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1 (* Title: HOL/Tools/SMT/z3_model.ML |
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2 Author: Sascha Boehme and Philipp Meyer, TU Muenchen |
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3 |
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4 Parser for counterexamples generated by Z3. |
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5 *) |
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6 |
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7 signature Z3_MODEL = |
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8 sig |
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9 val parse_counterex: SMT_Translate.recon -> string list -> term list |
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10 end |
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11 |
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12 structure Z3_Model: Z3_MODEL = |
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13 struct |
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14 |
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15 (* counterexample expressions *) |
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16 |
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17 datatype expr = True | False | Number of int * int option | Value of int | |
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18 Array of array |
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19 and array = Fresh of expr | Store of (array * expr) * expr |
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20 |
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21 |
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22 (* parsing *) |
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23 |
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24 val space = Scan.many Symbol.is_ascii_blank |
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25 fun in_parens p = Scan.$$ "(" |-- p --| Scan.$$ ")" |
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26 fun in_braces p = (space -- Scan.$$ "{") |-- p --| (space -- Scan.$$ "}") |
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27 |
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28 val digit = (fn |
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29 "0" => SOME 0 | "1" => SOME 1 | "2" => SOME 2 | "3" => SOME 3 | |
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30 "4" => SOME 4 | "5" => SOME 5 | "6" => SOME 6 | "7" => SOME 7 | |
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31 "8" => SOME 8 | "9" => SOME 9 | _ => NONE) |
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32 |
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33 val nat_num = Scan.repeat1 (Scan.some digit) >> |
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34 (fn ds => fold (fn d => fn i => i * 10 + d) ds 0) |
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35 val int_num = Scan.optional ($$ "-" >> K (fn i => ~i)) I :|-- |
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36 (fn sign => nat_num >> sign) |
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37 |
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38 val is_char = Symbol.is_ascii_letter orf Symbol.is_ascii_digit orf |
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39 member (op =) (explode "_+*-/%~=<>$&|?!.@^#") |
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40 val name = Scan.many1 is_char >> implode |
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41 |
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42 fun array_expr st = st |> |
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43 in_parens (space |-- ( |
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44 Scan.this_string "const" |-- expr >> Fresh || |
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45 Scan.this_string "store" -- space |-- array_expr -- expr -- expr >> Store)) |
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46 |
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47 and expr st = st |> (space |-- ( |
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48 Scan.this_string "true" >> K True || |
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49 Scan.this_string "false" >> K False || |
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50 int_num -- Scan.option (Scan.$$ "/" |-- int_num) >> Number || |
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51 Scan.this_string "val!" |-- nat_num >> Value || |
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52 array_expr >> Array)) |
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53 |
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54 val mapping = space -- Scan.this_string "->" |
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55 val value = mapping |-- expr |
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56 |
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57 val args_case = Scan.repeat expr -- value |
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58 val else_case = space -- Scan.this_string "else" |-- value >> |
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59 pair ([] : expr list) |
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60 |
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61 val func = |
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62 let fun cases st = (else_case >> single || args_case ::: cases) st |
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63 in in_braces cases end |
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64 |
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65 val cex = space |-- Scan.repeat (space |-- name --| mapping -- |
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66 (func || expr >> (single o pair []))) |
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67 |
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68 fun read_cex ls = |
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69 explode (cat_lines ls) |
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70 |> try (fst o Scan.finite Symbol.stopper cex) |
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71 |> the_default [] |
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72 |
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73 |
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74 (* translation into terms *) |
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75 |
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76 fun lookup_term tab (name, e) = Option.map (rpair e) (Symtab.lookup tab name) |
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77 |
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78 fun with_name_context tab f xs = |
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79 let |
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80 val ns = Symtab.fold (Term.add_free_names o snd) tab [] |
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81 val nctxt = Name.make_context ns |
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82 in fst (fold_map f xs (Inttab.empty, nctxt)) end |
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83 |
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84 fun fresh_term T (tab, nctxt) = |
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85 let val (n, nctxt') = yield_singleton Name.variants "" nctxt |
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86 in (Free (n, T), (tab, nctxt')) end |
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87 |
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88 fun term_of_value T i (cx as (tab, _)) = |
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89 (case Inttab.lookup tab i of |
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90 SOME t => (t, cx) |
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91 | NONE => |
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92 let val (t, (tab', nctxt')) = fresh_term T cx |
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93 in (t, (Inttab.update (i, t) tab', nctxt')) end) |
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94 |
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95 fun trans_expr _ True = pair @{term True} |
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96 | trans_expr _ False = pair @{term False} |
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97 | trans_expr T (Number (i, NONE)) = pair (HOLogic.mk_number T i) |
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98 | trans_expr T (Number (i, SOME j)) = |
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99 pair (Const (@{const_name divide}, [T, T] ---> T) $ |
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100 HOLogic.mk_number T i $ HOLogic.mk_number T j) |
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101 | trans_expr T (Value i) = term_of_value T i |
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102 | trans_expr T (Array a) = trans_array T a |
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103 |
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104 and trans_array T a = |
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105 let val dT = Term.domain_type T and rT = Term.range_type T |
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106 in |
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107 (case a of |
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108 Fresh e => trans_expr rT e #>> (fn t => Abs ("x", dT, t)) |
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109 | Store ((a', e1), e2) => |
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110 trans_array T a' ##>> trans_expr dT e1 ##>> trans_expr rT e2 #>> |
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111 (fn ((m, k), v) => |
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112 Const (@{const_name fun_upd}, [T, dT, rT] ---> T) $ m $ k $ v)) |
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113 end |
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114 |
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115 fun trans_pat i T f x = |
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116 f (Term.domain_type T) ##>> trans (i-1) (Term.range_type T) x #>> |
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117 (fn (u, (us, t)) => (u :: us, t)) |
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118 |
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119 and trans i T ([], v) = |
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120 if i > 0 then trans_pat i T fresh_term ([], v) |
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121 else trans_expr T v #>> pair [] |
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122 | trans i T (p :: ps, v) = trans_pat i T (fn U => trans_expr U p) (ps, v) |
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123 |
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124 fun mk_eq' t us u = HOLogic.mk_eq (Term.list_comb (t, us), u) |
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125 fun mk_eq (Const (@{const_name apply}, _)) (u' :: us', u) = mk_eq' u' us' u |
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126 | mk_eq t (us, u) = mk_eq' t us u |
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127 |
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128 fun translate (t, cs) = |
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129 let val T = Term.fastype_of t |
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130 in |
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131 (case (can HOLogic.dest_number t, cs) of |
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132 (true, [c]) => trans 0 T c #>> (fn (_, u) => [mk_eq u ([], t)]) |
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133 | (_, (es, _) :: _) => fold_map (trans (length es) T) cs #>> map (mk_eq t) |
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134 | _ => raise TERM ("translate: no cases", [t])) |
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135 end |
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136 |
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137 |
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138 (* overall procedure *) |
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139 |
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140 fun parse_counterex ({terms, ...} : SMT_Translate.recon) ls = |
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141 read_cex ls |
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142 |> map_filter (lookup_term terms) |
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143 |> with_name_context terms translate |
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144 |> flat |
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145 |
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146 end |