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1 (* extends Isabelle/src/Pure/term.ML |
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2 (c) Walther Neuper 1999 |
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3 |
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4 use"ProgLang/term.sml"; |
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5 use"term.sml"; |
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6 *) |
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7 |
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8 (* |
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9 > (cterm_of thy) a_term; |
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10 val it = "empty" : cterm *) |
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11 |
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12 (*2003 fun match thy t pat = |
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13 (snd (Pattern.match (Sign.tsig_of (sign_of thy)) (pat, t))) |
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14 handle _ => []; |
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15 fn : theory -> |
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16 Term.term -> Term.term -> (Term.indexname * Term.term) list*) |
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17 (*see src/Tools/eqsubst.ML fun clean_match*) |
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18 (*2003 fun matches thy tm pa = if match thy tm pa = [] then false else true;*) |
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19 fun matches thy tm pa = |
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20 (Pattern.match thy (pa, tm) (Vartab.empty, Vartab.empty); true) |
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21 handle _ => false |
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22 |
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23 fun atomtyp t = (*see raw_pp_typ*) |
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24 let |
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25 fun ato n (Type (s,[])) = |
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26 ("\n*** "^indent n^"Type ("^s^",[])") |
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27 | ato n (Type (s,Ts)) = |
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28 ("\n*** "^indent n^"Type ("^s^",["^ atol (n+1) Ts) |
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29 |
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30 | ato n (TFree (s,sort)) = |
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31 ("\n*** "^indent n^"TFree ("^s^",["^ strs2str' sort) |
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32 |
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33 | ato n (TVar ((s,i),sort)) = |
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34 ("\n*** "^indent n^"TVar (("^s^","^ |
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35 string_of_int i ^ strs2str' sort) |
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36 and atol n [] = |
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37 ("\n*** "^indent n^"]") |
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38 | atol n (T::Ts) = (ato n T ^ atol n Ts) |
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39 (*in print (ato 0 t ^ "\n") end; TODO TUM10*) |
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40 in writeln(ato 0 t) end; |
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41 |
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42 (*Prog.Tutorial.p.34*) |
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43 local |
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44 fun pp_pair (x, y) = Pretty.list "(" ")" [x, y] |
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45 fun pp_list xs = Pretty.list "[" "]" xs |
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46 fun pp_str s = Pretty.str s |
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47 fun pp_qstr s = Pretty.quote (pp_str s) |
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48 fun pp_int i = pp_str (string_of_int i) |
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49 fun pp_sort S = pp_list (map pp_qstr S) |
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50 fun pp_constr a args = Pretty.block [pp_str a, Pretty.brk 1, args] |
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51 in |
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52 fun raw_pp_typ (TVar ((a, i), S)) = |
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53 pp_constr "TVar" (pp_pair (pp_pair (pp_qstr a, pp_int i), pp_sort S)) |
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54 | raw_pp_typ (TFree (a, S)) = |
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55 pp_constr "TFree" (pp_pair (pp_qstr a, pp_sort S)) |
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56 | raw_pp_typ (Type (a, tys)) = |
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57 pp_constr "Type" (pp_pair (pp_qstr a, pp_list (map raw_pp_typ tys))) |
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58 end |
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59 (* install |
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60 PolyML.addPrettyPrinter |
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61 (fn _ => fn _ => ml_pretty o Pretty.to_ML o raw_pp_typ); |
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62 de-install |
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63 PolyML.addPrettyPrinter |
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64 (fn _ => fn _ => ml_pretty o Pretty.to_ML o Proof_Display.pp_typ Pure.thy); |
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65 *) |
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66 |
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67 (* |
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68 > val T = (type_of o term_of o the o (parse thy)) "a::[real,int] => nat"; |
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69 > atomtyp T; |
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70 *** Type (fun,[ |
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71 *** Type (RealDef.real,[]) |
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72 *** Type (fun,[ |
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73 *** Type (IntDef.int,[]) |
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74 *** Type (nat,[]) |
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75 *** ] |
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76 *** ] |
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77 *) |
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78 |
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79 fun atomt t = |
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80 let fun ato (Const(a,T)) n = |
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81 ("\n*** "^indent n^"Const ("^a^")") |
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82 | ato (Free (a,T)) n = |
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83 ("\n*** "^indent n^"Free ("^a^", "^")") |
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84 | ato (Var ((a,ix),T)) n = |
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85 ("\n*** "^indent n^"Var (("^a^", "^(string_of_int ix)^"), "^")") |
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86 | ato (Bound ix) n = |
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87 ("\n*** "^indent n^"Bound "^(string_of_int ix)) |
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88 | ato (Abs(a,T,body)) n = |
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89 ("\n*** "^indent n^"Abs("^a^",..")^ato body (n+1) |
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90 | ato (f$t') n = (ato f n; ato t' (n+1)) |
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91 in writeln("\n*** -------------"^ ato t 0 ^"\n***") end; |
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92 |
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93 fun term_detail2str t = |
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94 let fun ato (Const (a, T)) n = |
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95 "\n*** "^indent n^"Const ("^a^", "^string_of_typ T^")" |
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96 | ato (Free (a, T)) n = |
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97 "\n*** "^indent n^"Free ("^a^", "^string_of_typ T^")" |
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98 | ato (Var ((a, ix), T)) n = |
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99 "\n*** "^indent n^"Var (("^a^", "^string_of_int ix^"), "^ |
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100 string_of_typ T^")" |
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101 | ato (Bound ix) n = |
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102 "\n*** "^indent n^"Bound "^string_of_int ix |
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103 | ato (Abs(a, T, body)) n = |
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104 "\n*** "^indent n^"Abs ("^a^", "^ |
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105 (string_of_typ T)^",.." |
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106 ^ato body (n + 1) |
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107 | ato (f $ t') n = ato f n^ato t' (n+1) |
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108 in "\n*** "^ato t 0^"\n***" end; |
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109 fun atomty t = (writeln o term_detail2str) t; |
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110 |
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111 fun term_str thy (Const(s,_)) = s |
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112 | term_str thy (Free(s,_)) = s |
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113 | term_str thy (Var((s,i),_)) = s^(string_of_int i) |
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114 | term_str thy (Bound i) = "B."^(string_of_int i) |
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115 | term_str thy (Abs(s,_,_)) = s |
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116 | term_str thy t = raise error("term_str not for "^term2str t); |
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117 |
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118 (*.contains the fst argument the second argument (a leave! of term).*) |
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119 fun contains_term (Abs(_,_,body)) t = contains_term body t |
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120 | contains_term (f $ f') t = |
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121 contains_term f t orelse contains_term f' t |
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122 | contains_term s t = t = s; |
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123 (*.contains the term a VAR(("*",_),_) ?.*) |
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124 fun contains_Var (Abs(_,_,body)) = contains_Var body |
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125 | contains_Var (f $ f') = contains_Var f orelse contains_Var f' |
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126 | contains_Var (Var _) = true |
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127 | contains_Var _ = false; |
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128 (* contains_Var (str2term "?z = 3") (*true*); |
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129 contains_Var (str2term "z = 3") (*false*); |
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130 *) |
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131 |
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132 (*fun int_of_str str = |
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133 let val ss = explode str |
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134 val str' = case ss of |
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135 "("::s => drop_last s | _ => ss |
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136 in case BasisLibrary.Int.fromString (implode str') of |
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137 SOME i => SOME i |
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138 | NONE => NONE end;*) |
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139 fun int_of_str str = |
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140 let val ss = explode str |
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141 val str' = case ss of |
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142 "("::s => drop_last s | _ => ss |
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143 in (SOME (Thy_Output.integer (implode str'))) handle _ => NONE end; |
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144 (* |
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145 > int_of_str "123"; |
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146 val it = SOME 123 : int option |
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147 > int_of_str "(-123)"; |
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148 val it = SOME 123 : int option |
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149 > int_of_str "#123"; |
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150 val it = NONE : int option |
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151 > int_of_str "-123"; |
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152 val it = SOME ~123 : int option |
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153 *) |
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154 fun int_of_str' str = |
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155 case int_of_str str of |
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156 SOME i => i |
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157 | NONE => raise TERM ("int_of_string: no int-string",[]); |
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158 val str2int = int_of_str'; |
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159 |
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160 fun is_numeral str = case int_of_str str of |
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161 SOME _ => true |
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162 | NONE => false; |
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163 val is_no = is_numeral; |
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164 fun is_num (Free (s,_)) = if is_numeral s then true else false |
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165 | is_num _ = false; |
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166 (*> |
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167 > is_num ((term_of o the o (parse thy)) "#1"); |
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168 val it = true : bool |
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169 > is_num ((term_of o the o (parse thy)) "#-1"); |
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170 val it = true : bool |
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171 > is_num ((term_of o the o (parse thy)) "a123"); |
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172 val it = false : bool |
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173 *) |
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174 |
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175 (*fun int_of_Free (Free (intstr, _)) = |
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176 (case BasisLibrary.Int.fromString intstr of |
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177 SOME i => i |
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178 | NONE => raise error ("int_of_Free ( "^ intstr ^", _)")) |
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179 | int_of_Free t = raise error ("int_of_Free ( "^ term2str t ^" )");*) |
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180 fun int_of_Free (Free (intstr, _)) = (Thy_Output.integer intstr |
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181 handle _ => raise error ("int_of_Free ( "^ intstr ^", _)")) |
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182 | int_of_Free t = raise error ("int_of_Free ( "^ term2str t ^" )"); |
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183 |
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184 fun vars t = |
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185 let |
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186 fun scan vs (Const(s,T)) = vs |
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187 | scan vs (t as Free(s,T)) = if is_no s then vs else t::vs |
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188 | scan vs (t as Var((s,i),T)) = t::vs |
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189 | scan vs (Bound i) = vs |
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190 | scan vs (Abs(s,T,t)) = scan vs t |
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191 | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2) |
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192 in (distinct o (scan [])) t end; |
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193 |
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194 fun is_Free (Free _) = true |
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195 | is_Free _ = false; |
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196 fun is_fun_id (Const _) = true |
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197 | is_fun_id (Free _) = true |
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198 | is_fun_id _ = false; |
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199 fun is_f_x (f $ x) = is_fun_id f andalso is_Free x |
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200 | is_f_x _ = false; |
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201 (* is_f_x (str2term "q_0/2 * L * x") (*false*); |
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202 is_f_x (str2term "M_b x") (*true*); |
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203 *) |
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204 fun vars_str t = |
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205 let |
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206 fun scan vs (Const(s,T)) = vs |
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207 | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs |
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208 | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs |
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209 | scan vs (Bound i) = vs |
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210 | scan vs (Abs(s,T,t)) = scan vs t |
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211 | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2) |
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212 in (distinct o (scan [])) t end; |
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213 |
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214 fun ids2str t = |
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215 let |
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216 fun scan vs (Const(s,T)) = if is_no s then vs else s::vs |
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217 | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs |
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218 | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs |
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219 | scan vs (Bound i) = vs |
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220 | scan vs (Abs(s,T,t)) = scan (s::vs) t |
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221 | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2) |
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222 in (distinct o (scan [])) t end; |
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223 fun is_bdv str = |
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224 case explode str of |
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225 "b"::"d"::"v"::_ => true |
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226 | _ => false; |
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227 fun is_bdv_ (Free (s,_)) = is_bdv s |
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228 | is_bdv_ _ = false; |
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229 |
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230 fun free2str (Free (s,_)) = s |
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231 | free2str t = raise error ("free2str not for "^ term2str t); |
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232 fun free2int (t as Free (s, _)) = ((str2int s) |
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233 handle _ => raise error ("free2int: "^term_detail2str t)) |
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234 | free2int t = raise error ("free2int: "^term_detail2str t); |
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235 |
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236 (*27.8.01: unused*) |
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237 fun var2free (t as Const(s,T)) = t |
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238 | var2free (t as Free(s,T)) = t |
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239 | var2free (Var((s,i),T)) = Free(s,T) |
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240 | var2free (t as Bound i) = t |
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241 | var2free (Abs(s,T,t)) = Abs(s,T,var2free t) |
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242 | var2free (t1 $ t2) = (var2free t1) $ (var2free t2); |
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243 |
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244 (*27.8.01: doesn't find some subterm ???!???*) |
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245 (*2010 Logic.varify !!!*) |
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246 fun free2var (t as Const(s,T)) = t |
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247 | free2var (t as Free(s,T)) = if is_no s then t else Var((s,0),T) |
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248 | free2var (t as Var((s,i),T)) = t |
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249 | free2var (t as Bound i) = t |
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250 | free2var (Abs(s,T,t)) = Abs(s,T,free2var t) |
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251 | free2var (t1 $ t2) = (free2var t1) $ (free2var t2); |
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252 |
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253 |
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254 fun mk_listT T = Type ("List.list", [T]); |
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255 fun list_const T = |
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256 Const("List.list.Cons", [T, mk_listT T] ---> mk_listT T); |
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257 (*28.8.01: TODO: get type from head of list: 1 arg less!!!*) |
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258 fun list2isalist T [] = Const("List.list.Nil",mk_listT T) |
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259 | list2isalist T (t::ts) = (list_const T) $ t $ (list2isalist T ts); |
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260 (* |
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261 > val tt = (term_of o the o (parse thy)) "R=(R::real)"; |
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262 > val TT = type_of tt; |
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263 > val ss = list2isalist TT [tt,tt,tt]; |
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264 > (cterm_of thy) ss; |
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265 val it = "[R = R, R = R, R = R]" : cterm *) |
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266 |
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267 fun isapair2pair (Const ("Pair",_) $ a $ b) = (a,b) |
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268 | isapair2pair t = |
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269 raise error ("isapair2pair called with "^term2str t); |
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270 |
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271 val listType = Type ("List.list",[Type ("bool",[])]); |
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272 fun isalist2list ls = |
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273 let |
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274 fun get es (Const("List.list.Cons",_) $ t $ ls) = get (t::es) ls |
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275 | get es (Const("List.list.Nil",_)) = es |
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276 | get _ t = |
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277 raise error ("isalist2list applied to NON-list '"^term2str t^"'") |
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278 in (rev o (get [])) ls end; |
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279 (* |
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280 > val il = str2term "[a=b,c=d,e=f]"; |
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281 > val l = isalist2list il; |
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282 > (writeln o terms2str) l; |
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283 ["a = b","c = d","e = f"] |
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284 |
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285 > val il = str2term "ss___::bool list"; |
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286 > val l = isalist2list il; |
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287 [Free ("ss___", "bool List.list")] |
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288 *) |
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289 |
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290 |
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291 (*review Isabelle2009/src/HOL/Tools/hologic.ML*) |
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292 val prop = Type ("prop",[]); (* ~/Diss.99/Integers-Isa/tools.sml*) |
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293 val bool = Type ("bool",[]); (* 2002 Integ.int *) |
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294 val Trueprop = Const("Trueprop",bool-->prop); |
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295 fun mk_prop t = Trueprop $ t; |
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296 val true_as_term = Const("True",bool); |
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297 val false_as_term = Const("False",bool); |
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298 val true_as_cterm = cterm_of (theory "HOL") true_as_term; |
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299 val false_as_cterm = cterm_of (theory "HOL") false_as_term; |
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300 |
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301 infixr 5 -->; (*2002 /Pure/term.ML *) |
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302 infixr --->; (*2002 /Pure/term.ML *) |
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303 fun S --> T = Type("fun",[S,T]); (*2002 /Pure/term.ML *) |
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304 val op ---> = foldr (op -->); (*2002 /Pure/term.ML *) |
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305 fun list_implies ([], B) = B : term (*2002 /term.ML *) |
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306 | list_implies (A::AS, B) = Logic.implies $ A $ list_implies(AS,B); |
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307 |
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308 |
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309 |
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310 (** substitution **) |
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311 |
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312 fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = (* = thm.ML *) |
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313 match_bvs(s, t, if x="" orelse y="" then al |
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314 else (x,y)::al) |
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315 | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al)) |
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316 | match_bvs(_,_,al) = al; |
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317 fun ren_inst(insts,prop,pat,obj) = (* = thm.ML *) |
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318 let val ren = match_bvs(pat,obj,[]) |
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319 fun renAbs(Abs(x,T,b)) = |
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320 Abs(case assoc_string(ren,x) of NONE => x |
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321 | SOME(y) => y, T, renAbs(b)) |
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322 | renAbs(f$t) = renAbs(f) $ renAbs(t) |
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323 | renAbs(t) = t |
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324 in subst_vars insts (if null(ren) then prop else renAbs(prop)) end; |
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325 |
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326 |
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327 |
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328 |
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329 |
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330 |
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331 fun dest_equals' (Const("op =",_) $ t $ u) = (t,u)(* logic.ML: Const("=="*) |
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332 | dest_equals' t = raise TERM("dest_equals'", [t]); |
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333 val lhs_ = (fst o dest_equals'); |
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334 val rhs_ = (snd o dest_equals'); |
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335 |
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336 fun is_equality (Const("op =",_) $ t $ u) = true (* logic.ML: Const("=="*) |
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337 | is_equality _ = false; |
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338 fun mk_equality (t,u) = (Const("op =",[type_of t,type_of u]--->bool) $ t $ u); |
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339 fun is_expliceq (Const("op =",_) $ (Free _) $ u) = true |
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340 | is_expliceq _ = false; |
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341 fun strip_trueprop (Const("Trueprop",_) $ t) = t |
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342 | strip_trueprop t = t; |
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343 (* | strip_trueprop t = raise TERM("strip_trueprop", [t]); |
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344 *) |
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345 |
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346 (*.(A1==>...An==>B) goes to (A1==>...An==>).*) |
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347 fun strip_imp_prems' (Const("==>", T) $ A $ t) = |
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348 let fun coll_prems As (Const("==>", _) $ A $ t) = |
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349 coll_prems (As $ (Logic.implies $ A)) t |
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350 | coll_prems As _ = SOME As |
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351 in coll_prems (Logic.implies $ A) t end |
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352 | strip_imp_prems' _ = NONE; (* logic.ML: term -> term list*) |
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353 (* |
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354 val thm = real_mult_div_cancel1; |
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355 val prop = (#prop o rep_thm) thm; |
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356 atomt prop; |
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357 *** ------------- |
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358 *** Const ( ==>) |
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359 *** . Const ( Trueprop) |
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360 *** . . Const ( Not) |
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361 *** . . . Const ( op =) |
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362 *** . . . . Var ((k, 0), ) |
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363 *** . . . . Const ( 0) |
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364 *** . Const ( Trueprop) |
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365 *** . . Const ( op =) *** ............. |
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366 val SOME t = strip_imp_prems' ((#prop o rep_thm) thm); |
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367 atomt t; |
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368 *** ------------- |
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369 *** Const ( ==>) |
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370 *** . Const ( Trueprop) |
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371 *** . . Const ( Not) |
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372 *** . . . Const ( op =) |
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373 *** . . . . Var ((k, 0), ) |
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374 *** . . . . Const ( 0) |
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375 |
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376 val thm = real_le_anti_sym; |
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377 val prop = (#prop o rep_thm) thm; |
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378 atomt prop; |
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379 *** ------------- |
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380 *** Const ( ==>) |
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381 *** . Const ( Trueprop) |
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382 *** . . Const ( op <=) |
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383 *** . . . Var ((z, 0), ) |
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384 *** . . . Var ((w, 0), ) |
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385 *** . Const ( ==>) |
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386 *** . . Const ( Trueprop) |
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387 *** . . . Const ( op <=) |
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388 *** . . . . Var ((w, 0), ) |
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389 *** . . . . Var ((z, 0), ) |
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390 *** . . Const ( Trueprop) |
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391 *** . . . Const ( op =) |
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392 *** ............. |
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393 val SOME t = strip_imp_prems' ((#prop o rep_thm) thm); |
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394 atomt t; |
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395 *** ------------- |
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396 *** Const ( ==>) |
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397 *** . Const ( Trueprop) |
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398 *** . . Const ( op <=) |
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399 *** . . . Var ((z, 0), ) |
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400 *** . . . Var ((w, 0), ) |
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401 *** . Const ( ==>) |
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402 *** . . Const ( Trueprop) |
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403 *** . . . Const ( op <=) |
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404 *** . . . . Var ((w, 0), ) |
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405 *** . . . . Var ((z, 0), ) |
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406 *) |
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407 |
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408 (*. (A1==>...An==>) (B) goes to (A1==>...An==>B), where B is lowest branch.*) |
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409 fun ins_concl (Const("==>", T) $ A $ t) B = Logic.implies $ A $ (ins_concl t B) |
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410 | ins_concl (Const("==>", T) $ A ) B = Logic.implies $ A $ B |
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411 | ins_concl t B = raise TERM("ins_concl", [t, B]); |
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412 (* |
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413 val thm = real_le_anti_sym; |
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414 val prop = (#prop o rep_thm) thm; |
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415 val concl = Logic.strip_imp_concl prop; |
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416 val SOME prems = strip_imp_prems' prop; |
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417 val prop' = ins_concl prems concl; |
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418 prop = prop'; |
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419 atomt prop; |
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420 atomt prop'; |
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421 *) |
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422 |
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423 |
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424 fun vperm (Var _, Var _) = true (*2002 Pure/thm.ML *) |
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425 | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t) |
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426 | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2) |
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427 | vperm (t, u) = (t = u); |
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428 |
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429 (*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*) |
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430 fun mem_term (_, []) = false |
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431 | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts); |
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432 fun subset_term ([], ys) = true |
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433 | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys); |
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434 fun eq_set_term (xs, ys) = |
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435 xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs)); |
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436 (*a total, irreflexive ordering on index names*) |
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437 fun xless ((a,i), (b,j): indexname) = i<j orelse (i=j andalso a<b); |
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438 (*a partial ordering (not reflexive) for atomic terms*) |
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439 fun atless (Const (a,_), Const (b,_)) = a<b |
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440 | atless (Free (a,_), Free (b,_)) = a<b |
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441 | atless (Var(v,_), Var(w,_)) = xless(v,w) |
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442 | atless (Bound i, Bound j) = i<j |
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443 | atless _ = false; |
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444 (*insert atomic term into partially sorted list, suppressing duplicates (?)*) |
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445 fun insert_aterm (t,us) = |
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446 let fun inserta [] = [t] |
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447 | inserta (us as u::us') = |
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448 if atless(t,u) then t::us |
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449 else if t=u then us (*duplicate*) |
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450 else u :: inserta(us') |
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451 in inserta us end; |
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452 |
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453 (*Accumulates the Vars in the term, suppressing duplicates*) |
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454 fun add_term_vars (t, vars: term list) = case t of |
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455 Var _ => insert_aterm(t,vars) |
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456 | Abs (_,_,body) => add_term_vars(body,vars) |
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457 | f$t => add_term_vars (f, add_term_vars(t, vars)) |
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458 | _ => vars; |
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459 fun term_vars t = add_term_vars(t,[]); |
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460 |
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461 |
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462 fun var_perm (t, u) = (*2002 Pure/thm.ML *) |
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463 vperm (t, u) andalso eq_set_term (term_vars t, term_vars u); |
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464 |
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465 (*2002 fun decomp_simp, Pure/thm.ML *) |
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466 fun perm lhs rhs = var_perm (lhs, rhs) andalso not (lhs aconv rhs) |
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467 andalso not (is_Var lhs); |
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468 |
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469 |
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470 fun str_of_int n = |
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471 if n < 0 then "-"^((string_of_int o abs) n) |
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472 else string_of_int n; |
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473 (* |
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474 > str_of_int 1; |
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475 val it = "1" : string > str_of_int ~1; |
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476 val it = "-1" : string |
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477 *) |
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478 |
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479 |
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480 fun power b 0 = 1 |
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481 | power b n = |
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482 if n>0 then b*(power b (n-1)) |
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483 else raise error ("power "^(str_of_int b)^" "^(str_of_int n)); |
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484 (* |
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485 > power 2 3; |
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486 val it = 8 : int |
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487 > power ~2 3; |
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488 val it = ~8 : int |
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489 > power ~3 2; |
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490 val it = 9 : int |
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491 > power 3 ~2; |
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492 *) |
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493 fun gcd 0 b = b |
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494 | gcd a b = if a < b then gcd (b mod a) a |
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495 else gcd (a mod b) b; |
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496 fun sign n = if n < 0 then ~1 |
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497 else if n = 0 then 0 else 1; |
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498 fun sign2 n1 n2 = (sign n1) * (sign n2); |
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499 |
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500 infix dvd; |
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501 fun d dvd n = n mod d = 0; |
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502 |
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503 fun divisors n = |
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504 let fun pdiv ds d n = |
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505 if d=n then d::ds |
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506 else if d dvd n then pdiv (d::ds) d (n div d) |
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507 else pdiv ds (d+1) n |
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508 in pdiv [] 2 n end; |
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509 |
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510 divisors 30; |
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511 divisors 32; |
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512 divisors 60; |
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513 divisors 11; |
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514 |
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515 fun doubles ds = (* ds is ordered *) |
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516 let fun dbls ds [] = ds |
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517 | dbls ds [i] = ds |
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518 | dbls ds (i::i'::is) = if i=i' then dbls (i::ds) is |
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519 else dbls ds (i'::is) |
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520 in dbls [] ds end; |
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521 (*> doubles [2,3,4]; |
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522 val it = [] : int list |
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523 > doubles [2,3,3,5,5,7]; |
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524 val it = [5,3] : int list*) |
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525 |
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526 fun squfact 0 = 0 |
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527 | squfact 1 = 1 |
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528 | squfact n = foldl op* (1, (doubles o divisors) n); |
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529 (*> squfact 30; |
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530 val it = 1 : int |
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531 > squfact 32; |
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532 val it = 4 : int |
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533 > squfact 60; |
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534 val it = 2 : int |
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535 > squfact 11; |
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536 val it = 1 : int*) |
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537 |
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538 |
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539 fun dest_type (Type(T,[])) = T |
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540 | dest_type T = |
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541 (atomtyp T; |
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542 raise error ("... dest_type: not impl. for this type")); |
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543 |
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544 fun term_of_num ntyp n = Free (str_of_int n, ntyp); |
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545 |
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546 fun pairT T1 T2 = Type ("*", [T1, T2]); |
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547 (*> val t = str2term "(1,2)"; |
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548 > type_of t = pairT HOLogic.realT HOLogic.realT; |
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549 val it = true : bool |
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550 *) |
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551 fun PairT T1 T2 = ([T1, T2] ---> Type ("*", [T1, T2])); |
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552 (*> val t = str2term "(1,2)"; |
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553 > val Const ("Pair",pT) $ _ $ _ = t; |
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554 > pT = PairT HOLogic.realT HOLogic.realT; |
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555 val it = true : bool |
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556 *) |
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557 fun pairt t1 t2 = |
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558 Const ("Pair", PairT (type_of t1) (type_of t2)) $ t1 $ t2; |
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559 (*> val t = str2term "(1,2)"; |
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560 > val (t1, t2) = (str2term "1", str2term "2"); |
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561 > t = pairt t1 t2; |
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562 val it = true : bool*) |
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563 |
|
564 |
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565 fun num_of_term (t as Free (s,_)) = |
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566 (case int_of_str s of |
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567 SOME s' => s' |
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568 | NONE => raise error ("num_of_term not for "^ term2str t)) |
|
569 | num_of_term t = raise error ("num_of_term not for "^term2str t); |
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570 |
|
571 fun mk_factroot op_(*=thy.sqrt*) T fact root = |
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572 Const ("op *", [T, T] ---> T) $ (term_of_num T fact) $ |
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573 (Const (op_, T --> T) $ term_of_num T root); |
|
574 (* |
|
575 val T = (type_of o term_of o the) (parse thy "#12::real"); |
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576 val t = mk_factroot "SqRoot.sqrt" T 2 3; |
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577 (cterm_of thy) t; |
|
578 val it = "#2 * sqrt #3 " : cterm |
|
579 *) |
|
580 fun var_op_num v op_ optype ntyp n = |
|
581 Const (op_, optype) $ v $ |
|
582 Free (str_of_int n, ntyp); |
|
583 |
|
584 fun num_op_var v op_ optype ntyp n = |
|
585 Const (op_,optype) $ |
|
586 Free (str_of_int n, ntyp) $ v; |
|
587 |
|
588 fun num_op_num T1 T2 (op_,Top) n1 n2 = |
|
589 Const (op_,Top) $ |
|
590 Free (str_of_int n1, T1) $ Free (str_of_int n2, T2); |
|
591 (* |
|
592 > val t = num_op_num "Int" 3 4; |
|
593 > atomty t; |
|
594 > string_of_cterm ((cterm_of thy) t); |
|
595 *) |
|
596 |
|
597 fun const_in str (Const _) = false |
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598 | const_in str (Free (s,_)) = if strip_thy s = str then true else false |
|
599 | const_in str (Bound _) = false |
|
600 | const_in str (Var _) = false |
|
601 | const_in str (Abs (_,_,body)) = const_in str body |
|
602 | const_in str (f$u) = const_in str f orelse const_in str u; |
|
603 (* |
|
604 > val t = (term_of o the o (parse thy)) "6 + 5 * sqrt 4 + 3"; |
|
605 > const_in "sqrt" t; |
|
606 val it = true : bool |
|
607 > val t = (term_of o the o (parse thy)) "6 + 5 * 4 + 3"; |
|
608 > const_in "sqrt" t; |
|
609 val it = false : bool |
|
610 *) |
|
611 |
|
612 (*used for calculating built in binary operations in Isabelle2002->Float.ML*) |
|
613 (*fun calc "op +" (n1, n2) = n1+n2 |
|
614 | calc "op -" (n1, n2) = n1-n2 |
|
615 | calc "op *" (n1, n2) = n1*n2 |
|
616 | calc "HOL.divide"(n1, n2) = n1 div n2 |
|
617 | calc "Atools.pow"(n1, n2) = power n1 n2 |
|
618 | calc op_ _ = raise error ("calc: operator = "^op_^" not defined");-----*) |
|
619 fun calc_equ "op <" (n1, n2) = n1 < n2 |
|
620 | calc_equ "op <=" (n1, n2) = n1 <= n2 |
|
621 | calc_equ op_ _ = |
|
622 raise error ("calc_equ: operator = "^op_^" not defined"); |
|
623 fun sqrt (n:int) = if n < 0 then 0 |
|
624 (*FIXME ~~~*) else (trunc o Math.sqrt o Real.fromInt) n; |
|
625 |
|
626 fun mk_thmid thmid op_ n1 n2 = |
|
627 thmid ^ (strip_thy n1) ^ "_" ^ (strip_thy n2); |
|
628 |
|
629 fun dest_binop_typ (Type("fun",[range,Type("fun",[arg2,arg1])])) = |
|
630 (arg1,arg2,range) |
|
631 | dest_binop_typ _ = raise error "dest_binop_typ: not binary"; |
|
632 (* ----- |
|
633 > val t = (term_of o the o (parse thy)) "#3^#4"; |
|
634 > val hT = type_of (head_of t); |
|
635 > dest_binop_typ hT; |
|
636 val it = ("'a","nat","'a") : typ * typ * typ |
|
637 ----- *) |
|
638 |
|
639 |
|
640 (** transform binary numeralsstrings **) |
|
641 (*Makarius 100308, hacked by WN*) |
|
642 val numbers_to_string = |
|
643 let |
|
644 fun dest_num t = |
|
645 (case try HOLogic.dest_number t of |
|
646 SOME (T, i) => |
|
647 (*if T = @{typ int} orelse T = @{typ real} then WN*) |
|
648 SOME (Free (signed_string_of_int i, T)) |
|
649 (*else NONE WN*) |
|
650 | NONE => NONE); |
|
651 |
|
652 fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b) |
|
653 | to_str (t as (u1 $ u2)) = |
|
654 (case dest_num t of |
|
655 SOME t' => t' |
|
656 | NONE => to_str u1 $ to_str u2) |
|
657 | to_str t = perhaps dest_num t; |
|
658 in to_str end |
|
659 |
|
660 (*.make uminus uniform: |
|
661 Const ("uminus", _) $ Free ("2", "RealDef.real") --> Free ("-2", _) |
|
662 to be used immediately before evaluation of numerals; |
|
663 see Scripts/calculate.sml .*) |
|
664 (*2002 fun(*app_num_tr'2 (Const("0",T)) = Free("0",T) |
|
665 | app_num_tr'2 (Const("1",T)) = Free("1",T) |
|
666 |*)app_num_tr'2 (t as Const("uminus",_) $ Free(s,T)) = |
|
667 (case int_of_str s of SOME i => |
|
668 if i > 0 then Free("-"^s,T) else Free(s,T) |
|
669 | NONE => t) |
|
670 (*| app_num_tr'2 (t as Const(s,T)) = t |
|
671 | app_num_tr'2 (Const("Numeral.number_of",Type ("fun", [_, T])) $ t) = |
|
672 Free(NumeralSyntax.dest_bin_str t, T) |
|
673 | app_num_tr'2 (t as Free(s,T)) = t |
|
674 | app_num_tr'2 (t as Var(n,T)) = t |
|
675 | app_num_tr'2 (t as Bound i) = t |
|
676 *)| app_num_tr'2 (Abs(s,T,body)) = Abs(s,T, app_num_tr'2 body) |
|
677 | app_num_tr'2 (t1 $ t2) = (app_num_tr'2 t1) $ (app_num_tr'2 t2) |
|
678 | app_num_tr'2 t = t; |
|
679 *) |
|
680 val uminus_to_string = |
|
681 let |
|
682 fun dest_num t = |
|
683 (case t of |
|
684 (Const ("HOL.uminus_class.uminus", _) $ Free (s, T)) => |
|
685 (case int_of_str s of |
|
686 SOME i => |
|
687 SOME (Free (signed_string_of_int (~1 * i), T)) |
|
688 | NONE => NONE) |
|
689 | _ => NONE); |
|
690 |
|
691 fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b) |
|
692 | to_str (t as (u1 $ u2)) = |
|
693 (case dest_num t of |
|
694 SOME t' => t' |
|
695 | NONE => to_str u1 $ to_str u2) |
|
696 | to_str t = perhaps dest_num t; |
|
697 in to_str end; |
|
698 |
|
699 |
|
700 (*2002 fun num_str thm = |
|
701 let |
|
702 val {sign_ref = sign_ref, der = der, maxidx = maxidx, |
|
703 shyps = shyps, hyps = hyps, (*tpairs = tpairs,*) prop = prop} = |
|
704 rep_thm_G thm; |
|
705 val prop' = app_num_tr'1 prop; |
|
706 in assbl_thm sign_ref der maxidx shyps hyps (*tpairs*) prop' end;*) |
|
707 fun num_str thm = |
|
708 let val (deriv, |
|
709 {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps, |
|
710 hyps = hyps, tpairs = tpairs, prop = prop}) = rep_thm_G thm |
|
711 val prop' = numbers_to_string prop; |
|
712 in assbl_thm deriv thy_ref tags maxidx shyps hyps tpairs prop' end; |
|
713 |
|
714 fun get_thm' xstring = (*?covers 2009 Thm?!, replaces 2002 fun get_thm : |
|
715 val it = fn : theory -> xstring -> Thm.thm*) |
|
716 Thm (xstring, |
|
717 num_str (ProofContext.get_thm (thy2ctxt' "Isac") xstring)); |
|
718 |
|
719 (** get types of Free and Abs for parse' **) |
|
720 (*11.1.00: not used, fix-typed +,*,-,^ instead *) |
|
721 |
|
722 val dummyT = Type ("dummy",[]); |
|
723 val dummyT = TVar (("DUMMY",0),[]); |
|
724 |
|
725 (* assumes only 1 type for numerals |
|
726 and different identifiers for Const, Free and Abs *) |
|
727 fun get_types t = |
|
728 let |
|
729 fun get ts (Const(s,T)) = (s,T)::ts |
|
730 | get ts (Free(s,T)) = if is_no s |
|
731 then ("#",T)::ts else (s,T)::ts |
|
732 | get ts (Var(n,T)) = ts |
|
733 | get ts (Bound i) = ts |
|
734 | get ts (Abs(s,T,body)) = get ((s,T)::ts) body |
|
735 | get ts (t1 $ t2) = (get ts t1) @ (get ts t2) |
|
736 in distinct (get [] t) end; |
|
737 (* |
|
738 val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)"; |
|
739 get_types t; |
|
740 *) |
|
741 |
|
742 (*11.1.00: not used, fix-typed +,*,-,^ instead *) |
|
743 fun set_types al (Const(s,T)) = |
|
744 (case assoc (al,s) of |
|
745 SOME T' => Const(s,T') |
|
746 | NONE => (warning ("set_types: no type for "^s); Const(s,dummyT))) |
|
747 | set_types al (Free(s,T)) = |
|
748 if is_no s then |
|
749 (case assoc (al,"#") of |
|
750 SOME T' => Free(s,T') |
|
751 | NONE => (warning ("set_types: no type for numerals"); Free(s,T))) |
|
752 else (case assoc (al,s) of |
|
753 SOME T' => Free(s,T') |
|
754 | NONE => (warning ("set_types: no type for "^s); Free(s,T))) |
|
755 | set_types al (Var(n,T)) = Var(n,T) |
|
756 | set_types al (Bound i) = Bound i |
|
757 | set_types al (Abs(s,T,body)) = |
|
758 (case assoc (al,s) of |
|
759 SOME T' => Abs(s,T', set_types al body) |
|
760 | NONE => (warning ("set_types: no type for "^s); |
|
761 Abs(s,T, set_types al body))) |
|
762 | set_types al (t1 $ t2) = (set_types al t1) $ (set_types al t2); |
|
763 (* |
|
764 val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)"; |
|
765 val al = get_types t; |
|
766 |
|
767 val t = (term_of o the o (parse thy)) "x = #0 + #-1 * #-4"; |
|
768 atomty t; (* 'a *) |
|
769 val t' = set_types al t; |
|
770 atomty t'; (*real*) |
|
771 (cterm_of thy) t'; |
|
772 val it = "x = #0 + #-1 * #-4" : cterm |
|
773 |
|
774 val t = (term_of o the o (parse thy)) |
|
775 "#5 * x + x ^^^ #2 = (#2 + x) ^^^ #2"; |
|
776 atomty t; |
|
777 val t' = set_types al t; |
|
778 atomty t'; |
|
779 (cterm_of thy) t'; |
|
780 uncaught exception TYPE (*^^^ is new, NOT in al*) |
|
781 *) |
|
782 |
|
783 |
|
784 (** from Descript.ML **) |
|
785 |
|
786 (** decompose an isa-list to an ML-list |
|
787 i.e. [] belong to the meta-language, too **) |
|
788 |
|
789 fun is_list ((Const("List.list.Cons",_)) $ _ $ _) = true |
|
790 | is_list _ = false; |
|
791 (* val (SOME ct) = parse thy "lll::real list"; |
|
792 > val ty = (#t o rep_cterm) ct; |
|
793 > is_list ty; |
|
794 val it = false : bool |
|
795 > val (SOME ct) = parse thy "[lll]"; |
|
796 > val ty = (#t o rep_cterm) ct; |
|
797 > is_list ty; |
|
798 val it = true : bool *) |
|
799 |
|
800 |
|
801 |
|
802 fun mk_Free (s,T) = Free(s,T); |
|
803 fun mk_free T s = Free(s,T); |
|
804 |
|
805 (*instantiate let; necessary for ass_up*) |
|
806 fun inst_abs thy (Const sT) = Const sT |
|
807 | inst_abs thy (Free sT) = Free sT |
|
808 | inst_abs thy (Bound n) = Bound n |
|
809 | inst_abs thy (Var iT) = Var iT |
|
810 | inst_abs thy (Const ("Let",T1) $ e $ (Abs (v,T2,b))) = |
|
811 let val (v',b') = variant_abs (v,T2,b); (*fun variant_abs: term.ML*) |
|
812 in Const ("Let",T1) $ inst_abs thy e $ (Abs (v',T2,inst_abs thy b')) end |
|
813 | inst_abs thy (t1 $ t2) = inst_abs thy t1 $ inst_abs thy t2 |
|
814 | inst_abs thy t = |
|
815 (writeln("inst_abs: unchanged t= "^ term2str t); |
|
816 t); |
|
817 (*val scr as (Script sc) = Script ((term_of o the o (parse thy)) |
|
818 "Script Testeq (e_::bool) = \ |
|
819 \While (contains_root e_) Do \ |
|
820 \ (let e_ = Try (Repeat (Rewrite rroot_square_inv False e_)); \ |
|
821 \ e_ = Try (Repeat (Rewrite square_equation_left True e_)) \ |
|
822 \ in Try (Repeat (Rewrite radd_0 False e_))) "); |
|
823 ML> atomt sc; |
|
824 *** Const ( Script.Testeq) |
|
825 *** . Free ( e_, ) |
|
826 *** . Const ( Script.While) |
|
827 *** . . Const ( RatArith.contains'_root) |
|
828 *** . . . Free ( e_, ) |
|
829 *** . . Const ( Let) |
|
830 *** . . . Const ( Script.Try) |
|
831 *** . . . . Const ( Script.Repeat) |
|
832 *** . . . . . Const ( Script.Rewrite) |
|
833 *** . . . . . . Free ( rroot_square_inv, ) |
|
834 *** . . . . . . Const ( False) |
|
835 *** . . . . . . Free ( e_, ) |
|
836 *** . . . Abs( e_,.. |
|
837 *** . . . . Const ( Let) |
|
838 *** . . . . . Const ( Script.Try) |
|
839 *** . . . . . . Const ( Script.Repeat) |
|
840 *** . . . . . . . Const ( Script.Rewrite) |
|
841 *** . . . . . . . . Free ( square_equation_left, ) |
|
842 *** . . . . . . . . Const ( True) |
|
843 *** . . . . . . . . Bound 0 <-- !!! |
|
844 *** . . . . . Abs( e_,.. |
|
845 *** . . . . . . Const ( Script.Try) |
|
846 *** . . . . . . . Const ( Script.Repeat) |
|
847 *** . . . . . . . . Const ( Script.Rewrite) |
|
848 *** . . . . . . . . . Free ( radd_0, ) |
|
849 *** . . . . . . . . . Const ( False) |
|
850 *** . . . . . . . . . Bound 0 <-- !!! |
|
851 val it = () : unit |
|
852 ML> atomt (inst_abs thy sc); |
|
853 *** Const ( Script.Testeq) |
|
854 *** . Free ( e_, ) |
|
855 *** . Const ( Script.While) |
|
856 *** . . Const ( RatArith.contains'_root) |
|
857 *** . . . Free ( e_, ) |
|
858 *** . . Const ( Let) |
|
859 *** . . . Const ( Script.Try) |
|
860 *** . . . . Const ( Script.Repeat) |
|
861 *** . . . . . Const ( Script.Rewrite) |
|
862 *** . . . . . . Free ( rroot_square_inv, ) |
|
863 *** . . . . . . Const ( False) |
|
864 *** . . . . . . Free ( e_, ) |
|
865 *** . . . Abs( e_,.. |
|
866 *** . . . . Const ( Let) |
|
867 *** . . . . . Const ( Script.Try) |
|
868 *** . . . . . . Const ( Script.Repeat) |
|
869 *** . . . . . . . Const ( Script.Rewrite) |
|
870 *** . . . . . . . . Free ( square_equation_left, ) |
|
871 *** . . . . . . . . Const ( True) |
|
872 *** . . . . . . . . Free ( e_, ) <-- !!! |
|
873 *** . . . . . Abs( e_,.. |
|
874 *** . . . . . . Const ( Script.Try) |
|
875 *** . . . . . . . Const ( Script.Repeat) |
|
876 *** . . . . . . . . Const ( Script.Rewrite) |
|
877 *** . . . . . . . . . Free ( radd_0, ) |
|
878 *** . . . . . . . . . Const ( False) |
|
879 *** . . . . . . . . . Free ( e_, ) <-- ZUFALL vor 5.03!!! |
|
880 val it = () : unit*) |
|
881 |
|
882 |
|
883 |
|
884 |
|
885 fun inst_abs thy (Const sT) = Const sT |
|
886 | inst_abs thy (Free sT) = Free sT |
|
887 | inst_abs thy (Bound n) = Bound n |
|
888 | inst_abs thy (Var iT) = Var iT |
|
889 | inst_abs thy (Const ("Let",T1) $ e $ (Abs (v,T2,b))) = |
|
890 let val b' = subst_bound (Free(v,T2),b); |
|
891 (*fun variant_abs: term.ML*) |
|
892 in Const ("Let",T1) $ inst_abs thy e $ (Abs (v,T2,inst_abs thy b')) end |
|
893 | inst_abs thy (t1 $ t2) = inst_abs thy t1 $ inst_abs thy t2 |
|
894 | inst_abs thy t = |
|
895 (writeln("inst_abs: unchanged t= "^ term2str t); |
|
896 t); |
|
897 (*val scr = |
|
898 "Script Make_fun_by_explicit (f_::real) (v_::real) (eqs_::bool list) = \ |
|
899 \ (let h_ = (hd o (filterVar f_)) eqs_; \ |
|
900 \ e_1 = hd (dropWhile (ident h_) eqs_); \ |
|
901 \ vs_ = dropWhile (ident f_) (Vars h_); \ |
|
902 \ v_1 = hd (dropWhile (ident v_) vs_); \ |
|
903 \ (s_1::bool list)=(SubProblem(DiffApp_,[univar,equation],[no_met])\ |
|
904 \ [bool_ e_1, real_ v_1])\ |
|
905 \ in Substitute [(v_1 = (rhs o hd) s_1)] h_)"; |
|
906 > val ttt = (term_of o the o (parse thy)) scr; |
|
907 > writeln(term2str ttt); |
|
908 > atomt ttt; |
|
909 *** ------------- |
|
910 *** Const ( DiffApp.Make'_fun'_by'_explicit) |
|
911 *** . Free ( f_, ) |
|
912 *** . Free ( v_, ) |
|
913 *** . Free ( eqs_, ) |
|
914 *** . Const ( Let) |
|
915 *** . . Const ( Fun.op o) |
|
916 *** . . . Const ( List.hd) |
|
917 *** . . . Const ( DiffApp.filterVar) |
|
918 *** . . . . Free ( f_, ) |
|
919 *** . . . Free ( eqs_, ) |
|
920 *** . . Abs( h_,.. |
|
921 *** . . . Const ( Let) |
|
922 *** . . . . Const ( List.hd) |
|
923 *** . . . . . Const ( List.dropWhile) |
|
924 *** . . . . . . Const ( Atools.ident) |
|
925 *** . . . . . . . Bound 0 <---- Free ( h_, ) |
|
926 *** . . . . . . Free ( eqs_, ) |
|
927 *** . . . . Abs( e_1,.. |
|
928 *** . . . . . Const ( Let) |
|
929 *** . . . . . . Const ( List.dropWhile) |
|
930 *** . . . . . . . Const ( Atools.ident) |
|
931 *** . . . . . . . . Free ( f_, ) |
|
932 *** . . . . . . . Const ( Tools.Vars) |
|
933 *** . . . . . . . . Bound 1 <---- Free ( h_, ) |
|
934 *** . . . . . . Abs( vs_,.. |
|
935 *** . . . . . . . Const ( Let) |
|
936 *** . . . . . . . . Const ( List.hd) |
|
937 *** . . . . . . . . . Const ( List.dropWhile) |
|
938 *** . . . . . . . . . . Const ( Atools.ident) |
|
939 *** . . . . . . . . . . . Free ( v_, ) |
|
940 *** . . . . . . . . . . Bound 0 <---- Free ( vs_, ) |
|
941 *** . . . . . . . . Abs( v_1,.. |
|
942 *** . . . . . . . . . Const ( Let) |
|
943 *** . . . . . . . . . . Const ( Script.SubProblem) |
|
944 *** . . . . . . . . . . . Const ( Pair) |
|
945 *** . . . . . . . . . . . . Free ( DiffApp_, ) |
|
946 *** . . . . . . . . . . . . Const ( Pair) |
|
947 *** . . . . . . . . . . . . . Const ( List.list.Cons) |
|
948 *** . . . . . . . . . . . . . . Free ( univar, ) |
|
949 *** . . . . . . . . . . . . . . Const ( List.list.Cons) |
|
950 *** . . . . . . . . . . . . . . . Free ( equation, ) |
|
951 *** . . . . . . . . . . . . . . . Const ( List.list.Nil) |
|
952 *** . . . . . . . . . . . . . Const ( List.list.Cons) |
|
953 *** . . . . . . . . . . . . . . Free ( no_met, ) |
|
954 *** . . . . . . . . . . . . . . Const ( List.list.Nil) |
|
955 *** . . . . . . . . . . . Const ( List.list.Cons) |
|
956 *** . . . . . . . . . . . . Const ( Script.bool_) |
|
957 *** . . . . . . . . . . . . . Bound 2 <----- Free ( e_1, ) |
|
958 *** . . . . . . . . . . . . Const ( List.list.Cons) |
|
959 *** . . . . . . . . . . . . . Const ( Script.real_) |
|
960 *** . . . . . . . . . . . . . . Bound 0 <----- Free ( v_1, ) |
|
961 *** . . . . . . . . . . . . . Const ( List.list.Nil) |
|
962 *** . . . . . . . . . . Abs( s_1,.. |
|
963 *** . . . . . . . . . . . Const ( Script.Substitute) |
|
964 *** . . . . . . . . . . . . Const ( List.list.Cons) |
|
965 *** . . . . . . . . . . . . . Const ( Pair) |
|
966 *** . . . . . . . . . . . . . . Bound 1 <----- Free ( v_1, ) |
|
967 *** . . . . . . . . . . . . . . Const ( Fun.op o) |
|
968 *** . . . . . . . . . . . . . . . Const ( Tools.rhs) |
|
969 *** . . . . . . . . . . . . . . . Const ( List.hd) |
|
970 *** . . . . . . . . . . . . . . . Bound 0 <----- Free ( s_1, ) |
|
971 *** . . . . . . . . . . . . . Const ( List.list.Nil) |
|
972 *** . . . . . . . . . . . . Bound 4 <----- Free ( h_, ) |
|
973 |
|
974 > val ttt' = inst_abs thy ttt; |
|
975 > writeln(term2str ttt'); |
|
976 Script Make_fun_by_explicit f_ v_ eqs_ = |
|
977 ... as above ... |
|
978 > atomt ttt'; |
|
979 *** ------------- |
|
980 *** Const ( DiffApp.Make'_fun'_by'_explicit) |
|
981 *** . Free ( f_, ) |
|
982 *** . Free ( v_, ) |
|
983 *** . Free ( eqs_, ) |
|
984 *** . Const ( Let) |
|
985 *** . . Const ( Fun.op o) |
|
986 *** . . . Const ( List.hd) |
|
987 *** . . . Const ( DiffApp.filterVar) |
|
988 *** . . . . Free ( f_, ) |
|
989 *** . . . Free ( eqs_, ) |
|
990 *** . . Abs( h_,.. |
|
991 *** . . . Const ( Let) |
|
992 *** . . . . Const ( List.hd) |
|
993 *** . . . . . Const ( List.dropWhile) |
|
994 *** . . . . . . Const ( Atools.ident) |
|
995 *** . . . . . . . Free ( h_, ) <---- Bound 0 |
|
996 *** . . . . . . Free ( eqs_, ) |
|
997 *** . . . . Abs( e_1,.. |
|
998 *** . . . . . Const ( Let) |
|
999 *** . . . . . . Const ( List.dropWhile) |
|
1000 *** . . . . . . . Const ( Atools.ident) |
|
1001 *** . . . . . . . . Free ( f_, ) |
|
1002 *** . . . . . . . Const ( Tools.Vars) |
|
1003 *** . . . . . . . . Free ( h_, ) <---- Bound 1 |
|
1004 *** . . . . . . Abs( vs_,.. |
|
1005 *** . . . . . . . Const ( Let) |
|
1006 *** . . . . . . . . Const ( List.hd) |
|
1007 *** . . . . . . . . . Const ( List.dropWhile) |
|
1008 *** . . . . . . . . . . Const ( Atools.ident) |
|
1009 *** . . . . . . . . . . . Free ( v_, ) |
|
1010 *** . . . . . . . . . . Free ( vs_, ) <---- Bound 0 |
|
1011 *** . . . . . . . . Abs( v_1,.. |
|
1012 *** . . . . . . . . . Const ( Let) |
|
1013 *** . . . . . . . . . . Const ( Script.SubProblem) |
|
1014 *** . . . . . . . . . . . Const ( Pair) |
|
1015 *** . . . . . . . . . . . . Free ( DiffApp_, ) |
|
1016 *** . . . . . . . . . . . . Const ( Pair) |
|
1017 *** . . . . . . . . . . . . . Const ( List.list.Cons) |
|
1018 *** . . . . . . . . . . . . . . Free ( univar, ) |
|
1019 *** . . . . . . . . . . . . . . Const ( List.list.Cons) |
|
1020 *** . . . . . . . . . . . . . . . Free ( equation, ) |
|
1021 *** . . . . . . . . . . . . . . . Const ( List.list.Nil) |
|
1022 *** . . . . . . . . . . . . . Const ( List.list.Cons) |
|
1023 *** . . . . . . . . . . . . . . Free ( no_met, ) |
|
1024 *** . . . . . . . . . . . . . . Const ( List.list.Nil) |
|
1025 *** . . . . . . . . . . . Const ( List.list.Cons) |
|
1026 *** . . . . . . . . . . . . Const ( Script.bool_) |
|
1027 *** . . . . . . . . . . . . . Free ( e_1, ) <----- Bound 2 |
|
1028 *** . . . . . . . . . . . . Const ( List.list.Cons) |
|
1029 *** . . . . . . . . . . . . . Const ( Script.real_) |
|
1030 *** . . . . . . . . . . . . . . Free ( v_1, ) <----- Bound 0 |
|
1031 *** . . . . . . . . . . . . . Const ( List.list.Nil) |
|
1032 *** . . . . . . . . . . Abs( s_1,.. |
|
1033 *** . . . . . . . . . . . Const ( Script.Substitute) |
|
1034 *** . . . . . . . . . . . . Const ( List.list.Cons) |
|
1035 *** . . . . . . . . . . . . . Const ( Pair) |
|
1036 *** . . . . . . . . . . . . . . Free ( v_1, ) <----- Bound 1 |
|
1037 *** . . . . . . . . . . . . . . Const ( Fun.op o) |
|
1038 *** . . . . . . . . . . . . . . . Const ( Tools.rhs) |
|
1039 *** . . . . . . . . . . . . . . . Const ( List.hd) |
|
1040 *** . . . . . . . . . . . . . . . Free ( s_1, ) <----- Bound 0 |
|
1041 *** . . . . . . . . . . . . . Const ( List.list.Nil) |
|
1042 *** . . . . . . . . . . . . Free ( h_, ) <----- Bound 4 |
|
1043 |
|
1044 Note numbering of de Bruijn indexes ! |
|
1045 |
|
1046 Script Make_fun_by_explicit f_ v_ eqs_ = |
|
1047 let h_ = (hd o filterVar f_) eqs_; |
|
1048 e_1 = hd (dropWhile (ident h_ BOUND_0) eqs_); |
|
1049 vs_ = dropWhile (ident f_) (Vars h_ BOUND_1); |
|
1050 v_1 = hd (dropWhile (ident v_) vs_ BOUND_0); |
|
1051 s_1 = |
|
1052 SubProblem (DiffApp_, [univar, equation], [no_met]) |
|
1053 [bool_ e_1 BOUND_2, real_ v_1 BOUND_0] |
|
1054 in Substitute [(v_1 BOUND_1 = (rhs o hd) s_1 BOUND_0)] h_ BOUND_4 |
|
1055 *) |
|
1056 |
|
1057 |
|
1058 fun T_a2real (Type (s, [])) = |
|
1059 if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else Type (s, []) |
|
1060 | T_a2real (Type (s, Ts)) = Type (s, map T_a2real Ts) |
|
1061 | T_a2real (TFree (s, srt)) = |
|
1062 if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else TFree (s, srt) |
|
1063 | T_a2real (TVar (("DUMMY",_),srt)) = HOLogic.realT; |
|
1064 |
|
1065 (*FIXME .. fixes the type (+see Typefix.thy*) |
|
1066 fun typ_a2real (Const( s, T)) = (Const( s, T_a2real T)) |
|
1067 | typ_a2real (Free( s, T)) = (Free( s, T_a2real T)) |
|
1068 | typ_a2real (Var( n, T)) = (Var( n, T_a2real T)) |
|
1069 | typ_a2real (Bound i) = (Bound i) |
|
1070 | typ_a2real (Abs(s,T,t)) = Abs(s, T, typ_a2real t) |
|
1071 | typ_a2real (t1 $ t2) = (typ_a2real t1) $ (typ_a2real t2); |
|
1072 (* |
|
1073 ----------------6.8.02--------------------------------------------------- |
|
1074 val str = "1"; |
|
1075 val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[]))); |
|
1076 atomty (term_of t); |
|
1077 *** ------------- |
|
1078 *** Const ( 1, 'a) |
|
1079 val t = (app_num_tr' o term_of) t; |
|
1080 atomty t; |
|
1081 *** ------------- |
|
1082 *** Const ( 1, 'a) |
|
1083 val t = typ_a2real t; |
|
1084 atomty t; |
|
1085 *** ------------- |
|
1086 *** Const ( 1, real) |
|
1087 |
|
1088 val str = "2"; |
|
1089 val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[]))); |
|
1090 atomty (term_of t); |
|
1091 *** ------------- |
|
1092 *** Const ( Numeral.number_of, bin => 'a) |
|
1093 *** . Const ( Numeral.bin.Bit, [bin, bool] => bin) |
|
1094 *** . . Const ( Numeral.bin.Bit, [bin, bool] => bin) |
|
1095 *** . . . Const ( Numeral.bin.Pls, bin) |
|
1096 *** . . . Const ( True, bool) |
|
1097 *** . . Const ( False, bool) |
|
1098 val t = (app_num_tr' o term_of) t; |
|
1099 atomty t; |
|
1100 *** ------------- |
|
1101 *** Free ( 2, 'a) |
|
1102 val t = typ_a2real t; |
|
1103 atomty t; |
|
1104 *** ------------- |
|
1105 *** Free ( 2, real) |
|
1106 ----------------6.8.02--------------------------------------------------- |
|
1107 |
|
1108 |
|
1109 > val str = "R"; |
|
1110 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[])))); |
|
1111 val t = Free ("R","?DUMMY") : term |
|
1112 > val t' = typ_a2real t; |
|
1113 > (cterm_of thy) t'; |
|
1114 val it = "R::RealDef.real" : cterm |
|
1115 |
|
1116 > val str = "R=R"; |
|
1117 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[])))); |
|
1118 > atomty (typ_a2real t); |
|
1119 *** ------------- |
|
1120 *** Const ( op =, [RealDef.real, RealDef.real] => bool) |
|
1121 *** Free ( R, RealDef.real) |
|
1122 *** Free ( R, RealDef.real) |
|
1123 > val t' = typ_a2real t; |
|
1124 > (cterm_of thy) t'; |
|
1125 val it = "(R::RealDef.real) = R" : cterm |
|
1126 |
|
1127 > val str = "fixed_values [R=R]"; |
|
1128 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[])))); |
|
1129 > val t' = typ_a2real t; |
|
1130 > (cterm_of thy) t'; |
|
1131 val it = "fixed_values [(R::RealDef.real) = R]" : cterm |
|
1132 *) |
|
1133 |
|
1134 (*TODO.WN0609: parse should return a term or a string |
|
1135 (or even more comprehensive datastructure for error-messages) |
|
1136 i.e. in wrapping with SOME term or NONE the latter is not sufficient*) |
|
1137 (*2002 fun parseold thy str = |
|
1138 (let |
|
1139 val sgn = sign_of thy; |
|
1140 val t = ((*typ_a2real o*) app_num_tr'1 o term_of) |
|
1141 (read_cterm sgn (str,(TVar(("DUMMY",0),[])))); |
|
1142 in SOME (cterm_of sgn t) end) |
|
1143 handle _ => NONE;*) |
|
1144 |
|
1145 |
|
1146 |
|
1147 fun parseold thy str = |
|
1148 (let val t = ((*typ_a2real o*) numbers_to_string) |
|
1149 (Syntax.read_term_global thy str) |
|
1150 in SOME (cterm_of thy t) end) |
|
1151 handle _ => NONE; |
|
1152 (*2002 fun parseN thy str = |
|
1153 (let |
|
1154 val sgn = sign_of thy; |
|
1155 val t = ((*typ_a2real o app_num_tr'1 o*) term_of) |
|
1156 (read_cterm sgn (str,(TVar(("DUMMY",0),[])))); |
|
1157 in SOME (cterm_of sgn t) end) |
|
1158 handle _ => NONE;*) |
|
1159 fun parseN thy str = |
|
1160 (let val t = (*(typ_a2real o numbers_to_string)*) |
|
1161 (Syntax.read_term_global thy str) |
|
1162 in SOME (cterm_of thy t) end) |
|
1163 handle _ => NONE; |
|
1164 (*2002 fun parse thy str = |
|
1165 (let |
|
1166 val sgn = sign_of thy; |
|
1167 val t = (typ_a2real o app_num_tr'1 o term_of) |
|
1168 (read_cterm sgn (str,(TVar(("DUMMY",0),[])))); |
|
1169 in SOME (cterm_of sgn t) end) (*FIXXXXME 10.8.02: return term !!!*) |
|
1170 handle _ => NONE;*) |
|
1171 (*2010 fun parse thy str = |
|
1172 (let val t = (typ_a2real o app_num_tr'1) (Syntax.read_term_global thy str) |
|
1173 in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*) |
|
1174 handle _ => NONE;*) |
|
1175 fun parse thy str = |
|
1176 (let val t = (typ_a2real o numbers_to_string) |
|
1177 (Syntax.read_term_global thy str) |
|
1178 in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*) |
|
1179 handle _ => NONE; |
|
1180 |
|
1181 (* 10.8.02: for this reason we still have ^^^-------------------- |
|
1182 val thy = SqRoot.thy; |
|
1183 val str = "(1::real) ^ (2::nat)"; |
|
1184 val sgn = sign_of thy; |
|
1185 val ct = (read_cterm sgn (str,(TVar(("DUMMY",0),[])))) handle e =>print_exn e; |
|
1186 (*1*)"(1::real) ^ 2"; |
|
1187 atomty (term_of ct); |
|
1188 *** ------------- |
|
1189 *** Const ( Nat.power, [real, nat] => real) |
|
1190 *** . Const ( 1, real) |
|
1191 *** . Const ( Numeral.number_of, bin => nat) |
|
1192 *** . . Const ( Numeral.bin.Bit, [bin, bool] => bin) |
|
1193 *** . . . Const ( Numeral.bin.Bit, [bin, bool] => bin) |
|
1194 *** . . . . Const ( Numeral.bin.Pls, bin) |
|
1195 *** . . . . Const ( True, bool) |
|
1196 *** . . . Const ( False, bool) |
|
1197 val t = ((app_num_tr' o term_of) |
|
1198 (read_cterm sgn (str,(TVar(("DUMMY",0),[])))))handle e => print_exn e; |
|
1199 val ct = (cterm_of sgn t) handle e => print_exn e; |
|
1200 (*2*)"(1::real) ^ (2::nat)"; |
|
1201 atomty (term_of ct); |
|
1202 *** ------------- |
|
1203 *** Const ( Nat.power, [real, nat] => real) |
|
1204 *** . Free ( 1, real) |
|
1205 *** . Free ( 2, nat) (*1*) Const("2",_) (*2*) Free("2",_) |
|
1206 |
|
1207 |
|
1208 val str = "(2::real) ^ (2::nat)"; |
|
1209 val t = (read_cterm sgn (str,(TVar(("DUMMY",0),[])))) handle e => print_exn e; |
|
1210 val t = "(2::real) ^ 2" : cterm |
|
1211 val t = ((app_num_tr' o term_of) |
|
1212 (read_cterm sgn (str,(TVar(("DUMMY",0),[])))))handle e => print_exn e; |
|
1213 val ct = (cterm_of sgn t) handle e => print_exn e; |
|
1214 Variable "2" has two distinct types |
|
1215 real |
|
1216 nat |
|
1217 uncaught exception TYPE |
|
1218 raised at: sign.ML:672.26-673.56 |
|
1219 goals.ML:1100.61 |
|
1220 |
|
1221 |
|
1222 val str = "(3::real) ^ (2::nat)"; |
|
1223 val t = (read_cterm sgn (str,(TVar(("DUMMY",0),[])))) handle e => print_exn e; |
|
1224 val t = "(3::real) ^ 2" : cterm |
|
1225 val t = ((app_num_tr' o term_of) |
|
1226 (read_cterm sgn (str,(TVar(("DUMMY",0),[])))))handle e => print_exn e; |
|
1227 val ct = (cterm_of sgn t) handle e => print_exn e; |
|
1228 val ct = "(3::real) ^ (2::nat)" : cterm |
|
1229 |
|
1230 |
|
1231 Conclusion: The type inference allows different types |
|
1232 for one and the same Numeral.number_of |
|
1233 BUT the type inference doesn't allow |
|
1234 Free ( 2, real) and Free ( 2, nat) within one term |
|
1235 --------------- ~~~~ ~~~ *) |
|
1236 (* |
|
1237 > val (SOME ct) = parse thy "(-#5)^^^#3"; |
|
1238 > atomty (term_of ct); |
|
1239 *** ------------- |
|
1240 *** Const ( Nat.op ^, ['a, nat] => 'a) |
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1241 *** Const ( uminus, 'a => 'a) |
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1242 *** Free ( #5, 'a) |
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1243 *** Free ( #3, nat) |
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1244 > val (SOME ct) = parse thy "R=R"; |
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1245 > atomty (term_of ct); |
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1246 *** ------------- |
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1247 *** Const ( op =, [real, real] => bool) |
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1248 *** Free ( R, real) |
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1249 *** Free ( R, real) |
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1250 |
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1251 THIS IS THE OUTPUT FOR VERSION (3) above at typ_a2real !!!!! |
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1252 *** ------------- |
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1253 *** Const ( op =, [RealDef.real, RealDef.real] => bool) |
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1254 *** Free ( R, RealDef.real) |
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1255 *** Free ( R, RealDef.real) *) |
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1256 |
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1257 (*version for testing local to theories*) |
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1258 fun str2term_ thy str = (term_of o the o (parse thy)) str; |
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1259 fun str2term str = (term_of o the o (parse (theory "Isac"))) str; |
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1260 fun strs2terms ss = map str2term ss; |
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1261 fun str2termN str = (term_of o the o (parseN (theory "Isac"))) str; |
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1262 |
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1263 (*+ makes a substitution from the output of Pattern.match +*) |
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1264 (*fun mk_subs ((id, _):indexname, t:term) = (Free (id,type_of t), t);*) |
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1265 fun mk_subs (subs: ((string * int) * (Term.typ * Term.term)) list) = |
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1266 let fun mk_sub ((id, _), (ty, tm)) = (Free (id, ty), tm) in |
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1267 map mk_sub subs end; |
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1268 |
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1269 val atomthm = atomt o #prop o rep_thm; |
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1270 |
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1271 (*.instantiate #prop thm with bound variables (as Free).*) |
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1272 fun inst_bdv [] t = t : term |
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1273 | inst_bdv (instl: (term*term) list) t = |
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1274 let fun subst (v as Var((s,_),T)) = |
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1275 (case explode s of |
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1276 "b"::"d"::"v"::_ => |
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1277 if_none (assoc(instl,Free(s,T))) (Free(s,T)) |
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1278 | _ => v) |
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1279 | subst (Abs(a,T,body)) = Abs(a, T, subst body) |
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1280 | subst (f$t') = subst f $ subst t' |
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1281 | subst t = if_none (assoc(instl,t)) t |
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1282 in subst t end; |
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1283 |
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1284 |
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1285 (*WN050829 caution: is_atom (str2term"q_0/2 * L * x") = true !!! |
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1286 use length (vars term) = 1 instead*) |
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1287 fun is_atom (Const ("Float.Float",_) $ _) = true |
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1288 | is_atom (Const ("ComplexI.I'_'_",_)) = true |
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1289 | is_atom (Const ("op *",_) $ t $ Const ("ComplexI.I'_'_",_)) = is_atom t |
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1290 | is_atom (Const ("op +",_) $ t1 $ Const ("ComplexI.I'_'_",_)) = is_atom t1 |
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1291 | is_atom (Const ("op +",_) $ t1 $ |
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1292 (Const ("op *",_) $ t2 $ Const ("ComplexI.I'_'_",_))) = |
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1293 is_atom t1 andalso is_atom t2 |
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1294 | is_atom (Const _) = true |
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1295 | is_atom (Free _) = true |
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1296 | is_atom (Var _) = true |
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1297 | is_atom _ = false; |
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1298 (* val t = str2term "q_0/2 * L * x"; |
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1299 |
|
1300 |
|
1301 *) |
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1302 (*val t = str2term "Float ((1,2),(0,0))"; |
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1303 > is_atom t; |
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1304 val it = true : bool |
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1305 > val t = str2term "Float ((1,2),(0,0)) * I__"; |
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1306 > is_atom t; |
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1307 val it = true : bool |
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1308 > val t = str2term "Float ((1,2),(0,0)) + Float ((3,4),(0,0)) * I__"; |
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1309 > is_atom t; |
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1310 val it = true : bool |
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1311 > val t = str2term "1 + 2*I__"; |
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1312 > val Const ("op +",_) $ t1 $ (Const ("op *",_) $ t2 $ Const ("ComplexI.I'_'_",_)) = t; |
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1313 *) |
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1314 |
|
1315 (*.adaption from Isabelle/src/Pure/term.ML; reports if ALL Free's |
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1316 have found a substitution (required for evaluating the preconditions |
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1317 of _incomplete_ models).*) |
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1318 fun subst_atomic_all [] t = (false, (*TODO may be 'true' for some terms ?*) |
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1319 t : term) |
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1320 | subst_atomic_all (instl: (term*term) list) t = |
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1321 let fun subst (Abs(a,T,body)) = |
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1322 let val (all, body') = subst body |
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1323 in (all, Abs(a, T, body')) end |
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1324 | subst (f$tt) = |
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1325 let val (all1, f') = subst f |
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1326 val (all2, tt') = subst tt |
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1327 in (all1 andalso all2, f' $ tt') end |
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1328 | subst (t as Free _) = |
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1329 if is_num t then (true, t) (*numerals cannot be subst*) |
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1330 else (case assoc(instl,t) of |
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1331 SOME t' => (true, t') |
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1332 | NONE => (false, t)) |
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1333 | subst t = (true, if_none (assoc(instl,t)) t) |
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1334 in subst t end; |
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1335 |
|
1336 (*.add two terms with a type given.*) |
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1337 fun mk_add t1 t2 = |
|
1338 let val T1 = type_of t1 |
|
1339 val T2 = type_of t2 |
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1340 in if T1 <> T2 then raise TYPE ("mk_add gets ",[T1, T2],[t1,t2]) |
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1341 else (Const ("op +", [T1, T2] ---> T1) $ t1 $ t2) |
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1342 end; |
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1343 |