1 (* Title: HOL/Tools/res_reconstruct.ML |
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2 Author: Lawrence C Paulson and Claire Quigley, Cambridge University Computer Laboratory |
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3 |
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4 Transfer of proofs from external provers. |
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5 *) |
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6 |
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7 signature RES_RECONSTRUCT = |
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8 sig |
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9 val chained_hint: string |
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10 |
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11 val fix_sorts: sort Vartab.table -> term -> term |
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12 val invert_const: string -> string |
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13 val invert_type_const: string -> string |
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14 val num_typargs: theory -> string -> int |
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15 val make_tvar: string -> typ |
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16 val strip_prefix: string -> string -> string option |
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17 val setup: theory -> theory |
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18 (* extracting lemma list*) |
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19 val find_failure: string -> string option |
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20 val lemma_list: bool -> string -> |
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21 string * string vector * (int * int) * Proof.context * thm * int -> string * string list |
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22 (* structured proofs *) |
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23 val structured_proof: string -> |
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24 string * string vector * (int * int) * Proof.context * thm * int -> string * string list |
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25 end; |
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26 |
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27 structure Res_Reconstruct : RES_RECONSTRUCT = |
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28 struct |
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29 |
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30 val trace_path = Path.basic "atp_trace"; |
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31 |
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32 fun trace s = |
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33 if ! Res_Axioms.trace then File.append (File.tmp_path trace_path) s |
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34 else (); |
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35 |
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36 fun string_of_thm ctxt = PrintMode.setmp [] (Display.string_of_thm ctxt); |
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37 |
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38 (*For generating structured proofs: keep every nth proof line*) |
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39 val (modulus, modulus_setup) = Attrib.config_int "sledgehammer_modulus" 1; |
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40 |
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41 (*Indicates whether to include sort information in generated proofs*) |
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42 val (recon_sorts, recon_sorts_setup) = Attrib.config_bool "sledgehammer_sorts" true; |
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43 |
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44 (*Indicated whether to generate full proofs or just lemma lists - now via setup of atps*) |
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45 (* val (full_proofs, full_proofs_setup) = Attrib.config_bool "sledgehammer_full" false; *) |
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46 |
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47 val setup = modulus_setup #> recon_sorts_setup; |
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48 |
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49 (**** PARSING OF TSTP FORMAT ****) |
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50 |
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51 (*Syntax trees, either termlist or formulae*) |
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52 datatype stree = Int of int | Br of string * stree list; |
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53 |
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54 fun atom x = Br(x,[]); |
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55 |
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56 fun scons (x,y) = Br("cons", [x,y]); |
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57 val listof = List.foldl scons (atom "nil"); |
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58 |
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59 (*Strings enclosed in single quotes, e.g. filenames*) |
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60 val quoted = $$"'" |-- Scan.repeat (~$$"'") --| $$"'" >> implode; |
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61 |
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62 (*Intended for $true and $false*) |
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63 fun tf s = "c_" ^ str (Char.toUpper (String.sub(s,0))) ^ String.extract(s,1,NONE); |
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64 val truefalse = $$"$" |-- Symbol.scan_id >> (atom o tf); |
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65 |
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66 (*Integer constants, typically proof line numbers*) |
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67 fun is_digit s = Char.isDigit (String.sub(s,0)); |
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68 val integer = Scan.many1 is_digit >> (the o Int.fromString o implode); |
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69 |
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70 (*Generalized FO terms, which include filenames, numbers, etc.*) |
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71 fun termlist x = (term ::: Scan.repeat ($$"," |-- term)) x |
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72 and term x = (quoted >> atom || integer>>Int || truefalse || |
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73 Symbol.scan_id -- Scan.optional ($$"(" |-- termlist --| $$")") [] >> Br || |
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74 $$"(" |-- term --| $$")" || |
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75 $$"[" |-- Scan.optional termlist [] --| $$"]" >> listof) x; |
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76 |
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77 fun negate t = Br("c_Not", [t]); |
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78 fun equate (t1,t2) = Br("c_equal", [t1,t2]); |
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79 |
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80 (*Apply equal or not-equal to a term*) |
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81 fun syn_equal (t, NONE) = t |
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82 | syn_equal (t1, SOME (NONE, t2)) = equate (t1,t2) |
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83 | syn_equal (t1, SOME (SOME _, t2)) = negate (equate (t1,t2)); |
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84 |
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85 (*Literals can involve negation, = and !=.*) |
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86 fun literal x = ($$"~" |-- literal >> negate || |
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87 (term -- Scan.option (Scan.option ($$"!") --| $$"=" -- term) >> syn_equal)) x; |
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88 |
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89 val literals = literal ::: Scan.repeat ($$"|" |-- literal); |
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90 |
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91 (*Clause: a list of literals separated by the disjunction sign*) |
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92 val clause = $$"(" |-- literals --| $$")" || Scan.single literal; |
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93 |
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94 val annotations = $$"," |-- term -- Scan.option ($$"," |-- termlist); |
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95 |
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96 (*<cnf_annotated> ::= cnf(<name>,<formula_role>,<cnf_formula><annotations>). |
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97 The <name> could be an identifier, but we assume integers.*) |
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98 val tstp_line = (Scan.this_string "cnf" -- $$"(") |-- |
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99 integer --| $$"," -- Symbol.scan_id --| $$"," -- |
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100 clause -- Scan.option annotations --| $$ ")"; |
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101 |
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102 |
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103 (**** INTERPRETATION OF TSTP SYNTAX TREES ****) |
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104 |
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105 exception STREE of stree; |
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106 |
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107 (*If string s has the prefix s1, return the result of deleting it.*) |
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108 fun strip_prefix s1 s = |
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109 if String.isPrefix s1 s |
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110 then SOME (Res_Clause.undo_ascii_of (String.extract (s, size s1, NONE))) |
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111 else NONE; |
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112 |
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113 (*Invert the table of translations between Isabelle and ATPs*) |
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114 val type_const_trans_table_inv = |
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115 Symtab.make (map swap (Symtab.dest Res_Clause.type_const_trans_table)); |
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116 |
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117 fun invert_type_const c = |
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118 case Symtab.lookup type_const_trans_table_inv c of |
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119 SOME c' => c' |
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120 | NONE => c; |
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121 |
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122 fun make_tvar b = TVar(("'" ^ b, 0), HOLogic.typeS); |
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123 fun make_var (b,T) = Var((b,0),T); |
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124 |
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125 (*Type variables are given the basic sort, HOL.type. Some will later be constrained |
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126 by information from type literals, or by type inference.*) |
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127 fun type_of_stree t = |
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128 case t of |
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129 Int _ => raise STREE t |
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130 | Br (a,ts) => |
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131 let val Ts = map type_of_stree ts |
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132 in |
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133 case strip_prefix Res_Clause.tconst_prefix a of |
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134 SOME b => Type(invert_type_const b, Ts) |
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135 | NONE => |
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136 if not (null ts) then raise STREE t (*only tconsts have type arguments*) |
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137 else |
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138 case strip_prefix Res_Clause.tfree_prefix a of |
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139 SOME b => TFree("'" ^ b, HOLogic.typeS) |
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140 | NONE => |
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141 case strip_prefix Res_Clause.tvar_prefix a of |
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142 SOME b => make_tvar b |
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143 | NONE => make_tvar a (*Variable from the ATP, say X1*) |
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144 end; |
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145 |
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146 (*Invert the table of translations between Isabelle and ATPs*) |
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147 val const_trans_table_inv = |
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148 Symtab.update ("fequal", "op =") |
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149 (Symtab.make (map swap (Symtab.dest Res_Clause.const_trans_table))); |
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150 |
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151 fun invert_const c = |
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152 case Symtab.lookup const_trans_table_inv c of |
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153 SOME c' => c' |
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154 | NONE => c; |
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155 |
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156 (*The number of type arguments of a constant, zero if it's monomorphic*) |
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157 fun num_typargs thy s = length (Sign.const_typargs thy (s, Sign.the_const_type thy s)); |
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158 |
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159 (*Generates a constant, given its type arguments*) |
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160 fun const_of thy (a,Ts) = Const(a, Sign.const_instance thy (a,Ts)); |
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161 |
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162 (*First-order translation. No types are known for variables. HOLogic.typeT should allow |
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163 them to be inferred.*) |
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164 fun term_of_stree args thy t = |
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165 case t of |
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166 Int _ => raise STREE t |
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167 | Br ("hBOOL",[t]) => term_of_stree [] thy t (*ignore hBOOL*) |
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168 | Br ("hAPP",[t,u]) => term_of_stree (u::args) thy t |
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169 | Br (a,ts) => |
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170 case strip_prefix Res_Clause.const_prefix a of |
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171 SOME "equal" => |
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172 list_comb(Const ("op =", HOLogic.typeT), List.map (term_of_stree [] thy) ts) |
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173 | SOME b => |
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174 let val c = invert_const b |
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175 val nterms = length ts - num_typargs thy c |
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176 val us = List.map (term_of_stree [] thy) (List.take(ts,nterms) @ args) |
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177 (*Extra args from hAPP come AFTER any arguments given directly to the |
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178 constant.*) |
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179 val Ts = List.map type_of_stree (List.drop(ts,nterms)) |
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180 in list_comb(const_of thy (c, Ts), us) end |
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181 | NONE => (*a variable, not a constant*) |
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182 let val T = HOLogic.typeT |
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183 val opr = (*a Free variable is typically a Skolem function*) |
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184 case strip_prefix Res_Clause.fixed_var_prefix a of |
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185 SOME b => Free(b,T) |
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186 | NONE => |
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187 case strip_prefix Res_Clause.schematic_var_prefix a of |
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188 SOME b => make_var (b,T) |
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189 | NONE => make_var (a,T) (*Variable from the ATP, say X1*) |
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190 in list_comb (opr, List.map (term_of_stree [] thy) (ts@args)) end; |
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191 |
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192 (*Type class literal applied to a type. Returns triple of polarity, class, type.*) |
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193 fun constraint_of_stree pol (Br("c_Not",[t])) = constraint_of_stree (not pol) t |
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194 | constraint_of_stree pol t = case t of |
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195 Int _ => raise STREE t |
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196 | Br (a,ts) => |
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197 (case (strip_prefix Res_Clause.class_prefix a, map type_of_stree ts) of |
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198 (SOME b, [T]) => (pol, b, T) |
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199 | _ => raise STREE t); |
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200 |
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201 (** Accumulate type constraints in a clause: negative type literals **) |
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202 |
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203 fun addix (key,z) = Vartab.map_default (key,[]) (cons z); |
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204 |
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205 fun add_constraint ((false, cl, TFree(a,_)), vt) = addix ((a,~1),cl) vt |
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206 | add_constraint ((false, cl, TVar(ix,_)), vt) = addix (ix,cl) vt |
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207 | add_constraint (_, vt) = vt; |
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208 |
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209 (*False literals (which E includes in its proofs) are deleted*) |
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210 val nofalses = filter (not o equal HOLogic.false_const); |
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211 |
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212 (*Final treatment of the list of "real" literals from a clause.*) |
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213 fun finish [] = HOLogic.true_const (*No "real" literals means only type information*) |
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214 | finish lits = |
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215 case nofalses lits of |
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216 [] => HOLogic.false_const (*The empty clause, since we started with real literals*) |
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217 | xs => foldr1 HOLogic.mk_disj (rev xs); |
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218 |
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219 (*Accumulate sort constraints in vt, with "real" literals in lits.*) |
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220 fun lits_of_strees _ (vt, lits) [] = (vt, finish lits) |
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221 | lits_of_strees ctxt (vt, lits) (t::ts) = |
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222 lits_of_strees ctxt (add_constraint (constraint_of_stree true t, vt), lits) ts |
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223 handle STREE _ => |
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224 lits_of_strees ctxt (vt, term_of_stree [] (ProofContext.theory_of ctxt) t :: lits) ts; |
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225 |
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226 (*Update TVars/TFrees with detected sort constraints.*) |
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227 fun fix_sorts vt = |
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228 let fun tysubst (Type (a, Ts)) = Type (a, map tysubst Ts) |
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229 | tysubst (TVar (xi, s)) = TVar (xi, the_default s (Vartab.lookup vt xi)) |
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230 | tysubst (TFree (x, s)) = TFree (x, the_default s (Vartab.lookup vt (x, ~1))) |
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231 fun tmsubst (Const (a, T)) = Const (a, tysubst T) |
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232 | tmsubst (Free (a, T)) = Free (a, tysubst T) |
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233 | tmsubst (Var (xi, T)) = Var (xi, tysubst T) |
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234 | tmsubst (t as Bound _) = t |
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235 | tmsubst (Abs (a, T, t)) = Abs (a, tysubst T, tmsubst t) |
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236 | tmsubst (t $ u) = tmsubst t $ tmsubst u; |
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237 in fn t => if Vartab.is_empty vt then t else tmsubst t end; |
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238 |
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239 (*Interpret a list of syntax trees as a clause, given by "real" literals and sort constraints. |
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240 vt0 holds the initial sort constraints, from the conjecture clauses.*) |
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241 fun clause_of_strees ctxt vt0 ts = |
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242 let val (vt, dt) = lits_of_strees ctxt (vt0,[]) ts in |
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243 singleton (Syntax.check_terms ctxt) (TypeInfer.constrain HOLogic.boolT (fix_sorts vt dt)) |
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244 end; |
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245 |
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246 fun gen_all_vars t = fold_rev Logic.all (OldTerm.term_vars t) t; |
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247 |
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248 fun ints_of_stree_aux (Int n, ns) = n::ns |
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249 | ints_of_stree_aux (Br(_,ts), ns) = List.foldl ints_of_stree_aux ns ts; |
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250 |
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251 fun ints_of_stree t = ints_of_stree_aux (t, []); |
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252 |
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253 fun decode_tstp vt0 (name, role, ts, annots) ctxt = |
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254 let val deps = case annots of NONE => [] | SOME (source,_) => ints_of_stree source |
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255 val cl = clause_of_strees ctxt vt0 ts |
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256 in ((name, role, cl, deps), fold Variable.declare_term (OldTerm.term_frees cl) ctxt) end; |
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257 |
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258 fun dest_tstp ((((name, role), ts), annots), chs) = |
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259 case chs of |
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260 "."::_ => (name, role, ts, annots) |
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261 | _ => error ("TSTP line not terminated by \".\": " ^ implode chs); |
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262 |
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263 |
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264 (** Global sort constraints on TFrees (from tfree_tcs) are positive unit clauses. **) |
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265 |
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266 fun add_tfree_constraint ((true, cl, TFree(a,_)), vt) = addix ((a,~1),cl) vt |
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267 | add_tfree_constraint (_, vt) = vt; |
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268 |
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269 fun tfree_constraints_of_clauses vt [] = vt |
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270 | tfree_constraints_of_clauses vt ([lit]::tss) = |
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271 (tfree_constraints_of_clauses (add_tfree_constraint (constraint_of_stree true lit, vt)) tss |
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272 handle STREE _ => (*not a positive type constraint: ignore*) |
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273 tfree_constraints_of_clauses vt tss) |
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274 | tfree_constraints_of_clauses vt (_::tss) = tfree_constraints_of_clauses vt tss; |
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275 |
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276 |
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277 (**** Translation of TSTP files to Isar Proofs ****) |
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278 |
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279 fun decode_tstp_list ctxt tuples = |
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280 let val vt0 = tfree_constraints_of_clauses Vartab.empty (map #3 tuples) |
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281 in #1 (fold_map (decode_tstp vt0) tuples ctxt) end; |
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282 |
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283 (** Finding a matching assumption. The literals may be permuted, and variable names |
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284 may disagree. We have to try all combinations of literals (quadratic!) and |
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285 match up the variable names consistently. **) |
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286 |
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287 fun strip_alls_aux n (Const("all",_)$Abs(a,T,t)) = |
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288 strip_alls_aux (n+1) (subst_bound (Var ((a,n), T), t)) |
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289 | strip_alls_aux _ t = t; |
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290 |
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291 val strip_alls = strip_alls_aux 0; |
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292 |
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293 exception MATCH_LITERAL; |
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294 |
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295 (*Ignore types: they are not to be trusted...*) |
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296 fun match_literal (t1$u1) (t2$u2) env = |
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297 match_literal t1 t2 (match_literal u1 u2 env) |
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298 | match_literal (Abs (_,_,t1)) (Abs (_,_,t2)) env = |
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299 match_literal t1 t2 env |
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300 | match_literal (Bound i1) (Bound i2) env = |
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301 if i1=i2 then env else raise MATCH_LITERAL |
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302 | match_literal (Const(a1,_)) (Const(a2,_)) env = |
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303 if a1=a2 then env else raise MATCH_LITERAL |
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304 | match_literal (Free(a1,_)) (Free(a2,_)) env = |
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305 if a1=a2 then env else raise MATCH_LITERAL |
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306 | match_literal (Var(ix1,_)) (Var(ix2,_)) env = insert (op =) (ix1,ix2) env |
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307 | match_literal _ _ _ = raise MATCH_LITERAL; |
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308 |
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309 (*Checking that all variable associations are unique. The list env contains no |
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310 repetitions, but does it contain say (x,y) and (y,y)? *) |
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311 fun good env = |
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312 let val (xs,ys) = ListPair.unzip env |
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313 in not (has_duplicates (op=) xs orelse has_duplicates (op=) ys) end; |
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314 |
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315 (*Match one list of literals against another, ignoring types and the order of |
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316 literals. Sorting is unreliable because we don't have types or variable names.*) |
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317 fun matches_aux _ [] [] = true |
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318 | matches_aux env (lit::lits) ts = |
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319 let fun match1 us [] = false |
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320 | match1 us (t::ts) = |
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321 let val env' = match_literal lit t env |
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322 in (good env' andalso matches_aux env' lits (us@ts)) orelse |
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323 match1 (t::us) ts |
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324 end |
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325 handle MATCH_LITERAL => match1 (t::us) ts |
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326 in match1 [] ts end; |
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327 |
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328 (*Is this length test useful?*) |
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329 fun matches (lits1,lits2) = |
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330 length lits1 = length lits2 andalso |
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331 matches_aux [] (map Envir.eta_contract lits1) (map Envir.eta_contract lits2); |
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332 |
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333 fun permuted_clause t = |
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334 let val lits = HOLogic.disjuncts t |
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335 fun perm [] = NONE |
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336 | perm (ctm::ctms) = |
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337 if matches (lits, HOLogic.disjuncts (HOLogic.dest_Trueprop (strip_alls ctm))) |
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338 then SOME ctm else perm ctms |
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339 in perm end; |
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340 |
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341 fun have_or_show "show " _ = "show \"" |
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342 | have_or_show have lname = have ^ lname ^ ": \"" |
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343 |
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344 (*ctms is a list of conjecture clauses as yielded by Isabelle. Those returned by the |
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345 ATP may have their literals reordered.*) |
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346 fun isar_lines ctxt ctms = |
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347 let val string_of = PrintMode.setmp [] (fn term => Syntax.string_of_term ctxt term) |
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348 val _ = trace ("\n\nisar_lines: start\n") |
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349 fun doline _ (lname, t, []) = (*No deps: it's a conjecture clause, with no proof.*) |
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350 (case permuted_clause t ctms of |
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351 SOME u => "assume " ^ lname ^ ": \"" ^ string_of u ^ "\"\n" |
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352 | NONE => "assume? " ^ lname ^ ": \"" ^ string_of t ^ "\"\n") (*no match!!*) |
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353 | doline have (lname, t, deps) = |
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354 have_or_show have lname ^ string_of (gen_all_vars (HOLogic.mk_Trueprop t)) ^ |
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355 "\"\n by (metis " ^ space_implode " " deps ^ ")\n" |
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356 fun dolines [(lname, t, deps)] = [doline "show " (lname, t, deps)] |
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357 | dolines ((lname, t, deps)::lines) = doline "have " (lname, t, deps) :: dolines lines |
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358 in setmp_CRITICAL show_sorts (Config.get ctxt recon_sorts) dolines end; |
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359 |
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360 fun notequal t (_,t',_) = not (t aconv t'); |
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361 |
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362 (*No "real" literals means only type information*) |
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363 fun eq_types t = t aconv HOLogic.true_const; |
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364 |
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365 fun replace_dep (old:int, new) dep = if dep=old then new else [dep]; |
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366 |
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367 fun replace_deps (old:int, new) (lno, t, deps) = |
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368 (lno, t, List.foldl (uncurry (union (op =))) [] (map (replace_dep (old, new)) deps)); |
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369 |
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370 (*Discard axioms; consolidate adjacent lines that prove the same clause, since they differ |
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371 only in type information.*) |
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372 fun add_prfline ((lno, "axiom", t, []), lines) = (*axioms are not proof lines*) |
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373 if eq_types t (*must be clsrel/clsarity: type information, so delete refs to it*) |
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374 then map (replace_deps (lno, [])) lines |
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375 else |
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376 (case take_prefix (notequal t) lines of |
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377 (_,[]) => lines (*no repetition of proof line*) |
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378 | (pre, (lno', _, _) :: post) => (*repetition: replace later line by earlier one*) |
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379 pre @ map (replace_deps (lno', [lno])) post) |
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380 | add_prfline ((lno, _, t, []), lines) = (*no deps: conjecture clause*) |
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381 (lno, t, []) :: lines |
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382 | add_prfline ((lno, _, t, deps), lines) = |
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383 if eq_types t then (lno, t, deps) :: lines |
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384 (*Type information will be deleted later; skip repetition test.*) |
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385 else (*FIXME: Doesn't this code risk conflating proofs involving different types??*) |
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386 case take_prefix (notequal t) lines of |
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387 (_,[]) => (lno, t, deps) :: lines (*no repetition of proof line*) |
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388 | (pre, (lno', t', _) :: post) => |
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389 (lno, t', deps) :: (*repetition: replace later line by earlier one*) |
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390 (pre @ map (replace_deps (lno', [lno])) post); |
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391 |
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392 (*Recursively delete empty lines (type information) from the proof.*) |
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393 fun add_nonnull_prfline ((lno, t, []), lines) = (*no dependencies, so a conjecture clause*) |
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394 if eq_types t (*must be type information, tfree_tcs, clsrel, clsarity: delete refs to it*) |
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395 then delete_dep lno lines |
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396 else (lno, t, []) :: lines |
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397 | add_nonnull_prfline ((lno, t, deps), lines) = (lno, t, deps) :: lines |
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398 and delete_dep lno lines = List.foldr add_nonnull_prfline [] (map (replace_deps (lno, [])) lines); |
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399 |
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400 fun bad_free (Free (a,_)) = String.isPrefix "sko_" a |
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401 | bad_free _ = false; |
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402 |
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403 (*TVars are forbidden in goals. Also, we don't want lines with <2 dependencies. |
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404 To further compress proofs, setting modulus:=n deletes every nth line, and nlines |
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405 counts the number of proof lines processed so far. |
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406 Deleted lines are replaced by their own dependencies. Note that the "add_nonnull_prfline" |
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407 phase may delete some dependencies, hence this phase comes later.*) |
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408 fun add_wanted_prfline ctxt ((lno, t, []), (nlines, lines)) = |
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409 (nlines, (lno, t, []) :: lines) (*conjecture clauses must be kept*) |
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410 | add_wanted_prfline ctxt ((lno, t, deps), (nlines, lines)) = |
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411 if eq_types t orelse not (null (Term.add_tvars t [])) orelse |
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412 exists_subterm bad_free t orelse |
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413 (not (null lines) andalso (*final line can't be deleted for these reasons*) |
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414 (length deps < 2 orelse nlines mod (Config.get ctxt modulus) <> 0)) |
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415 then (nlines+1, map (replace_deps (lno, deps)) lines) (*Delete line*) |
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416 else (nlines+1, (lno, t, deps) :: lines); |
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417 |
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418 (*Replace numeric proof lines by strings, either from thm_names or sequential line numbers*) |
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419 fun stringify_deps thm_names deps_map [] = [] |
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420 | stringify_deps thm_names deps_map ((lno, t, deps) :: lines) = |
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421 if lno <= Vector.length thm_names (*axiom*) |
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422 then (Vector.sub(thm_names,lno-1), t, []) :: stringify_deps thm_names deps_map lines |
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423 else let val lname = Int.toString (length deps_map) |
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424 fun fix lno = if lno <= Vector.length thm_names |
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425 then SOME(Vector.sub(thm_names,lno-1)) |
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426 else AList.lookup op= deps_map lno; |
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427 in (lname, t, map_filter fix (distinct (op=) deps)) :: |
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428 stringify_deps thm_names ((lno,lname)::deps_map) lines |
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429 end; |
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430 |
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431 val proofstart = "proof (neg_clausify)\n"; |
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432 |
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433 fun isar_header [] = proofstart |
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434 | isar_header ts = proofstart ^ "fix " ^ space_implode " " ts ^ "\n"; |
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435 |
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436 fun decode_tstp_file cnfs ctxt th sgno thm_names = |
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437 let val _ = trace "\ndecode_tstp_file: start\n" |
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438 val tuples = map (dest_tstp o tstp_line o explode) cnfs |
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439 val _ = trace (Int.toString (length tuples) ^ " tuples extracted\n") |
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440 val ctxt = ProofContext.set_mode ProofContext.mode_schematic ctxt |
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441 val raw_lines = List.foldr add_prfline [] (decode_tstp_list ctxt tuples) |
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442 val _ = trace (Int.toString (length raw_lines) ^ " raw_lines extracted\n") |
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443 val nonnull_lines = List.foldr add_nonnull_prfline [] raw_lines |
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444 val _ = trace (Int.toString (length nonnull_lines) ^ " nonnull_lines extracted\n") |
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445 val (_,lines) = List.foldr (add_wanted_prfline ctxt) (0,[]) nonnull_lines |
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446 val _ = trace (Int.toString (length lines) ^ " lines extracted\n") |
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447 val (ccls,fixes) = Res_Axioms.neg_conjecture_clauses ctxt th sgno |
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448 val _ = trace (Int.toString (length ccls) ^ " conjecture clauses\n") |
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449 val ccls = map forall_intr_vars ccls |
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450 val _ = |
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451 if ! Res_Axioms.trace then app (fn th => trace ("\nccl: " ^ string_of_thm ctxt th)) ccls |
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452 else () |
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453 val ilines = isar_lines ctxt (map prop_of ccls) (stringify_deps thm_names [] lines) |
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454 val _ = trace "\ndecode_tstp_file: finishing\n" |
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455 in |
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456 isar_header (map #1 fixes) ^ implode ilines ^ "qed\n" |
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457 end handle STREE _ => error "Could not extract proof (ATP output malformed?)"; |
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458 |
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459 |
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460 (*=== EXTRACTING PROOF-TEXT === *) |
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461 |
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462 val begin_proof_strings = ["# SZS output start CNFRefutation.", |
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463 "=========== Refutation ==========", |
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464 "Here is a proof"]; |
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465 |
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466 val end_proof_strings = ["# SZS output end CNFRefutation", |
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467 "======= End of refutation =======", |
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468 "Formulae used in the proof"]; |
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469 |
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470 fun get_proof_extract proof = |
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471 let |
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472 (*splits to_split by the first possible of a list of splitters*) |
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473 val (begin_string, end_string) = |
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474 (find_first (fn s => String.isSubstring s proof) begin_proof_strings, |
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475 find_first (fn s => String.isSubstring s proof) end_proof_strings) |
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476 in |
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477 if is_none begin_string orelse is_none end_string |
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478 then error "Could not extract proof (no substring indicating a proof)" |
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479 else proof |> first_field (the begin_string) |> the |> snd |
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480 |> first_field (the end_string) |> the |> fst |
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481 end; |
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482 |
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483 (* ==== CHECK IF PROOF OF E OR VAMPIRE WAS SUCCESSFUL === *) |
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484 |
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485 val failure_strings_E = ["SZS status: Satisfiable","SZS status Satisfiable", |
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486 "SZS status: ResourceOut","SZS status ResourceOut","# Cannot determine problem status"]; |
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487 val failure_strings_vampire = ["Satisfiability detected", "Refutation not found", "CANNOT PROVE"]; |
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488 val failure_strings_SPASS = ["SPASS beiseite: Completion found.", |
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489 "SPASS beiseite: Ran out of time.", "SPASS beiseite: Maximal number of loops exceeded."]; |
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490 val failure_strings_remote = ["Remote-script could not extract proof"]; |
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491 fun find_failure proof = |
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492 let val failures = |
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493 map_filter (fn s => if String.isSubstring s proof then SOME s else NONE) |
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494 (failure_strings_E @ failure_strings_vampire @ failure_strings_SPASS @ failure_strings_remote) |
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495 val correct = null failures andalso |
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496 exists (fn s => String.isSubstring s proof) begin_proof_strings andalso |
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497 exists (fn s => String.isSubstring s proof) end_proof_strings |
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498 in |
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499 if correct then NONE |
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500 else if null failures then SOME "Output of ATP not in proper format" |
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501 else SOME (hd failures) end; |
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502 |
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503 (* === EXTRACTING LEMMAS === *) |
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504 (* lines have the form "cnf(108, axiom, ...", |
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505 the number (108) has to be extracted)*) |
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506 fun get_step_nums false proofextract = |
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507 let val toks = String.tokens (not o Char.isAlphaNum) |
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508 fun inputno ("cnf"::ntok::"axiom"::_) = Int.fromString ntok |
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509 | inputno ("cnf"::ntok::"negated"::"conjecture"::_) = Int.fromString ntok |
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510 | inputno _ = NONE |
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511 val lines = split_lines proofextract |
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512 in map_filter (inputno o toks) lines end |
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513 (*String contains multiple lines. We want those of the form |
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514 "253[0:Inp] et cetera..." |
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515 A list consisting of the first number in each line is returned. *) |
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516 | get_step_nums true proofextract = |
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517 let val toks = String.tokens (not o Char.isAlphaNum) |
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518 fun inputno (ntok::"0"::"Inp"::_) = Int.fromString ntok |
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519 | inputno _ = NONE |
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520 val lines = split_lines proofextract |
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521 in map_filter (inputno o toks) lines end |
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522 |
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523 (*extracting lemmas from tstp-output between the lines from above*) |
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524 fun extract_lemmas get_step_nums (proof, thm_names, conj_count, _, _, _) = |
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525 let |
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526 (* get the names of axioms from their numbers*) |
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527 fun get_axiom_names thm_names step_nums = |
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528 let |
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529 val last_axiom = Vector.length thm_names |
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530 fun is_axiom n = n <= last_axiom |
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531 fun is_conj n = n >= fst conj_count andalso n < fst conj_count + snd conj_count |
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532 fun getname i = Vector.sub(thm_names, i-1) |
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533 in |
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534 (sort_distinct string_ord (filter (fn x => x <> "??.unknown") |
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535 (map getname (filter is_axiom step_nums))), |
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536 exists is_conj step_nums) |
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537 end |
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538 val proofextract = get_proof_extract proof |
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539 in |
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540 get_axiom_names thm_names (get_step_nums proofextract) |
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541 end; |
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542 |
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543 (*Used to label theorems chained into the sledgehammer call*) |
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544 val chained_hint = "CHAINED"; |
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545 val nochained = filter_out (fn y => y = chained_hint) |
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546 |
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547 (* metis-command *) |
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548 fun metis_line [] = "apply metis" |
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549 | metis_line xs = "apply (metis " ^ space_implode " " xs ^ ")" |
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550 |
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551 (* atp_minimize [atp=<prover>] <lemmas> *) |
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552 fun minimize_line _ [] = "" |
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553 | minimize_line name lemmas = "For minimizing the number of lemmas try this command:\n" ^ |
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554 (Markup.markup Markup.sendback) ("atp_minimize [atp=" ^ name ^ "] " ^ |
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555 space_implode " " (nochained lemmas)) |
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556 |
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557 fun sendback_metis_nochained lemmas = |
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558 (Markup.markup Markup.sendback o metis_line) (nochained lemmas) |
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559 |
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560 fun lemma_list dfg name result = |
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561 let val (lemmas, used_conj) = extract_lemmas (get_step_nums dfg) result |
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562 in (sendback_metis_nochained lemmas ^ "\n" ^ minimize_line name lemmas ^ |
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563 (if used_conj then "" |
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564 else "\nWarning: Goal is provable because context is inconsistent."), |
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565 nochained lemmas) |
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566 end; |
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567 |
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568 (* === Extracting structured Isar-proof === *) |
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569 fun structured_proof name (result as (proof, thm_names, conj_count, ctxt, goal, subgoalno)) = |
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570 let |
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571 (*Could use split_lines, but it can return blank lines...*) |
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572 val lines = String.tokens (equal #"\n"); |
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573 val nospaces = String.translate (fn c => if Char.isSpace c then "" else str c) |
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574 val proofextract = get_proof_extract proof |
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575 val cnfs = filter (String.isPrefix "cnf(") (map nospaces (lines proofextract)) |
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576 val (one_line_proof, lemma_names) = lemma_list false name result |
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577 val structured = |
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578 if chained_hint mem_string (String.tokens (fn c => c = #" ") one_line_proof) then "" |
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579 else decode_tstp_file cnfs ctxt goal subgoalno thm_names |
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580 in |
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581 (one_line_proof ^ "\n\n" ^ Markup.markup Markup.sendback structured, lemma_names) |
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582 end |
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583 |
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584 end; |
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