264 is_package_def name0) orelse |
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265 exists (fn s => String.isSuffix s name0) |
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266 (multi_base_blacklist ctxt ho_atp)) then |
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267 I |
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268 else |
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269 let |
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270 val multi = length ths > 1 |
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271 val backquote_thm = |
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272 backquote o hackish_string_for_term ctxt o close_form o prop_of |
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273 fun check_thms a = |
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274 case try (Proof_Context.get_thms ctxt) a of |
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275 NONE => false |
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276 | SOME ths' => eq_list Thm.eq_thm_prop (ths, ths') |
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277 in |
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278 pair 1 |
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279 #> fold (fn th => fn (j, (multis, unis)) => |
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280 (j + 1, |
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281 if not (member Thm.eq_thm_prop add_ths th) andalso |
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282 is_theorem_bad_for_atps ho_atp exporter th then |
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283 (multis, unis) |
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284 else |
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285 let |
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286 val new = |
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287 (((fn () => |
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288 if name0 = "" then |
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289 th |> backquote_thm |
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290 else |
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291 [Facts.extern ctxt facts name0, |
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292 Name_Space.extern ctxt full_space name0, |
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293 name0] |
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294 |> find_first check_thms |
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295 |> (fn SOME name => |
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296 make_name reserved multi j name |
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297 | NONE => "")), |
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298 stature_of_thm global assms chained_ths |
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299 css_table name0 th), th) |
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300 in |
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301 if multi then (new :: multis, unis) |
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302 else (multis, new :: unis) |
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303 end)) ths |
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304 #> snd |
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305 end) |
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306 in |
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307 (* The single-name theorems go after the multiple-name ones, so that single |
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308 names are preferred when both are available. *) |
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309 ([], []) |> add_facts false fold local_facts (unnamed_locals @ named_locals) |
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310 |> add_facts true Facts.fold_static global_facts global_facts |
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311 |> op @ |
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312 end |
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313 |
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314 fun clasimpset_rule_table_of ctxt = |
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315 let |
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316 val thy = Proof_Context.theory_of ctxt |
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317 val atomize = HOLogic.mk_Trueprop o Object_Logic.atomize_term thy |
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318 fun add stature normalizers get_th = |
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319 fold (fn rule => |
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320 let |
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321 val th = rule |> get_th |
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322 val t = |
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323 th |> Thm.maxidx_of th > 0 ? zero_var_indexes |> prop_of |
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324 in |
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325 fold (fn normalize => Termtab.update (normalize t, stature)) |
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326 (I :: normalizers) |
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327 end) |
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328 val {safeIs, (* safeEs, *) hazIs, (* hazEs, *) ...} = |
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329 ctxt |> claset_of |> Classical.rep_cs |
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330 val intros = Item_Net.content safeIs @ Item_Net.content hazIs |
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331 (* Add once it is used: |
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332 val elims = |
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333 Item_Net.content safeEs @ Item_Net.content hazEs |
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334 |> map Classical.classical_rule |
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335 *) |
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336 val simps = ctxt |> simpset_of |> dest_ss |> #simps |
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337 val specs = ctxt |> Spec_Rules.get |
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338 val (rec_defs, nonrec_defs) = |
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339 specs |> filter (curry (op =) Spec_Rules.Equational o fst) |
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340 |> maps (snd o snd) |
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341 |> filter_out (member Thm.eq_thm_prop risky_defs) |
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342 |> List.partition (is_rec_def o prop_of) |
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343 val spec_intros = |
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344 specs |> filter (member (op =) [Spec_Rules.Inductive, |
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345 Spec_Rules.Co_Inductive] o fst) |
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346 |> maps (snd o snd) |
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347 in |
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348 Termtab.empty |> add Simp [atomize] snd simps |
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349 |> add Simp [] I rec_defs |
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350 |> add Def [] I nonrec_defs |
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351 (* Add once it is used: |
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352 |> add Elim [] I elims |
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353 *) |
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354 |> add Intro [] I intros |
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355 |> add Inductive [] I spec_intros |
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356 end |
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357 |
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358 fun uniquify xs = |
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359 Termtab.fold (cons o snd) |
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360 (fold (Termtab.update o `(prop_of o snd)) xs Termtab.empty) [] |
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361 |
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362 fun struct_induct_rule_on th = |
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363 case Logic.strip_horn (prop_of th) of |
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364 (prems, @{const Trueprop} |
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365 $ ((p as Var ((p_name, 0), _)) $ (a as Var (_, ind_T)))) => |
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366 if not (is_TVar ind_T) andalso length prems > 1 andalso |
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367 exists (exists_subterm (curry (op aconv) p)) prems andalso |
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368 not (exists (exists_subterm (curry (op aconv) a)) prems) then |
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369 SOME (p_name, ind_T) |
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370 else |
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371 NONE |
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372 | _ => NONE |
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373 |
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374 fun instantiate_induct_rule ctxt concl_prop p_name ((name, stature), th) ind_x = |
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375 let |
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376 fun varify_noninducts (t as Free (s, T)) = |
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377 if (s, T) = ind_x orelse can dest_funT T then t else Var ((s, 0), T) |
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378 | varify_noninducts t = t |
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379 val p_inst = |
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380 concl_prop |> map_aterms varify_noninducts |> close_form |
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381 |> lambda (Free ind_x) |
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382 |> hackish_string_for_term ctxt |
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383 in |
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384 ((fn () => name () ^ "[where " ^ p_name ^ " = " ^ quote p_inst ^ "]", |
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385 stature), th |> read_instantiate ctxt [((p_name, 0), p_inst)]) |
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386 end |
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387 |
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388 fun type_match thy (T1, T2) = |
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389 (Sign.typ_match thy (T2, T1) Vartab.empty; true) |
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390 handle Type.TYPE_MATCH => false |
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391 |
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392 fun instantiate_if_induct_rule ctxt stmt stmt_xs (ax as (_, th)) = |
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393 case struct_induct_rule_on th of |
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394 SOME (p_name, ind_T) => |
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395 let val thy = Proof_Context.theory_of ctxt in |
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396 stmt_xs |> filter (fn (_, T) => type_match thy (T, ind_T)) |
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397 |> map_filter (try (instantiate_induct_rule ctxt stmt p_name ax)) |
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398 end |
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399 | NONE => [ax] |
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400 |
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401 fun external_frees t = |
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402 [] |> Term.add_frees t |> filter_out (can Name.dest_internal o fst) |
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403 |
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404 fun maybe_instantiate_inducts ctxt hyp_ts concl_t = |
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405 if Config.get ctxt instantiate_inducts then |
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406 let |
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407 val thy = Proof_Context.theory_of ctxt |
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408 val ind_stmt = |
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409 (hyp_ts |> filter_out (null o external_frees), concl_t) |
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410 |> Logic.list_implies |> Object_Logic.atomize_term thy |
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411 val ind_stmt_xs = external_frees ind_stmt |
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412 in maps (instantiate_if_induct_rule ctxt ind_stmt ind_stmt_xs) end |
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413 else |
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414 I |
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415 |
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416 fun maybe_filter_no_atps ctxt = |
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417 not (Config.get ctxt ignore_no_atp) ? filter_out (No_ATPs.member ctxt o snd) |
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418 |
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419 fun nearly_all_facts ctxt ho_atp ({add, only, ...} : relevance_override) |
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420 chained_ths hyp_ts concl_t = |
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421 if only andalso null add then |
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422 [] |
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423 else |
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424 let |
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425 val reserved = reserved_isar_keyword_table () |
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426 val add_ths = Attrib.eval_thms ctxt add |
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427 val css_table = clasimpset_rule_table_of ctxt |
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428 in |
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429 (if only then |
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430 maps (map (fn ((name, stature), th) => ((K name, stature), th)) |
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431 o fact_from_ref ctxt reserved chained_ths css_table) add |
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432 else |
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433 all_facts ctxt ho_atp reserved false add_ths chained_ths css_table) |
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434 |> maybe_instantiate_inducts ctxt hyp_ts concl_t |
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435 |> not only ? maybe_filter_no_atps ctxt |
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436 |> uniquify |
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437 end |
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438 |
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439 end; |