1 (* Title: HOLCF/Tools/Domain/domain_library.ML |
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2 Author: David von Oheimb |
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3 |
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4 Library for domain command. |
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5 *) |
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6 |
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7 |
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8 (* infix syntax *) |
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9 |
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10 infixr 5 -->; |
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11 infixr 6 ->>; |
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12 infixr 0 ===>; |
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13 infixr 0 ==>; |
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14 infix 0 ==; |
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15 infix 1 ===; |
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16 infix 1 ~=; |
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17 |
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18 infix 9 ` ; |
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19 infix 9 `% ; |
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20 infix 9 `%%; |
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21 |
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22 |
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23 (* ----- specific support for domain ---------------------------------------- *) |
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24 |
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25 signature DOMAIN_LIBRARY = |
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26 sig |
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27 val first : 'a * 'b * 'c -> 'a |
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28 val second : 'a * 'b * 'c -> 'b |
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29 val third : 'a * 'b * 'c -> 'c |
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30 val upd_second : ('b -> 'd) -> 'a * 'b * 'c -> 'a * 'd * 'c |
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31 val upd_third : ('c -> 'd) -> 'a * 'b * 'c -> 'a * 'b * 'd |
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32 val mapn : (int -> 'a -> 'b) -> int -> 'a list -> 'b list |
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33 val atomize : Proof.context -> thm -> thm list |
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34 |
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35 val Imposs : string -> 'a; |
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36 val cpo_type : theory -> typ -> bool; |
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37 val pcpo_type : theory -> typ -> bool; |
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38 val string_of_typ : theory -> typ -> string; |
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39 |
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40 (* Creating HOLCF types *) |
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41 val mk_ssumT : typ * typ -> typ; |
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42 val mk_sprodT : typ * typ -> typ; |
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43 val mk_uT : typ -> typ; |
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44 val oneT : typ; |
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45 val pcpoS : sort; |
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46 |
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47 (* Creating HOLCF terms *) |
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48 val %: : string -> term; |
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49 val %%: : string -> term; |
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50 val ` : term * term -> term; |
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51 val `% : term * string -> term; |
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52 val UU : term; |
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53 val ID : term; |
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54 val list_ccomb : term * term list -> term; |
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55 val con_app2 : string -> ('a -> term) -> 'a list -> term; |
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56 val prj : ('a -> 'b -> 'a) -> ('a -> 'b -> 'a) -> 'a -> 'b list -> int -> 'a |
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57 val proj : term -> 'a list -> int -> term; |
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58 |
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59 (* Creating propositions *) |
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60 val mk_conj : term * term -> term; |
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61 val mk_disj : term * term -> term; |
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62 val mk_imp : term * term -> term; |
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63 val mk_lam : string * term -> term; |
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64 val mk_all : string * term -> term; |
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65 val mk_ex : string * term -> term; |
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66 val mk_constrainall : string * typ * term -> term; |
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67 val === : term * term -> term; |
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68 val defined : term -> term; |
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69 val mk_adm : term -> term; |
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70 val lift : ('a -> term) -> 'a list * term -> term; |
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71 val lift_defined : ('a -> term) -> 'a list * term -> term; |
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72 |
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73 (* Creating meta-propositions *) |
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74 val mk_trp : term -> term; (* HOLogic.mk_Trueprop *) |
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75 val == : term * term -> term; |
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76 val ===> : term * term -> term; |
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77 val mk_All : string * term -> term; |
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78 |
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79 (* Domain specifications *) |
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80 eqtype arg; |
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81 type cons = string * arg list; |
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82 type eq = (string * typ list) * cons list; |
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83 val mk_arg : (bool * Datatype.dtyp) * string -> arg; |
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84 val is_lazy : arg -> bool; |
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85 val rec_of : arg -> int; |
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86 val dtyp_of : arg -> Datatype.dtyp; |
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87 val vname : arg -> string; |
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88 val upd_vname : (string -> string) -> arg -> arg; |
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89 val is_rec : arg -> bool; |
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90 val is_nonlazy_rec : arg -> bool; |
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91 val nonlazy : arg list -> string list; |
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92 val nonlazy_rec : arg list -> string list; |
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93 val %# : arg -> term; |
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94 val bound_arg : ''a list -> ''a -> term; (* ''a = arg or string *) |
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95 val idx_name : 'a list -> string -> int -> string; |
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96 val con_app : string -> arg list -> term; |
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97 end; |
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98 |
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99 structure Domain_Library :> DOMAIN_LIBRARY = |
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100 struct |
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101 |
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102 fun first (x,_,_) = x; |
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103 fun second (_,x,_) = x; |
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104 fun third (_,_,x) = x; |
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105 |
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106 fun upd_first f (x,y,z) = (f x, y, z); |
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107 fun upd_second f (x,y,z) = ( x, f y, z); |
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108 fun upd_third f (x,y,z) = ( x, y, f z); |
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109 |
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110 fun mapn f n [] = [] |
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111 | mapn f n (x::xs) = (f n x) :: mapn f (n+1) xs; |
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112 |
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113 fun foldr'' f (l,f2) = |
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114 let fun itr [] = raise Fail "foldr''" |
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115 | itr [a] = f2 a |
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116 | itr (a::l) = f(a, itr l) |
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117 in itr l end; |
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118 |
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119 fun atomize ctxt thm = |
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120 let |
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121 val r_inst = read_instantiate ctxt; |
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122 fun at thm = |
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123 case concl_of thm of |
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124 _$(Const(@{const_name HOL.conj},_)$_$_) => at(thm RS conjunct1)@at(thm RS conjunct2) |
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125 | _$(Const(@{const_name All} ,_)$Abs(s,_,_))=> at(thm RS (r_inst [(("x", 0), "?" ^ s)] spec)) |
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126 | _ => [thm]; |
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127 in map zero_var_indexes (at thm) end; |
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128 |
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129 exception Impossible of string; |
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130 fun Imposs msg = raise Impossible ("Domain:"^msg); |
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131 |
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132 fun cpo_type sg t = Sign.of_sort sg (Sign.certify_typ sg t, @{sort cpo}); |
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133 fun pcpo_type sg t = Sign.of_sort sg (Sign.certify_typ sg t, @{sort pcpo}); |
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134 fun string_of_typ sg = Syntax.string_of_typ_global sg o Sign.certify_typ sg; |
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135 |
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136 (* ----- constructor list handling ----- *) |
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137 |
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138 type arg = |
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139 (bool * Datatype.dtyp) * (* (lazy, recursive element) *) |
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140 string; (* argument name *) |
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141 |
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142 type cons = |
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143 string * (* operator name of constr *) |
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144 arg list; (* argument list *) |
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145 |
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146 type eq = |
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147 (string * (* name of abstracted type *) |
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148 typ list) * (* arguments of abstracted type *) |
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149 cons list; (* represented type, as a constructor list *) |
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150 |
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151 val mk_arg = I; |
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152 |
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153 fun rec_of ((_,dtyp),_) = |
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154 case dtyp of Datatype_Aux.DtRec i => i | _ => ~1; |
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155 (* FIXME: what about indirect recursion? *) |
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156 |
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157 fun is_lazy arg = fst (fst arg); |
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158 fun dtyp_of arg = snd (fst arg); |
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159 val vname = snd; |
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160 val upd_vname = apsnd; |
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161 fun is_rec arg = rec_of arg >=0; |
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162 fun is_nonlazy_rec arg = is_rec arg andalso not (is_lazy arg); |
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163 fun nonlazy args = map vname (filter_out is_lazy args); |
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164 fun nonlazy_rec args = map vname (filter is_nonlazy_rec args); |
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165 |
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166 |
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167 (* ----- support for type and mixfix expressions ----- *) |
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168 |
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169 fun mk_uT T = Type(@{type_name "u"}, [T]); |
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170 fun mk_sprodT (T, U) = Type(@{type_name sprod}, [T, U]); |
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171 fun mk_ssumT (T, U) = Type(@{type_name ssum}, [T, U]); |
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172 val oneT = @{typ one}; |
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173 |
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174 (* ----- support for term expressions ----- *) |
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175 |
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176 fun %: s = Free(s,dummyT); |
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177 fun %# arg = %:(vname arg); |
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178 fun %%: s = Const(s,dummyT); |
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179 |
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180 local open HOLogic in |
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181 val mk_trp = mk_Trueprop; |
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182 fun mk_conj (S,T) = conj $ S $ T; |
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183 fun mk_disj (S,T) = disj $ S $ T; |
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184 fun mk_imp (S,T) = imp $ S $ T; |
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185 fun mk_lam (x,T) = Abs(x,dummyT,T); |
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186 fun mk_all (x,P) = HOLogic.mk_all (x,dummyT,P); |
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187 fun mk_ex (x,P) = mk_exists (x,dummyT,P); |
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188 fun mk_constrainall (x,typ,P) = %%: @{const_name All} $ (Type.constraint (typ --> boolT) (mk_lam(x,P))); |
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189 end |
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190 |
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191 fun mk_All (x,P) = %%:"all" $ mk_lam(x,P); (* meta universal quantification *) |
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192 |
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193 infixr 0 ===>; fun S ===> T = %%: "==>" $ S $ T; |
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194 infix 0 ==; fun S == T = %%: "==" $ S $ T; |
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195 infix 1 ===; fun S === T = %%: @{const_name HOL.eq} $ S $ T; |
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196 infix 1 ~=; fun S ~= T = HOLogic.mk_not (S === T); |
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197 |
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198 infix 9 ` ; fun f ` x = %%: @{const_name Rep_CFun} $ f $ x; |
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199 infix 9 `% ; fun f`% s = f` %: s; |
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200 infix 9 `%%; fun f`%%s = f` %%:s; |
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201 |
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202 fun mk_adm t = %%: @{const_name adm} $ t; |
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203 val ID = %%: @{const_name ID}; |
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204 fun mk_strictify t = %%: @{const_name strictify}`t; |
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205 fun mk_ssplit t = %%: @{const_name ssplit}`t; |
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206 fun mk_sscase (x, y) = %%: @{const_name sscase}`x`y; |
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207 fun mk_fup (t,u) = %%: @{const_name fup} ` t ` u; |
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208 |
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209 val pcpoS = @{sort pcpo}; |
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210 |
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211 val list_ccomb = Library.foldl (op `); (* continuous version of list_comb *) |
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212 fun con_app2 con f args = list_ccomb(%%:con,map f args); |
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213 fun con_app con = con_app2 con %#; |
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214 fun prj _ _ x ( _::[]) _ = x |
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215 | prj _ _ _ [] _ = raise Fail "Domain_Library.prj: empty list" |
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216 | prj f1 _ x (_::y::ys) 0 = f1 x y |
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217 | prj f1 f2 x (y:: ys) j = prj f1 f2 (f2 x y) ys (j-1); |
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218 fun proj x = prj (fn S => K (%%: @{const_name fst} $ S)) (fn S => K (%%: @{const_name snd} $ S)) x; |
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219 fun lift tfn = Library.foldr (fn (x,t)=> (mk_trp(tfn x) ===> t)); |
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220 |
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221 val UU = %%: @{const_name UU}; |
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222 fun defined t = t ~= UU; |
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223 fun cpair (t,u) = %%: @{const_name Pair} $ t $ u; |
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224 fun spair (t,u) = %%: @{const_name spair}`t`u; |
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225 fun lift_defined f = lift (fn x => defined (f x)); |
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226 fun bound_arg vns v = Bound (length vns - find_index (fn v' => v' = v) vns - 1); |
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227 |
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228 fun cont_eta_contract (Const("Cfun.Abs_CFun",TT) $ Abs(a,T,body)) = |
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229 (case cont_eta_contract body of |
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230 body' as (Const("Cfun.Rep_CFun",Ta) $ f $ Bound 0) => |
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231 if not (member (op =) (loose_bnos f) 0) then incr_boundvars ~1 f |
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232 else Const("Cfun.Abs_CFun",TT) $ Abs(a,T,body') |
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233 | body' => Const("Cfun.Abs_CFun",TT) $ Abs(a,T,body')) |
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234 | cont_eta_contract(f$t) = cont_eta_contract f $ cont_eta_contract t |
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235 | cont_eta_contract t = t; |
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236 |
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237 fun idx_name dnames s n = s^(if length dnames = 1 then "" else string_of_int n); |
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238 |
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239 end; (* struct *) |
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