1 (* Title: HOL/SMT/Tools/smt_translate.ML |
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2 Author: Sascha Boehme, TU Muenchen |
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3 |
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4 Translate theorems into an SMT intermediate format and serialize them. |
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5 *) |
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6 |
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7 signature SMT_TRANSLATE = |
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8 sig |
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9 (* intermediate term structure *) |
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10 datatype squant = SForall | SExists |
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11 datatype 'a spattern = SPat of 'a list | SNoPat of 'a list |
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12 datatype sterm = |
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13 SVar of int | |
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14 SApp of string * sterm list | |
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15 SLet of string * sterm * sterm | |
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16 SQua of squant * string list * sterm spattern list * sterm |
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17 |
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18 (* configuration options *) |
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19 type prefixes = {sort_prefix: string, func_prefix: string} |
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20 type strict = { |
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21 is_builtin_conn: string * typ -> bool, |
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22 is_builtin_pred: string * typ -> bool, |
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23 is_builtin_distinct: bool} |
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24 type builtins = { |
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25 builtin_typ: typ -> string option, |
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26 builtin_num: typ -> int -> string option, |
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27 builtin_fun: string * typ -> term list -> (string * term list) option } |
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28 datatype smt_theory = Integer | Real | Bitvector |
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29 type sign = { |
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30 theories: smt_theory list, |
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31 sorts: string list, |
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32 funcs: (string * (string list * string)) list } |
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33 type config = { |
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34 prefixes: prefixes, |
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35 strict: strict option, |
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36 builtins: builtins, |
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37 serialize: sign -> sterm list -> string } |
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38 type recon = { |
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39 typs: typ Symtab.table, |
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40 terms: term Symtab.table, |
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41 unfolds: thm list, |
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42 assms: thm list option } |
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43 |
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44 val translate: config -> Proof.context -> thm list -> string * recon |
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45 end |
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46 |
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47 structure SMT_Translate: SMT_TRANSLATE = |
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48 struct |
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49 |
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50 (* intermediate term structure *) |
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51 |
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52 datatype squant = SForall | SExists |
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53 |
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54 datatype 'a spattern = SPat of 'a list | SNoPat of 'a list |
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55 |
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56 datatype sterm = |
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57 SVar of int | |
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58 SApp of string * sterm list | |
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59 SLet of string * sterm * sterm | |
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60 SQua of squant * string list * sterm spattern list * sterm |
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61 |
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62 |
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63 |
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64 (* configuration options *) |
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65 |
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66 type prefixes = {sort_prefix: string, func_prefix: string} |
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67 |
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68 type strict = { |
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69 is_builtin_conn: string * typ -> bool, |
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70 is_builtin_pred: string * typ -> bool, |
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71 is_builtin_distinct: bool} |
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72 |
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73 type builtins = { |
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74 builtin_typ: typ -> string option, |
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75 builtin_num: typ -> int -> string option, |
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76 builtin_fun: string * typ -> term list -> (string * term list) option } |
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77 |
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78 datatype smt_theory = Integer | Real | Bitvector |
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79 |
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80 type sign = { |
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81 theories: smt_theory list, |
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82 sorts: string list, |
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83 funcs: (string * (string list * string)) list } |
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84 |
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85 type config = { |
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86 prefixes: prefixes, |
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87 strict: strict option, |
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88 builtins: builtins, |
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89 serialize: sign -> sterm list -> string } |
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90 |
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91 type recon = { |
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92 typs: typ Symtab.table, |
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93 terms: term Symtab.table, |
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94 unfolds: thm list, |
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95 assms: thm list option } |
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96 |
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97 |
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98 |
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99 (* utility functions *) |
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100 |
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101 val dest_funT = |
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102 let |
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103 fun dest Ts 0 T = (rev Ts, T) |
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104 | dest Ts i (Type ("fun", [T, U])) = dest (T::Ts) (i-1) U |
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105 | dest _ _ T = raise TYPE ("dest_funT", [T], []) |
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106 in dest [] end |
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107 |
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108 val quantifier = (fn |
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109 @{const_name All} => SOME SForall |
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110 | @{const_name Ex} => SOME SExists |
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111 | _ => NONE) |
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112 |
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113 fun group_quant qname Ts (t as Const (q, _) $ Abs (_, T, u)) = |
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114 if q = qname then group_quant qname (T :: Ts) u else (Ts, t) |
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115 | group_quant _ Ts t = (Ts, t) |
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116 |
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117 fun dest_pat ts (Const (@{const_name pat}, _) $ t) = SPat (rev (t :: ts)) |
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118 | dest_pat ts (Const (@{const_name nopat}, _) $ t) = SNoPat (rev (t :: ts)) |
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119 | dest_pat ts (Const (@{const_name andpat}, _) $ p $ t) = dest_pat (t::ts) p |
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120 | dest_pat _ t = raise TERM ("dest_pat", [t]) |
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121 |
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122 fun dest_trigger (@{term trigger} $ tl $ t) = |
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123 (map (dest_pat []) (HOLogic.dest_list tl), t) |
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124 | dest_trigger t = ([], t) |
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125 |
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126 fun dest_quant qn T t = quantifier qn |> Option.map (fn q => |
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127 let |
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128 val (Ts, u) = group_quant qn [T] t |
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129 val (ps, b) = dest_trigger u |
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130 in (q, rev Ts, ps, b) end) |
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131 |
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132 fun fold_map_pat f (SPat ts) = fold_map f ts #>> SPat |
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133 | fold_map_pat f (SNoPat ts) = fold_map f ts #>> SNoPat |
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134 |
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135 fun prop_of thm = HOLogic.dest_Trueprop (Thm.prop_of thm) |
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136 |
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137 |
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138 |
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139 (* enforce a strict separation between formulas and terms *) |
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140 |
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141 val term_eq_rewr = @{lemma "x term_eq y == x = y" by (simp add: term_eq_def)} |
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142 |
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143 val term_bool = @{lemma "~(True term_eq False)" by (simp add: term_eq_def)} |
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144 val term_bool' = Simplifier.rewrite_rule [term_eq_rewr] term_bool |
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145 |
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146 |
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147 val needs_rewrite = Thm.prop_of #> Term.exists_subterm (fn |
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148 Const (@{const_name Let}, _) => true |
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149 | @{term "op = :: bool => _"} $ _ $ @{term True} => true |
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150 | Const (@{const_name If}, _) $ _ $ @{term True} $ @{term False} => true |
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151 | _ => false) |
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152 |
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153 val rewrite_rules = [ |
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154 Let_def, |
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155 @{lemma "P = True == P" by (rule eq_reflection) simp}, |
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156 @{lemma "if P then True else False == P" by (rule eq_reflection) simp}] |
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157 |
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158 fun rewrite ctxt = Simplifier.full_rewrite |
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159 (Simplifier.context ctxt empty_ss addsimps rewrite_rules) |
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160 |
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161 fun normalize ctxt thm = |
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162 if needs_rewrite thm then Conv.fconv_rule (rewrite ctxt) thm else thm |
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163 |
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164 val unfold_rules = term_eq_rewr :: rewrite_rules |
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165 |
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166 |
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167 val revert_types = |
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168 let |
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169 fun revert @{typ prop} = @{typ bool} |
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170 | revert (Type (n, Ts)) = Type (n, map revert Ts) |
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171 | revert T = T |
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172 in Term.map_types revert end |
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173 |
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174 |
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175 fun strictify {is_builtin_conn, is_builtin_pred, is_builtin_distinct} ctxt = |
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176 let |
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177 |
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178 fun is_builtin_conn' (@{const_name True}, _) = false |
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179 | is_builtin_conn' (@{const_name False}, _) = false |
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180 | is_builtin_conn' c = is_builtin_conn c |
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181 |
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182 val propT = @{typ prop} and boolT = @{typ bool} |
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183 val as_propT = (fn @{typ bool} => propT | T => T) |
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184 fun mapTs f g = Term.strip_type #> (fn (Ts, T) => map f Ts ---> g T) |
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185 fun conn (n, T) = (n, mapTs as_propT as_propT T) |
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186 fun pred (n, T) = (n, mapTs I as_propT T) |
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187 |
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188 val term_eq = @{term "op = :: bool => _"} |> Term.dest_Const |> pred |
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189 fun as_term t = Const term_eq $ t $ @{term True} |
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190 |
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191 val if_term = Const (@{const_name If}, [propT, boolT, boolT] ---> boolT) |
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192 fun wrap_in_if t = if_term $ t $ @{term True} $ @{term False} |
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193 |
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194 fun in_list T f t = HOLogic.mk_list T (map f (HOLogic.dest_list t)) |
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195 |
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196 fun in_term t = |
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197 (case Term.strip_comb t of |
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198 (c as Const (@{const_name If}, _), [t1, t2, t3]) => |
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199 c $ in_form t1 $ in_term t2 $ in_term t3 |
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200 | (h as Const c, ts) => |
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201 if is_builtin_conn' (conn c) orelse is_builtin_pred (pred c) |
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202 then wrap_in_if (in_form t) |
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203 else Term.list_comb (h, map in_term ts) |
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204 | (h as Free _, ts) => Term.list_comb (h, map in_term ts) |
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205 | _ => t) |
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206 |
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207 and in_pat ((c as Const (@{const_name pat}, _)) $ t) = c $ in_term t |
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208 | in_pat ((c as Const (@{const_name nopat}, _)) $ t) = c $ in_term t |
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209 | in_pat ((c as Const (@{const_name andpat}, _)) $ p $ t) = |
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210 c $ in_pat p $ in_term t |
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211 | in_pat t = raise TERM ("in_pat", [t]) |
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212 |
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213 and in_pats p = in_list @{typ pattern} in_pat p |
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214 |
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215 and in_trig ((c as @{term trigger}) $ p $ t) = c $ in_pats p $ in_form t |
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216 | in_trig t = in_form t |
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217 |
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218 and in_form t = |
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219 (case Term.strip_comb t of |
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220 (q as Const (qn, _), [Abs (n, T, t')]) => |
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221 if is_some (quantifier qn) then q $ Abs (n, T, in_trig t') |
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222 else as_term (in_term t) |
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223 | (Const (c as (@{const_name distinct}, T)), [t']) => |
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224 if is_builtin_distinct then Const (pred c) $ in_list T in_term t' |
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225 else as_term (in_term t) |
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226 | (Const c, ts) => |
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227 if is_builtin_conn (conn c) |
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228 then Term.list_comb (Const (conn c), map in_form ts) |
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229 else if is_builtin_pred (pred c) |
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230 then Term.list_comb (Const (pred c), map in_term ts) |
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231 else as_term (in_term t) |
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232 | _ => as_term (in_term t)) |
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233 in |
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234 map (normalize ctxt) #> (fn thms => ((unfold_rules, term_bool' :: thms), |
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235 map (in_form o prop_of) (term_bool :: thms))) |
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236 end |
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237 |
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238 |
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239 |
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240 (* translation from Isabelle terms into SMT intermediate terms *) |
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241 |
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242 val empty_context = (1, Typtab.empty, 1, Termtab.empty, []) |
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243 |
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244 fun make_sign (_, typs, _, terms, thys) = { |
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245 theories = thys, |
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246 sorts = Typtab.fold (cons o snd) typs [], |
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247 funcs = Termtab.fold (cons o snd) terms [] } |
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248 |
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249 fun make_recon (unfolds, assms) (_, typs, _, terms, _) = { |
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250 typs = Symtab.make (map swap (Typtab.dest typs)), |
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251 terms = Symtab.make (map (fn (t, (n, _)) => (n, t)) (Termtab.dest terms)), |
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252 unfolds = unfolds, |
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253 assms = SOME assms } |
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254 |
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255 fun string_of_index pre i = pre ^ string_of_int i |
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256 |
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257 fun add_theory T (Tidx, typs, idx, terms, thys) = |
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258 let |
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259 fun add @{typ int} = insert (op =) Integer |
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260 | add @{typ real} = insert (op =) Real |
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261 | add (Type (@{type_name word}, _)) = insert (op =) Bitvector |
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262 | add (Type (_, Ts)) = fold add Ts |
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263 | add _ = I |
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264 in (Tidx, typs, idx, terms, add T thys) end |
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265 |
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266 fun fresh_typ sort_prefix T (cx as (Tidx, typs, idx, terms, thys)) = |
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267 (case Typtab.lookup typs T of |
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268 SOME s => (s, cx) |
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269 | NONE => |
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270 let |
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271 val s = string_of_index sort_prefix Tidx |
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272 val typs' = Typtab.update (T, s) typs |
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273 in (s, (Tidx+1, typs', idx, terms, thys)) end) |
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274 |
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275 fun fresh_fun func_prefix t ss (cx as (Tidx, typs, idx, terms, thys)) = |
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276 (case Termtab.lookup terms t of |
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277 SOME (f, _) => (f, cx) |
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278 | NONE => |
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279 let |
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280 val f = string_of_index func_prefix idx |
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281 val terms' = Termtab.update (revert_types t, (f, ss)) terms |
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282 in (f, (Tidx, typs, idx+1, terms', thys)) end) |
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283 |
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284 fun relaxed thms = (([], thms), map prop_of thms) |
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285 |
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286 fun with_context f (ths, ts) = |
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287 let val (us, context) = fold_map f ts empty_context |
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288 in ((make_sign context, us), make_recon ths context) end |
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289 |
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290 |
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291 fun translate {prefixes, strict, builtins, serialize} ctxt = |
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292 let |
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293 val {sort_prefix, func_prefix} = prefixes |
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294 val {builtin_typ, builtin_num, builtin_fun} = builtins |
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295 |
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296 fun transT T = add_theory T #> |
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297 (case builtin_typ T of |
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298 SOME n => pair n |
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299 | NONE => fresh_typ sort_prefix T) |
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300 |
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301 fun app n ts = SApp (n, ts) |
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302 |
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303 fun trans t = |
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304 (case Term.strip_comb t of |
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305 (Const (qn, _), [Abs (_, T, t1)]) => |
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306 (case dest_quant qn T t1 of |
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307 SOME (q, Ts, ps, b) => |
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308 fold_map transT Ts ##>> fold_map (fold_map_pat trans) ps ##>> |
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309 trans b #>> (fn ((Ts', ps'), b') => SQua (q, Ts', ps', b')) |
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310 | NONE => raise TERM ("intermediate", [t])) |
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311 | (Const (@{const_name Let}, _), [t1, Abs (_, T, t2)]) => |
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312 transT T ##>> trans t1 ##>> trans t2 #>> |
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313 (fn ((U, u1), u2) => SLet (U, u1, u2)) |
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314 | (h as Const (c as (@{const_name distinct}, T)), [t1]) => |
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315 (case builtin_fun c (HOLogic.dest_list t1) of |
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316 SOME (n, ts) => add_theory T #> fold_map trans ts #>> app n |
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317 | NONE => transs h T [t1]) |
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318 | (h as Const (c as (_, T)), ts) => |
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319 (case try HOLogic.dest_number t of |
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320 SOME (T, i) => |
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321 (case builtin_num T i of |
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322 SOME n => add_theory T #> pair (SApp (n, [])) |
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323 | NONE => transs t T []) |
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324 | NONE => |
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325 (case builtin_fun c ts of |
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326 SOME (n, ts') => add_theory T #> fold_map trans ts' #>> app n |
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327 | NONE => transs h T ts)) |
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328 | (h as Free (_, T), ts) => transs h T ts |
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329 | (Bound i, []) => pair (SVar i) |
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330 | _ => raise TERM ("intermediate", [t])) |
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331 |
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332 and transs t T ts = |
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333 let val (Us, U) = dest_funT (length ts) T |
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334 in |
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335 fold_map transT Us ##>> transT U #-> (fn Up => |
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336 fresh_fun func_prefix t Up ##>> fold_map trans ts #>> SApp) |
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337 end |
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338 in |
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339 (if is_some strict then strictify (the strict) ctxt else relaxed) #> |
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340 with_context trans #>> uncurry serialize |
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341 end |
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342 |
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343 end |
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