1 (* Title: HOL/BNF/Tools/bnf_decl.ML |
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2 Author: Dmitriy Traytel, TU Muenchen |
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3 Copyright 2013 |
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4 |
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5 Axiomatic declaration of bounded natural functors. |
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6 *) |
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7 |
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8 signature BNF_DECL = |
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9 sig |
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10 val bnf_decl: (binding option * (typ * sort)) list -> binding -> mixfix -> binding -> binding -> |
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11 typ list -> local_theory -> BNF_Def.bnf * local_theory |
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12 end |
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13 |
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14 structure BNF_Decl : BNF_DECL = |
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15 struct |
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16 |
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17 open BNF_Util |
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18 open BNF_Def |
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19 |
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20 fun prepare_decl prepare_constraint prepare_typ raw_vars b mx user_mapb user_relb user_witTs lthy = |
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21 let |
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22 fun prepare_type_arg (set_opt, (ty, c)) = |
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23 let val s = fst (dest_TFree (prepare_typ lthy ty)) in |
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24 (set_opt, (s, prepare_constraint lthy c)) |
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25 end; |
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26 val ((user_setbs, vars), raw_vars') = |
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27 map prepare_type_arg raw_vars |
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28 |> `split_list |
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29 |>> apfst (map_filter I); |
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30 val deads = map_filter (fn (NONE, x) => SOME x | _ => NONE) raw_vars'; |
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31 |
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32 fun mk_b name user_b = |
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33 (if Binding.is_empty user_b then Binding.prefix_name (name ^ "_") b else user_b) |
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34 |> Binding.qualify false (Binding.name_of b); |
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35 val (Tname, lthy) = Typedecl.basic_typedecl (b, length vars, mx) lthy; |
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36 val (bd_type_Tname, lthy) = |
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37 Typedecl.basic_typedecl (mk_b "bd_type" Binding.empty, length deads, NoSyn) lthy; |
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38 val T = Type (Tname, map TFree vars); |
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39 val bd_type_T = Type (bd_type_Tname, map TFree deads); |
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40 val lives = map TFree (filter_out (member (op =) deads) vars); |
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41 val live = length lives; |
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42 val _ = "Trying to declare a BNF with no live variables" |> null lives ? error; |
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43 val (lives', _) = BNF_Util.mk_TFrees (length lives) |
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44 (fold Variable.declare_typ (map TFree vars) lthy); |
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45 val T' = Term.typ_subst_atomic (lives ~~ lives') T; |
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46 val mapT = map2 (curry op -->) lives lives' ---> T --> T'; |
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47 val setTs = map (fn U => T --> HOLogic.mk_setT U) lives; |
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48 val bdT = BNF_Util.mk_relT (bd_type_T, bd_type_T); |
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49 val mapb = mk_b BNF_Def.mapN user_mapb; |
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50 val bdb = mk_b "bd" Binding.empty; |
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51 val setbs = map2 (fn b => fn i => mk_b (BNF_Def.mk_setN i) b) user_setbs |
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52 (if live = 1 then [0] else 1 upto live); |
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53 |
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54 val witTs = map (prepare_typ lthy) user_witTs; |
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55 val nwits = length witTs; |
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56 val witbs = map (fn i => mk_b (BNF_Def.mk_witN i) Binding.empty) |
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57 (if nwits = 1 then [0] else 1 upto nwits); |
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58 |
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59 val lthy = Local_Theory.background_theory |
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60 (Sign.add_consts_i ((mapb, mapT, NoSyn) :: (bdb, bdT, NoSyn) :: |
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61 map2 (fn b => fn T => (b, T, NoSyn)) setbs setTs @ |
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62 map2 (fn b => fn T => (b, T, NoSyn)) witbs witTs)) |
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63 lthy; |
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64 val Fmap = Const (Local_Theory.full_name lthy mapb, mapT); |
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65 val Fsets = map2 (fn setb => fn setT => |
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66 Const (Local_Theory.full_name lthy setb, setT)) setbs setTs; |
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67 val Fbd = Const (Local_Theory.full_name lthy bdb, bdT); |
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68 val Fwits = map2 (fn witb => fn witT => |
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69 Const (Local_Theory.full_name lthy witb, witT)) witbs witTs; |
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70 val (key, goals, (triv_tac_opt, wit_goalss), after_qed, lthy, _) = |
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71 prepare_def Do_Inline (user_policy Note_Some) I (K I) (K I) (SOME (map TFree deads)) |
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72 user_mapb user_relb user_setbs ((((((Binding.empty, T), Fmap), Fsets), Fbd), Fwits), NONE) |
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73 lthy; |
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74 |
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75 fun mk_wits_tac set_maps = K (TRYALL Goal.conjunction_tac) THEN' the triv_tac_opt set_maps; |
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76 val wit_goals = map Logic.mk_conjunction_balanced wit_goalss; |
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77 val all_goalss = map single goals @ (if nwits > 0 then wit_goalss else []); |
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78 |
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79 val (((_, [raw_thms])), (lthy_old, lthy)) = Local_Theory.background_theory_result |
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80 (Specification.axiomatization [] [((mk_b "axioms" Binding.empty, []), flat all_goalss)]) lthy |
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81 ||> `Local_Theory.restore; |
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82 |
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83 fun mk_wit_thms set_maps = |
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84 Goal.prove_sorry lthy [] [] (Logic.mk_conjunction_balanced wit_goals) (mk_wits_tac set_maps) |
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85 |> Conjunction.elim_balanced (length wit_goals) |
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86 |> map2 (Conjunction.elim_balanced o length) wit_goalss |
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87 |> map (map (Thm.close_derivation o Thm.forall_elim_vars 0)); |
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88 val phi = Proof_Context.export_morphism lthy_old lthy; |
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89 val thms = unflat all_goalss (Morphism.fact phi raw_thms); |
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90 in |
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91 BNF_Def.register_bnf key (after_qed mk_wit_thms thms lthy) |
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92 end; |
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93 |
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94 val bnf_decl = prepare_decl (K I) (K I); |
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95 |
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96 fun read_constraint _ NONE = HOLogic.typeS |
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97 | read_constraint ctxt (SOME s) = Syntax.read_sort ctxt s; |
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98 |
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99 val bnf_decl_cmd = prepare_decl read_constraint Syntax.read_typ; |
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100 |
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101 val parse_witTs = |
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102 @{keyword "["} |-- (Parse.short_ident --| @{keyword ":"} -- Scan.repeat Parse.typ |
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103 >> (fn ("wits", Ts) => Ts |
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104 | (s, _) => error ("Unknown label " ^ quote s ^ " (expected \"wits\")"))) --| |
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105 @{keyword "]"} || Scan.succeed []; |
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106 |
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107 val parse_bnf_decl = |
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108 parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings -- |
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109 parse_witTs -- Parse.opt_mixfix; |
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110 |
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111 val _ = |
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112 Outer_Syntax.local_theory @{command_spec "bnf_decl"} "bnf declaration" |
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113 (parse_bnf_decl >> |
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114 (fn ((((bsTs, b), (mapb, relb)), witTs), mx) => |
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115 bnf_decl_cmd bsTs b mx mapb relb witTs #> snd)); |
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116 |
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117 end; |
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