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1 (* Title: HOLCF/Tools/domain/domain_axioms.ML |
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2 ID: $Id$ |
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3 Author: David von Oheimb |
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4 |
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5 Syntax generator for domain command. |
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6 *) |
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7 |
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8 structure Domain_Axioms = struct |
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9 |
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10 local |
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11 |
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12 open Domain_Library; |
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13 infixr 0 ===>;infixr 0 ==>;infix 0 == ; |
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14 infix 1 ===; infix 1 ~= ; infix 1 <<; infix 1 ~<<; |
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15 infix 9 ` ; infix 9 `% ; infix 9 `%%; infixr 9 oo; |
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16 |
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17 fun calc_axioms comp_dname (eqs : eq list) n (((dname,_),cons) : eq)= |
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18 let |
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19 |
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20 (* ----- axioms and definitions concerning the isomorphism ------------------ *) |
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21 |
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22 val dc_abs = %%:(dname^"_abs"); |
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23 val dc_rep = %%:(dname^"_rep"); |
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24 val x_name'= "x"; |
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25 val x_name = idx_name eqs x_name' (n+1); |
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26 val dnam = Sign.base_name dname; |
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27 |
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28 val abs_iso_ax = ("abs_iso", mk_trp(dc_rep`(dc_abs`%x_name') === %:x_name')); |
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29 val rep_iso_ax = ("rep_iso", mk_trp(dc_abs`(dc_rep`%x_name') === %:x_name')); |
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30 |
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31 val when_def = ("when_def",%%:(dname^"_when") == |
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32 foldr (uncurry /\ ) (/\x_name'((when_body cons (fn (x,y) => |
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33 Bound(1+length cons+x-y)))`(dc_rep`Bound 0))) (when_funs cons)); |
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34 |
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35 val copy_def = let |
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36 fun idxs z x arg = if is_rec arg |
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37 then (cproj (Bound z) eqs (rec_of arg))`Bound(z-x) |
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38 else Bound(z-x); |
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39 fun one_con (con,args) = |
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40 foldr /\# (list_ccomb (%%:con, mapn (idxs (length args)) 1 args)) args; |
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41 in ("copy_def", %%:(dname^"_copy") == |
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42 /\"f" (list_ccomb (%%:(dname^"_when"), map one_con cons))) end; |
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43 |
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44 (* -- definitions concerning the constructors, discriminators and selectors - *) |
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45 |
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46 fun con_def m n (_,args) = let |
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47 fun idxs z x arg = (if is_lazy arg then fn t => %%:upN`t else I) (Bound(z-x)); |
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48 fun parms vs = mk_stuple (mapn (idxs(length vs)) 1 vs); |
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49 fun inj y 1 _ = y |
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50 | inj y _ 0 = %%:sinlN`y |
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51 | inj y i j = %%:sinrN`(inj y (i-1) (j-1)); |
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52 in foldr /\# (dc_abs`(inj (parms args) m n)) args end; |
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53 |
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54 val con_defs = mapn (fn n => fn (con,args) => |
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55 (extern_name con ^"_def", %%:con == con_def (length cons) n (con,args))) 0 cons; |
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56 |
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57 val dis_defs = let |
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58 fun ddef (con,_) = (dis_name con ^"_def",%%:(dis_name con) == |
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59 list_ccomb(%%:(dname^"_when"),map |
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60 (fn (con',args) => (foldr /\# |
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61 (if con'=con then %%:TT_N else %%:FF_N) args)) cons)) |
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62 in map ddef cons end; |
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63 |
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64 val mat_defs = let |
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65 fun mdef (con,_) = (mat_name con ^"_def",%%:(mat_name con) == |
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66 list_ccomb(%%:(dname^"_when"),map |
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67 (fn (con',args) => (foldr /\# |
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68 (if con'=con |
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69 then %%:returnN`(mk_ctuple (map (bound_arg args) args)) |
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70 else %%:failN) args)) cons)) |
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71 in map mdef cons end; |
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72 |
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73 val pat_defs = |
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74 let |
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75 fun pdef (con,args) = |
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76 let |
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77 val ps = mapn (fn n => fn _ => %:("pat" ^ string_of_int n)) 1 args; |
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78 val xs = map (bound_arg args) args; |
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79 val r = Bound (length args); |
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80 val rhs = case args of [] => %%:returnN ` HOLogic.unit |
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81 | _ => foldr1 cpair_pat ps ` mk_ctuple xs; |
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82 fun one_con (con',args') = foldr /\# (if con'=con then rhs else %%:failN) args'; |
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83 in (pat_name con ^"_def", list_comb (%%:(pat_name con), ps) == |
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84 list_ccomb(%%:(dname^"_when"), map one_con cons)) |
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85 end |
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86 in map pdef cons end; |
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87 |
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88 val sel_defs = let |
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89 fun sdef con n arg = Option.map (fn sel => (sel^"_def",%%:sel == |
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90 list_ccomb(%%:(dname^"_when"),map |
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91 (fn (con',args) => if con'<>con then UU else |
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92 foldr /\# (Bound (length args - n)) args) cons))) (sel_of arg); |
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93 in List.mapPartial I (List.concat(map (fn (con,args) => mapn (sdef con) 1 args) cons)) end; |
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94 |
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95 |
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96 (* ----- axiom and definitions concerning induction ------------------------- *) |
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97 |
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98 val reach_ax = ("reach", mk_trp(cproj (%%:fixN`%%(comp_dname^"_copy")) eqs n |
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99 `%x_name === %:x_name)); |
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100 val take_def = ("take_def",%%:(dname^"_take") == mk_lam("n",cproj |
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101 (%%:iterateN $ Bound 0 ` %%:(comp_dname^"_copy") ` UU) eqs n)); |
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102 val finite_def = ("finite_def",%%:(dname^"_finite") == mk_lam(x_name, |
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103 mk_ex("n",(%%:(dname^"_take") $ Bound 0)`Bound 1 === Bound 1))); |
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104 |
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105 in (dnam, |
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106 [abs_iso_ax, rep_iso_ax, reach_ax], |
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107 [when_def, copy_def] @ |
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108 con_defs @ dis_defs @ mat_defs @ pat_defs @ sel_defs @ |
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109 [take_def, finite_def]) |
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110 end; (* let *) |
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111 |
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112 fun infer_props thy = map (apsnd (FixrecPackage.legacy_infer_prop thy)); |
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113 |
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114 fun add_axioms_i x = snd o PureThy.add_axioms_i (map Thm.no_attributes x); |
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115 fun add_axioms_infer axms thy = add_axioms_i (infer_props thy axms) thy; |
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116 |
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117 fun add_defs_i x = snd o (PureThy.add_defs_i false) (map Thm.no_attributes x); |
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118 fun add_defs_infer defs thy = add_defs_i (infer_props thy defs) thy; |
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119 |
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120 in (* local *) |
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121 |
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122 fun add_axioms (comp_dnam, eqs : eq list) thy' = let |
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123 val comp_dname = Sign.full_name thy' comp_dnam; |
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124 val dnames = map (fst o fst) eqs; |
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125 val x_name = idx_name dnames "x"; |
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126 fun copy_app dname = %%:(dname^"_copy")`Bound 0; |
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127 val copy_def = ("copy_def" , %%:(comp_dname^"_copy") == |
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128 /\"f"(foldr1 cpair (map copy_app dnames))); |
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129 val bisim_def = ("bisim_def",%%:(comp_dname^"_bisim")==mk_lam("R", |
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130 let |
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131 fun one_con (con,args) = let |
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132 val nonrec_args = filter_out is_rec args; |
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133 val rec_args = List.filter is_rec args; |
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134 val recs_cnt = length rec_args; |
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135 val allargs = nonrec_args @ rec_args |
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136 @ map (upd_vname (fn s=> s^"'")) rec_args; |
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137 val allvns = map vname allargs; |
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138 fun vname_arg s arg = if is_rec arg then vname arg^s else vname arg; |
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139 val vns1 = map (vname_arg "" ) args; |
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140 val vns2 = map (vname_arg "'") args; |
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141 val allargs_cnt = length nonrec_args + 2*recs_cnt; |
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142 val rec_idxs = (recs_cnt-1) downto 0; |
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143 val nonlazy_idxs = map snd (filter_out (fn (arg,_) => is_lazy arg) |
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144 (allargs~~((allargs_cnt-1) downto 0))); |
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145 fun rel_app i ra = proj (Bound(allargs_cnt+2)) eqs (rec_of ra) $ |
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146 Bound (2*recs_cnt-i) $ Bound (recs_cnt-i); |
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147 val capps = foldr mk_conj (mk_conj( |
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148 Bound(allargs_cnt+1)===list_ccomb(%%:con,map (bound_arg allvns) vns1), |
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149 Bound(allargs_cnt+0)===list_ccomb(%%:con,map (bound_arg allvns) vns2))) |
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150 (mapn rel_app 1 rec_args); |
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151 in foldr mk_ex (Library.foldr mk_conj |
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152 (map (defined o Bound) nonlazy_idxs,capps)) allvns end; |
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153 fun one_comp n (_,cons) =mk_all(x_name(n+1),mk_all(x_name(n+1)^"'",mk_imp( |
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154 proj (Bound 2) eqs n $ Bound 1 $ Bound 0, |
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155 foldr1 mk_disj (mk_conj(Bound 1 === UU,Bound 0 === UU) |
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156 ::map one_con cons)))); |
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157 in foldr1 mk_conj (mapn one_comp 0 eqs)end )); |
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158 fun add_one (thy,(dnam,axs,dfs)) = thy |
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159 |> Theory.add_path dnam |
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160 |> add_defs_infer dfs |
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161 |> add_axioms_infer axs |
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162 |> Theory.parent_path; |
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163 val thy = Library.foldl add_one (thy', mapn (calc_axioms comp_dname eqs) 0 eqs); |
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164 in thy |> Theory.add_path comp_dnam |
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165 |> add_defs_infer (bisim_def::(if length eqs>1 then [copy_def] else [])) |
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166 |> Theory.parent_path |
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167 end; |
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168 |
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169 end; (* local *) |
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170 end; (* struct *) |