1 (* ID: $Id$ |
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2 Author: Claire Quigley |
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3 Copyright 2004 University of Cambridge |
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4 *) |
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5 |
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6 structure Recon_Transfer = |
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7 struct |
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8 |
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9 open Recon_Parse |
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10 |
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11 infixr 8 ++; infixr 7 >>; infixr 6 ||; |
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12 |
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13 val trace_path = Path.basic "transfer_trace"; |
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14 |
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15 fun trace s = if !Output.show_debug_msgs then File.append (File.tmp_path trace_path) s |
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16 else (); |
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17 |
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18 |
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19 (* Versions that include type information *) |
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20 |
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21 (* FIXME rename to str_of_thm *) |
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22 fun string_of_thm thm = |
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23 setmp show_sorts true (Pretty.str_of o Display.pretty_thm) thm; |
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24 |
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25 |
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26 (* check separate args in the watcher program for separating strings with a * or ; or something *) |
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27 |
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28 fun clause_strs_to_string [] str = str |
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29 | clause_strs_to_string (x::xs) str = clause_strs_to_string xs (str^x^"%") |
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30 |
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31 fun thmvars_to_string [] str = str |
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32 | thmvars_to_string (x::xs) str = thmvars_to_string xs (str^x^"%") |
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33 |
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34 |
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35 fun proofstep_to_string Axiom = "Axiom()" |
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36 | proofstep_to_string (Binary ((a,b), (c,d)))= |
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37 "Binary(("^(string_of_int a)^","^(string_of_int b)^"),("^(string_of_int c)^","^(string_of_int d)^"))" |
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38 | proofstep_to_string (Factor (a,b,c)) = |
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39 "Factor("^(string_of_int a)^","^(string_of_int b)^","^(string_of_int c)^")" |
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40 | proofstep_to_string (Para ((a,b), (c,d)))= |
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41 "Para(("^(string_of_int a)^","^(string_of_int b)^"),("^(string_of_int c)^","^(string_of_int d)^"))" |
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42 | proofstep_to_string (MRR ((a,b), (c,d))) = |
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43 "MRR(("^(string_of_int a)^","^(string_of_int b)^"),("^(string_of_int c)^","^(string_of_int d)^"))" |
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44 (*| proofstep_to_string (Rewrite((a,b),(c,d))) = |
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45 "Rewrite(("^(string_of_int a)^","^(string_of_int b)^"),("^(string_of_int c)^","^(string_of_int d)^"))"*) |
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46 |
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47 |
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48 fun proof_to_string (num,(step,clause_strs, thmvars)) = |
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49 (string_of_int num)^(proofstep_to_string step)^ |
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50 "["^(clause_strs_to_string clause_strs "")^"]["^(thmvars_to_string thmvars "")^"]" |
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51 |
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52 |
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53 fun proofs_to_string [] str = str |
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54 | proofs_to_string (x::xs) str = proofs_to_string xs (str ^ proof_to_string x) |
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55 |
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56 |
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57 fun init_proofstep_to_string (num, step, clause_strs) = |
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58 (string_of_int num)^" "^(proofstep_to_string step)^" "^ |
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59 (clause_strs_to_string clause_strs "")^" " |
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60 |
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61 fun init_proofsteps_to_string [] str = str |
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62 | init_proofsteps_to_string (x::xs) str = |
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63 init_proofsteps_to_string xs (str ^ init_proofstep_to_string x) |
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64 |
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65 |
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66 |
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67 (*** get a string representing the Isabelle ordered axioms ***) |
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68 |
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69 fun origAx_to_string (num,(meta,thmvars)) = |
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70 let val clause_strs = ReconOrderClauses.get_meta_lits_bracket meta |
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71 in |
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72 (string_of_int num)^"OrigAxiom()["^ |
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73 (clause_strs_to_string clause_strs "")^"]["^ |
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74 (thmvars_to_string thmvars "")^"]" |
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75 end |
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76 |
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77 |
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78 fun origAxs_to_string [] str = str |
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79 | origAxs_to_string (x::xs) str = |
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80 origAxs_to_string xs (str ^ origAx_to_string x ) |
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81 |
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82 |
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83 (*** get a string representing the Isabelle ordered axioms not used in the spass proof***) |
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84 |
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85 fun extraAx_to_string (num, (meta,thmvars)) = |
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86 let val clause_strs = ReconOrderClauses.get_meta_lits_bracket meta |
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87 in |
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88 (string_of_int num)^"ExtraAxiom()["^ |
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89 (clause_strs_to_string clause_strs "")^"]"^ |
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90 "["^(thmvars_to_string thmvars "")^"]" |
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91 end; |
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92 |
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93 fun extraAxs_to_string [] str = str |
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94 | extraAxs_to_string (x::xs) str = |
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95 let val newstr = extraAx_to_string x |
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96 in |
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97 extraAxs_to_string xs (str^newstr) |
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98 end; |
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99 |
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100 fun is_axiom (_,Axiom,str) = true |
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101 | is_axiom (_,_,_) = false |
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102 |
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103 fun get_step_nums [] nums = nums |
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104 | get_step_nums (( num:int,Axiom, str)::xs) nums = get_step_nums xs (nums@[num]) |
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105 |
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106 exception Noassoc; |
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107 |
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108 fun assoc_snd a [] = raise Noassoc |
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109 | assoc_snd a ((x, y)::t) = if a = y then x else assoc_snd a t; |
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110 |
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111 (* change to be something using check_order instead of a = y --> returns true if ASSERTION not raised in checkorder, false otherwise *) |
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112 |
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113 (*fun get_assoc_snds [] xs assocs= assocs |
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114 | get_assoc_snds (x::xs) ys assocs = get_assoc_snds xs ys (assocs@[((assoc_snd x ys))]) |
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115 *) |
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116 (*FIX - should this have vars in it? *) |
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117 fun there_out_of_order xs ys = (ReconOrderClauses.checkorder xs ys [] ([],[],[]); true) |
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118 handle _ => false |
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119 |
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120 fun assoc_out_of_order a [] = raise Noassoc |
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121 | assoc_out_of_order a ((b,c)::t) = if there_out_of_order a c then b else assoc_out_of_order a t; |
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122 |
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123 fun get_assoc_snds [] xs assocs= assocs |
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124 | get_assoc_snds (x::xs) ys assocs = get_assoc_snds xs ys (assocs@[((assoc_out_of_order x ys))]) |
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125 |
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126 fun add_if_not_inlist eq [] xs newlist = newlist |
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127 | add_if_not_inlist eq (y::ys) xs newlist = |
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128 if not (member eq xs y) then add_if_not_inlist eq ys xs (y::newlist) |
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129 else add_if_not_inlist eq ys xs newlist |
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130 |
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131 (*Flattens a list of list of strings to one string*) |
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132 fun onestr ls = String.concat (map String.concat ls); |
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133 |
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134 |
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135 (**** retrieve the axioms that were obtained from the clasimpset ****) |
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136 |
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137 (*Get names of axioms used. Axioms are indexed from 1, while the array is indexed from 0*) |
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138 fun get_axiom_names (names_arr: string array) step_nums = |
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139 let fun is_axiom n = n <= Array.length names_arr |
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140 fun index i = Array.sub(names_arr, i-1) |
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141 val axnums = List.filter is_axiom step_nums |
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142 val axnames = sort_distinct string_ord (map index axnums) |
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143 in |
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144 if length axnums = length step_nums then "UNSOUND!!" :: axnames |
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145 else axnames |
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146 end |
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147 |
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148 (*String contains multiple lines. We want those of the form |
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149 "253[0:Inp] et cetera..." |
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150 A list consisting of the first number in each line is returned. *) |
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151 fun get_spass_linenums proofstr = |
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152 let val toks = String.tokens (not o Char.isAlphaNum) |
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153 fun inputno (ntok::"0"::"Inp"::_) = Int.fromString ntok |
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154 | inputno _ = NONE |
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155 val lines = String.tokens (fn c => c = #"\n") proofstr |
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156 in List.mapPartial (inputno o toks) lines end |
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157 |
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158 fun get_axiom_names_spass proofstr names_arr = |
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159 get_axiom_names names_arr (get_spass_linenums proofstr); |
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160 |
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161 (*String contains multiple lines. We want those of the form |
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162 "number : ...: ...: initial..." *) |
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163 fun get_e_linenums proofstr = |
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164 let val fields = String.fields (fn c => c = #":") |
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165 val nospaces = String.translate (fn c => if c = #" " then "" else str c) |
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166 fun initial s = String.isPrefix "initial" (nospaces s) |
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167 fun firstno (line :: _ :: _ :: rule :: _) = |
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168 if initial rule then Int.fromString line else NONE |
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169 | firstno _ = NONE |
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170 val lines = String.tokens (fn c => c = #"\n") proofstr |
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171 in List.mapPartial (firstno o fields) lines end |
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172 |
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173 fun get_axiom_names_e proofstr names_arr = |
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174 get_axiom_names names_arr (get_e_linenums proofstr); |
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175 |
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176 (*String contains multiple lines. We want those of the form |
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177 "*********** [448, input] ***********". |
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178 A list consisting of the first number in each line is returned. *) |
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179 fun get_vamp_linenums proofstr = |
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180 let val toks = String.tokens (not o Char.isAlphaNum) |
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181 fun inputno [ntok,"input"] = Int.fromString ntok |
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182 | inputno _ = NONE |
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183 val lines = String.tokens (fn c => c = #"\n") proofstr |
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184 in List.mapPartial (inputno o toks) lines end |
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185 |
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186 fun get_axiom_names_vamp proofstr names_arr = |
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187 get_axiom_names names_arr (get_vamp_linenums proofstr); |
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188 |
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189 |
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190 (***********************************************) |
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191 (* get axioms for reconstruction *) |
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192 (***********************************************) |
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193 fun numclstr (vars, []) str = str |
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194 | numclstr ( vars, ((num, thm)::rest)) str = |
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195 let val newstr = str^(string_of_int num)^" "^(string_of_thm thm)^" " |
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196 in |
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197 numclstr (vars,rest) newstr |
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198 end |
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199 |
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200 fun addvars c (a,b) = (a,b,c) |
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201 |
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202 fun get_axioms_used proof_steps thms names_arr = |
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203 let val axioms = (List.filter is_axiom) proof_steps |
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204 val step_nums = get_step_nums axioms [] |
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205 |
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206 val clauses = make_clauses thms (*FIXME: must this be repeated??*) |
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207 |
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208 val vars = map thm_varnames clauses |
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209 |
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210 val distvars = distinct (op =) (fold append vars []) |
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211 val clause_terms = map prop_of clauses |
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212 val clause_frees = List.concat (map term_frees clause_terms) |
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213 |
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214 val frees = map lit_string_with_nums clause_frees; |
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215 |
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216 val distfrees = distinct (op =) frees |
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217 |
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218 val metas = map Meson.make_meta_clause clauses |
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219 val ax_strs = map #3 axioms |
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220 |
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221 (* literals of -all- axioms, not just those used by spass *) |
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222 val meta_strs = map ReconOrderClauses.get_meta_lits metas |
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223 |
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224 val metas_and_strs = ListPair.zip (metas,meta_strs) |
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225 val _ = trace ("\nAxioms: " ^ onestr ax_strs) |
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226 val _ = trace ("\nMeta_strs: " ^ onestr meta_strs) |
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227 |
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228 (* get list of axioms as thms with their variables *) |
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229 |
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230 val ax_metas = get_assoc_snds ax_strs metas_and_strs [] |
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231 val ax_vars = map thm_varnames ax_metas |
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232 val ax_with_vars = ListPair.zip (ax_metas,ax_vars) |
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233 |
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234 (* get list of extra axioms as thms with their variables *) |
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235 val extra_metas = add_if_not_inlist Thm.eq_thm metas ax_metas [] |
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236 val extra_vars = map thm_varnames extra_metas |
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237 val extra_with_vars = if not (null extra_metas) |
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238 then ListPair.zip (extra_metas,extra_vars) |
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239 else [] |
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240 in |
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241 (distfrees,distvars, extra_with_vars,ax_with_vars, ListPair.zip (step_nums,ax_metas)) |
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242 end; |
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243 |
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244 |
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245 (*********************************************************************) |
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246 (* Pass in spass string of proof and string version of isabelle goal *) |
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247 (* Get out reconstruction steps as a string to be sent to Isabelle *) |
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248 (*********************************************************************) |
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249 |
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250 fun rules_to_string [] = "NONE" |
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251 | rules_to_string xs = space_implode " " xs |
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252 |
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253 |
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254 (*The signal handler in watcher.ML must be able to read the output of this.*) |
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255 fun prover_lemma_list_aux getax proofstr probfile toParent ppid names_arr = |
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256 let val _ = trace |
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257 ("\n\nGetting lemma names. proofstr is " ^ proofstr ^ |
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258 "\nprobfile is " ^ probfile ^ |
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259 " num of clauses is " ^ string_of_int (Array.length names_arr)) |
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260 val axiom_names = getax proofstr names_arr |
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261 val ax_str = rules_to_string axiom_names |
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262 in |
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263 trace ("\nDone. Lemma list is " ^ ax_str); |
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264 TextIO.output (toParent, "Success. Lemmas used in automatic proof: " ^ |
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265 ax_str ^ "\n"); |
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266 TextIO.output (toParent, probfile ^ "\n"); |
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267 TextIO.flushOut toParent; |
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268 Posix.Process.kill(Posix.Process.K_PROC ppid, Posix.Signal.usr2) |
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269 end |
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270 handle exn => (*FIXME: exn handler is too general!*) |
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271 (trace ("\nprover_lemma_list_aux: In exception handler: " ^ |
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272 Toplevel.exn_message exn); |
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273 TextIO.output (toParent, "Translation failed for the proof: " ^ |
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274 String.toString proofstr ^ "\n"); |
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275 TextIO.output (toParent, probfile); |
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276 TextIO.flushOut toParent; |
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277 Posix.Process.kill(Posix.Process.K_PROC ppid, Posix.Signal.usr2)); |
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278 |
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279 val e_lemma_list = prover_lemma_list_aux get_axiom_names_e; |
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280 |
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281 val vamp_lemma_list = prover_lemma_list_aux get_axiom_names_vamp; |
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282 |
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283 val spass_lemma_list = prover_lemma_list_aux get_axiom_names_spass; |
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284 |
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285 |
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286 (**** Full proof reconstruction for SPASS (not really working) ****) |
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287 |
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288 fun spass_reconstruct proofstr probfile toParent ppid thms names_arr = |
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289 let val _ = trace ("\nspass_reconstruct. Proofstr is "^proofstr) |
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290 val tokens = #1(lex proofstr) |
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291 |
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292 (* parse spass proof into datatype *) |
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293 (***********************************) |
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294 val proof_steps = parse tokens |
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295 val _ = trace "\nParsing finished" |
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296 |
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297 (************************************) |
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298 (* recreate original subgoal as thm *) |
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299 (************************************) |
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300 (* get axioms as correctly numbered clauses w.r.t. the Spass proof *) |
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301 (* need to get prems_of thm, then get right one of the prems, relating to whichever*) |
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302 (* subgoal this is, and turn it into meta_clauses *) |
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303 (* should prob add array and table here, so that we can get axioms*) |
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304 (* produced from the clasimpset rather than the problem *) |
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305 val (frees,vars,extra_with_vars ,ax_with_vars,numcls) = get_axioms_used proof_steps thms names_arr |
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306 |
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307 (*val numcls_string = numclstr ( vars, numcls) ""*) |
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308 val _ = trace "\ngot axioms" |
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309 |
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310 (************************************) |
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311 (* translate proof *) |
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312 (************************************) |
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313 val _ = trace ("\nabout to translate proof, steps: " |
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314 ^ (init_proofsteps_to_string proof_steps "")) |
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315 val (newthm,proof) = translate_proof numcls proof_steps vars |
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316 val _ = trace ("translated proof, steps: "^(init_proofsteps_to_string proof_steps "")) |
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317 (***************************************************) |
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318 (* transfer necessary steps as strings to Isabelle *) |
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319 (***************************************************) |
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320 (* turn the proof into a string *) |
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321 val reconProofStr = proofs_to_string proof "" |
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322 (* do the bit for the Isabelle ordered axioms at the top *) |
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323 val ax_nums = map #1 numcls |
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324 val ax_strs = map ReconOrderClauses.get_meta_lits_bracket (map #2 numcls) |
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325 val numcls_strs = ListPair.zip (ax_nums,ax_strs) |
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326 val num_cls_vars = map (addvars vars) numcls_strs; |
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327 val reconIsaAxStr = origAxs_to_string (ListPair.zip (ax_nums,ax_with_vars)) "" |
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328 |
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329 val extra_nums = if not (null extra_with_vars) then (1 upto (length extra_with_vars)) |
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330 else [] |
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331 val reconExtraAxStr = extraAxs_to_string ( ListPair.zip (extra_nums,extra_with_vars)) "" |
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332 val frees_str = "["^(thmvars_to_string frees "")^"]" |
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333 val reconstr = (frees_str^reconExtraAxStr^reconIsaAxStr^reconProofStr) |
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334 val _ = trace ("\nReconstruction:\n" ^ reconstr) |
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335 in |
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336 TextIO.output (toParent, reconstr^"\n"); |
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337 TextIO.output (toParent, probfile ^ "\n"); |
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338 TextIO.flushOut toParent; |
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339 Posix.Process.kill(Posix.Process.K_PROC ppid, Posix.Signal.usr2); |
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340 all_tac |
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341 end |
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342 handle exn => (*FIXME: exn handler is too general!*) |
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343 (trace ("\nspass_reconstruct. In exception handler: " ^ Toplevel.exn_message exn); |
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344 TextIO.output (toParent,"Translation failed for SPASS proof:"^ |
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345 String.toString proofstr ^"\n"); |
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346 TextIO.output (toParent, probfile ^ "\n"); |
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347 TextIO.flushOut toParent; |
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348 Posix.Process.kill(Posix.Process.K_PROC ppid, Posix.Signal.usr2); all_tac) |
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349 |
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350 (**********************************************************************************) |
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351 (* At other end, want to turn back into datatype so can apply reconstruct_proof. *) |
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352 (* This will be done by the signal handler *) |
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353 (**********************************************************************************) |
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354 |
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355 (* Parse in the string version of the proof steps for reconstruction *) |
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356 (* Isar format: cl1 [BINARY 0 cl2 0];cl1 [PARAMOD 0 cl2 0]; cl1 [DEMOD 0 cl2];cl1 [FACTOR 1 2];*) |
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357 |
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358 |
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359 val term_numstep = |
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360 (number ++ (a (Other ",")) ++ number) >> (fn (a, (_, c)) => (a, c)) |
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361 |
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362 val extraaxiomstep = (a (Word "ExtraAxiom"))++ (a (Other "(")) ++(a (Other ")")) |
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363 >> (fn (_) => ExtraAxiom) |
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364 |
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365 |
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366 |
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367 val origaxiomstep = (a (Word "OrigAxiom"))++ (a (Other "(")) ++(a (Other ")")) |
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368 >> (fn (_) => OrigAxiom) |
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369 |
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370 |
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371 val axiomstep = (a (Word "Axiom"))++ (a (Other "(")) ++(a (Other ")")) |
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372 >> (fn (_) => Axiom) |
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373 |
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374 |
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375 |
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376 |
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377 val binarystep = (a (Word "Binary")) ++ (a (Other "(")) ++ (a (Other "(")) |
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378 ++ term_numstep ++ (a (Other ")")) ++ (a (Other ",")) |
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379 ++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")")) |
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380 >> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => Binary (c,e)) |
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381 |
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382 |
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383 val parastep = (a (Word "Para")) ++ (a (Other "(")) ++ (a (Other "(")) |
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384 ++ term_numstep ++ (a (Other ")")) ++ (a (Other ",")) |
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385 ++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")")) |
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386 >> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => Para(c, e)) |
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387 |
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388 val mrrstep = (a (Word "MRR")) ++ (a (Other "(")) ++ (a (Other "(")) |
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389 ++ term_numstep ++ (a (Other ")")) ++ (a (Other ",")) |
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390 ++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")")) |
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391 >> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => MRR(c, e)) |
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392 |
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393 |
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394 val factorstep = (a (Word "Factor")) ++ (a (Other "(")) |
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395 ++ number ++ (a (Other ",")) |
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396 ++ number ++ (a (Other ",")) |
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397 ++ number ++ (a (Other ")")) |
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398 |
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399 >> (fn (_, (_, (c, (_, (e,(_,(f,_))))))) => Factor (c,e,f)) |
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400 |
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401 |
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402 (*val rewritestep = (a (Word "Rewrite")) ++ (a (Other "(")) ++ (a (Other "(")) |
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403 ++ term_numstep ++ (a (Other ")")) ++ (a (Other ",")) |
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404 ++ (a (Other "(")) ++ term_numstep ++ (a (Other ")")) ++ (a (Other ")")) |
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405 >> (fn (_, (_, (_, (c, (_,(_,(_, (e,(_,_))))))))) => Rewrite (c,e))*) |
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406 |
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407 val obviousstep = (a (Word "Obvious")) ++ (a (Other "(")) |
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408 ++ term_numstep ++ (a (Other ")")) |
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409 >> (fn (_, (_, (c,_))) => Obvious (c)) |
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410 |
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411 val methodstep = extraaxiomstep || origaxiomstep || axiomstep ||binarystep || factorstep|| parastep || mrrstep || (*rewritestep ||*) obviousstep |
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412 |
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413 |
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414 val number_list_step = |
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415 ( number ++ many ((a (Other ",") ++ number)>> #2)) |
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416 >> (fn (a,b) => (a::b)) |
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417 |
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418 val numberlist_step = a (Other "[") ++ a (Other "]") |
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419 >>(fn (_,_) => ([]:int list)) |
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420 || a (Other "[") ++ number_list_step ++ a (Other "]") |
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421 >>(fn (_,(a,_)) => a) |
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422 |
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423 |
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424 |
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425 (** change this to allow P (x U) *) |
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426 fun arglist_step input = |
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427 ( word ++ many word >> (fn (a, b) => (a^" "^(space_implode " " b))) |
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428 ||word >> (fn (a) => (a)))input |
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429 |
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430 |
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431 fun literal_step input = (word ++ a (Other "(") ++ arglist_step ++ a (Other ")") |
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432 >>(fn (a, (b, (c,d))) => (a^" ("^(c)^")")) |
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433 || arglist_step >> (fn (a) => (a)))input |
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434 |
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435 |
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436 |
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437 (* fun term_step input = (a (Other "~") ++ arglist_step ++ a (Other "%")>> (fn (a,(b,c)) => ("~ "^b)) |
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438 || arglist_step ++ a (Other "%")>> (fn (a,b) => a ))input |
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439 *) |
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440 |
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441 |
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442 fun term_step input = (a (Other "~") ++ literal_step ++ a (Other "%")>> (fn (a,(b,c)) => ("~ "^b)) |
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443 || literal_step ++ a (Other "%")>> (fn (a,b) => a ))input |
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444 |
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445 |
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446 |
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447 |
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448 val term_list_step = |
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449 ( term_step ++ many ( term_step)) |
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450 >> (fn (a,b) => (a::b)) |
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451 |
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452 |
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453 val term_lists_step = a (Other "[") ++ a (Other "]") |
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454 >>(fn (_,_) => ([]:string list)) |
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455 || a (Other "[") ++ term_list_step ++ a (Other "]") |
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456 >>(fn (_,(a,_)) => a) |
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457 |
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458 |
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459 val linestep = number ++ methodstep ++ term_lists_step ++ term_lists_step |
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460 >> (fn (a, (b, (c,d))) => (a,(b,c,d))) |
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461 |
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462 val lines_step = many linestep |
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463 |
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464 val alllines_step = (term_lists_step ++ lines_step ) ++ finished >> #1 |
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465 |
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466 val parse_step = #1 o alllines_step |
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467 |
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468 |
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469 (* |
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470 val reconstr ="[P%x%xa%xb%]1OrigAxiom()[P x%~ P U%][U%]3OrigAxiom()[P U%~ P x%][U%]5OrigAxiom()[~ P xa%~ P U%][U%]7OrigAxiom()[P U%P xb%][U%]1Axiom()[P x%~ P U%][U%]3Axiom()[P U%~ P x%][U%]5Axiom()[~ P U%~ P xa%][U%]7Axiom()[P U%P xb%][U%]9Factor(5,0,1)[~ P xa%][]10Binary((9,0),(3,0))[~ P x%][]11Binary((10,0),(1,0))[~ P U%][U%]12Factor(7,0,1)[P xb%][]14Binary((11,0),(12,0))[][]%(EX x::'a::type. ALL y::'a::type. (P::'a::type => bool) x = P y) -->(EX x::'a::type. P x) = (ALL y::'a::type. P y)" |
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471 *) |
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472 |
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473 (************************************************************) |
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474 (* Construct an Isar style proof from a list of proof steps *) |
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475 (************************************************************) |
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476 (* want to assume all axioms, then do haves for the other clauses*) |
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477 (* then show for the last step *) |
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478 |
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479 (* replace ~ by not here *) |
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480 val change_nots = String.translate (fn c => if c = #"~" then "\\<not>" else str c); |
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481 |
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482 fun clstrs_to_string xs = space_implode "; " (map change_nots xs); |
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483 |
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484 fun thmvars_to_quantstring [] str = str |
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485 | thmvars_to_quantstring (x::[]) str =str^x^". " |
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486 | thmvars_to_quantstring (x::xs) str = thmvars_to_quantstring xs (str^(x^" ")) |
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487 |
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488 |
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489 fun clause_strs_to_isar clstrs [] = |
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490 "\"\\<lbrakk>"^(clstrs_to_string clstrs)^"\\<rbrakk> \\<Longrightarrow> False\"" |
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491 | clause_strs_to_isar clstrs thmvars = |
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492 "\"\\<And>"^(thmvars_to_quantstring thmvars "")^ |
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493 "\\<lbrakk>"^(clstrs_to_string clstrs)^"\\<rbrakk> \\<Longrightarrow> False\"" |
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494 |
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495 fun frees_to_isar_str clstrs = space_implode " " (map change_nots clstrs) |
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496 |
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497 |
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498 (***********************************************************************) |
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499 (* functions for producing assumptions for the Isabelle ordered axioms *) |
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500 (***********************************************************************) |
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501 (*val str = "[P%x%xa%xb%]1OrigAxiom()[P x%~ P U%][U%]3OrigAxiom()[P U%~ P x%][U%]5OrigAxiom()[~ P xa%~ P U%][U%]7OrigAxiom()[P U%P xb%][U%]1Axiom()[P x%~ P U%][U%]3Axiom()[P U%~ P x%][U%]5Axiom()[~ P U%~ P xa%][U%]7Axiom()[P U%P xb%][U%]9Factor(5,0,1)[~ P xa%][]10Binary((9,0),(3,0))[~ P x%][]11Binary((10,0),(1,0))[~ P U%][U%]12Factor(7,0,1)[P xb%][]14Binary((11,0),(12,0))[][]"; |
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502 num, rule, clausestrs, vars*) |
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503 |
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504 |
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505 (* assume the extra clauses - not used in Spass proof *) |
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506 |
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507 fun is_extraaxiom_step ( num:int,(ExtraAxiom, str, tstr)) = true |
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508 | is_extraaxiom_step (num, _) = false |
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509 |
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510 fun get_extraaxioms xs = List.filter (is_extraaxiom_step) ( xs) |
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511 |
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512 fun assume_isar_extraaxiom [] str = str |
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513 | assume_isar_extraaxiom ((numb,(step, clstr, thmvars))::xs) str = assume_isar_extraaxiom xs (str^"and cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstr thmvars)^"\n " ) |
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514 |
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515 |
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516 |
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517 fun assume_isar_extraaxioms [] = "" |
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518 |assume_isar_extraaxioms ((numb,(step, clstrs, thmstrs))::xs) = let val str = "assume cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstrs thmstrs)^"\n" |
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519 in |
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520 assume_isar_extraaxiom xs str |
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521 end |
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522 |
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523 (* assume the Isabelle ordered clauses *) |
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524 |
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525 fun is_origaxiom_step ( num:int,(OrigAxiom, str, tstr)) = true |
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526 | is_origaxiom_step (num, _) = false |
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527 |
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528 fun get_origaxioms xs = List.filter (is_origaxiom_step) ( xs) |
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529 |
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530 fun assume_isar_origaxiom [] str = str |
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531 | assume_isar_origaxiom ((numb,(step, clstr, thmvars))::xs) str = assume_isar_origaxiom xs (str^"and cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstr thmvars)^"\n " ) |
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532 |
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533 |
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534 |
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535 fun assume_isar_origaxioms ((numb,(step, clstrs, thmstrs))::xs) = let val str = "assume cl"^(string_of_int numb)^"': "^(clause_strs_to_isar clstrs thmstrs)^"\n" |
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536 in |
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537 assume_isar_origaxiom xs str |
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538 end |
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539 |
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540 |
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541 |
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542 fun is_axiom_step ( num:int,(Axiom, str, tstr)) = true |
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543 | is_axiom_step (num, _) = false |
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544 |
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545 fun get_axioms xs = List.filter (is_axiom_step) ( xs) |
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546 |
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547 fun have_isar_axiomline (numb,(step, clstrs, thmstrs))="have cl"^(string_of_int numb)^": "^(clause_strs_to_isar clstrs thmstrs)^"\n" |
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548 |
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549 fun by_isar_axiomline (numb,(step, clstrs, thmstrs))="by (rule cl"^ (string_of_int numb)^"') \n" |
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550 |
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551 |
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552 fun isar_axiomline (numb, (step, clstrs, thmstrs)) = (have_isar_axiomline (numb,(step,clstrs, thmstrs )))^( by_isar_axiomline(numb,(step,clstrs, thmstrs )) ) |
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553 |
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554 |
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555 fun isar_axiomlines [] str = str |
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556 | isar_axiomlines (x::xs) str = isar_axiomlines xs (str^(isar_axiomline x)) |
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557 |
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558 |
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559 fun have_isar_line (numb,(step, clstrs, thmstrs))="have cl"^(string_of_int numb)^": "^(clause_strs_to_isar clstrs thmstrs)^"\n" |
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560 (*FIX: ask Larry to add and mrr attribute *) |
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561 |
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562 fun by_isar_line ((Binary ((a,b), (c,d)))) = |
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563 "by(rule cl"^ |
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564 (string_of_int a)^" [binary "^(string_of_int b)^" cl"^ |
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565 (string_of_int c)^" "^(string_of_int d)^"])\n" |
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566 |by_isar_line ((MRR ((a,b), (c,d)))) = |
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567 "by(rule cl"^ |
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568 (string_of_int a)^" [binary "^(string_of_int b)^" cl"^ |
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569 (string_of_int c)^" "^(string_of_int d)^"])\n" |
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570 | by_isar_line ( (Para ((a,b), (c,d)))) = |
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571 "by (rule cl"^ |
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572 (string_of_int a)^" [paramod "^(string_of_int b)^" cl"^ |
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573 (string_of_int c)^" "^(string_of_int d)^"])\n" |
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574 | by_isar_line ((Factor ((a,b,c)))) = |
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575 "by (rule cl"^(string_of_int a)^" [factor "^(string_of_int b)^" "^ |
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576 (string_of_int c)^" ])\n" |
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577 (*| by_isar_line ( (Rewrite ((a,b),(c,d)))) = |
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578 "by (rule cl"^(string_of_int a)^" [demod "^(string_of_int b)^" "^ |
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579 (string_of_int c)^" "^(string_of_int d)^" ])\n"*) |
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580 | by_isar_line ( (Obvious ((a,b)))) = |
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581 "by (rule cl"^(string_of_int a)^" [obvious "^(string_of_int b)^" ])\n" |
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582 |
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583 fun isar_line (numb, (step, clstrs, thmstrs)) = (have_isar_line (numb,(step,clstrs, thmstrs )))^( by_isar_line step) |
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584 |
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585 |
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586 fun isar_lines [] str = str |
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587 | isar_lines (x::xs) str = isar_lines xs (str^(isar_line x)) |
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588 |
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589 fun last_isar_line (numb,( step, clstrs,thmstrs)) = "show \"False\"\n"^(by_isar_line step) |
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590 |
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591 |
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592 fun to_isar_proof (frees, xs) = |
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593 let val extraaxioms = get_extraaxioms xs |
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594 val extraax_num = length extraaxioms |
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595 val origaxioms_and_steps = Library.drop (extraax_num, xs) |
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596 |
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597 val origaxioms = get_origaxioms origaxioms_and_steps |
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598 val origax_num = length origaxioms |
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599 val axioms_and_steps = Library.drop (origax_num + extraax_num, xs) |
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600 val axioms = get_axioms axioms_and_steps |
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601 |
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602 val steps = Library.drop (origax_num, axioms_and_steps) |
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603 val (firststeps, laststep) = split_last steps |
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604 |
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605 val isar_proof = |
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606 ("show \"[your goal]\"\n")^ |
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607 ("proof (rule ccontr,skolemize, make_clauses) \n")^ |
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608 ("fix "^(frees_to_isar_str frees)^"\n")^ |
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609 (assume_isar_extraaxioms extraaxioms)^ |
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610 (assume_isar_origaxioms origaxioms)^ |
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611 (isar_axiomlines axioms "")^ |
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612 (isar_lines firststeps "")^ |
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613 (last_isar_line laststep)^ |
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614 ("qed") |
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615 val _ = trace ("\nto_isar_proof returns " ^ isar_proof) |
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616 in |
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617 isar_proof |
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618 end; |
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619 |
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620 (* get fix vars from axioms - all Frees *) |
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621 (* check each clause for meta-vars and /\ over them at each step*) |
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622 |
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623 (*******************************************************) |
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624 (* This assumes the thm list "numcls" is still there *) |
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625 (* In reality, should probably label it with an *) |
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626 (* ID number identifying the subgoal. This could *) |
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627 (* be passed over to the watcher, e.g. numcls25 *) |
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628 (*******************************************************) |
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629 |
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630 fun apply_res_thm str = |
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631 let val tokens = #1 (lex str); |
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632 val _ = trace ("\napply_res_thm. str is: "^str^"\n") |
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633 val (frees,recon_steps) = parse_step tokens |
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634 in |
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635 to_isar_proof (frees, recon_steps) |
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636 end |
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637 |
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638 end; |
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